Observation of Transverse Spin-Dependent Azimuthal Correlations of Charged Pion Pairs in $p^\uparrow+p$ at $\sqrt{s
L.~Adamczyk
J.~K.~Adkins
G.~Agakishiev
M.~M.~Aggarwal
Z.~Ahammed
I.~Alekseev
J.~Alford
A.~Aparin
D.~Arkhipkin
E.~C.~Aschenauer
G.~S.~Averichev
A.~Banerjee
R.~Bellwied
A.~Bhasin
A.~K.~Bhati
P.~Bhattarai
J.~Bielcik
J.~Bielcikova
L.~C.~Bland
I.~G.~Bordyuzhin
J.~Bouchet
A.~V.~Brandin
I.~Bunzarov
T.~P.~Burton
J.~Butterworth
H.~Caines
M.~Calder'on~de~la~Barca~S'anchez
J.~M.~Campbell
D.~Cebra
M.~C.~Cervantes
I.~Chakaberia
P.~Chaloupka
Z.~Chang
S.~Chattopadhyay
J.~H.~Chen
X.~Chen
J.~Cheng
M.~Cherney
W.~Christie
G.~Contin
H.~J.~Crawford
S.~Das
L.~C.~De~Silva
R.~R.~Debbe
T.~G.~Dedovich
J.~Deng
A.~A.~Derevschikov
B.~di~Ruzza
L.~Didenko
C.~Dilks
X.~Dong
J.~L.~Drachenberg
J.~E.~Draper
C.~M.~Du
L.~E.~Dunkelberger
J.~C.~Dunlop
L.~G.~Efimov
J.~Engelage
G.~Eppley
R.~Esha
O.~Evdokimov
O.~Eyser
R.~Fatemi
S.~Fazio
P.~Federic
J.~Fedorisin
Z.~Feng
P.~Filip
Y.~Fisyak
C.~E.~Flores
L.~Fulek
C.~A.~Gagliardi
D.~ Garand
F.~Geurts
A.~Gibson
M.~Girard
L.~Greiner
D.~Grosnick
D.~S.~Gunarathne
Y.~Guo
S.~Gupta
A.~Gupta
W.~Guryn
A.~Hamad
A.~Hamed
R.~Haque
J.~W.~Harris
L.~He
S.~Heppelmann
S.~Heppelmann
A.~Hirsch
G.~W.~Hoffmann
D.~J.~Hofman
S.~Horvat
B.~Huang
X.~ Huang
H.~Z.~Huang
P.~Huck
T.~J.~Humanic
G.~Igo
W.~W.~Jacobs
H.~Jang
K.~Jiang
E.~G.~Judd
S.~Kabana
D.~Kalinkin
K.~Kang
K.~Kauder
H.~W.~Ke
D.~Keane
A.~Kechechyan
Z.~H.~Khan
D.~P.~Kikola
I.~Kisel
A.~Kisiel
L.~Kochenda
D.~D.~Koetke
T.~Kollegger
L.~K.~Kosarzewski
A.~F.~Kraishan
P.~Kravtsov
K.~Krueger
I.~Kulakov
L.~Kumar
R.~A.~Kycia
M.~A.~C.~Lamont
J.~M.~Landgraf
K.~D.~ Landry
J.~Lauret
A.~Lebedev
R.~Lednicky
J.~H.~Lee
X.~Li
C.~Li
W.~Li
Z.~M.~Li
Y.~Li
X.~Li
M.~A.~Lisa
F.~Liu
T.~Ljubicic
W.~J.~Llope
M.~Lomnitz
R.~S.~Longacre
X.~Luo
Y.~G.~Ma
G.~L.~Ma
L.~Ma
R.~Ma
N.~Magdy
R.~Majka
A.~Manion
S.~Margetis
C.~Markert
H.~Masui
H.~S.~Matis
D.~McDonald
K.~Meehan
N.~G.~Minaev
S.~Mioduszewski
B.~Mohanty
M.~M.~Mondal
D.~Morozov
M.~K.~Mustafa
B.~K.~Nandi
Md.~Nasim
T.~K.~Nayak
G.~Nigmatkulov
L.~V.~Nogach
S.~Y.~Noh
J.~Novak
S.~B.~Nurushev
G.~Odyniec
A.~Ogawa
K.~Oh
V.~Okorokov
D.~Olvitt~Jr.
B.~S.~Page
R.~Pak
Y.~X.~Pan
Y.~Pandit
Y.~Panebratsev
B.~Pawlik
H.~Pei
C.~Perkins
A.~Peterson
P.~ Pile
M.~Planinic
J.~Pluta
N.~Poljak
K.~Poniatowska
J.~Porter
M.~Posik
A.~M.~Poskanzer
N.~K.~Pruthi
J.~Putschke
H.~Qiu
A.~Quintero
S.~Ramachandran
R.~Raniwala
S.~Raniwala
R.~L.~Ray
H.~G.~Ritter
J.~B.~Roberts
O.~V.~Rogachevskiy
J.~L.~Romero
A.~Roy
L.~Ruan
J.~Rusnak
O.~Rusnakova
N.~R.~Sahoo
P.~K.~Sahu
I.~Sakrejda
S.~Salur
J.~Sandweiss
A.~ Sarkar
J.~Schambach
R.~P.~Scharenberg
A.~M.~Schmah
W.~B.~Schmidke
N.~Schmitz
J.~Seger
P.~Seyboth
N.~Shah
E.~Shahaliev
P.~V.~Shanmuganathan
M.~Shao
M.~K.~Sharma
B.~Sharma
W.~Q.~Shen
S.~S.~Shi
Q.~Y.~Shou
E.~P.~Sichtermann
R.~Sikora
M.~Simko
M.~J.~Skoby
D.~Smirnov
N.~Smirnov
L.~Song
P.~Sorensen
H.~M.~Spinka
B.~Srivastava
T.~D.~S.~Stanislaus
M.~ Stepanov
R.~Stock
M.~Strikhanov
B.~Stringfellow
M.~Sumbera
B.~Summa
X.~Sun
Z.~Sun
X.~M.~Sun
Y.~Sun
B.~Surrow
N.~Svirida
M.~A.~Szelezniak
A.~H.~Tang
Z.~Tang
T.~Tarnowsky
A.~N.~Tawfik
J.~H.~Thomas
A.~R.~Timmins
D.~Tlusty
M.~Tokarev
S.~Trentalange
R.~E.~Tribble
P.~Tribedy
S.~K.~Tripathy
B.~A.~Trzeciak
O.~D.~Tsai
T.~Ullrich
D.~G.~Underwood
I.~Upsal
G.~Van~Buren
G.~van~Nieuwenhuizen
M.~Vandenbroucke
R.~Varma
A.~N.~Vasiliev
R.~Vertesi
F.~Videb{ae
Y.~P.~Viyogi
S.~Vokal
S.~A.~Voloshin
A.~Vossen
G.~Wang
Y.~Wang
F.~Wang
Y.~Wang
H.~Wang
J.~S.~Wang
J.~C.~Webb
G.~Webb
L.~Wen
G.~D.~Westfall
H.~Wieman
S.~W.~Wissink
R.~Witt
Y.~F.~Wu
Z.~G.~Xiao
W.~Xie
K.~Xin
Q.~H.~Xu
Z.~Xu
H.~Xu
N.~Xu
Y.~F.~Xu
Q.~Yang
Y.~Yang
S.~Yang
Y.~Yang
C.~Yang
Z.~Ye
P.~Yepes
L.~Yi
K.~Yip
I.~-K.~Yoo
N.~Yu
H.~Zbroszczyk
W.~Zha
X.~P.~Zhang
J.~Zhang
Y.~Zhang
J.~Zhang
J.~B.~Zhang
S.~Zhang
Z.~Zhang
J.~Zhao
C.~Zhong
L.~Zhou
X.~Zhu
Y.~Zoulkarneeva
M.~Zyzak
We report the observation of transverse polarization-dependent azimuthal correlations in charged pion pair production with the STAR experiment in $p^\uparrow+p$ collisions at RHIC. These correlations directly probe quark transversity distributions. We measure signals in excess of five standard deviations at high transverse momenta, at high pseudorapidities $\eta>0.5$, and for pair masses around the mass of the $\rho$-meson. This is the first direct transversity measurement in {p+p collisions. Comparing the results to data from lepton-nucleon scattering will test the universality of these spin-dependent quantities. %%% TOO LONG ----> %We report the observation of transverse polarization-dependent azimuthal correlations in charged pion pair production with the STAR experiment in $p^\uparrow+p$ collisions at RHIC. %These correlations originate from the fragmentation of transversely polarized quarks via the spin-dependent di-hadron interference fragmentation function and thus directly probe the quark transversity distribution. %The correlations are extracted as a function of the hadron pair transverse momentum, invariant mass, and pseudorapidity. We measure signals in excess of 5~$\sigma$ statistical uncertainty at high transverse momenta, at high pseudorapidities $\eta>0.5$, and for pair masses around the mass of the $\rho$-meson. %This is the first direct transversity measurement in {p+p collisions and allows an independent determination of quantities that up to now have only been accessed in semi-inclusive deep inelastic scattering. The results can test the universality of these transverse polarization-dependent quantities.
acknowledgements.tex
We thank the RHIC Operations Group and RCF at BNL, the NERSC Center at LBNL, the KISTI Center in Korea, and the Open Science Grid consortium for providing resources and support. This work was supported in part by the Office of Nuclear Physics within the U.S. DOE Office of Science, the U.S. NSF, the Ministry of Education and Science of the Russian Federation, NNSFC, CAS, MoST and MoE of China, the Korean Research Foundation, GA and MSMT of the Czech Republic, FIAS of Germany, DAE, DST, and UGC of India, the National Science Centre of Poland, National Research Foundation, the Ministry of Science, Education and Sports of the Republic of Croatia, and RosAtom of Russia.
authors.tex
\affiliation{AGH University of Science and Technology, Cracow 30-059, Poland}
\affiliation{Argonne National Laboratory, Argonne, Illinois 60439, USA}
\affiliation{Brookhaven National Laboratory, Upton, New York 11973, USA}
\affiliation{University of California, Berkeley, California 94720, USA}
\affiliation{University of California, Davis, California 95616, USA}
\affiliation{University of California, Los Angeles, California 90095, USA}
\affiliation{Central China Normal University (HZNU), Wuhan 430079, China}
\affiliation{University of Illinois at Chicago, Chicago, Illinois 60607, USA}
\affiliation{Creighton University, Omaha, Nebraska 68178, USA}
\affiliation{Czech Technical University in Prague, FNSPE, Prague, 115 19, Czech Republic}
\affiliation{Nuclear Physics Institute AS CR, 250 68 \v{R}e\v{z}/Prague, Czech Republic}
\affiliation{Frankfurt Institute for Advanced Studies FIAS, Frankfurt 60438, Germany}
\affiliation{Institute of Physics, Bhubaneswar 751005, India}
\affiliation{Indian Institute of Technology, Mumbai 400076, India}
\affiliation{Indiana University, Bloomington, Indiana 47408, USA}
\affiliation{Alikhanov Institute for Theoretical and Experimental Physics, Moscow 117218, Russia}
\affiliation{University of Jammu, Jammu 180001, India}
\affiliation{Joint Institute for Nuclear Research, Dubna, 141 980, Russia}
\affiliation{Kent State University, Kent, Ohio 44242, USA}
\affiliation{University of Kentucky, Lexington, Kentucky, 40506-0055, USA}
\affiliation{Korea Institute of Science and Technology Information, Daejeon 305-701, Korea}
\affiliation{Institute of Modern Physics, Lanzhou 730000, China}
\affiliation{Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA}
\affiliation{Max-Planck-Institut fur Physik, Munich 80805, Germany}
\affiliation{Michigan State University, East Lansing, Michigan 48824, USA}
\affiliation{Moscow Engineering Physics Institute, Moscow 115409, Russia}
\affiliation{National Institute of Science Education and Research, Bhubaneswar 751005, India}
\affiliation{Ohio State University, Columbus, Ohio 43210, USA}
\affiliation{Institute of Nuclear Physics PAN, Cracow 31-342, Poland}
\affiliation{Panjab University, Chandigarh 160014, India}
\affiliation{Pennsylvania State University, University Park, Pennsylvania 16802, USA}
\affiliation{Institute of High Energy Physics, Protvino 142281, Russia}
\affiliation{Purdue University, West Lafayette, Indiana 47907, USA}
\affiliation{Pusan National University, Pusan 609735, Republic of Korea}
\affiliation{University of Rajasthan, Jaipur 302004, India}
\affiliation{Rice University, Houston, Texas 77251, USA}
\affiliation{University of Science and Technology of China, Hefei 230026, China}
\affiliation{Shandong University, Jinan, Shandong 250100, China}
\affiliation{Shanghai Institute of Applied Physics, Shanghai 201800, China}
\affiliation{Temple University, Philadelphia, Pennsylvania 19122, USA}
\affiliation{Texas A\&M University, College Station, Texas 77843, USA}
\affiliation{University of Texas, Austin, Texas 78712, USA}
\affiliation{University of Houston, Houston, Texas 77204, USA}
\affiliation{Tsinghua University, Beijing 100084, China}
\affiliation{United States Naval Academy, Annapolis, Maryland, 21402, USA}
\affiliation{Valparaiso University, Valparaiso, Indiana 46383, USA}
\affiliation{Variable Energy Cyclotron Centre, Kolkata 700064, India}
\affiliation{Warsaw University of Technology, Warsaw 00-661, Poland}
\affiliation{Wayne State University, Detroit, Michigan 48201, USA}
\affiliation{World Laboratory for Cosmology and Particle Physics (WLCAPP), Cairo 11571, Egypt}
\affiliation{Yale University, New Haven, Connecticut 06520, USA}
\affiliation{University of Zagreb, Zagreb, HR-10002, Croatia}

\author{L.~Adamczyk}\affiliation{AGH University of Science and Technology, Cracow 30-059, Poland}
\author{J.~K.~Adkins}\affiliation{University of Kentucky, Lexington, Kentucky, 40506-0055, USA}
\author{G.~Agakishiev}\affiliation{Joint Institute for Nuclear Research, Dubna, 141 980, Russia}
\author{M.~M.~Aggarwal}\affiliation{Panjab University, Chandigarh 160014, India}
\author{Z.~Ahammed}\affiliation{Variable Energy Cyclotron Centre, Kolkata 700064, India}
\author{I.~Alekseev}\affiliation{Alikhanov Institute for Theoretical and Experimental Physics, Moscow 117218, Russia}
\author{J.~Alford}\affiliation{Kent State University, Kent, Ohio 44242, USA}
\author{A.~Aparin}\affiliation{Joint Institute for Nuclear Research, Dubna, 141 980, Russia}
\author{D.~Arkhipkin}\affiliation{Brookhaven National Laboratory, Upton, New York 11973, USA}
\author{E.~C.~Aschenauer}\affiliation{Brookhaven National Laboratory, Upton, New York 11973, USA}
\author{G.~S.~Averichev}\affiliation{Joint Institute for Nuclear Research, Dubna, 141 980, Russia}
\author{A.~Banerjee}\affiliation{Variable Energy Cyclotron Centre, Kolkata 700064, India}
\author{R.~Bellwied}\affiliation{University of Houston, Houston, Texas 77204, USA}
\author{A.~Bhasin}\affiliation{University of Jammu, Jammu 180001, India}
\author{A.~K.~Bhati}\affiliation{Panjab University, Chandigarh 160014, India}
\author{P.~Bhattarai}\affiliation{University of Texas, Austin, Texas 78712, USA}
\author{J.~Bielcik}\affiliation{Czech Technical University in Prague, FNSPE, Prague, 115 19, Czech Republic}
\author{J.~Bielcikova}\affiliation{Nuclear Physics Institute AS CR, 250 68 \v{R}e\v{z}/Prague, Czech Republic}
\author{L.~C.~Bland}\affiliation{Brookhaven National Laboratory, Upton, New York 11973, USA}
\author{I.~G.~Bordyuzhin}\affiliation{Alikhanov Institute for Theoretical and Experimental Physics, Moscow 117218, Russia}
\author{J.~Bouchet}\affiliation{Kent State University, Kent, Ohio 44242, USA}
\author{A.~V.~Brandin}\affiliation{Moscow Engineering Physics Institute, Moscow 115409, Russia}
\author{I.~Bunzarov}\affiliation{Joint Institute for Nuclear Research, Dubna, 141 980, Russia}
\author{T.~P.~Burton}\affiliation{Brookhaven National Laboratory, Upton, New York 11973, USA}
\author{J.~Butterworth}\affiliation{Rice University, Houston, Texas 77251, USA}
\author{H.~Caines}\affiliation{Yale University, New Haven, Connecticut 06520, USA}
\author{M.~Calder'on~de~la~Barca~S'anchez}\affiliation{University of California, Davis, California 95616, USA}
\author{J.~M.~Campbell}\affiliation{Ohio State University, Columbus, Ohio 43210, USA}
\author{D.~Cebra}\affiliation{University of California, Davis, California 95616, USA}
\author{M.~C.~Cervantes}\affiliation{Texas A\&M University, College Station, Texas 77843, USA}
\author{I.~Chakaberia}\affiliation{Brookhaven National Laboratory, Upton, New York 11973, USA}
\author{P.~Chaloupka}\affiliation{Czech Technical University in Prague, FNSPE, Prague, 115 19, Czech Republic}
\author{Z.~Chang}\affiliation{Texas A\&M University, College Station, Texas 77843, USA}
\author{S.~Chattopadhyay}\affiliation{Variable Energy Cyclotron Centre, Kolkata 700064, India}
\author{J.~H.~Chen}\affiliation{Shanghai Institute of Applied Physics, Shanghai 201800, China}
\author{X.~Chen}\affiliation{Institute of Modern Physics, Lanzhou 730000, China}
\author{J.~Cheng}\affiliation{Tsinghua University, Beijing 100084, China}
\author{M.~Cherney}\affiliation{Creighton University, Omaha, Nebraska 68178, USA}
\author{W.~Christie}\affiliation{Brookhaven National Laboratory, Upton, New York 11973, USA}
\author{G.~Contin}\affiliation{Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA}
\author{H.~J.~Crawford}\affiliation{University of California, Berkeley, California 94720, USA}
\author{S.~Das}\affiliation{Institute of Physics, Bhubaneswar 751005, India}
\author{L.~C.~De~Silva}\affiliation{Creighton University, Omaha, Nebraska 68178, USA}
\author{R.~R.~Debbe}\affiliation{Brookhaven National Laboratory, Upton, New York 11973, USA}
\author{T.~G.~Dedovich}\affiliation{Joint Institute for Nuclear Research, Dubna, 141 980, Russia}
\author{J.~Deng}\affiliation{Shandong University, Jinan, Shandong 250100, China}
\author{A.~A.~Derevschikov}\affiliation{Institute of High Energy Physics, Protvino 142281, Russia}
\author{B.~di~Ruzza}\affiliation{Brookhaven National Laboratory, Upton, New York 11973, USA}
\author{L.~Didenko}\affiliation{Brookhaven National Laboratory, Upton, New York 11973, USA}
\author{C.~Dilks}\affiliation{Pennsylvania State University, University Park, Pennsylvania 16802, USA}
\author{X.~Dong}\affiliation{Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA}
\author{J.~L.~Drachenberg}\affiliation{Valparaiso University, Valparaiso, Indiana 46383, USA}
\author{J.~E.~Draper}\affiliation{University of California, Davis, California 95616, USA}
\author{C.~M.~Du}\affiliation{Institute of Modern Physics, Lanzhou 730000, China}
\author{L.~E.~Dunkelberger}\affiliation{University of California, Los Angeles, California 90095, USA}
\author{J.~C.~Dunlop}\affiliation{Brookhaven National Laboratory, Upton, New York 11973, USA}
\author{L.~G.~Efimov}\affiliation{Joint Institute for Nuclear Research, Dubna, 141 980, Russia}
\author{J.~Engelage}\affiliation{University of California, Berkeley, California 94720, USA}
\author{G.~Eppley}\affiliation{Rice University, Houston, Texas 77251, USA}
\author{R.~Esha}\affiliation{University of California, Los Angeles, California 90095, USA}
\author{O.~Evdokimov}\affiliation{University of Illinois at Chicago, Chicago, Illinois 60607, USA}
\author{O.~Eyser}\affiliation{Brookhaven National Laboratory, Upton, New York 11973, USA}
\author{R.~Fatemi}\affiliation{University of Kentucky, Lexington, Kentucky, 40506-0055, USA}
\author{S.~Fazio}\affiliation{Brookhaven National Laboratory, Upton, New York 11973, USA}
\author{P.~Federic}\affiliation{Nuclear Physics Institute AS CR, 250 68 \v{R}e\v{z}/Prague, Czech Republic}
\author{J.~Fedorisin}\affiliation{Joint Institute for Nuclear Research, Dubna, 141 980, Russia}
\author{Z.~Feng}\affiliation{Central China Normal University (HZNU), Wuhan 430079, China}
\author{P.~Filip}\affiliation{Joint Institute for Nuclear Research, Dubna, 141 980, Russia}
\author{Y.~Fisyak}\affiliation{Brookhaven National Laboratory, Upton, New York 11973, USA}
\author{C.~E.~Flores}\affiliation{University of California, Davis, California 95616, USA}
\author{L.~Fulek}\affiliation{AGH University of Science and Technology, Cracow 30-059, Poland}
\author{C.~A.~Gagliardi}\affiliation{Texas A\&M University, College Station, Texas 77843, USA}
\author{D.~ Garand}\affiliation{Purdue University, West Lafayette, Indiana 47907, USA}
\author{F.~Geurts}\affiliation{Rice University, Houston, Texas 77251, USA}
\author{A.~Gibson}\affiliation{Valparaiso University, Valparaiso, Indiana 46383, USA}
\author{M.~Girard}\affiliation{Warsaw University of Technology, Warsaw 00-661, Poland}
\author{L.~Greiner}\affiliation{Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA}
\author{D.~Grosnick}\affiliation{Valparaiso University, Valparaiso, Indiana 46383, USA}
\author{D.~S.~Gunarathne}\affiliation{Temple University, Philadelphia, Pennsylvania 19122, USA}
\author{Y.~Guo}\affiliation{University of Science and Technology of China, Hefei 230026, China}
\author{S.~Gupta}\affiliation{University of Jammu, Jammu 180001, India}
\author{A.~Gupta}\affiliation{University of Jammu, Jammu 180001, India}
\author{W.~Guryn}\affiliation{Brookhaven National Laboratory, Upton, New York 11973, USA}
\author{A.~Hamad}\affiliation{Kent State University, Kent, Ohio 44242, USA}
\author{A.~Hamed}\affiliation{Texas A\&M University, College Station, Texas 77843, USA}
\author{R.~Haque}\affiliation{National Institute of Science Education and Research, Bhubaneswar 751005, India}
\author{J.~W.~Harris}\affiliation{Yale University, New Haven, Connecticut 06520, USA}
\author{L.~He}\affiliation{Purdue University, West Lafayette, Indiana 47907, USA}
\author{S.~Heppelmann}\affiliation{Pennsylvania State University, University Park, Pennsylvania 16802, USA}
\author{S.~Heppelmann}\affiliation{Brookhaven National Laboratory, Upton, New York 11973, USA}
\author{A.~Hirsch}\affiliation{Purdue University, West Lafayette, Indiana 47907, USA}
\author{G.~W.~Hoffmann}\affiliation{University of Texas, Austin, Texas 78712, USA}
\author{D.~J.~Hofman}\affiliation{University of Illinois at Chicago, Chicago, Illinois 60607, USA}
\author{S.~Horvat}\affiliation{Yale University, New Haven, Connecticut 06520, USA}
\author{B.~Huang}\affiliation{University of Illinois at Chicago, Chicago, Illinois 60607, USA}
\author{X.~ Huang}\affiliation{Tsinghua University, Beijing 100084, China}
\author{H.~Z.~Huang}\affiliation{University of California, Los Angeles, California 90095, USA}
\author{P.~Huck}\affiliation{Central China Normal University (HZNU), Wuhan 430079, China}
\author{T.~J.~Humanic}\affiliation{Ohio State University, Columbus, Ohio 43210, USA}
\author{G.~Igo}\affiliation{University of California, Los Angeles, California 90095, USA}
\author{W.~W.~Jacobs}\affiliation{Indiana University, Bloomington, Indiana 47408, USA}
\author{H.~Jang}\affiliation{Korea Institute of Science and Technology Information, Daejeon 305-701, Korea}
\author{K.~Jiang}\affiliation{University of Science and Technology of China, Hefei 230026, China}
\author{E.~G.~Judd}\affiliation{University of California, Berkeley, California 94720, USA}
\author{S.~Kabana}\affiliation{Kent State University, Kent, Ohio 44242, USA}
\author{D.~Kalinkin}\affiliation{Alikhanov Institute for Theoretical and Experimental Physics, Moscow 117218, Russia}
\author{K.~Kang}\affiliation{Tsinghua University, Beijing 100084, China}
\author{K.~Kauder}\affiliation{Wayne State University, Detroit, Michigan 48201, USA}
\author{H.~W.~Ke}\affiliation{Brookhaven National Laboratory, Upton, New York 11973, USA}
\author{D.~Keane}\affiliation{Kent State University, Kent, Ohio 44242, USA}
\author{A.~Kechechyan}\affiliation{Joint Institute for Nuclear Research, Dubna, 141 980, Russia}
\author{Z.~H.~Khan}\affiliation{University of Illinois at Chicago, Chicago, Illinois 60607, USA}
\author{D.~P.~Kikola}\affiliation{Warsaw University of Technology, Warsaw 00-661, Poland}
\author{I.~Kisel}\affiliation{Frankfurt Institute for Advanced Studies FIAS, Frankfurt 60438, Germany}
\author{A.~Kisiel}\affiliation{Warsaw University of Technology, Warsaw 00-661, Poland}
\author{L.~Kochenda}\affiliation{Moscow Engineering Physics Institute, Moscow 115409, Russia}
\author{D.~D.~Koetke}\affiliation{Valparaiso University, Valparaiso, Indiana 46383, USA}
\author{T.~Kollegger}\affiliation{Frankfurt Institute for Advanced Studies FIAS, Frankfurt 60438, Germany}
\author{L.~K.~Kosarzewski}\affiliation{Warsaw University of Technology, Warsaw 00-661, Poland}
\author{A.~F.~Kraishan}\affiliation{Temple University, Philadelphia, Pennsylvania 19122, USA}
\author{P.~Kravtsov}\affiliation{Moscow Engineering Physics Institute, Moscow 115409, Russia}
\author{K.~Krueger}\affiliation{Argonne National Laboratory, Argonne, Illinois 60439, USA}
\author{I.~Kulakov}\affiliation{Frankfurt Institute for Advanced Studies FIAS, Frankfurt 60438, Germany}
\author{L.~Kumar}\affiliation{Panjab University, Chandigarh 160014, India}
\author{R.~A.~Kycia}\affiliation{Institute of Nuclear Physics PAN, Cracow 31-342, Poland}
\author{M.~A.~C.~Lamont}\affiliation{Brookhaven National Laboratory, Upton, New York 11973, USA}
\author{J.~M.~Landgraf}\affiliation{Brookhaven National Laboratory, Upton, New York 11973, USA}
\author{K.~D.~ Landry}\affiliation{University of California, Los Angeles, California 90095, USA}
\author{J.~Lauret}\affiliation{Brookhaven National Laboratory, Upton, New York 11973, USA}
\author{A.~Lebedev}\affiliation{Brookhaven National Laboratory, Upton, New York 11973, USA}
\author{R.~Lednicky}\affiliation{Joint Institute for Nuclear Research, Dubna, 141 980, Russia}
\author{J.~H.~Lee}\affiliation{Brookhaven National Laboratory, Upton, New York 11973, USA}
\author{X.~Li}\affiliation{Brookhaven National Laboratory, Upton, New York 11973, USA}
\author{C.~Li}\affiliation{University of Science and Technology of China, Hefei 230026, China}
\author{W.~Li}\affiliation{Shanghai Institute of Applied Physics, Shanghai 201800, China}
\author{Z.~M.~Li}\affiliation{Central China Normal University (HZNU), Wuhan 430079, China}
\author{Y.~Li}\affiliation{Tsinghua University, Beijing 100084, China}
\author{X.~Li}\affiliation{Temple University, Philadelphia, Pennsylvania 19122, USA}
\author{M.~A.~Lisa}\affiliation{Ohio State University, Columbus, Ohio 43210, USA}
\author{F.~Liu}\affiliation{Central China Normal University (HZNU), Wuhan 430079, China}
\author{T.~Ljubicic}\affiliation{Brookhaven National Laboratory, Upton, New York 11973, USA}
\author{W.~J.~Llope}\affiliation{Wayne State University, Detroit, Michigan 48201, USA}
\author{M.~Lomnitz}\affiliation{Kent State University, Kent, Ohio 44242, USA}
\author{R.~S.~Longacre}\affiliation{Brookhaven National Laboratory, Upton, New York 11973, USA}
\author{X.~Luo}\affiliation{Central China Normal University (HZNU), Wuhan 430079, China}
\author{Y.~G.~Ma}\affiliation{Shanghai Institute of Applied Physics, Shanghai 201800, China}
\author{G.~L.~Ma}\affiliation{Shanghai Institute of Applied Physics, Shanghai 201800, China}
\author{L.~Ma}\affiliation{Shanghai Institute of Applied Physics, Shanghai 201800, China}
\author{R.~Ma}\affiliation{Brookhaven National Laboratory, Upton, New York 11973, USA}
\author{N.~Magdy}\affiliation{World Laboratory for Cosmology and Particle Physics (WLCAPP), Cairo 11571, Egypt}
\author{R.~Majka}\affiliation{Yale University, New Haven, Connecticut 06520, USA}
\author{A.~Manion}\affiliation{Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA}
\author{S.~Margetis}\affiliation{Kent State University, Kent, Ohio 44242, USA}
\author{C.~Markert}\affiliation{University of Texas, Austin, Texas 78712, USA}
\author{H.~Masui}\affiliation{Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA}
\author{H.~S.~Matis}\affiliation{Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA}
\author{D.~McDonald}\affiliation{University of Houston, Houston, Texas 77204, USA}
\author{K.~Meehan}\affiliation{University of California, Davis, California 95616, USA}
\author{N.~G.~Minaev}\affiliation{Institute of High Energy Physics, Protvino 142281, Russia}
\author{S.~Mioduszewski}\affiliation{Texas A\&M University, College Station, Texas 77843, USA}
\author{B.~Mohanty}\affiliation{National Institute of Science Education and Research, Bhubaneswar 751005, India}
\author{M.~M.~Mondal}\affiliation{Texas A\&M University, College Station, Texas 77843, USA}
\author{D.~Morozov}\affiliation{Institute of High Energy Physics, Protvino 142281, Russia}
\author{M.~K.~Mustafa}\affiliation{Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA}
\author{B.~K.~Nandi}\affiliation{Indian Institute of Technology, Mumbai 400076, India}
\author{Md.~Nasim}\affiliation{University of California, Los Angeles, California 90095, USA}
\author{T.~K.~Nayak}\affiliation{Variable Energy Cyclotron Centre, Kolkata 700064, India}
\author{G.~Nigmatkulov}\affiliation{Moscow Engineering Physics Institute, Moscow 115409, Russia}
\author{L.~V.~Nogach}\affiliation{Institute of High Energy Physics, Protvino 142281, Russia}
\author{S.~Y.~Noh}\affiliation{Korea Institute of Science and Technology Information, Daejeon 305-701, Korea}
\author{J.~Novak}\affiliation{Michigan State University, East Lansing, Michigan 48824, USA}
\author{S.~B.~Nurushev}\affiliation{Institute of High Energy Physics, Protvino 142281, Russia}
\author{G.~Odyniec}\affiliation{Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA}
\author{A.~Ogawa}\affiliation{Brookhaven National Laboratory, Upton, New York 11973, USA}
\author{K.~Oh}\affiliation{Pusan National University, Pusan 609735, Republic of Korea}
\author{V.~Okorokov}\affiliation{Moscow Engineering Physics Institute, Moscow 115409, Russia}
\author{D.~Olvitt~Jr.}\affiliation{Temple University, Philadelphia, Pennsylvania 19122, USA}
\author{B.~S.~Page}\affiliation{Brookhaven National Laboratory, Upton, New York 11973, USA}
\author{R.~Pak}\affiliation{Brookhaven National Laboratory, Upton, New York 11973, USA}
\author{Y.~X.~Pan}\affiliation{University of California, Los Angeles, California 90095, USA}
\author{Y.~Pandit}\affiliation{University of Illinois at Chicago, Chicago, Illinois 60607, USA}
\author{Y.~Panebratsev}\affiliation{Joint Institute for Nuclear Research, Dubna, 141 980, Russia}
\author{B.~Pawlik}\affiliation{Institute of Nuclear Physics PAN, Cracow 31-342, Poland}
\author{H.~Pei}\affiliation{Central China Normal University (HZNU), Wuhan 430079, China}
\author{C.~Perkins}\affiliation{University of California, Berkeley, California 94720, USA}
\author{A.~Peterson}\affiliation{Ohio State University, Columbus, Ohio 43210, USA}
\author{P.~ Pile}\affiliation{Brookhaven National Laboratory, Upton, New York 11973, USA}
\author{M.~Planinic}\affiliation{University of Zagreb, Zagreb, HR-10002, Croatia}
\author{J.~Pluta}\affiliation{Warsaw University of Technology, Warsaw 00-661, Poland}
\author{N.~Poljak}\affiliation{University of Zagreb, Zagreb, HR-10002, Croatia}
\author{K.~Poniatowska}\affiliation{Warsaw University of Technology, Warsaw 00-661, Poland}
\author{J.~Porter}\affiliation{Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA}
\author{M.~Posik}\affiliation{Temple University, Philadelphia, Pennsylvania 19122, USA}
\author{A.~M.~Poskanzer}\affiliation{Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA}
\author{N.~K.~Pruthi}\affiliation{Panjab University, Chandigarh 160014, India}
\author{J.~Putschke}\affiliation{Wayne State University, Detroit, Michigan 48201, USA}
\author{H.~Qiu}\affiliation{Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA}
\author{A.~Quintero}\affiliation{Kent State University, Kent, Ohio 44242, USA}
\author{S.~Ramachandran}\affiliation{University of Kentucky, Lexington, Kentucky, 40506-0055, USA}
\author{R.~Raniwala}\affiliation{University of Rajasthan, Jaipur 302004, India}
\author{S.~Raniwala}\affiliation{University of Rajasthan, Jaipur 302004, India}
\author{R.~L.~Ray}\affiliation{University of Texas, Austin, Texas 78712, USA}
\author{H.~G.~Ritter}\affiliation{Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA}
\author{J.~B.~Roberts}\affiliation{Rice University, Houston, Texas 77251, USA}
\author{O.~V.~Rogachevskiy}\affiliation{Joint Institute for Nuclear Research, Dubna, 141 980, Russia}
\author{J.~L.~Romero}\affiliation{University of California, Davis, California 95616, USA}
\author{A.~Roy}\affiliation{Variable Energy Cyclotron Centre, Kolkata 700064, India}
\author{L.~Ruan}\affiliation{Brookhaven National Laboratory, Upton, New York 11973, USA}
\author{J.~Rusnak}\affiliation{Nuclear Physics Institute AS CR, 250 68 \v{R}e\v{z}/Prague, Czech Republic}
\author{O.~Rusnakova}\affiliation{Czech Technical University in Prague, FNSPE, Prague, 115 19, Czech Republic}
\author{N.~R.~Sahoo}\affiliation{Texas A\&M University, College Station, Texas 77843, USA}
\author{P.~K.~Sahu}\affiliation{Institute of Physics, Bhubaneswar 751005, India}
\author{I.~Sakrejda}\affiliation{Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA}
\author{S.~Salur}\affiliation{Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA}
\author{J.~Sandweiss}\affiliation{Yale University, New Haven, Connecticut 06520, USA}
\author{A.~ Sarkar}\affiliation{Indian Institute of Technology, Mumbai 400076, India}
\author{J.~Schambach}\affiliation{University of Texas, Austin, Texas 78712, USA}
\author{R.~P.~Scharenberg}\affiliation{Purdue University, West Lafayette, Indiana 47907, USA}
\author{A.~M.~Schmah}\affiliation{Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA}
\author{W.~B.~Schmidke}\affiliation{Brookhaven National Laboratory, Upton, New York 11973, USA}
\author{N.~Schmitz}\affiliation{Max-Planck-Institut fur Physik, Munich 80805, Germany}
\author{J.~Seger}\affiliation{Creighton University, Omaha, Nebraska 68178, USA}
\author{P.~Seyboth}\affiliation{Max-Planck-Institut fur Physik, Munich 80805, Germany}
\author{N.~Shah}\affiliation{University of California, Los Angeles, California 90095, USA}
\author{E.~Shahaliev}\affiliation{Joint Institute for Nuclear Research, Dubna, 141 980, Russia}
\author{P.~V.~Shanmuganathan}\affiliation{Kent State University, Kent, Ohio 44242, USA}
\author{M.~Shao}\affiliation{University of Science and Technology of China, Hefei 230026, China}
\author{M.~K.~Sharma}\affiliation{University of Jammu, Jammu 180001, India}
\author{B.~Sharma}\affiliation{Panjab University, Chandigarh 160014, India}
\author{W.~Q.~Shen}\affiliation{Shanghai Institute of Applied Physics, Shanghai 201800, China}
\author{S.~S.~Shi}\affiliation{Central China Normal University (HZNU), Wuhan 430079, China}
\author{Q.~Y.~Shou}\affiliation{Shanghai Institute of Applied Physics, Shanghai 201800, China}
\author{E.~P.~Sichtermann}\affiliation{Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA}
\author{R.~Sikora}\affiliation{AGH University of Science and Technology, Cracow 30-059, Poland}
\author{M.~Simko}\affiliation{Nuclear Physics Institute AS CR, 250 68 \v{R}e\v{z}/Prague, Czech Republic}
\author{M.~J.~Skoby}\affiliation{Indiana University, Bloomington, Indiana 47408, USA}
\author{D.~Smirnov}\affiliation{Brookhaven National Laboratory, Upton, New York 11973, USA}
\author{N.~Smirnov}\affiliation{Yale University, New Haven, Connecticut 06520, USA}
\author{L.~Song}\affiliation{University of Houston, Houston, Texas 77204, USA}
\author{P.~Sorensen}\affiliation{Brookhaven National Laboratory, Upton, New York 11973, USA}
\author{H.~M.~Spinka}\affiliation{Argonne National Laboratory, Argonne, Illinois 60439, USA}
\author{B.~Srivastava}\affiliation{Purdue University, West Lafayette, Indiana 47907, USA}
\author{T.~D.~S.~Stanislaus}\affiliation{Valparaiso University, Valparaiso, Indiana 46383, USA}
\author{M.~ Stepanov}\affiliation{Purdue University, West Lafayette, Indiana 47907, USA}
\author{R.~Stock}\affiliation{Frankfurt Institute for Advanced Studies FIAS, Frankfurt 60438, Germany}
\author{M.~Strikhanov}\affiliation{Moscow Engineering Physics Institute, Moscow 115409, Russia}
\author{B.~Stringfellow}\affiliation{Purdue University, West Lafayette, Indiana 47907, USA}
\author{M.~Sumbera}\affiliation{Nuclear Physics Institute AS CR, 250 68 \v{R}e\v{z}/Prague, Czech Republic}
\author{B.~Summa}\affiliation{Pennsylvania State University, University Park, Pennsylvania 16802, USA}
\author{X.~Sun}\affiliation{Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA}
\author{Z.~Sun}\affiliation{Institute of Modern Physics, Lanzhou 730000, China}
\author{X.~M.~Sun}\affiliation{Central China Normal University (HZNU), Wuhan 430079, China}
\author{Y.~Sun}\affiliation{University of Science and Technology of China, Hefei 230026, China}
\author{B.~Surrow}\affiliation{Temple University, Philadelphia, Pennsylvania 19122, USA}
\author{N.~Svirida}\affiliation{Alikhanov Institute for Theoretical and Experimental Physics, Moscow 117218, Russia}
\author{M.~A.~Szelezniak}\affiliation{Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA}
\author{A.~H.~Tang}\affiliation{Brookhaven National Laboratory, Upton, New York 11973, USA}
\author{Z.~Tang}\affiliation{University of Science and Technology of China, Hefei 230026, China}
\author{T.~Tarnowsky}\affiliation{Michigan State University, East Lansing, Michigan 48824, USA}
\author{A.~N.~Tawfik}\affiliation{World Laboratory for Cosmology and Particle Physics (WLCAPP), Cairo 11571, Egypt}
\author{J.~H.~Thomas}\affiliation{Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA}
\author{A.~R.~Timmins}\affiliation{University of Houston, Houston, Texas 77204, USA}
\author{D.~Tlusty}\affiliation{Nuclear Physics Institute AS CR, 250 68 \v{R}e\v{z}/Prague, Czech Republic}
\author{M.~Tokarev}\affiliation{Joint Institute for Nuclear Research, Dubna, 141 980, Russia}
\author{S.~Trentalange}\affiliation{University of California, Los Angeles, California 90095, USA}
\author{R.~E.~Tribble}\affiliation{Texas A\&M University, College Station, Texas 77843, USA}
\author{P.~Tribedy}\affiliation{Variable Energy Cyclotron Centre, Kolkata 700064, India}
\author{S.~K.~Tripathy}\affiliation{Institute of Physics, Bhubaneswar 751005, India}
\author{B.~A.~Trzeciak}\affiliation{Czech Technical University in Prague, FNSPE, Prague, 115 19, Czech Republic}
\author{O.~D.~Tsai}\affiliation{University of California, Los Angeles, California 90095, USA}
\author{T.~Ullrich}\affiliation{Brookhaven National Laboratory, Upton, New York 11973, USA}
\author{D.~G.~Underwood}\affiliation{Argonne National Laboratory, Argonne, Illinois 60439, USA}
\author{I.~Upsal}\affiliation{Ohio State University, Columbus, Ohio 43210, USA}
\author{G.~Van~Buren}\affiliation{Brookhaven National Laboratory, Upton, New York 11973, USA}
\author{G.~van~Nieuwenhuizen}\affiliation{Brookhaven National Laboratory, Upton, New York 11973, USA}
\author{M.~Vandenbroucke}\affiliation{Temple University, Philadelphia, Pennsylvania 19122, USA}
\author{R.~Varma}\affiliation{Indian Institute of Technology, Mumbai 400076, India}
\author{A.~N.~Vasiliev}\affiliation{Institute of High Energy Physics, Protvino 142281, Russia}
\author{R.~Vertesi}\affiliation{Nuclear Physics Institute AS CR, 250 68 \v{R}e\v{z}/Prague, Czech Republic}
\author{F.~Videb{ae}k}\affiliation{Brookhaven National Laboratory, Upton, New York 11973, USA}
\author{Y.~P.~Viyogi}\affiliation{Variable Energy Cyclotron Centre, Kolkata 700064, India}
\author{S.~Vokal}\affiliation{Joint Institute for Nuclear Research, Dubna, 141 980, Russia}
\author{S.~A.~Voloshin}\affiliation{Wayne State University, Detroit, Michigan 48201, USA}
\author{A.~Vossen}\affiliation{Indiana University, Bloomington, Indiana 47408, USA}
\author{G.~Wang}\affiliation{University of California, Los Angeles, California 90095, USA}
\author{Y.~Wang}\affiliation{Central China Normal University (HZNU), Wuhan 430079, China}
\author{F.~Wang}\affiliation{Purdue University, West Lafayette, Indiana 47907, USA}
\author{Y.~Wang}\affiliation{Tsinghua University, Beijing 100084, China}
\author{H.~Wang}\affiliation{Brookhaven National Laboratory, Upton, New York 11973, USA}
\author{J.~S.~Wang}\affiliation{Institute of Modern Physics, Lanzhou 730000, China}
\author{J.~C.~Webb}\affiliation{Brookhaven National Laboratory, Upton, New York 11973, USA}
\author{G.~Webb}\affiliation{Brookhaven National Laboratory, Upton, New York 11973, USA}
\author{L.~Wen}\affiliation{University of California, Los Angeles, California 90095, USA}
\author{G.~D.~Westfall}\affiliation{Michigan State University, East Lansing, Michigan 48824, USA}
\author{H.~Wieman}\affiliation{Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA}
\author{S.~W.~Wissink}\affiliation{Indiana University, Bloomington, Indiana 47408, USA}
\author{R.~Witt}\affiliation{United States Naval Academy, Annapolis, Maryland, 21402, USA}
\author{Y.~F.~Wu}\affiliation{Central China Normal University (HZNU), Wuhan 430079, China}
\author{Z.~G.~Xiao}\affiliation{Tsinghua University, Beijing 100084, China}
\author{W.~Xie}\affiliation{Purdue University, West Lafayette, Indiana 47907, USA}
\author{K.~Xin}\affiliation{Rice University, Houston, Texas 77251, USA}
\author{Q.~H.~Xu}\affiliation{Shandong University, Jinan, Shandong 250100, China}
\author{Z.~Xu}\affiliation{Brookhaven National Laboratory, Upton, New York 11973, USA}
\author{H.~Xu}\affiliation{Institute of Modern Physics, Lanzhou 730000, China}
\author{N.~Xu}\affiliation{Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA}
\author{Y.~F.~Xu}\affiliation{Shanghai Institute of Applied Physics, Shanghai 201800, China}
\author{Q.~Yang}\affiliation{University of Science and Technology of China, Hefei 230026, China}
\author{Y.~Yang}\affiliation{Institute of Modern Physics, Lanzhou 730000, China}
\author{S.~Yang}\affiliation{University of Science and Technology of China, Hefei 230026, China}
\author{Y.~Yang}\affiliation{Central China Normal University (HZNU), Wuhan 430079, China}
\author{C.~Yang}\affiliation{University of Science and Technology of China, Hefei 230026, China}
\author{Z.~Ye}\affiliation{University of Illinois at Chicago, Chicago, Illinois 60607, USA}
\author{P.~Yepes}\affiliation{Rice University, Houston, Texas 77251, USA}
\author{L.~Yi}\affiliation{Purdue University, West Lafayette, Indiana 47907, USA}
\author{K.~Yip}\affiliation{Brookhaven National Laboratory, Upton, New York 11973, USA}
\author{I.~-K.~Yoo}\affiliation{Pusan National University, Pusan 609735, Republic of Korea}
\author{N.~Yu}\affiliation{Central China Normal University (HZNU), Wuhan 430079, China}
\author{H.~Zbroszczyk}\affiliation{Warsaw University of Technology, Warsaw 00-661, Poland}
\author{W.~Zha}\affiliation{University of Science and Technology of China, Hefei 230026, China}
\author{X.~P.~Zhang}\affiliation{Tsinghua University, Beijing 100084, China}
\author{J.~Zhang}\affiliation{Shandong University, Jinan, Shandong 250100, China}
\author{Y.~Zhang}\affiliation{University of Science and Technology of China, Hefei 230026, China}
\author{J.~Zhang}\affiliation{Institute of Modern Physics, Lanzhou 730000, China}
\author{J.~B.~Zhang}\affiliation{Central China Normal University (HZNU), Wuhan 430079, China}
\author{S.~Zhang}\affiliation{Shanghai Institute of Applied Physics, Shanghai 201800, China}
\author{Z.~Zhang}\affiliation{Shanghai Institute of Applied Physics, Shanghai 201800, China}
\author{J.~Zhao}\affiliation{Central China Normal University (HZNU), Wuhan 430079, China}
\author{C.~Zhong}\affiliation{Shanghai Institute of Applied Physics, Shanghai 201800, China}
\author{L.~Zhou}\affiliation{University of Science and Technology of China, Hefei 230026, China}
\author{X.~Zhu}\affiliation{Tsinghua University, Beijing 100084, China}
\author{Y.~Zoulkarneeva}\affiliation{Joint Institute for Nuclear Research, Dubna, 141 980, Russia}
\author{M.~Zyzak}\affiliation{Frankfurt Institute for Advanced Studies FIAS, Frankfurt 60438, Germany}

\collaboration{STAR Collaboration}\noaffiliation
main.tex
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\title{Observation of Transverse Spin-Dependent Azimuthal Correlations of Charged Pion Pairs in $p^\uparrow+p$ at $\sqrt{s}=200~GeV$}

% repeat the \author .. \affiliation  etc. as needed
% \email, \thanks, \homepage, \altaffiliation all apply to the current
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\date{\today}

\begin{abstract}
We report the observation of transverse polarization-dependent azimuthal correlations in charged pion pair production with the STAR experiment in $p^\uparrow+p$ collisions at RHIC.
These correlations directly probe quark transversity distributions.
We measure signals in excess of five standard deviations at high transverse momenta, at high pseudorapidities $\eta>0.5$, and for pair masses around the mass of the $\rho$-meson.
This is the first direct transversity measurement in {\it p+p} collisions. Comparing the results to data from lepton-nucleon scattering will test the universality of these spin-dependent quantities.


%%% TOO LONG ---->
%We report the observation of transverse polarization-dependent azimuthal correlations in charged pion pair production with the STAR experiment in $p^\uparrow+p$ collisions at RHIC.
%These correlations originate from the fragmentation of transversely polarized quarks via the spin-dependent  di-hadron interference fragmentation function and thus directly probe the quark transversity distribution.
%The correlations are extracted as a function of the hadron pair transverse momentum, invariant mass, and pseudorapidity. We measure signals in excess of 5~$\sigma$ statistical uncertainty at high transverse momenta, at high pseudorapidities $\eta>0.5$, and for pair masses around the mass of the $\rho$-meson.
%This is the first direct transversity measurement in {\it p+p} collisions and allows an independent determination of quantities that up to now have only been accessed in semi-inclusive deep inelastic scattering. The results can test the universality of these transverse polarization-dependent quantities.

\end{abstract}

\pacs{25.40.Ep, 14.20.Dh, 13.85.Ni}

\maketitle

%A - Introduction
%1-definition of transversity in PDF context (this is mostly there now)
%2-Why measuring h1 is interesting and important (likely needs more than 
%than what is there at the moment to sell this to PRL)
%3-What observable(s) can be measured to get to h1. In general a 
%paragraph should not be much longer than 1/2 of a PRL column. In the 
%current text, information about why the data is important is mixed in 
%with the info on how to extract h1. Those two topics might be split into 
%separate paragraphs.
%---

% INTRODUCTION
The non-perturbative structure of the nucleon can be described in terms of parton distribution functions (PDFs), equivalent to number densities of quarks and gluons in a fast moving nucleon.
Transversity, $h^q_1(x)$, is the least well known of the PDFs.
It represents the transverse quark polarization in transversely polarized nucleons for quark flavor $q$ and momentum fraction $x$.
Due to its chiral odd nature, transversity vanishes for gluons in the nucleon ($s_z=\frac{1}{2} \hbar$) and is primarily a property of the valence quarks~\cite{Barone:2001sp}.
An experimental measurement of the nucleon tensor charge $\delta q=\int_0^1 dx (h^{q}_{1}(x)-h^{\bar{q}}_{1}(x)) $ will directly test our theory of quantum chromodynamics (QCD) when compared to calculations on the lattice or model calculations ~\cite{Anselmino:2013vqa,Gamberg:2001qc,Bacchetta:2012ty,Cloet:2007em,Wakamatsu:2007nc,Gockeler:2005cj,He:1996wy,Schweitzer:2001sr,Pasquini:2005dk,Bacchetta:2008af}.
%--->our understanding of QCD when compared to calculations on the lattice or models
$h_1$ becomes accessible in physics observables when it is coupled with an additional chiral-odd partner, e.g. a transverse spin-dependent fragmentation process.
This second part has to be measured independently in order to extract $h_1$.
Our current knowledge of $h_1$~\cite{Anselmino:2013vqa,Bacchetta:2012ty} is based on fixed-target semi-inclusive deep inelastic lepton-nucleon scattering (SIDIS)~\cite{Airapetian:2004tw,Airapetian:2008sk,Adolph:2012nw,Alekseev:2010rw,Alekseev:2008aa} in combination with data from electron-positron annihilation ~\cite{Seidl:2008xc,Vossen:2011fk}.
Proton-proton collisions allow us to reach into the dominant valence quark region, but the framework of perturbative QCD introduces complications when the intrinsic transverse momentum from the hadronization process has to be considered~\cite{Rogers:2010dm}.
%//// Mention process dependence? ////
It has been shown that di-hadron correlations in the final state persist when integrated over intrinsic transverse momenta.
This so-called Interference Fragmentation Function (IFF), $H_1^{\sphericalangle}$, can therefore be described collinearly~\cite{PhysRevLett.80.1166}. Therefore the contributions to the cross section can be factorized~\cite{Boer:2003ya}
and the IFF should be universal between electron-positron annihilation, SIDIS, and proton-proton scattering.

We present measurements of charged pion correlations from the STAR experiment at the Relativistic Heavy Ion Collider (RHIC) at a center-of-mass energy $\sqrt{s}=200$~GeV.
The data, the first measurement of transversity in polarized proton collisions, show non-zero $h^q_1(x)$ at $0.15<x<0.30$.
In this range, transversity is not well constrained by previous SIDIS measurements and our result will be particularly 
important to restrict the $d$-quark transversity which is charge suppressed in lepton-proton scattering. 


% EXPERIMENTAL SETUP: RHIC + STAR
RHIC, located at Brookhaven National Laboratory, collides bunched beams of heavy ions as well as polarized protons.
The stable beam polarization orientation is transverse to the collider plane and the polarization direction alternates between subsequent bunches or pairs thereof (polarization up $\uparrow$ or down $\downarrow$).
The bunch polarization pattern is changed from fill to fill in order to reduce systematic effects.
While typically both beams are polarized, a single-spin measurement is achieved by summing over the bunches in one beam, effectively reducing its polarization to near zero.
The polarization of each beam is measured by polarimeters using the elastic scattering of protons on very thin carbon targets, several times during a RHIC fill.
The polarimeter are calibrated using a polarized hydrogen gas jet target~\cite{polarimeter}.
We report results from the RHIC run in 2006 with an integrated luminosity of 1.8~pb$^{-1}$ and an average beam polarization of about 60\%.

The STAR experiment is located at one of the collision points in RHIC.
This analysis is based on data in the central pseudorapidity range $-1<\eta<1$.
Data are collected by the Time Projection Chamber (TPC) providing tracking and charged pion identification~\cite{Ackermann:2002ad} and by the Barrel Electromagnetic Calorimeter (BEMC), a lead scintillator sampling calorimeter~\cite{Beddo:2002zx}.
Data from a pair of scintillator-based beam-beam counters (BBC) at forward rapidities $3.3<|\eta|<5.0$ in combination with the BEMC provides a trigger for hard QCD events~\cite{Da:2011da}.
The trigger requires a coincidence between the BBCs and either a minimum transverse energy, $E_T>5$~GeV in a single BEMC tower or one of several jet patch triggers in $\Delta\phi\times\Delta\eta=1.0\times 1.0$ ($E_T>$ 4.0 or 7.8 GeV).


Charged pion pairs are selected by requiring tracks that originate
within $\pm 60$~cm in the longitudinal direction and 1~cm in the transverse direction from the nominal interaction vertex and that are required to point into the central region.
Tracks are required to have a minimum transverse momentum $p_T$ of 1.5 GeV/$c$. Using $dE/dx$ measurements in the TPC to select pions, a purity of the single pion sample of greater than 95\% over the whole kinematic range is achieved.
All pion pairs in an event are considered where the pions are close enough in ($\eta,\phi$) space to originate from the fragmentation
of the same parton. The default value of this opening angle cut is $\sqrt{(\eta_{\pi_1}-\eta_{\pi_2})^2+(\phi_{\pi_1}-\phi_{\pi_2})^2}<0.3$. 
Pion pairs produced in the weak decay of the $K^0$ meson are not expected to contribute to the asymmetry, therefore the corresponding mass range (497.6 $\pm$ 10 MeV) was excluded from the analysis.

%<----------

%how is it measured?

%---
%B-Definition of the observable

%This seems to begin here: "Bacchetta et. al. proposed [11] to use the 
%single spin asymmetry..." But at this point you should say: We 
%measured ..., proposed by Bacchetta\ et.\ al... so the reader understands 
%you are stating on the definition of what will be presented and are no longer
%speaking hypothetically.

%Maybe the discussion beginning "Then the amplitude A_N¦ provides direct 
%access to transversity,..." would be better moved to the conclusion 
%section.
%----

%new below

\begin{figure}[h]
\includegraphics[width=0.5\textwidth]{IFF_frame.pdf}
\caption{Azimuthal angle defintions in the dihadron system.
$\vec{s}_{a}$ is the direction of the spin of the polarized proton, $\vec{p}_{h,\{1,2\}}$ are the
momenta of the positive and negative pion, respectively and $\phi_R$ is
the angle between the production and dihadron plane.
\label{fig:angles}}
\end{figure}

The transversely polarized cross-section of hadron pairs in $p^\uparrow+p$ collisions can be written similar to~\cite{Bacchetta:2004it}:
\begin{equation}
d\sigma_{UT}\propto \sin(\phi_{RS})
\int dx_a dx_b f_1(x_a) h_1(x_b) \frac{d\Delta\hat{\sigma}}{d\hat{t}} H_{1,q}^\sphericalangle(z,M).
\label{eq:xsect}
\end{equation}
%\begin{multline}
%removed o,t from H: this is just one part of the legendre polynomials, so eq. is also true w/o
%\sigma_{UT}=2|\vec{P}_{\perp}| \sum_{a,b,c,d}\frac{\vec{R}}{M} |\vec{S}_{T}|\sin(\phi_{RS}) \\
%\int \frac{dx_a dx_b}{16\pi z} f_1^a(x_a)h_1^b(x_b)\frac{d\Delta \sigma_{ab^\uparrow\rightarrow cd^\uparrow}}{d\hat{t}}H_1^{\sphericalangle}(z_{\pi^+\pi^-},M_{\pi^+\pi^-}^2). 
%\label{eq:xsect}
%\end{multline}
Here, $\hat{\sigma}$ is the polarized scattering cross section of partons $a$ and $b$ with four momentum transfer $\hat{t}$. The unpolarized parton distribution is $f_1(x)$.
The fragmentation function $H_{1,q}^\sphericalangle$ is a function of $z$, the fractional energy with respect to the fragmenting quark  carried by the hadron pair and its invariant mass, $M$.
The angle $\phi_{RS}=\phi_R - \phi_S$ is derived according to Fig.~\ref{fig:angles} from the angle between the polarization vector and the production plane, $\phi_S$ and the angle between the two hadron plane and the production plane, $\phi_R$.
The production plane is spanned by the incident proton momentum, $\vec{p}_{beam}$, and the sum of the two hadron momenta, $\vec{p}_h=\vec{p}_{h,1}+\vec{p}_{h,2}$.
The difference of the momenta $\vec{R}=\vec{p}_{h,1}-\vec{p}_{h,2}$ lies in the hadron plane. 
The convolution of $h_1(x)$ and $H_{1,q}^{\sphericalangle}$ will introduce an asymmetry, modulated by $\sin(\phi_{RS})$.
%Here, $\phi_{RS}=\phi_R-\phi_S$ and $\phi_S$ is the angle between the polarization vector of the polarized proton to the production plane and $\phi_R$ is the azimuthal angle between the difference vector of the two hadron momenta: $\vec{R}=\vec{P}_{h_1}-\vec{P}_{h_2}$ and the production plane. 
%The production plane is spanned by the vectors parallel to the polarized beam direction and $\vec{P}_h=\vec{P}_{h_1}+\vec{P}_{h_2}$.
%The product of the transversity $h(x)$ and IFF $H_1^{\sphericalangle}$ can then be accessed by extracting the modulation of $\sigma_{UT}$ in $\phi_{RS}$.
The effect will inherit the dependence on the partonic variable $x$ from $h_1(x)$ and the final state variables $M$ and $z$.

%---


An experimental observable directly proportional to the differential cross-section is constructed for each RHIC fill:
\begin{equation}
\frac{N^\uparrow(\phi_{RS})-r\cdot N^\downarrow(\phi_{RS})}{N^\uparrow(\phi_{RS})+r\cdot N^\downarrow(\phi_{RS})} = P_{beam}\cdot A_{UT}\cdot\sin(\phi_{RS}).
\label{eq:simpleForm}
\end{equation}
where $N^{\uparrow/\downarrow}$ is the number of pion pairs meeting the selection criteria for each polarization state, $P_{beam}$ the beam polarization and  $r$ the ratio $L^{\uparrow}/L^{\downarrow}$ between the integrated luminosities of the two polarization states.
%Both are required external input to the asymmetry measurement.
%We define  $N^{\uparrow/\downarrow}(\phi_{RS})$ as the number of hadron pairs in a specific angular bin when an up- or downward polarized beam hits an unpolarized target beam. Since the two polarization states are not equally populated, eq.~\ref{eq:simpleForm} has to be corrected for  the relative luminosity $R$ of the two polarization states and then divided by the beam polarization $P$ to get the intrinsic asymmetry. This leads to the relative luminosity formula: 
%\begin{equation}
%A_{UT}^{\sin\phi}(\phi_{RS})\sin(\phi_{RS})=\frac{1}{P}\frac{N^\uparrow(\phi_{RS})-RN^\downarrow(\phi_{RS})}{N^\uparrow(\phi_{RS})+RN^\downarrow(\phi_{RS})}
%\end{equation}
% for a specific angular bin. 
%One can therefore write:
%\begin{multline}
%A_{UT}(\phi_{RS})=\\\frac{1}{P}   \frac{\sqrt{N^\uparrow(\phi_{RS})N^\downarrow(\phi_{RS}+\pi)}-\sqrt{N^\downarrow(\phi_{RS})N^\uparrow(\phi_{RS}+\pi)}}{\sqrt{N^\uparrow(\phi_{RS})N^\downarrow(\phi_{RS}+\pi)}+\sqrt{N^\downarrow(\phi_{RS})N^\uparrow(\phi_{RS}+\pi)}}. 
%\end{multline}

%%%% C - STAR Analysis

The data is binned in 16 equal bins covering $2\pi$ in azimuth. The amplitude $A_{UT}$ of $\sin(\phi_{RS})$ is extracted by a fit to the data.
%For this analysis we calculate the asymmetries on the left side of eq.~\ref{eq:simpleForm} for 16 separate azimuthal bins and then fit with a sine function to extract $A_{UT}$.
The description of the functional form is very good, with a reduced $\chi^2$ per degree of freedom of $0.975\pm 0.007$ over all kinematic bins.
We include all pion pairs with opposite charges from an event and define $\vec{p}_{h,1}$ to be the momentum of the positive particle (and $\vec{p}_{h,2}$ the negative particle accordingly).
Note that this charge ordering is essential because it establishes the direction of $\vec{R}$.
A random charge assignment would lead to a vanishing asymmetry since it would randomize the sign of $\phi_{RS}$.


%%%% D - Results

\begin{figure}[h]
\begin{center}
	\includegraphics[width=0.45\textwidth]{IFF_fig2.pdf}
	\caption{$A_{UT}$ as a function of $M$ (upper panel) and corresponding partonic variables $x$ and $z$ (lower panel).
    A clear enhancement of the signal around the $\rho$  mass region can be observed.\label{fig:fwdBwdAsymM} }. 
\end{center}
\end{figure}

Figure~\ref{fig:fwdBwdAsymM} shows the results for $A_{UT}$ as a function of the invariant mass $M$ of the pion pair, both for forward ($\eta>0$)and backward ($\eta<0$) going particles.
We define the forward direction here along the momentum of the polarized beam.
The results combine independent measurements of the asymmetries for both polarized RHIC beams in the two halves of the STAR detector, which provides internal consistency checks.

% In addition to the s-p interference, contributions from p-p interference are possible at our kinematics.
%However the p-p contribution is proportional to $\cos\theta$ whereas the s-p interference term is proportional to $\sin\theta$, with $\theta$ being the decay angle in %the two-hadron center of mass frame. For this measurement, the average $\sin\theta$ value in each kinematic bin is close to unity and conversely the $\cos\theta$ d%istribution has a mean of zero. Therefore only the s-p contribution is of relevance.

We used a Pythia~\cite{Sjostrand:2006za} simulation in conjunction with a  model of the STAR detector response implemented in GEANT~\cite{Brun:1978fy} to determine the partonic scattering processes as well as the partonic variables $x$ and $z$, the fractional momentum of the parent quark carried by the two hadrons.
These are shown in the lower panel of Fig.~\ref{fig:fwdBwdAsymM}.
%The lower panel Fig.~\ref{fig:fwdBwdAsymM} in Fig.~\ref{fig:fwdBwdAsymM} shows the partonic variables $x$ and $z$.
The simulation agrees reasonably well with the data and detector resolutions are small compared to the presented bin sizes.
The mean $x$ value, $\langle x\rangle$, of the recorded data at midrapidity is around 0.2 and it changes very little over the available invariant mass range.
This is well in the valence region, $x>0.1$, where transversity is expected to be sizable.
On the other hand, $\langle z\rangle$ rises more strongly with the invariant mass.
This is essentially a consequence of the opening angle cut and the required minimum $p_T$ for each hadron.
Naively one expects that the IFF is uniformly rising in $z$, since hadrons at high $z$ carry more of the parent quark spin information.
This is consistent with measurements in $e^+e^-$ annihilation ~\cite{Vossen:2011fk} where sizable values have been observed at similar $z$ and $M$.

In model calculations, the transverse spin dependence of the IFF originates from an interference of amplitudes with different angular momenta~\cite{Bianconi:1999uc}.
In our kinematic region, this will mainly be contributions from vector meson decays in a relative p-wave which interfere with non-resonant background in a relative s-wave.
Therefore, it is expected that the invariant mass dependence will show an enhancement around the mass of the $\rho$ meson~\cite{Bianconi:1999uc}.
Our results confirm these expectations and show a clear signal in the forward direction around the $\rho$ mass.

Backward asymmetries, $\eta<0$, are sensitive to quarks at small $x$.
They are consistent with zero, as is expected since transversity is primarily carried by the valence quarks.

\begin{figure}[h!]
\begin{center}
	\includegraphics[width=0.45\textwidth]{IFF_fig3.pdf}
	\caption{$A_{UT}$ as a function of $\eta$ (upper panel) and corresponding partonic variables $x$ and $z_{\pi^+\pi^-}$ (lower panel). \label{fig:etaAsym}}
\end{center}
\end{figure}

%The $M_{\pi^+\pi^-}$  dependence 
%	\begin{figure}[h]
%	\begin{center}
% \includegraphics[width=0.45\textwidth]{../paperPlots//cPt_kinematics.png}
%				\caption{$A_{UT}^{\sin\phi}$ as a function of $p_{T_{\pi^+\pi^-}}$ (upper panel) and corresponding $M_{\pi^+\pi^-}$ and partonic variables $x$ and $z_{\pi^+\pi^-}$ (lower panel). Only the largest transverse momenta contribute to the asymmetry indicating a steep rise of transversity in this $x$ range.\label{fig:fwdBwdAsymPt}}
%	\end{center}
%\end{figure}
%Figure~\ref{fig:fwdBwdAsymPt} also shows significant asymmetries at large transverse momenta of the hadron pair $p_{T_{\pi^+\pi^-}}$ where the average $x$ of the scattered parton is larger, rising to a value of about 0.27, and $z_{\pi^+\pi^-}$ is higher, increasing the magnitude of the spin dependent fragmentation function.

Figure~\ref{fig:etaAsym} shows $A_{UT}$ as a function of $\eta$ in more detail.
The $\langle x\rangle$ of the polarized beam rises approximately linearly with $\eta$ from 0.15 to 0.25 while $\langle z\rangle \approx 0.4$ in the covered acceptance.
The measured asymmetries reflect the $x$-dependence and valence quark nature of transversity and rise monotonically with $\eta$. The partonic spin transfer coefficient becomes larger in the forward direction as well, but its contribution to the $\eta$ dependence of the asymmetry is small compared to the shape of the transversity distribution.

%The asymmetries mirror this behavior and clearly reflect the $x$-dependence and valence quark nature of transversity. At large $\eta$ the asymmetries are enhanced by larger values of the spin transfer coefficient. 
We show the corresponding distributions of $x$ in Fig.~\ref{fig:xdist} for the highest and lowest $\eta$ ranges from Fig.~\ref{fig:etaAsym}.
The distributions are fairly wide and asymmetrical as is expected for hadronic collisions.
They also partially overlap, but the different pseudrapdidities clearly are sensitive to different partonic kinematics.
%Spin transfer coefficients can partially account for the observed $\eta$ dependence, but the monotonous behavior of $h_1(x)$ persists in simulations studies even when the partonic spin transfer kinematics are included.

\begin{figure}[h]
\begin{center}
	\includegraphics[width=0.45\textwidth]{IFF_fig4.pdf}
	\caption{Comparison of the shape of the partonic momentum distributions in the polarized protons for different pseudorapidity regions of the pion pair as determined from embedded event simulation studies.
    The distributions are not fully normalized.
    \label{fig:xdist}}
\end{center}
\end{figure}

%\begin{figure}[h]
%	\begin{center}	
%\includegraphics[width=0.45\textwidth]{../paperPlots//cPt_conePaper.png}
%			\caption{$A_{UT}^{\sin\phi}(p_{T_{\pi^+\pi^-}})$  with different cone cuts. In a given $p_{T_{\pi^+\pi^-}}$ bin the dependence on the cone cut and thus on %the mean $M_{\pi^+\pi^-}$ is only weak. Data points are offset for visibility.\label{fig:coneAsymPt}}
%	\end{center}
%\end{figure}	

% The $x$ distributions for the smallest and largest $\eta$ bin are shown in Fig.~\ref{fig:xdist}. As is typical in $p+p$ collisions, the distributions are wide and do partially overlap, which has to be taken into account when extracting transversity from this data.

We also investigated the effect of different upper values for the opening angle, ranging from 0.2 to 0.4 as shown in Fig.~\ref{fig:coneAsymM}.
\begin{figure}[h]
\begin{center}
	\includegraphics[width=0.45\textwidth]{IFF_fig5.pdf}
	\caption{$A_{UT}(M)$ with different opening angle cuts. The signal in each  $M$ bin exhibits a strong dependence on the mean $p_{T}$.
Data points are slightly shifted in $M$ for better visibility.\label{fig:coneAsymM}}
\end{center}
\end{figure}
At intermediate invariant masses, $M>0.7~$GeV$/c^2$, the asymmetries depend strongly on this geometric limitation; wider opening angles result in smaller asymmetries.
As can be seen in the bottom panel, the opening angle cut also directly affects the mean $\langle p_{T}\rangle$ of the pion pair.
Larger opening angles typically allow for more pions with low momentum, so a tighter cut selects high transverse momenta; supplemental data tables list the details and are available online.
This, in effect would also increase the contributions of pion pairs with high $z$ and high $x$ which (see above) have been found to scale with the asymmetries~\cite{Vossen:2011fk}.
While there is a clear distinction between the asymmetries with increasing invariant mass, at the largest masses the statistical uncertainty, especially for the most restrictive cuts on the opening angle, does not allow for a decisive statement at this point.
It might be that the $z$-dependence of the asymmetries is a minor contribution and what we observe is actually largely driven by the change in the relative contribution of the resonant production of pions from $\rho$-decays and the non-resonant channel.
Non-resonant pions are more likely at low $p_T$ and their dominance in the data sample will dilute the asymmetry when using wider opening angle cuts.

%As the mean $p_{T_{\pi^+\pi^-}}$ is dependent on the size of the cone, larger cone sizes allowing for more pions at low transverse momenta we can observe the combined $p_{T_{\pi^+\pi^-}}$, $M_{\pi^+\pi^-}$ dependence of the asymmetries.
%Our results show a correlation between the mean $\langle p_T \rangle$ and the size of the observed asymmetries.
%At fixed $M_\textrm{Inv}$, higher values of $\langle p_T\rangle$ lead to higher observed asymmetries.
%One explanation is that the mean $\langle x \rangle$ and $\langle z \rangle$ are $p_T$ dependent and thus one would expect higher asymmetries at higher $p_T$.

%At fixed $M_{\pi^+\pi^-}$, the asymmetries reflect the $p_{T_{\pi^+\pi^-}}$ dependence for different cone cuts which is mainly a consequence of the $z_{\pi^+\pi^-}$ dependence of the IFF. 

%Supplemental tables (available online) list the corresponding mean values of the partonic variables as obtained from simulations.
%For the more restrictive cone cut of 0.2 an average $x$ value of 0.3 is reached at high $p_{T_{\pi^+\pi^-}}$ and the $\langle z \rangle$ for the most restrictive cone cut is more than 0.1 larger than for the least restrictive cut in the three highest $M_\textrm{Inv}$ bins.
%However, there might also be a more subtle effect, which has an influence on the difference of observed asymmetries between the different cone cuts.
%Since non-resonant pion production is more likely to produce low $p_T$ pions, the different cone cuts will also have an effect on the relative s- and p-wave contributions to the fragmentation function, which will change the strength of the spin dependent effect.


%%%% SYSTEMATIC UNCERTAINTIES

The leading systematic uncertainty for our results comes from the ~4.8\% scale uncertainty of the beam polarization.
On average the purity of the single pion sample is 96\% which has been determined in simulation studies.
The purity shows a slight dependence on the transverse momentum, starting at around 94\% and rising up to 97\% at with $p_{T}$.
The asymmetry in $\pi-p$ correlations is expected to be very small in model calculations.
Data from $\pi-K$ asymmetries~\cite{compassPiK} are of the same sign as those of the two-pion system and of similar or smaller size.
We do not assign a systematic uncertainty to the results due to the unknown size of background asymmetry.
In the worst case the dilution of the asymmetry is on the same order of magnitude as the impurity of the pion sample. Triggering on large electromagnetic energy deposits introduces a bias in the sampled event kinematics and partonic processes~\cite{Adamczyk:2012qj}. From simulations, we determine that our trigger bias in selecting the partonic subprocess leads to an enhancement of the fraction of quark-quark scattering sampled of up to 20\% whereas quark-gluon and gluon-gluon scattering processes are suppressed by up to 10\%.
Overall, systematic uncertainties are very small compared to the statistical precision of the measurement, and they are not shown in the figures.

A variety of systematic checks have been carried out
to ensure the correctness of the results. A random assignment of the polarization states of the beam bunches leads to vanishing spin asymmetries. The $\chi^2$ values of the individual fits are distributed according to a $\chi^2$ distribution (within the relevant statistics).
An alternative way of computing the asymmetry takes advantage of the fact
that the asymmetry is antisymmetric in $\phi_{RS}$ and therefore a shift of
$\pi$ and a flip of the beam polarization both lead to a sign change of the
asymmetry~\cite{Ohlsen:1973}. The advantage of this "proper-flip" method is that the relative luminosity dependence cancels. It leads to the same result as~(\ref{eq:simpleForm}). In addition, the consistency between asymmetries for both RHIC beams is an important check, as is the stability of the results over the duration of the measurement.



%%%% E - Conclusion

%Maybe you should summarize the measurements and statistical significance 
%first. Then describe how this measurement implies significant, non-zero 
%transversity. Once you are happy with the concluding paragraph or 
%paragraphs, try to summarize them in a few sentences for the conclusion of 
%the abstract

In summary, STAR has observed transverse spin-dependent charged pion pair correlation asymmetries with a statistical significance of more than five standard deviations away from zero.
Using the collinear factorization framework, the distribution of transversely polarized quarks described by the proton's transversity distribution function can be extracted from these results. 
This constitutes the first signal of transversity in $p^\uparrow+p$ collisions.
The observed signal is enhanced for invariant masses of the hadron pair around the  $\rho$ mass and rises with $p_{T}$ and $\eta$ consistent with qualitative expectations from the transversity distribution function and the dependence of the IFF on $z$ and $M$.
These results can be included in an extraction of transversity from world data in a collinear framework that is currently underway~\cite{Bacchetta:2011ab}.
Compared with previous measurements of two hadron correlations in SIDIS, the RHIC data allows access to a complementary kinematic regime.
Proton-proton collisions do not suffer from $u$-quark dominance and will therefore help constrain the $d$-quark transversity. 
This is the first measurement of transverse spin asymmetries in $p^{\uparrow}+p$ collisions  which can be directly compared to those in SIDIS and $e^+-e^-$ annihilation.
Thus it is an important test of factorization and universality in these processes, particularly so in light of the recent discovery that factorization is broken for transverse spin asymmetries in $p+p$ collisions that vanish in a collinear framework~\cite{Rogers:2010dm}.


\input{acknowledgements}


%One example is the Collins asymmetry, which originates from the correlation of the intrinsic transverse momentum in the fragmentation with the outgoing quark spin.
%The comparison of the measurement presented in this paper with the Collins asymmetries extracted from p+p data will provide bounds on the effect of the expected factorization breaking in the transverse momentum dependent framework used to describe the Collins asymmetries.

%A large dataset taken in 2012 will allow us to reduce the error bars on this measurement by about a factor of 3 and hadron pairs involving neutral pions will be investigated. 


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\section{Supplemental Information}
%\input{paperTables}
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\end{document}
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% ****** End of file apstemplate.tex ******
tables2.tex
\begin{center}
	\begin{table}[h!]
%\hspace{-1cm}
\caption{\label{trigTable1}$p_T$ asymmetries, $\eta<0$, maximum opening angle of 0.2}
		\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c| } \hline
		%\begin{tabular}{| >{\centering\arraybackslash}p{.5in} |  >{\centering\arraybackslash}p{.5in}| >{\centering\arraybackslash}p{.5in}| >{\centering\arraybackslash}p{.5in}| >{\centering\arraybackslash}p{.5in}| >{\centering\arraybackslash}p{.5in}| >{\centering\arraybackslash}p{.5in}| >{\centering\arraybackslash}p{.5in}| >{\centering\arraybackslash}p{.5in}| >{\centering\arraybackslash}p{.5in}| >{\centering\arraybackslash}p{.5in}| >{\centering\arraybackslash}p{.5in}|} \hline
\vtop{\hbox{\strut $\left<p_T\right>$}\hbox{ \strut [GeV/c] } }& $\left<\sin\theta\right>$ & \vtop{\hbox{\strut $\left<M_\textrm{Inv}\right>$}\hbox{ \strut [GeV/c$^2$] } } & $A_{\textrm{UT}}^{\sin\phi}$ & $\sigma_{A_{\textrm{UT}}^{\sin\phi}}$ & $\left<z\right>$ & $\sigma_{\left<z\right>}$ & $\left<x_1\right>$ & $\sigma_{\left<x_1\right>}$ & $\left<x_2\right>$& $\sigma_{\left<x_2\right>}$ & $\left<\eta\right>$   \\                                                                 \hline                                                                                                                                


3.62& 0.99 & 0.38 & -0.031& 0.014 & 0.29 & 0.10 &  0.15 & 0.10 & 0.20  & 0.11 & -0.50\\
4.49& 0.96 & 0.41 & -0.010& 0.012 & 0.35 & 0.12 & 0.15 & 0.10 & 0.20 & 0.11 & -0.51\\
5.70& 0.93 & 0.47 & 0.023& 0.011 &0.44 & 0.16 & 0.16 & 0.11 &  0.21 & 0.11 & -0.51\\
7.18& 0.91 & 0.55 & 0.016& 0.014 &  0.48 & 0.15 & 0.16 & 0.11& 0.23 & 0.11 & -0.51\\
10.45& 0.88 & 0.68 & 0.0085& 0.013 &  0.57 & 0.17 & 0.20 & 0.12 & 0.27 & 0.12 & -0.51\\
\hline
           			\end{tabular}
\end{table}
\end{center}


 \begin{center}
	\begin{table}[h!]
%\hspace{-1cm}
\caption{$\left<M_\textrm{Inv}\right>$ asymmetries, $\eta<0$, maximum opening angle of 0.2}
\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|} \hline
 \vtop{\hbox{\strut $\left<M_\textrm{Inv}\right>$}\hbox{ \strut [GeV/c$^2$] } } & $\left<\sin\theta\right>$ & \vtop{\hbox{\strut $\left<p_T\right>$}\hbox{ \strut [GeV/c] } } & $A_{\textrm{UT}}^{\sin\phi}$ & $\sigma_{A_{\textrm{UT}}^{\sin\phi}}$ & $\left<z\right>$ & $\sigma_{\left<z\right>}$ & $\left<x_1\right>$ & $\sigma_{\left<x_1\right>}$ & $\left<x_2\right>$& $\sigma_{\left<x_2\right>}$ & $\left<\eta\right>$ \\    
 \hline                                                               
0.36& 0.95 & 4.73 & -0.013& 0.010 &  0.38 & 0.15 & 0.16 & 0.11 & 0.22 & 0.12 & -0.51\\                                                                                                   
0.48& 0.94 & 5.93 & 0.015& 0.0080 &  0.43 & 0.17 & 0.16 & 0.11 & 0.22 & 0.11 & -0.51\\                                                                                                    
0.68& 0.91 & 8.58 & -0.0044& 0.014 & 0.53 & 0.17 & 0.17 & 0.11 & 0.24 & 0.12  & -0.51\\                                                                                                   
0.88& 0.90 & 11.13 & 0.022& 0.027 &  0.59 & 0.17 & 0.21 & 0.12 & 0.28 & 0.13 & -0.51\\                                                                                                   
1.15& 0.90 & 14.57 & 0.0042& 0.062 &  0.63 & 0.15 & 0.23 & 0.13 & 0.34 & 0.13 & -0.48\\   
\hline                                                                                                		\end{tabular}
	\end{table}
\end{center}
                                                                           \begin{center}
	\begin{table}[h!]
%\hspace{-1cm}
\caption{$p_T$ asymmetries, $\eta>0$, maximum opening angle 0.2}
		\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|} \hline
  \vtop{\hbox{\strut $\left<p_T\right>$}\hbox{ \strut [GeV/c] } } & $\left<\sin\theta\right>$ & \vtop{\hbox{\strut $\left<M_\textrm{Inv}\right>$}\hbox{ \strut [GeV/c$^2$] } } & $A_{\textrm{UT}}^{\sin\phi}$ & $\sigma_{A_{\textrm{UT}}^{\sin\phi}}$ & $\left<z\right>$ & $\sigma_{\left<z\right>}$ & $\left<x_1\right>$ & $\sigma_{\left<x_1\right>}$ & $\left<x_2\right>$& $\sigma_{\left<x_2\right>}$ & $\left<\eta\right>$\\
 \hline
3.62& 0.99 & 0.38 & 0.0090& 0.014 &  0.28 & 0.10 & 0.21 & 0.11 & 0.15 & 0.11 &0.50\\
4.49& 0.96 & 0.41 & 0.0095& 0.012 & 0.34 & 0.12 & 0.21 & 0.11 & 0.15 & 0.11 &0.51\\
5.70& 0.93 & 0.47 & 0.022& 0.011 & 0.42 & 0.15 & 0.22 & 0.12 & 0.15 & 0.10 &0.51\\
7.18& 0.91 & 0.55 & 0.0050& 0.014 &  0.50 & 0.19 & 0.23 & 0.12 & 0.16 & 0.10 &0.51\\
10.45& 0.88 & 0.68 & 0.057& 0.012 & 0.58 & 0.17 & 0.27 & 0.13 & 0.20 & 0.12 & 0.51\\
\hline
           		\end{tabular}
	\end{table}
\end{center}
 \begin{center}
	\begin{table}[h!]
%\hspace{-1cm}
\caption{$\left<M_\textrm{Inv}\right>$ asymmetries, $\eta>0$, maximum opening angle 0.2}
		\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|} \hline
\vtop{\hbox{\strut $\left<M_\textrm{Inv}\right>$}\hbox{ \strut [GeV/c$^2$] } }  & $\left<\sin\theta\right>$ & \vtop{\hbox{\strut $\left<p_T\right>$}\hbox{ \strut [GeV/c] } }& $A_{\textrm{UT}}^{\sin\phi}$ & $\sigma_{A_{\textrm{UT}}^{\sin\phi}}$ & $\left<z\right>$ & $\sigma_{\left<z\right>}$ & $\left<x_1\right>$ & $\sigma_{\left<x_1\right>}$ & $\left<x_2\right>$& $\sigma_{\left<x_2\right>}$ & $\left<\eta\right>$   \\                                                                   \hline
0.36& 0.95 & 4.73 & 0.0054& 0.010 &  0.38 & 0.16 & 0.23 & 0.12 & 0.16 & 0.11 & 0.51\\  
0.48& 0.94 & 5.93 & 0.019& 0.0081 &  0.42 & 0.16 & 0.22 & 0.12 & 0.16 & 0.11 & 0.51\\                                                                                                     
0.68& 0.91 & 8.58 & 0.033& 0.014 &  0.55 & 0.20 & 0.25 & 0.12 & 0.17 & 0.11 & 0.51\\                                                                                                     
0.88& 0.90 & 11.13 & 0.11& 0.027 &  0.60 & 0.17 & 0.27 & 0.13 & 0.20 & 0.12 & 0.51\\                                                                                                    
1.15& 0.90 & 14.57 & 0.13& 0.060 &  0.65 & 0.17 & 0.31 & 0.13 & 0.24 & 0.13 & 0.48\\  
\hline

           		\end{tabular}
	\end{table}
\end{center}
  \begin{center}
	\begin{table}[h!]
%\hspace{-1cm}
\caption{$p_T$ asymmetries, $\eta<0$, maximum opening angle 0.3}
		\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|} \hline                                                                                                                                                                                               
 \vtop{\hbox{\strut $\left<p_T\right>$}\hbox{ \strut [GeV/c] } } & $\left<\sin\theta\right>$ & \vtop{\hbox{\strut $\left<M_\textrm{Inv}\right>$}\hbox{ \strut [GeV/c$^2$] } } & $A_{\textrm{UT}}^{\sin\phi}$ & $\sigma_{A_{\textrm{UT}}^{\sin\phi}}$ & $\left<z\right>$ & $\sigma_{\left<z\right>}$ & $\left<x_1\right>$ & $\sigma_{\left<x_1\right>}$ & $\left<x_2\right>$& $\sigma_{\left<x_2\right>}$ & $\left<\eta\right>$ \\
 \hline
3.61& 0.99 & 0.45 & -0.022& 0.010 & 0.30 & 0.13 & 0.15 & 0.10 & 0.20 & 0.11  & -0.49\\
4.49& 0.97 & 0.51 & -0.007& 0.0087 & 0.36 & 0.13 & 0.15 & 0.11 & 0.20 & 0.11  & -0.50\\
5.68& 0.94 & 0.59 & 0.018& 0.0082 &  0.43 & 0.16 & 0.16 & 0.11 & 0.22 & 0.11 & -0.51\\
7.17& 0.92 & 0.67 & 0.021& 0.011 &  0.48 & 0.15 & 0.16 & 0.11 & 0.23 & 0.11 & -0.51\\
10.32& 0.88 & 0.81 & 0.0088& 0.011 & 0.57 & 0.17 & 0.19 & 0.12 & 0.27 & 0.12 & -0.51\\
\hline
           		\end{tabular}
	\end{table}
\end{center}
 \begin{center}
	\begin{table}[h!]
%\hspace{-1cm}
\caption{$\left<M_\textrm{Inv}\right>$ asymmetries, $\eta<0$, maximum opening angle 0.3}
		\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|} \hline
 \vtop{\hbox{\strut $\left<M_\textrm{Inv}\right>$}\hbox{ \strut [GeV/c$^2$] } } & $\left<\sin\theta\right>$ & \vtop{\hbox{\strut $\left<p_T\right>$}\hbox{ \strut [GeV/c] } } & $A_{\textrm{UT}}^{\sin\phi}$ &$\sigma_{A_{\textrm{UT}}^{\sin\phi}}$ & $\left<z\right>$ & $\sigma_{\left<z\right>}$ & $\left<x_1\right>$ & $\sigma_{\left<x_1\right>}$ & $\left<x_2\right>$& $\sigma_{\left<x_2\right>}$ & $\left<\eta\right>$ \\           
 \hline                                                                                                                                  
0.36& 0.95 & 4.73 & -0.013& 0.010 & 0.38 & 0.15 & 0.16 & 0.11 & 0.22 & 0.12 & -0.51\\
0.50& 0.95 & 5.35 & 0.0063& 0.0068 &  0.41 & 0.17  & 0.16 & 0.11 & 0.21& 0.11 & -0.50\\ 
0.69& 0.94 & 6.35 & 0.00020 & 0.0081 &  0.44 & 0.17 & 0.16 & 0.11 & 0.22 & 0.11 & -0.51\\
0.88& 0.92 & 7.98 & 0.025& 0.013 &  0.50 & 0.17 & 0.17 & 0.11 & 0.25 & 0.12 & -0.51\\
1.19& 0.90 & 10.63 & 0.017& 0.020 & 0.56 & 0.17 & 0.19 & 0.12 & 0.27 & 0.13 & -0.50\\     
\hline                                                                                                          		\end{tabular}
	\end{table}
\end{center}                                                                         
                                                                                                                                                                                  
  \begin{center}
	\begin{table}[h!]
%\hspace{-1cm}
\caption{$p_T$ asymmetries, $\eta>0$,maximum opening angle 0.3}
		\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|} \hline                                                                          
 \vtop{\hbox{\strut $\left<p_T\right>$}\hbox{ \strut [GeV/c] } }& $\left<\sin\theta\right>$ & \vtop{\hbox{\strut $\left<M_\textrm{Inv}\right>$}\hbox{ \strut [GeV/c$^2$] } } & $A_{\textrm{UT}}^{\sin\phi}$ & $\sigma_{A_{\textrm{UT}}^{\sin\phi}}$ & $\left<z\right>$ & $\sigma_{\left<z\right>}$ & $\left<x_1\right>$ & $\sigma_{\left<x_1\right>}$ & $\left<x_2\right>$& $\sigma_{\left<x_2\right>}$ & $\left<\eta\right>$  \\
 \hline
3.61& 0.99 & 0.45 & 0.0092& 0.010 &   0.29 & 0.10 & 0.20 & 0.11 & 0.14 & 0.10 & 0.49\\
4.49& 0.97 & 0.51 & 0.011& 0.0086 &   0.35 & 0.12  & 0.21 & 0.11 & 0.15 & 0.11 & 0.50\\
5.68& 0.94 & 0.59 & 0.029& 0.0082 &   0.43 & 0.15 & 0.22 & 0.12 & 0.15 & 0.10 & 0.51\\
7.17& 0.92 & 0.67 & 0.0071& 0.011 &   0.50 & 0.18 & 0.23 & 0.12 & 0.16 & 01.0 & 0.51\\
10.32& 0.88 & 0.81 & 0.053& 0.011 &  0.58 & 0.18 & 0.27 & 0.13 & 0.19 & 0.12 & 0.51\\
\hline
           		\end{tabular}
	\end{table}
\end{center}


 \begin{center}
	\begin{table}[h!]
%\hspace{-1cm}
\caption{$\left<M_\textrm{Inv}\right>$ asymmetries, $\eta>0$, maximum opening angle 0.3}
		\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|} \hline
\vtop{\hbox{\strut $\left<M_\textrm{Inv}\right>$}\hbox{ \strut [GeV/c$^2$] } }  & $\left<\sin\theta\right>$ & \vtop{\hbox{\strut $\left<p_T\right>$}\hbox{ \strut [GeV/c] } } & $A_{\textrm{UT}}^{\sin\phi}$ &$\sigma_{A_{\textrm{UT}}^{\sin\phi}}$ & $\left<z\right>$ & $\sigma_{\left<z\right>}$ & $\left<x_1\right>$ & $\sigma_{\left<x_1\right>}$ & $\left<x_2\right>$& $\sigma_{\left<x_2\right>}$ & $\left<\eta\right>$ \\                                                                   \hline                                                                          
0.36& 0.95 & 4.73 & 0.0054& 0.010 &   0.38 & 0.16 & 0.23 & 0.12  & 0.16 & 0.11 & 0.51\\
0.50& 0.95 & 5.35 & 0.018& 0.0068 &  0.40  & 0.16 & 0.22 & 0.12 & 0.16 & 0.11 & 0.50\\
0.69& 0.94 & 6.35 & 0.023& 0.0081 &  0.46 & 0.18 & 0.23 & 0.12 & 0.15  & 0.11 & 0.51\\
0.88& 0.92 & 7.98 & 0.070& 0.013 &  0.51 & 0.17 & 0.24 & 0.12 & 0.17 & 0.11  & 0.51\\
1.19& 0.90 & 10.63 & 0.039& 0.020 & 0.59 & 0.19 & 0.27 & 0.12 & 0.19 & 0.12 & 0.50\\ 
\hline
           		\end{tabular}
	\end{table}
\end{center}
                                                                                                         \begin{center}
	\begin{table}[h!]
%\hspace{-1cm}
\caption{$p_T$ asymmetries, $\eta<0$, maximum opening angle 0.4}
		\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|} \hline                                                     
 \vtop{\hbox{\strut $\left<p_T\right>$}\hbox{ \strut [GeV/c] } }& $\left<\sin\theta\right>$ & \vtop{\hbox{\strut $\left<M_\textrm{Inv}\right>$}\hbox{ \strut [GeV/c$^2$] } } & $A_{\textrm{UT}}^{\sin\phi}$ &$\sigma_{A_{\textrm{UT}}^{\sin\phi}}$ & $\left<z\right>$ & $\sigma_{\left<z\right>}$ & $\left<x_1\right>$ & $\sigma_{\left<x_1\right>}$ & $\left<x_2\right>$& $\sigma_{\left<x_2\right>}$ & $\left<\eta\right>$  \\
 \hline
3.60& 0.99 & 0.53 & -0.016& 0.0084 &0.30 & 0.12 & 0.14 & 0.10 & 0.20 & 0.11 & -0.49\\
4.48& 0.97 & 0.60 & -0.0081& 0.0073 &0.36 & 0.13 & 0.15 & 0.11 & 0.20 & 0.11 & -0.50\\
5.67& 0.94 & 0.68 & 0.013& 0.0073 & 0.43 & 0.16 & 0.15 & 0.11 & 0.21 & 0.11 & -0.50\\
7.17& 0.92 & 0.76 & 0.016& 0.010 & 0.48 & 0.15 & 0.16 & 0.11 & 0.24 & 0.11 &-0.51\\
10.28& 0.88 & 0.89 & 0.015& 0.0099 &0.57 & 0.17 & 0.19 & 0.12 & 0.27 & 0.12 & -0.51\\
\hline
           		\end{tabular}
	\end{table}
\end{center}
                                                             \begin{center}
	\begin{table}[h!]
%\hspace{-1cm}
\caption{$\left<M_\textrm{Inv}\right>$ asymmetries, $\eta<0$, maximum opening angle 0.4}
		\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|} \hline  
		 \vtop{\hbox{\strut $\left<M_\textrm{Inv}\right>$}\hbox{ \strut [GeV/c$^2$] } }  & $\left<\sin\theta\right>$ & \vtop{\hbox{\strut $\left<p_T\right>$}\hbox{ \strut [GeV/c] } }& $A_{\textrm{UT}}^{\sin\phi}$ & $\sigma_{A_{\textrm{UT}}^{\sin\phi}}$ & $\left<z\right>$ & $\sigma_{\left<z\right>}$ & $\left<x_1\right>$ & $\sigma_{\left<x_1\right>}$ & $\left<x_2\right>$& $\sigma_{\left<x_2\right>}$ & $\left<\eta\right>$  \\                        
		 \hline                                                       
0.36& 0.95 & 4.73 & -0.013& 0.010 &0.38 & 0.15 & 0.16 & 0.11 & 0.22 & 0.12 & -0.51\\                                
0.50& 0.95 & 5.31 & 0.0054& 0.0067 & 0.41 & 0.17 & 0.16 & 0.11  & 0.21 & 0.11 & -0.50\\
0.70& 0.96 & 5.60 & -0.0022& 0.0068 & 0.41 & 0.17 & 0.16 & 0.11 & 0.22 & 0.11 & -0.50\\
0.88& 0.94 & 6.45 & 0.010& 0.0094 & 0.44 & 0.16 & 0.16 & 0.11 & 0.23 & 0.12 & -0.50\\ 
1.22& 0.91 & 8.55 & 0.011& 0.012 & 0.52 & 0.18 & 0.17 & 0.11 & 0.24 & 0.12 & -0.49     \\
\hline                                                                                
           		\end{tabular}
	\end{table}
\end{center}                                                                                      
                                                                                                                                                      \begin{center}
	\begin{table}[h!]
%\hspace{-1cm}
\caption{$p_T$ asymmetries, $\eta>0$, maximum opening angle 0.4}
		\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|} \hline                                                                          
 \vtop{\hbox{\strut $\left<p_T\right>$}\hbox{ \strut [GeV/c] } } & $\left<\sin\theta\right>$ &\vtop{\hbox{\strut $\left<M_\textrm{Inv}\right>$}\hbox{ \strut [GeV/c$^2$] } }  & $A_{\textrm{UT}}^{\sin\phi}$ & $\sigma_{A_{\textrm{UT}}^{\sin\phi}}$ & $\left<z\right>$ & $\sigma_{\left<z\right>}$ & $\left<x_1\right>$ & $\sigma_{\left<x_1\right>}$ & $\left<x_2\right>$& $\sigma_{\left<x_2\right>}$ & $\left<\eta\right>$ \\
 \hline
3.60& 0.99 & 0.53 & 0.013& 0.0084 & 0.29 & 0.10 & 0.20 & 0.11 & 0.14 & 0.10 &  0.49\\
4.48& 0.97 & 0.60 & 0.0060& 0.0073& 0.35 & 0.12 & 0.21 & 0.11 & 0.15 & 0.11 &  0.50\\
5.67& 0.94 & 0.68 & 0.025& 0.0073 &0.42 & 0.14 & 0.22 & 0.12 & 0.15 & 0.10 &  0.50\\
7.17& 0.92 & 0.76 & 0.0096& 0.010 &0.50 & 0.18 & 0.23 & 0.12 & 0.16 & 0.10 &  0.51\\
10.28& 0.88 & 0.89 & 0.053& 0.0099&0.58 & 0.18 & 0.27 & 0.13 & 0.19 & 0.12 & 0.51\\
\hline
           		\end{tabular}
	\end{table}
\end{center}

 \begin{center}
	\begin{table}[h!]
%\hspace{-1cm}
\caption{$\left<M_\textrm{Inv}\right>$ asymmetries, $\eta>0$, maximum opening angle 0.4}
		\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|} \hline
 \vtop{\hbox{\strut $\left<M_\textrm{Inv}\right>$}\hbox{ \strut [GeV/c$^2$] } }  & $\left<\sin\theta\right>$ & \vtop{\hbox{\strut $\left<p_T\right>$}\hbox{ \strut [GeV/c] } } & $A_{\textrm{UT}}^{\sin\phi}$ & $\sigma_{A_{\textrm{UT}}^{\sin\phi}}$ & $\left<z\right>$ & $\sigma_{\left<z\right>}$ & $\left<x_1\right>$ & $\sigma_{\left<x_1\right>}$ & $\left<x_2\right>$& $\sigma_{\left<x_2\right>}$ & $\left<\eta\right>$ \\   
 \hline                                                                                                                                          
0.36& 0.95 & 4.73 & 0.0054& 0.010 &0.38 & 0.16 & 0.23 & 0.12 & 0.16 & 0.11   & 0.51\\ 
0.50& 0.95 & 5.31 & 0.018& 0.0067 &0.39 & 0.16 & 0.22 & 0.12  & 0.16 & 0.11  & 0.50\\ 
0.70& 0.96 & 5.60 & 0.018& 0.0068 & 0.42 & 0.18 & 0.22 & 0.12 & 0.15 & 0.11  & 0.50\\ 
0.88& 0.94 & 6.45 & 0.031& 0.0095 &0.44 & 0.16 & 0.22 & 0.12 & 0.16 & 0.10   & 0.50\\ 
1.22& 0.91 & 8.55 & 0.033& 0.012 &0.53 & 0.18 & 0.24 & 0.12 & 0.17 & 0.11   & 0.49\\                                                                                          \hline
           		\end{tabular}
	\end{table}
\end{center}

 \begin{center}
	\begin{table}[h!]
%\hspace{-1cm}
\caption{$\eta$ asymmetries, maximum opening angle 0.2}
		\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|} \hline
 \vtop{\hbox{\strut $\left<p_T\right>$}\hbox{ \strut [GeV/c] } }& $\left<\sin\theta\right>$ & \vtop{\hbox{\strut $\left<M_\textrm{Inv}\right>$}\hbox{ \strut [GeV/c$^2$] } }  & $A_{\textrm{UT}}^{\sin\phi}$ & $\sigma_{A_{\textrm{UT}}^{\sin\phi}}$ & $\left<z\right>$ & $\sigma_{\left<z\right>}$ & $\left<x_1\right>$ & $\sigma_{\left<x_1\right>}$ & $\left<x_2\right>$& $\sigma_{\left<x_2\right>}$ & $\left<\eta\right>$ \\     
 \hline
 6.30 & 0.93 & 0.50 & 0.0010 &0.0079 &   0.46 & 0.18 & 0.15 & 0.11 & 0.25 & 0.12 & -0.75 \\               
 6.27 & 0.94 & 0.50 & 0.0054 &0.0080 &   0.41 & 0.16 & 0.18 & 0.11 & 0.20 & 0.11 & -0.26 \\
 6.27 & 0.94 & 0.50 & 0.015   &0.0080 &   0.43 & 0.18 & 0.21 & 0.12 & 0.17 & 0.11 & 0.26\\
 6.30 & 0.93 & 0.50 & 0.028   &0.0079 &   0.45 & 0.19 & 0.26 & 0.12 & 0.15 & 0.11 & 0.75  \\
 \hline
                       		\end{tabular}
	\end{table}
\end{center}           
       
        \begin{center}
	\begin{table}[h!]
%\hspace{-1cm}
\caption{$\eta$ asymmetries, maximum opening angle 0.3}
		\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|} \hline
 \vtop{\hbox{\strut $\left<p_T\right>$}\hbox{ \strut [GeV/c] } }& $\left<\sin\theta\right>$ & \vtop{\hbox{\strut $\left<M_\textrm{Inv}\right>$}\hbox{ \strut [GeV/c$^2$] } }  & $A_{\textrm{UT}}^{\sin\phi}$ & $\sigma_{A_{\textrm{UT}}^{\sin\phi}}$ & $\left<z\right>$ & $\sigma_{\left<z\right>}$ & $\left<x_1\right>$ & $\sigma_{\left<x_1\right>}$ & $\left<x_2\right>$& $\sigma_{\left<x_2\right>}$ & $\left<\eta\right>$\\  
\hline
 6.04 & 0.94 & 0.59 & -0.00020 &0.0060&0.45 & 0.18 & 0.15 & 0.11 & 0.24 & 0.12  & -0.75\\ 
 5.99 & 0.94 & 0.60 & 0.0075 &0.0061& 0.40 & 0.16 & 0.18 & 0.11 & 0.20 & 0.11 & -0.26 \\
 5.99 & 0.94 & 0.60 & 0.013 &0.0061& 0.42 & 0.17 & 0.20 & 0.11 & 0.17 & 0.11 & 0.26  \\
 6.04 & 0.94 & 0.59 & 0.031 &0.0060& 0.44 & 0.18 & 0.25 & 0.12 & 0.15 & 0.10  &0.75 \\
 \hline
 \end{tabular}
	\end{table}
\end{center}           
 \begin{center}
	\begin{table}[h!]
%\hspace{-1cm}
\caption{\label{trigTableN}$\eta$ asymmetries, maximum opening angle 0.4}
		\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|} \hline
		\vtop{\hbox{\strut $\left<p_T\right>$}\hbox{ \strut [GeV/c] } }& $\left<\sin\theta\right>$ & \vtop{\hbox{\strut $\left<M_\textrm{Inv}\right>$}\hbox{ \strut [GeV/c$^2$] } }  &$A_{\textrm{UT}}^{\sin\phi}$ & $\sigma_{A_{\textrm{UT}}^{\sin\phi}}$ & $\left<z\right>$ & $\sigma_{\left<z\right>}$ & $\left<x_1\right>$ & $\sigma_{\left<X_1\right>}$ & $\left<x_2\right>$& $\sigma_{\left<x_2\right>}$ & $\left<\eta\right>$\\
		\hline
5.84 & 0.95 & 0.67 & -0.0027 &0.0053&0.44 & 0.18 & 0.14 & 0.11 & 0.24 & 0.12 &-0.75    \\
5.78 & 0.95 & 0.67 & 0.0074 &0.0053& 0.40 & 0.16 & 0.17 & 0.11 & 0.20 & 0.11 &-0.26 \\
5.78 & 0.95 & 0.67 & 0.0095 &0.0053& 0.41 & 0.17 & 0.20 & 0.11 & 0.17 & 0.11 &0.26 \\
5.84 & 0.95 & 0.67 & 0.030 &0.0053& 0.43 & 0.18 & 0.24 & 0.12 & 0.14 & 0.10 & 0.75 \\
\hline
\end{tabular}
	\end{table}
\end{center}
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  \bibfield  {author} {\bibinfo {author} {\bibfnamefont {T.}~\bibnamefont
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%%CITATION = HEP-PH/0603175;%%
\bibitem [{\citenamefont {Brun}\ \emph {et~al.}(1978)\citenamefont {Brun},
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  \BibitemOpen
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  \bibinfo {author} {\bibfnamefont {J.}~\bibnamefont {Lassalle}},\ }\href@noop
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%%CITATION = CERN-DD-78-2-REV ETC.;%%
\bibitem [{\citenamefont {Bianconi}\ \emph {et~al.}(2000)\citenamefont
  {Bianconi}, \citenamefont {Boffi}, \citenamefont {Jakob},\ and\ \citenamefont
  {Radici}}]{Bianconi:1999uc}%
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\bibitem [{\citenamefont {Braun}(2013)}]{compassPiK}%
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  \bibfield  {author} {\bibinfo {author} {\bibfnamefont {C.}~\bibnamefont
  {Braun}}\ }(\bibinfo  {publisher} {{presented at the workshop Structure of
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  {NoStop}%
\bibitem [{\citenamefont {Adamczyk}\ \emph {et~al.}(2012)\citenamefont
  {Adamczyk} \emph {et~al.}}]{Adamczyk:2012qj}%
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  {Adamczyk}} \emph {et~al.} (\bibinfo {collaboration} {STAR Collaboration}),\
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%%CITATION = ARXIV:1205.2735;%%
\bibitem [{\citenamefont {Ohlsen}\ and\ \citenamefont
  {Keaton}(1973)}]{Ohlsen:1973}%
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\bibitem [{\citenamefont {Bacchetta}\ \emph {et~al.}(2011)\citenamefont
  {Bacchetta}, \citenamefont {Courtoy},\ and\ \citenamefont
  {Radici}}]{Bacchetta:2011ab}%
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  \bibfield  {author} {\bibinfo {author} {\bibfnamefont {A.}~\bibnamefont
  {Bacchetta}}, \bibinfo {author} {\bibfnamefont {A.}~\bibnamefont {Courtoy}},
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  {\doibase 10.1103/PhysRevLett.107.012001} {\bibfield  {journal} {\bibinfo
  {journal} {Phys. Rev. Lett.}\ }\textbf {\bibinfo {volume} {107}},\ \bibinfo
  {pages} {012001} (\bibinfo {year} {2011})}\BibitemShut {NoStop}%
\end{thebibliography}%
