Minijet deformation and charge-independent angular correlations on momentum subspace $(\eta,\phi)$ in Au-Au collisions at $\sqrt{s_{NN}}$ = 130 GeV
J.~Adams
First measurements of charge-independent correlations on angular difference variables $\eta_1 - \eta_2$ (pseudorapidity) and $\phi_1 - \phi_2$ (azimuth) are presented for primary charged hadrons with transverse momentum $0.15 \leq p_t \leq 2$~GeV/$c$ and $|\eta| \leq 1.3$ from Au-Au collisions at $\sqrt{s_{NN}} = 130$~GeV. Strong charge-independent angular correlations are observed associated with jet-like structures and elliptic flow. The width of the jet-like peak on $\eta_1 - \eta_2$ increases by a factor 2.3 from peripheral to central collisions, suggesting strong coupling of semi-hard scattered partons to a longitudinally-expanding medium. New methods of jet analysis introduced here provide evidence for nonperturbative QCD medium effects in heavy ion collisions.
axial_ci_plb_v2-7revtex.tex
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\title{Minijet deformation and charge-independent angular correlations on momentum subspace $(\eta,\phi)$ in Au-Au collisions at $\sqrt{s_{NN}}$ = 130 GeV}


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\affiliation{Argonne National Laboratory, Argonne, Illinois 60439}
\affiliation{University of Bern, 3012 Bern, Switzerland}
\affiliation{University of Birmingham, Birmingham, United Kingdom}
\affiliation{Brookhaven National Laboratory, Upton, New York 11973}
\affiliation{California Institute of Technology, Pasadena, California 91125}
\affiliation{University of California, Berkeley, California 94720}
\affiliation{University of California, Davis, California 95616}
\affiliation{University of California, Los Angeles, California 90095}
\affiliation{Carnegie Mellon University, Pittsburgh, Pennsylvania 15213}
\affiliation{Creighton University, Omaha, Nebraska 68178}
\affiliation{Nuclear Physics Institute AS CR, 250 68 \v{R}e\v{z}/Prague, Czech Republic}
\affiliation{Laboratory for High Energy (JINR), Dubna, Russia}
\affiliation{Particle Physics Laboratory (JINR), Dubna, Russia}
\affiliation{University of Frankfurt, Frankfurt, Germany}
\affiliation{Institute of Physics, Bhubaneswar 751005, India}
\affiliation{Indian Institute of Technology, Mumbai, India}
\affiliation{Indiana University, Bloomington, Indiana 47408}
\affiliation{Institut de Recherches Subatomiques, Strasbourg, France}
\affiliation{University of Jammu, Jammu 180001, India}
\affiliation{Kent State University, Kent, Ohio 44242}
\affiliation{Lawrence Berkeley National Laboratory, Berkeley, California 94720}
\affiliation{Massachusetts Institute of Technology, Cambridge, MA 02139-4307}
\affiliation{Max-Planck-Institut f\"ur Physik, Munich, Germany}
\affiliation{Michigan State University, East Lansing, Michigan 48824}
\affiliation{Moscow Engineering Physics Institute, Moscow Russia}
\affiliation{City College of New York, New York City, New York 10031}
\affiliation{NIKHEF and Utrecht University, Amsterdam, The Netherlands}
\affiliation{Ohio State University, Columbus, Ohio 43210}
\affiliation{Panjab University, Chandigarh 160014, India}
\affiliation{Pennsylvania State University, University Park, Pennsylvania 16802}
\affiliation{Institute of High Energy Physics, Protvino, Russia}
\affiliation{Purdue University, West Lafayette, Indiana 47907}
\affiliation{Pusan National University, Pusan, Republic of Korea}
\affiliation{University of Rajasthan, Jaipur 302004, India}
\affiliation{Rice University, Houston, Texas 77251}
\affiliation{Universidade de Sao Paulo, Sao Paulo, Brazil}
\affiliation{University of Science \& Technology of China, Hefei 230026, China}
\affiliation{Shanghai Institute of Applied Physics, Shanghai 201800, China}
\affiliation{SUBATECH, Nantes, France}
\affiliation{Texas A\&M University, College Station, Texas 77843}
\affiliation{University of Texas, Austin, Texas 78712}
\affiliation{Tsinghua University, Beijing 100084, China}
\affiliation{Valparaiso University, Valparaiso, Indiana 46383}
\affiliation{Variable Energy Cyclotron Centre, Kolkata 700064, India}
\affiliation{Warsaw University of Technology, Warsaw, Poland}
\affiliation{University of Washington, Seattle, Washington 98195}
\affiliation{Wayne State University, Detroit, Michigan 48201}
\affiliation{Institute of Particle Physics, CCNU (HZNU), Wuhan 430079, China}
\affiliation{Yale University, New Haven, Connecticut 06520}
\affiliation{University of Zagreb, Zagreb, HR-10002, Croatia}

\author{J.~Adams}\affiliation{University of Birmingham, Birmingham, United Kingdom}
\author{M.M.~Aggarwal}\affiliation{Panjab University, Chandigarh 160014, India}
\author{Z.~Ahammed}\affiliation{Variable Energy Cyclotron Centre, Kolkata 700064, India}
\author{J.~Amonett}\affiliation{Kent State University, Kent, Ohio 44242}
\author{B.D.~Anderson}\affiliation{Kent State University, Kent, Ohio 44242}
\author{D.~Arkhipkin}\affiliation{Particle Physics Laboratory (JINR), Dubna, Russia}
\author{G.S.~Averichev}\affiliation{Laboratory for High Energy (JINR), Dubna, Russia}
\author{S.K.~Badyal}\affiliation{University of Jammu, Jammu 180001, India}
\author{Y.~Bai}\affiliation{NIKHEF and Utrecht University, Amsterdam, The Netherlands}
\author{J.~Balewski}\affiliation{Indiana University, Bloomington, Indiana 47408}
\author{O.~Barannikova}\affiliation{Purdue University, West Lafayette, Indiana 47907}
\author{L.S.~Barnby}\affiliation{University of Birmingham, Birmingham, United Kingdom}
\author{J.~Baudot}\affiliation{Institut de Recherches Subatomiques, Strasbourg, France}
\author{S.~Bekele}\affiliation{Ohio State University, Columbus, Ohio 43210}
\author{V.V.~Belaga}\affiliation{Laboratory for High Energy (JINR), Dubna, Russia}
\author{A.~Bellingeri-Laurikainen}\affiliation{SUBATECH, Nantes, France}
\author{R.~Bellwied}\affiliation{Wayne State University, Detroit, Michigan 48201}
\author{J.~Berger}\affiliation{University of Frankfurt, Frankfurt, Germany}
\author{B.I.~Bezverkhny}\affiliation{Yale University, New Haven, Connecticut 06520}
\author{S.~Bharadwaj}\affiliation{University of Rajasthan, Jaipur 302004, India}
\author{A.~Bhasin}\affiliation{University of Jammu, Jammu 180001, India}
\author{A.K.~Bhati}\affiliation{Panjab University, Chandigarh 160014, India}
\author{V.S.~Bhatia}\affiliation{Panjab University, Chandigarh 160014, India}
\author{H.~Bichsel}\affiliation{University of Washington, Seattle, Washington 98195}
\author{J.~Bielcik}\affiliation{Yale University, New Haven, Connecticut 06520}
\author{J.~Bielcikova}\affiliation{Yale University, New Haven, Connecticut 06520}
\author{A.~Billmeier}\affiliation{Wayne State University, Detroit, Michigan 48201}
\author{L.C.~Bland}\affiliation{Brookhaven National Laboratory, Upton, New York 11973}
\author{C.O.~Blyth}\affiliation{University of Birmingham, Birmingham, United Kingdom}
\author{S-L.~Blyth}\affiliation{Lawrence Berkeley National Laboratory, Berkeley, California 94720}
\author{B.E.~Bonner}\affiliation{Rice University, Houston, Texas 77251}
\author{M.~Botje}\affiliation{NIKHEF and Utrecht University, Amsterdam, The Netherlands}
\author{A.~Boucham}\affiliation{SUBATECH, Nantes, France}
\author{J.~Bouchet}\affiliation{SUBATECH, Nantes, France}
\author{A.V.~Brandin}\affiliation{Moscow Engineering Physics Institute, Moscow Russia}
\author{A.~Bravar}\affiliation{Brookhaven National Laboratory, Upton, New York 11973}
\author{M.~Bystersky}\affiliation{Nuclear Physics Institute AS CR, 250 68 \v{R}e\v{z}/Prague, Czech Republic}
\author{R.V.~Cadman}\affiliation{Argonne National Laboratory, Argonne, Illinois 60439}
\author{X.Z.~Cai}\affiliation{Shanghai Institute of Applied Physics, Shanghai 201800, China}
\author{H.~Caines}\affiliation{Yale University, New Haven, Connecticut 06520}
\author{M.~Calder\'on~de~la~Barca~S\'anchez}\affiliation{Indiana University, Bloomington, Indiana 47408}
\author{J.~Castillo}\affiliation{Lawrence Berkeley National Laboratory, Berkeley, California 94720}
\author{O.~Catu}\affiliation{Yale University, New Haven, Connecticut 06520}
\author{D.~Cebra}\affiliation{University of California, Davis, California 95616}
\author{Z.~Chajecki}\affiliation{Ohio State University, Columbus, Ohio 43210}
\author{P.~Chaloupka}\affiliation{Nuclear Physics Institute AS CR, 250 68 \v{R}e\v{z}/Prague, Czech Republic}
\author{S.~Chattopadhyay}\affiliation{Variable Energy Cyclotron Centre, Kolkata 700064, India}
\author{H.F.~Chen}\affiliation{University of Science \& Technology of China, Hefei 230026, China}
\author{J.H.~Chen}\affiliation{Shanghai Institute of Applied Physics, Shanghai 201800, China}
\author{Y.~Chen}\affiliation{University of California, Los Angeles, California 90095}
\author{J.~Cheng}\affiliation{Tsinghua University, Beijing 100084, China}
\author{M.~Cherney}\affiliation{Creighton University, Omaha, Nebraska 68178}
\author{A.~Chikanian}\affiliation{Yale University, New Haven, Connecticut 06520}
\author{H.A.~Choi}\affiliation{Pusan National University, Pusan, Republic of Korea}
\author{W.~Christie}\affiliation{Brookhaven National Laboratory, Upton, New York 11973}
\author{J.P.~Coffin}\affiliation{Institut de Recherches Subatomiques, Strasbourg, France}
\author{T.M.~Cormier}\affiliation{Wayne State University, Detroit, Michigan 48201}
\author{M.R.~Cosentino}\affiliation{Universidade de Sao Paulo, Sao Paulo, Brazil}
\author{J.G.~Cramer}\affiliation{University of Washington, Seattle, Washington 98195}
\author{H.J.~Crawford}\affiliation{University of California, Berkeley, California 94720}
\author{D.~Das}\affiliation{Variable Energy Cyclotron Centre, Kolkata 700064, India}
\author{S.~Das}\affiliation{Variable Energy Cyclotron Centre, Kolkata 700064, India}
\author{M.~Daugherity}\affiliation{University of Texas, Austin, Texas 78712}
\author{M.M.~de Moura}\affiliation{Universidade de Sao Paulo, Sao Paulo, Brazil}
\author{T.G.~Dedovich}\affiliation{Laboratory for High Energy (JINR), Dubna, Russia}
\author{M.~DePhillips}\affiliation{Brookhaven National Laboratory, Upton, New York 11973}
\author{A.A.~Derevschikov}\affiliation{Institute of High Energy Physics, Protvino, Russia}
\author{L.~Didenko}\affiliation{Brookhaven National Laboratory, Upton, New York 11973}
\author{T.~Dietel}\affiliation{University of Frankfurt, Frankfurt, Germany}
\author{S.M.~Dogra}\affiliation{University of Jammu, Jammu 180001, India}
\author{W.J.~Dong}\affiliation{University of California, Los Angeles, California 90095}
\author{X.~Dong}\affiliation{University of Science \& Technology of China, Hefei 230026, China}
\author{J.E.~Draper}\affiliation{University of California, Davis, California 95616}
\author{F.~Du}\affiliation{Yale University, New Haven, Connecticut 06520}
\author{A.K.~Dubey}\affiliation{Institute of Physics, Bhubaneswar 751005, India}
\author{V.B.~Dunin}\affiliation{Laboratory for High Energy (JINR), Dubna, Russia}
\author{J.C.~Dunlop}\affiliation{Brookhaven National Laboratory, Upton, New York 11973}
\author{M.R.~Dutta Mazumdar}\affiliation{Variable Energy Cyclotron Centre, Kolkata 700064, India}
\author{V.~Eckardt}\affiliation{Max-Planck-Institut f\"ur Physik, Munich, Germany}
\author{W.R.~Edwards}\affiliation{Lawrence Berkeley National Laboratory, Berkeley, California 94720}
\author{L.G.~Efimov}\affiliation{Laboratory for High Energy (JINR), Dubna, Russia}
\author{V.~Emelianov}\affiliation{Moscow Engineering Physics Institute, Moscow Russia}
\author{J.~Engelage}\affiliation{University of California, Berkeley, California 94720}
\author{G.~Eppley}\affiliation{Rice University, Houston, Texas 77251}
\author{B.~Erazmus}\affiliation{SUBATECH, Nantes, France}
\author{M.~Estienne}\affiliation{SUBATECH, Nantes, France}
\author{P.~Fachini}\affiliation{Brookhaven National Laboratory, Upton, New York 11973}
\author{J.~Faivre}\affiliation{Institut de Recherches Subatomiques, Strasbourg, France}
\author{R.~Fatemi}\affiliation{Massachusetts Institute of Technology, Cambridge, MA 02139-4307}
\author{J.~Fedorisin}\affiliation{Laboratory for High Energy (JINR), Dubna, Russia}
\author{K.~Filimonov}\affiliation{Lawrence Berkeley National Laboratory, Berkeley, California 94720}
\author{P.~Filip}\affiliation{Nuclear Physics Institute AS CR, 250 68 \v{R}e\v{z}/Prague, Czech Republic}
\author{E.~Finch}\affiliation{Yale University, New Haven, Connecticut 06520}
\author{V.~Fine}\affiliation{Brookhaven National Laboratory, Upton, New York 11973}
\author{Y.~Fisyak}\affiliation{Brookhaven National Laboratory, Upton, New York 11973}
\author{K.S.F.~Fornazier}\affiliation{Universidade de Sao Paulo, Sao Paulo, Brazil}
\author{J.~Fu}\affiliation{Tsinghua University, Beijing 100084, China}
\author{C.A.~Gagliardi}\affiliation{Texas A\&M University, College Station, Texas 77843}
\author{L.~Gaillard}\affiliation{University of Birmingham, Birmingham, United Kingdom}
\author{J.~Gans}\affiliation{Yale University, New Haven, Connecticut 06520}
\author{M.S.~Ganti}\affiliation{Variable Energy Cyclotron Centre, Kolkata 700064, India}
\author{F.~Geurts}\affiliation{Rice University, Houston, Texas 77251}
\author{V.~Ghazikhanian}\affiliation{University of California, Los Angeles, California 90095}
\author{P.~Ghosh}\affiliation{Variable Energy Cyclotron Centre, Kolkata 700064, India}
\author{J.E.~Gonzalez}\affiliation{University of California, Los Angeles, California 90095}
\author{Y.G.~Gorbunov}\affiliation{Creighton University, Omaha, Nebraska 68178}
\author{H.~Gos}\affiliation{Warsaw University of Technology, Warsaw, Poland}
\author{O.~Grachov}\affiliation{Wayne State University, Detroit, Michigan 48201}
\author{O.~Grebenyuk}\affiliation{NIKHEF and Utrecht University, Amsterdam, The Netherlands}
\author{D.~Grosnick}\affiliation{Valparaiso University, Valparaiso, Indiana 46383}
\author{S.M.~Guertin}\affiliation{University of California, Los Angeles, California 90095}
\author{Y.~Guo}\affiliation{Wayne State University, Detroit, Michigan 48201}
\author{A.~Gupta}\affiliation{University of Jammu, Jammu 180001, India}
\author{N.~Gupta}\affiliation{University of Jammu, Jammu 180001, India}
\author{T.D.~Gutierrez}\affiliation{University of California, Davis, California 95616}
\author{T.J.~Hallman}\affiliation{Brookhaven National Laboratory, Upton, New York 11973}
\author{A.~Hamed}\affiliation{Wayne State University, Detroit, Michigan 48201}
\author{D.~Hardtke}\affiliation{Lawrence Berkeley National Laboratory, Berkeley, California 94720}
\author{J.W.~Harris}\affiliation{Yale University, New Haven, Connecticut 06520}
\author{M.~Heinz}\affiliation{University of Bern, 3012 Bern, Switzerland}
\author{T.W.~Henry}\affiliation{Texas A\&M University, College Station, Texas 77843}
\author{S.~Hepplemann}\affiliation{Pennsylvania State University, University Park, Pennsylvania 16802}
\author{B.~Hippolyte}\affiliation{Institut de Recherches Subatomiques, Strasbourg, France}
\author{A.~Hirsch}\affiliation{Purdue University, West Lafayette, Indiana 47907}
\author{E.~Hjort}\affiliation{Lawrence Berkeley National Laboratory, Berkeley, California 94720}
\author{G.W.~Hoffmann}\affiliation{University of Texas, Austin, Texas 78712}
\author{M.J.~Horner}\affiliation{Lawrence Berkeley National Laboratory, Berkeley, California 94720}
\author{H.Z.~Huang}\affiliation{University of California, Los Angeles, California 90095}
\author{S.L.~Huang}\affiliation{University of Science \& Technology of China, Hefei 230026, China}
\author{E.W.~Hughes}\affiliation{California Institute of Technology, Pasadena, California 91125}
\author{T.J.~Humanic}\affiliation{Ohio State University, Columbus, Ohio 43210}
\author{G.~Igo}\affiliation{University of California, Los Angeles, California 90095}
\author{A.~Ishihara}\affiliation{University of Texas, Austin, Texas 78712}
\author{P.~Jacobs}\affiliation{Lawrence Berkeley National Laboratory, Berkeley, California 94720}
\author{W.W.~Jacobs}\affiliation{Indiana University, Bloomington, Indiana 47408}
\author{H.~Jiang}\affiliation{University of California, Los Angeles, California 90095}
\author{P.G.~Jones}\affiliation{University of Birmingham, Birmingham, United Kingdom}
\author{E.G.~Judd}\affiliation{University of California, Berkeley, California 94720}
\author{S.~Kabana}\affiliation{University of Bern, 3012 Bern, Switzerland}
\author{K.~Kang}\affiliation{Tsinghua University, Beijing 100084, China}
\author{M.~Kaplan}\affiliation{Carnegie Mellon University, Pittsburgh, Pennsylvania 15213}
\author{D.~Keane}\affiliation{Kent State University, Kent, Ohio 44242}
\author{A.~Kechechyan}\affiliation{Laboratory for High Energy (JINR), Dubna, Russia}
\author{V.Yu.~Khodyrev}\affiliation{Institute of High Energy Physics, Protvino, Russia}
\author{B.C.~Kim}\affiliation{Pusan National University, Pusan, Republic of Korea}
\author{J.~Kiryluk}\affiliation{Massachusetts Institute of Technology, Cambridge, MA 02139-4307}
\author{A.~Kisiel}\affiliation{Warsaw University of Technology, Warsaw, Poland}
\author{E.M.~Kislov}\affiliation{Laboratory for High Energy (JINR), Dubna, Russia}
\author{J.~Klay}\affiliation{Lawrence Berkeley National Laboratory, Berkeley, California 94720}
\author{S.R.~Klein}\affiliation{Lawrence Berkeley National Laboratory, Berkeley, California 94720}
\author{D.D.~Koetke}\affiliation{Valparaiso University, Valparaiso, Indiana 46383}
\author{T.~Kollegger}\affiliation{University of Frankfurt, Frankfurt, Germany}
\author{M.~Kopytine}\affiliation{Kent State University, Kent, Ohio 44242}
\author{L.~Kotchenda}\affiliation{Moscow Engineering Physics Institute, Moscow Russia}
\author{K.L.~Kowalik}\affiliation{Lawrence Berkeley National Laboratory, Berkeley, California 94720}
\author{M.~Kramer}\affiliation{City College of New York, New York City, New York 10031}
\author{P.~Kravtsov}\affiliation{Moscow Engineering Physics Institute, Moscow Russia}
\author{V.I.~Kravtsov}\affiliation{Institute of High Energy Physics, Protvino, Russia}
\author{K.~Krueger}\affiliation{Argonne National Laboratory, Argonne, Illinois 60439}
\author{C.~Kuhn}\affiliation{Institut de Recherches Subatomiques, Strasbourg, France}
\author{A.I.~Kulikov}\affiliation{Laboratory for High Energy (JINR), Dubna, Russia}
\author{A.~Kumar}\affiliation{Panjab University, Chandigarh 160014, India}
\author{R.Kh.~Kutuev}\affiliation{Particle Physics Laboratory (JINR), Dubna, Russia}
\author{A.A.~Kuznetsov}\affiliation{Laboratory for High Energy (JINR), Dubna, Russia}
\author{M.A.C.~Lamont}\affiliation{Yale University, New Haven, Connecticut 06520}
\author{J.M.~Landgraf}\affiliation{Brookhaven National Laboratory, Upton, New York 11973}
\author{S.~Lange}\affiliation{University of Frankfurt, Frankfurt, Germany}
\author{F.~Laue}\affiliation{Brookhaven National Laboratory, Upton, New York 11973}
\author{J.~Lauret}\affiliation{Brookhaven National Laboratory, Upton, New York 11973}
\author{A.~Lebedev}\affiliation{Brookhaven National Laboratory, Upton, New York 11973}
\author{R.~Lednicky}\affiliation{Laboratory for High Energy (JINR), Dubna, Russia}
\author{C-H.~Lee}\affiliation{Pusan National University, Pusan, Republic of Korea}
\author{S.~Lehocka}\affiliation{Laboratory for High Energy (JINR), Dubna, Russia}
\author{M.J.~LeVine}\affiliation{Brookhaven National Laboratory, Upton, New York 11973}
\author{C.~Li}\affiliation{University of Science \& Technology of China, Hefei 230026, China}
\author{Q.~Li}\affiliation{Wayne State University, Detroit, Michigan 48201}
\author{Y.~Li}\affiliation{Tsinghua University, Beijing 100084, China}
\author{G.~Lin}\affiliation{Yale University, New Haven, Connecticut 06520}
\author{S.J.~Lindenbaum}\affiliation{City College of New York, New York City, New York 10031}
\author{M.A.~Lisa}\affiliation{Ohio State University, Columbus, Ohio 43210}
\author{F.~Liu}\affiliation{Institute of Particle Physics, CCNU (HZNU), Wuhan 430079, China}
\author{H.~Liu}\affiliation{University of Science \& Technology of China, Hefei 230026, China}
\author{J.~Liu}\affiliation{Rice University, Houston, Texas 77251}
\author{L.~Liu}\affiliation{Institute of Particle Physics, CCNU (HZNU), Wuhan 430079, China}
\author{Q.J.~Liu}\affiliation{University of Washington, Seattle, Washington 98195}
\author{Z.~Liu}\affiliation{Institute of Particle Physics, CCNU (HZNU), Wuhan 430079, China}
\author{T.~Ljubicic}\affiliation{Brookhaven National Laboratory, Upton, New York 11973}
\author{W.J.~Llope}\affiliation{Rice University, Houston, Texas 77251}
\author{H.~Long}\affiliation{University of California, Los Angeles, California 90095}
\author{R.S.~Longacre}\affiliation{Brookhaven National Laboratory, Upton, New York 11973}
\author{M.~Lopez-Noriega}\affiliation{Ohio State University, Columbus, Ohio 43210}
\author{W.A.~Love}\affiliation{Brookhaven National Laboratory, Upton, New York 11973}
\author{Y.~Lu}\affiliation{Institute of Particle Physics, CCNU (HZNU), Wuhan 430079, China}
\author{T.~Ludlam}\affiliation{Brookhaven National Laboratory, Upton, New York 11973}
\author{D.~Lynn}\affiliation{Brookhaven National Laboratory, Upton, New York 11973}
\author{G.L.~Ma}\affiliation{Shanghai Institute of Applied Physics, Shanghai 201800, China}
\author{J.G.~Ma}\affiliation{University of California, Los Angeles, California 90095}
\author{Y.G.~Ma}\affiliation{Shanghai Institute of Applied Physics, Shanghai 201800, China}
\author{D.~Magestro}\affiliation{Ohio State University, Columbus, Ohio 43210}
\author{S.~Mahajan}\affiliation{University of Jammu, Jammu 180001, India}
\author{D.P.~Mahapatra}\affiliation{Institute of Physics, Bhubaneswar 751005, India}
\author{R.~Majka}\affiliation{Yale University, New Haven, Connecticut 06520}
\author{L.K.~Mangotra}\affiliation{University of Jammu, Jammu 180001, India}
\author{R.~Manweiler}\affiliation{Valparaiso University, Valparaiso, Indiana 46383}
\author{S.~Margetis}\affiliation{Kent State University, Kent, Ohio 44242}
\author{C.~Markert}\affiliation{Kent State University, Kent, Ohio 44242}
\author{L.~Martin}\affiliation{SUBATECH, Nantes, France}
\author{J.N.~Marx}\affiliation{Lawrence Berkeley National Laboratory, Berkeley, California 94720}
\author{H.S.~Matis}\affiliation{Lawrence Berkeley National Laboratory, Berkeley, California 94720}
\author{Yu.A.~Matulenko}\affiliation{Institute of High Energy Physics, Protvino, Russia}
\author{C.J.~McClain}\affiliation{Argonne National Laboratory, Argonne, Illinois 60439}
\author{T.S.~McShane}\affiliation{Creighton University, Omaha, Nebraska 68178}
\author{F.~Meissner}\affiliation{Lawrence Berkeley National Laboratory, Berkeley, California 94720}
\author{Yu.~Melnick}\affiliation{Institute of High Energy Physics, Protvino, Russia}
\author{A.~Meschanin}\affiliation{Institute of High Energy Physics, Protvino, Russia}
\author{M.L.~Miller}\affiliation{Massachusetts Institute of Technology, Cambridge, MA 02139-4307}
\author{N.G.~Minaev}\affiliation{Institute of High Energy Physics, Protvino, Russia}
\author{C.~Mironov}\affiliation{Kent State University, Kent, Ohio 44242}
\author{A.~Mischke}\affiliation{NIKHEF and Utrecht University, Amsterdam, The Netherlands}
\author{D.K.~Mishra}\affiliation{Institute of Physics, Bhubaneswar 751005, India}
\author{J.~Mitchell}\affiliation{Rice University, Houston, Texas 77251}
\author{B.~Mohanty}\affiliation{Variable Energy Cyclotron Centre, Kolkata 700064, India}
\author{L.~Molnar}\affiliation{Purdue University, West Lafayette, Indiana 47907}
\author{C.F.~Moore}\affiliation{University of Texas, Austin, Texas 78712}
\author{D.A.~Morozov}\affiliation{Institute of High Energy Physics, Protvino, Russia}
\author{M.G.~Munhoz}\affiliation{Universidade de Sao Paulo, Sao Paulo, Brazil}
\author{B.K.~Nandi}\affiliation{Variable Energy Cyclotron Centre, Kolkata 700064, India}
\author{S.K.~Nayak}\affiliation{University of Jammu, Jammu 180001, India}
\author{T.K.~Nayak}\affiliation{Variable Energy Cyclotron Centre, Kolkata 700064, India}
\author{J.M.~Nelson}\affiliation{University of Birmingham, Birmingham, United Kingdom}
\author{P.K.~Netrakanti}\affiliation{Variable Energy Cyclotron Centre, Kolkata 700064, India}
\author{V.A.~Nikitin}\affiliation{Particle Physics Laboratory (JINR), Dubna, Russia}
\author{L.V.~Nogach}\affiliation{Institute of High Energy Physics, Protvino, Russia}
\author{S.B.~Nurushev}\affiliation{Institute of High Energy Physics, Protvino, Russia}
\author{G.~Odyniec}\affiliation{Lawrence Berkeley National Laboratory, Berkeley, California 94720}
\author{A.~Ogawa}\affiliation{Brookhaven National Laboratory, Upton, New York 11973}
\author{V.~Okorokov}\affiliation{Moscow Engineering Physics Institute, Moscow Russia}
\author{M.~Oldenburg}\affiliation{Lawrence Berkeley National Laboratory, Berkeley, California 94720}
\author{D.~Olson}\affiliation{Lawrence Berkeley National Laboratory, Berkeley, California 94720}
\author{S.K.~Pal}\affiliation{Variable Energy Cyclotron Centre, Kolkata 700064, India}
\author{Y.~Panebratsev}\affiliation{Laboratory for High Energy (JINR), Dubna, Russia}
\author{S.Y.~Panitkin}\affiliation{Brookhaven National Laboratory, Upton, New York 11973}
\author{A.I.~Pavlinov}\affiliation{Wayne State University, Detroit, Michigan 48201}
\author{T.~Pawlak}\affiliation{Warsaw University of Technology, Warsaw, Poland}
\author{T.~Peitzmann}\affiliation{NIKHEF and Utrecht University, Amsterdam, The Netherlands}
\author{V.~Perevoztchikov}\affiliation{Brookhaven National Laboratory, Upton, New York 11973}
\author{C.~Perkins}\affiliation{University of California, Berkeley, California 94720}
\author{W.~Peryt}\affiliation{Warsaw University of Technology, Warsaw, Poland}
\author{V.A.~Petrov}\affiliation{Wayne State University, Detroit, Michigan 48201}
\author{S.C.~Phatak}\affiliation{Institute of Physics, Bhubaneswar 751005, India}
\author{R.~Picha}\affiliation{University of California, Davis, California 95616}
\author{M.~Planinic}\affiliation{University of Zagreb, Zagreb, HR-10002, Croatia}
\author{J.~Pluta}\affiliation{Warsaw University of Technology, Warsaw, Poland}
\author{N.~Porile}\affiliation{Purdue University, West Lafayette, Indiana 47907}
\author{J.~Porter}\affiliation{University of Washington, Seattle, Washington 98195}
\author{A.M.~Poskanzer}\affiliation{Lawrence Berkeley National Laboratory, Berkeley, California 94720}
\author{M.~Potekhin}\affiliation{Brookhaven National Laboratory, Upton, New York 11973}
\author{E.~Potrebenikova}\affiliation{Laboratory for High Energy (JINR), Dubna, Russia}
\author{B.V.K.S.~Potukuchi}\affiliation{University of Jammu, Jammu 180001, India}
\author{D.~Prindle}\affiliation{University of Washington, Seattle, Washington 98195}
\author{C.~Pruneau}\affiliation{Wayne State University, Detroit, Michigan 48201}
\author{J.~Putschke}\affiliation{Lawrence Berkeley National Laboratory, Berkeley, California 94720}
\author{G.~Rakness}\affiliation{Pennsylvania State University, University Park, Pennsylvania 16802}
\author{R.~Raniwala}\affiliation{University of Rajasthan, Jaipur 302004, India}
\author{S.~Raniwala}\affiliation{University of Rajasthan, Jaipur 302004, India}
\author{O.~Ravel}\affiliation{SUBATECH, Nantes, France}
\author{R.L.~Ray}\affiliation{University of Texas, Austin, Texas 78712}
\author{S.V.~Razin}\affiliation{Laboratory for High Energy (JINR), Dubna, Russia}
\author{D.~Reichhold}\affiliation{Purdue University, West Lafayette, Indiana 47907}
\author{J.G.~Reid}\affiliation{University of Washington, Seattle, Washington 98195}
\author{J.~Reinnarth}\affiliation{SUBATECH, Nantes, France}
\author{G.~Renault}\affiliation{SUBATECH, Nantes, France}
\author{F.~Retiere}\affiliation{Lawrence Berkeley National Laboratory, Berkeley, California 94720}
\author{A.~Ridiger}\affiliation{Moscow Engineering Physics Institute, Moscow Russia}
\author{H.G.~Ritter}\affiliation{Lawrence Berkeley National Laboratory, Berkeley, California 94720}
\author{J.B.~Roberts}\affiliation{Rice University, Houston, Texas 77251}
\author{O.V.~Rogachevskiy}\affiliation{Laboratory for High Energy (JINR), Dubna, Russia}
\author{J.L.~Romero}\affiliation{University of California, Davis, California 95616}
\author{A.~Rose}\affiliation{Lawrence Berkeley National Laboratory, Berkeley, California 94720}
\author{C.~Roy}\affiliation{SUBATECH, Nantes, France}
\author{L.~Ruan}\affiliation{University of Science \& Technology of China, Hefei 230026, China}
\author{M.J.~Russcher}\affiliation{NIKHEF and Utrecht University, Amsterdam, The Netherlands}
\author{R.~Sahoo}\affiliation{Institute of Physics, Bhubaneswar 751005, India}
\author{I.~Sakrejda}\affiliation{Lawrence Berkeley National Laboratory, Berkeley, California 94720}
\author{S.~Salur}\affiliation{Yale University, New Haven, Connecticut 06520}
\author{J.~Sandweiss}\affiliation{Yale University, New Haven, Connecticut 06520}
\author{M.~Sarsour}\affiliation{Texas A\&M University, College Station, Texas 77843}
\author{I.~Savin}\affiliation{Particle Physics Laboratory (JINR), Dubna, Russia}
\author{P.S.~Sazhin}\affiliation{Laboratory for High Energy (JINR), Dubna, Russia}
\author{J.~Schambach}\affiliation{University of Texas, Austin, Texas 78712}
\author{R.P.~Scharenberg}\affiliation{Purdue University, West Lafayette, Indiana 47907}
\author{N.~Schmitz}\affiliation{Max-Planck-Institut f\"ur Physik, Munich, Germany}
\author{K.~Schweda}\affiliation{Lawrence Berkeley National Laboratory, Berkeley, California 94720}
\author{J.~Seger}\affiliation{Creighton University, Omaha, Nebraska 68178}
\author{I.~Selyuzhenkov}\affiliation{Wayne State University, Detroit, Michigan 48201}
\author{P.~Seyboth}\affiliation{Max-Planck-Institut f\"ur Physik, Munich, Germany}
\author{E.~Shahaliev}\affiliation{Laboratory for High Energy (JINR), Dubna, Russia}
\author{M.~Shao}\affiliation{University of Science \& Technology of China, Hefei 230026, China}
\author{W.~Shao}\affiliation{California Institute of Technology, Pasadena, California 91125}
\author{M.~Sharma}\affiliation{Panjab University, Chandigarh 160014, India}
\author{W.Q.~Shen}\affiliation{Shanghai Institute of Applied Physics, Shanghai 201800, China}
\author{K.E.~Shestermanov}\affiliation{Institute of High Energy Physics, Protvino, Russia}
\author{S.S.~Shimanskiy}\affiliation{Laboratory for High Energy (JINR), Dubna, Russia}
\author{E~Sichtermann}\affiliation{Lawrence Berkeley National Laboratory, Berkeley, California 94720}
\author{F.~Simon}\affiliation{Massachusetts Institute of Technology, Cambridge, MA 02139-4307}
\author{R.N.~Singaraju}\affiliation{Variable Energy Cyclotron Centre, Kolkata 700064, India}
\author{N.~Smirnov}\affiliation{Yale University, New Haven, Connecticut 06520}
\author{R.~Snellings}\affiliation{NIKHEF and Utrecht University, Amsterdam, The Netherlands}
\author{G.~Sood}\affiliation{Valparaiso University, Valparaiso, Indiana 46383}
\author{P.~Sorensen}\affiliation{Brookhaven National Laboratory, Upton, New York 11973}
\author{J.~Sowinski}\affiliation{Indiana University, Bloomington, Indiana 47408}
\author{J.~Speltz}\affiliation{Institut de Recherches Subatomiques, Strasbourg, France}
\author{H.M.~Spinka}\affiliation{Argonne National Laboratory, Argonne, Illinois 60439}
\author{B.~Srivastava}\affiliation{Purdue University, West Lafayette, Indiana 47907}
\author{A.~Stadnik}\affiliation{Laboratory for High Energy (JINR), Dubna, Russia}
\author{T.D.S.~Stanislaus}\affiliation{Valparaiso University, Valparaiso, Indiana 46383}
\author{R.~Stock}\affiliation{University of Frankfurt, Frankfurt, Germany}
\author{A.~Stolpovsky}\affiliation{Wayne State University, Detroit, Michigan 48201}
\author{M.~Strikhanov}\affiliation{Moscow Engineering Physics Institute, Moscow Russia}
\author{B.~Stringfellow}\affiliation{Purdue University, West Lafayette, Indiana 47907}
\author{A.A.P.~Suaide}\affiliation{Universidade de Sao Paulo, Sao Paulo, Brazil}
\author{E.~Sugarbaker}\affiliation{Ohio State University, Columbus, Ohio 43210}
\author{M.~Sumbera}\affiliation{Nuclear Physics Institute AS CR, 250 68 \v{R}e\v{z}/Prague, Czech Republic}
\author{B.~Surrow}\affiliation{Massachusetts Institute of Technology, Cambridge, MA 02139-4307}
\author{M.~Swanger}\affiliation{Creighton University, Omaha, Nebraska 68178}
\author{T.J.M.~Symons}\affiliation{Lawrence Berkeley National Laboratory, Berkeley, California 94720}
\author{A.~Szanto de Toledo}\affiliation{Universidade de Sao Paulo, Sao Paulo, Brazil}
\author{A.~Tai}\affiliation{University of California, Los Angeles, California 90095}
\author{J.~Takahashi}\affiliation{Universidade de Sao Paulo, Sao Paulo, Brazil}
\author{A.H.~Tang}\affiliation{NIKHEF and Utrecht University, Amsterdam, The Netherlands}
\author{T.~Tarnowsky}\affiliation{Purdue University, West Lafayette, Indiana 47907}
\author{D.~Thein}\affiliation{University of California, Los Angeles, California 90095}
\author{J.H.~Thomas}\affiliation{Lawrence Berkeley National Laboratory, Berkeley, California 94720}
\author{A.R.~Timmins}\affiliation{University of Birmingham, Birmingham, United Kingdom}
\author{S.~Timoshenko}\affiliation{Moscow Engineering Physics Institute, Moscow Russia}
\author{M.~Tokarev}\affiliation{Laboratory for High Energy (JINR), Dubna, Russia}
\author{T.A.~Trainor}\affiliation{University of Washington, Seattle, Washington 98195}
\author{S.~Trentalange}\affiliation{University of California, Los Angeles, California 90095}
\author{R.E.~Tribble}\affiliation{Texas A\&M University, College Station, Texas 77843}
\author{O.D.~Tsai}\affiliation{University of California, Los Angeles, California 90095}
\author{J.~Ulery}\affiliation{Purdue University, West Lafayette, Indiana 47907}
\author{T.~Ullrich}\affiliation{Brookhaven National Laboratory, Upton, New York 11973}
\author{D.G.~Underwood}\affiliation{Argonne National Laboratory, Argonne, Illinois 60439}
\author{G.~Van Buren}\affiliation{Brookhaven National Laboratory, Upton, New York 11973}
\author{N.~van der Kolk}\affiliation{NIKHEF and Utrecht University, Amsterdam, The Netherlands}
\author{M.~van Leeuwen}\affiliation{Lawrence Berkeley National Laboratory, Berkeley, California 94720}
\author{A.M.~Vander Molen}\affiliation{Michigan State University, East Lansing, Michigan 48824}
\author{R.~Varma}\affiliation{Indian Institute of Technology, Mumbai, India}
\author{I.M.~Vasilevski}\affiliation{Particle Physics Laboratory (JINR), Dubna, Russia}
\author{A.N.~Vasiliev}\affiliation{Institute of High Energy Physics, Protvino, Russia}
\author{R.~Vernet}\affiliation{Institut de Recherches Subatomiques, Strasbourg, France}
\author{S.E.~Vigdor}\affiliation{Indiana University, Bloomington, Indiana 47408}
\author{Y.P.~Viyogi}\affiliation{Variable Energy Cyclotron Centre, Kolkata 700064, India}
\author{S.~Vokal}\affiliation{Laboratory for High Energy (JINR), Dubna, Russia}
\author{S.A.~Voloshin}\affiliation{Wayne State University, Detroit, Michigan 48201}
\author{W.T.~Waggoner}\affiliation{Creighton University, Omaha, Nebraska 68178}
\author{F.~Wang}\affiliation{Purdue University, West Lafayette, Indiana 47907}
\author{G.~Wang}\affiliation{Kent State University, Kent, Ohio 44242}
\author{G.~Wang}\affiliation{California Institute of Technology, Pasadena, California 91125}
\author{X.L.~Wang}\affiliation{University of Science \& Technology of China, Hefei 230026, China}
\author{Y.~Wang}\affiliation{University of Texas, Austin, Texas 78712}
\author{Y.~Wang}\affiliation{Tsinghua University, Beijing 100084, China}
\author{Z.M.~Wang}\affiliation{University of Science \& Technology of China, Hefei 230026, China}
\author{H.~Ward}\affiliation{University of Texas, Austin, Texas 78712}
\author{J.W.~Watson}\affiliation{Kent State University, Kent, Ohio 44242}
\author{J.C.~Webb}\affiliation{Indiana University, Bloomington, Indiana 47408}
\author{G.D.~Westfall}\affiliation{Michigan State University, East Lansing, Michigan 48824}
\author{A.~Wetzler}\affiliation{Lawrence Berkeley National Laboratory, Berkeley, California 94720}
\author{C.~Whitten Jr.}\affiliation{University of California, Los Angeles, California 90095}
\author{H.~Wieman}\affiliation{Lawrence Berkeley National Laboratory, Berkeley, California 94720}
\author{S.W.~Wissink}\affiliation{Indiana University, Bloomington, Indiana 47408}
\author{R.~Witt}\affiliation{University of Bern, 3012 Bern, Switzerland}
\author{J.~Wood}\affiliation{University of California, Los Angeles, California 90095}
\author{J.~Wu}\affiliation{University of Science \& Technology of China, Hefei 230026, China}
\author{N.~Xu}\affiliation{Lawrence Berkeley National Laboratory, Berkeley, California 94720}
\author{Z.~Xu}\affiliation{Brookhaven National Laboratory, Upton, New York 11973}
\author{Z.Z.~Xu}\affiliation{University of Science \& Technology of China, Hefei 230026, China}
\author{E.~Yamamoto}\affiliation{Lawrence Berkeley National Laboratory, Berkeley, California 94720}
\author{P.~Yepes}\affiliation{Rice University, Houston, Texas 77251}
\author{I-K.~Yoo}\affiliation{Pusan National University, Pusan, Republic of Korea}
\author{V.I.~Yurevich}\affiliation{Laboratory for High Energy (JINR), Dubna, Russia}
\author{I.~Zborovsky}\affiliation{Nuclear Physics Institute AS CR, 250 68 \v{R}e\v{z}/Prague, Czech Republic}
\author{H.~Zhang}\affiliation{Brookhaven National Laboratory, Upton, New York 11973}
\author{W.M.~Zhang}\affiliation{Kent State University, Kent, Ohio 44242}
\author{Y.~Zhang}\affiliation{University of Science \& Technology of China, Hefei 230026, China}
\author{Z.P.~Zhang}\affiliation{University of Science \& Technology of China, Hefei 230026, China}
\author{C.~Zhong}\affiliation{Shanghai Institute of Applied Physics, Shanghai 201800, China}
\author{R.~Zoulkarneev}\affiliation{Particle Physics Laboratory (JINR), Dubna, Russia}
\author{Y.~Zoulkarneeva}\affiliation{Particle Physics Laboratory (JINR), Dubna, Russia}
\author{A.N.~Zubarev}\affiliation{Laboratory for High Energy (JINR), Dubna, Russia}
\author{J.X.~Zuo}\affiliation{Shanghai Institute of Applied Physics, Shanghai 201800, China}


\collaboration{STAR Collaboration}\noaffiliation


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\date{\today}

\begin{abstract}
First measurements of charge-independent correlations on angular difference variables $\eta_1 - \eta_2$ (pseudorapidity) and $\phi_1 - \phi_2$ (azimuth) are presented for primary charged hadrons with transverse momentum $0.15 \leq p_t \leq 2$~GeV/$c$ and $|\eta| \leq 1.3$ from Au-Au collisions at $\sqrt{s_{NN}} = 130$~GeV. Strong charge-independent angular correlations are observed associated with jet-like structures and elliptic flow. The width of the jet-like peak on $\eta_1 - \eta_2$ increases by a factor 2.3 from peripheral to central collisions, suggesting strong coupling of semi-hard scattered partons to a longitudinally-expanding medium. New methods of jet analysis introduced here provide evidence for nonperturbative QCD medium effects in heavy ion collisions.
\end{abstract}

\pacs{24.60.-k, 24.60.Ky, 25.75.Gz}
%\keywords{Suggested keywords}

\maketitle

\section{Introduction}

Correlations and fluctuations can provide essential information on the nature of the medium produced in ultrarelativistic heavy ion collisions~\cite{stock,poly,dcc}. {\em In-medium modification} of parton scattering and fragmentation of energetic partons and the bulk medium can be observed {\em via} large-momentum-scale correlations. Charge-independent angular correlations result from initial-state multiple scattering (Cronin effect~\cite{iss}, hard parton scattering~\cite{jetquench}) with subsequent in-medium parton dissipation~\cite{newref} and elliptic flow. Medium modification of minimum-bias, semi-hard parton scattering and fragmentation ({\em i.e., minijets}) is the subject of this paper. 

Previous studies of parton-medium interactions have included angular correlations of high-$p_t$ particles based on a {\em leading-particle} technique ({\em e.g.,} leading-particle $p_t > 4$ GeV/c, associated particle $p_t < 4$ GeV/c) in which the away-side jet structure was observed to be strongly reduced in central Au-Au collisions~\cite{backjet}. Theoretical descriptions of parton energy loss and medium-modified fragmentation include perturbative quantum chromodynamics (pQCD) based jet-quenching models~\cite{jetquench,salgado} and parton recombination models~\cite{reco}.

In this Letter we report the first measurements in heavy ion collisions of charge-independent {\em joint autocorrelations}~\cite{auto} on angular difference variables $\phi_{\Delta} \equiv \phi_1 - \phi_2$ (azimuth) {\em and}\, $\eta_{\Delta} \equiv \eta_1 - \eta_2$ (pseudorapidity) for charged particles with $0.15 \leq p_t \leq 2$ GeV/c. This analysis is based on $\sqrt{s_{NN}} = 130$~GeV Au-Au collisions observed with the STAR detector~\cite{star} at the Relativistic Heavy Ion Collider (RHIC). 
The measurements involve no {\em a priori} jet model (specifically, no trigger particle). 
%The observed correlations are dominated by a peaked structure for pairs of particles with $\phi_{\Delta} < \pi/2$ (same-side) and elliptic flow.   The same-side correlation is maximum at $\phi_{\Delta} = \eta_{\Delta} = 0$. We hypothesize that the peaked structure is caused by {\em minimum-bias} initial-stage parton scattering and fragmentation detected without imposing a jet model. 
The autocorrelation technique, combined with the large angular acceptance of the STAR detector, enables statistically weak correlation structures, which are individually undetectable but occur multiple times in each event, to be measured in the aggregate with good statistical accuracy. 
These novel {\em low}-$p_t$ measurements reveal jet-like correlations which suggest that in central Au-Au collisions strong non-perturbative coupling of partons to a {\em longitudinally-expanding medium}~\cite{schukraft} produces dramatic changes in the angular distribution of parton fragments (hadrons) not anticipated by pQCD-based theory~\cite{jetquench,rqmd}. 

\section{Analysis Method}

Our goal is to access the complete {\em charge-independent} (CI - all charged particles) structure of two-particle density $\rho(\vec{p_1},\vec{p_2})$ {\em without imposing a correlation model}. The full two-particle momentum space is projected onto angular subspace $(\eta_1,\eta_2,\phi_1,\phi_2)$, integrating over a specific transverse momentum interval. Correlation structure on {transverse momentum} with specific angular constraints is considered in a separate analysis~\cite{mtxmt}. We further project the 4D (four dimensional) subspace onto a 2D subspace of angular {\em difference variables} to form a {\em joint autocorrelation} which is observed to retain essentially all angular correlation information~\cite{cdpaper}. The autocorrelations obtained in this study thus access the {\em complete CI angular structure} of two-particle density $\rho(\vec{p_1},\vec{p_2})$.

Differential correlation analysis is achieved by comparing an object distribution $\rho_{sib}$ of particle pairs taken from single events (sibling pairs) with a reference distribution $\rho_{mix}$ where each particle in the pair is taken from different but similar events (mixed pairs). The corresponding correlation function and pair-number density ratio are defined by
\bea
C(\vec{p}_1,\vec{p}_2) & = &
\rho_{sib}(\vec{p}_1,\vec{p}_2) - \rho_{mix}(\vec{p}_1,\vec{p}_2) \nonumber \\
r(\vec{p}_1,\vec{p}_2) & \equiv & \rho_{sib}(\vec{p}_1,\vec{p}_2)/
\rho_{mix}(\vec{p}_1,\vec{p}_2).
\label{Eq1}
\eea
Pair densities $\rho(\vec{p}_1,\vec{p}_2)$ are first projected onto subspaces $(\eta_1,\eta_2)$, $(\phi_1,\phi_2)$ as histograms $n_{ab} \simeq  \epsilon_x \, \epsilon_y \,\rho(x_a,y_b)$, where $ab$ are 2D bin indices and $\epsilon_x, \epsilon_y$ are bin widths on $x,y \in \{\eta, \phi, \eta_\Delta, \phi_\Delta\}$. Sibling- and mixed-pair histograms are separately normalized to the total number of detected pairs in each event class: $\hat n_{ab} = n_{ab} / \sum_{ab} n_{ab}$. Normalized pair-number ratios $\hat{r}_{ab} = \hat{n}_{ab,sib}/\hat{n}_{ab,mix}$ are the basis for this analysis. Ratios are formed from subsets of events with similar centrality (multiplicities differ by $\leq 100$, except $\leq 50$ for most-central) and primary-vertex location (within 7.5~cm along the beam axis) and combined as weighted (by sibling pair number) averages within each centrality class.
If correlation structure is invariant on sum variables $\eta_1 + \eta_2$ and $\phi_1 + \phi_2$ (stationarity), as observed previously in heavy ion collisions~\cite{cdpaper}, histograms $\hat r_{ab}$ may be projected {\em by averaging} along parallel diagonals to form 2D {joint}\, autocorrelations~\cite{auto,inverse} on difference variables $\eta_\Delta , \phi_\Delta$. Autocorrelation details are described in~\cite{inverse,mitmeths}. The autocorrelations in this study should not be confused with {\em conditional distributions} obtained from leading-particle jet analyses. 2D joint autocorrelations compactly represent all angular correlations on 4D subspace $(\eta_1,\eta_2,\phi_1,\phi_2)$ {\em without information loss} (distortion).

%The projection is done by filling pair-number histograms $n_{ab} \simeq  \epsilon_x \, \epsilon_y \,\rho(x_a,y_b)$, where subscripts $ab$ denote 2D bin indices and $\epsilon_x, \epsilon_y$ are histogram bin widths on variables $x,y \in \{\eta_1, \eta_2, \phi_1, \phi_2, \eta_\Delta, \phi_\Delta\}$. Sibling and mixed pair-number histograms for each charge-pair combination are separately normalized to the total number of detected pairs in each centrality class: $\hat n_{ab,sib} = n_{ab,sib} / \sum_{ab} n_{ab,sib}$ and $\hat n_{ab,mix} = n_{ab,mix} / \sum_{ab} n_{ab,mix}$. Normalized pair-number ratios $\hat{r}_{ab} = \hat{n}_{ab,sib}/\hat{n}_{ab,mix}$ are the basis for this analysis. 

%To reduce systematic error, ratio histograms are obtained for subsets of events within a given centrality class which have similar multiplicities (differences $\leq 50$) and primary collision vertex location within the detector (within 7.5~cm along the beam axis). Ratios $\hat r_{ab}$ for each centrality class were defined as weighted (by total number of sibling pairs) averages over all subsets in that centrality class. 

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%In order to visualize the CD correlation structure in the 4D subspace $(\eta_1,\eta_2,\phi_1,\phi_2)$ pair densities can be projected onto separate 2D subspaces ($\eta_1,\eta_2$) and ($\phi_1,\phi_2$).  Those projections, discussed further below, discard a substantial amount of the information in the full two-particle space. However, they reveal that the principal variation is on differences $\eta_1 - \eta_2$ and $\phi_1 - \phi_2$.  

%For this analysis we simultaneously project the 4D subspace onto angular {\em difference variables} $\phi_{\Delta} \equiv \phi_1 - \phi_2$ and $\eta_{\Delta} \equiv \eta_1 - \eta_2$. 

% The resulting 2D distribution is referred to as a {\em joint  autocorrelation}. 


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[t]
\includegraphics[keepaspectratio,width=3.3in]{cidata}
\caption{\label{Figure1}
Perspective views of two-particle CI joint autocorrelations $\bar N (\hat r-1)$ on  $(\eta_{\Delta},\phi_{\Delta})$ for central (a) to peripheral (d) collisions.}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\section{Data}
\label{SecData}

Data for this analysis were obtained with the STAR detector~\cite{star}
using a 0.25~T uniform magnetic field parallel to the beam axis. Event triggering and charged-particle measurements with the time projection chamber (TPC) are described in \cite{star}. Track definitions, tracking efficiencies, quality cuts and primary-particle definition are described in~\cite{meanptprl,spectra}.  Tracks were accepted in $|\eta| \leq 1.3$, $0.15 \leq p_t \leq 2$~GeV/$c$ and full azimuth. Particle identification was not implemented. Corrections were made to $\hat{r}$ for two-track inefficiencies due to track merging and intersecting trajectories reconstructed as $>2$ particles (splitting)~\cite{trackcuts}. Small-scale momentum correlations due to HBT and Coulomb effects~\cite{starhbt} were suppressed by eliminating sibling and mixed track pairs with $|\eta_{\Delta}| < 0.3$, $|\phi_{\Delta}| < \pi/6$, $|p_{t1} - p_{t2}| < 0.15$~GeV/$c$, if $p_t < 0.8$~GeV/$c$ for either particle. These pair cuts have negligible effect on the correlations studied here. Four centrality classes for 300k events labeled (a) - (d) for central to peripheral were defined by cuts on TPC track multiplicity $N$ within the acceptance relative to minimum-bias event multiplicity frequency distribution end-point $N_0$~\cite{endpoint}, which corresponds to the maximum participant number~\cite{meanptprl,nu}. The four centrality classes used here were defined by (d) $0.03 < N/N_0 \leq 0.21$, (c) $0.21 < N/N_0 \leq 0.56$, (b) $0.56 < N/N_0 \leq 0.79$ and (a) $N/N_0 > 0.79$, corresponding respectively to fraction of total cross section ranges 40-70\%, 17-40\%, 5-17\% and 0-5\%.

%Ratios were formed from subsets of events with similar centrality (multiplicity differs by $\leq 50$) and primary-vertex location (within 7.5~cm along beam axis) and combined as weighted averages within each centrality class. 

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[t]
\includegraphics[keepaspectratio,width=1.65in]{ciautomod1}
\includegraphics[keepaspectratio,width=1.65in]{ciautomod2}
\includegraphics[keepaspectratio,width=1.65in]{ciautomod3}
\includegraphics[keepaspectratio,width=1.65in]{ciautomod4}
%\includegraphics[keepaspectratio,width=3.3in]{cidatamod}
\caption{\label{Figure2}
The same data as in Fig.~\ref{Figure1}, but with $\eta_\Delta$-independent dipole and quadrupole components on $\phi_\Delta$ (see text) subtracted to reveal `same-side' ($|\phi_\Delta| < \pi / 2$) structures which can be associated with minijets.}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\section{Two-particle Distributions}

Plotted in Fig.~\ref{Figure1}  are perspective views of CI joint autocorrelations of quantity $\bar N(\hat r - 1)$ (measuring the density of correlated pairs {\em per final-state particle}~\cite{cdpaper}, typically $O(1)$ for all centralities, $\bar N$ is the mean multiplicity in the acceptance) for four centrality classes of Au-Au collisions. $\bar N(\hat r - 1)$ would be independent of centrality if Au-Au collisions were linear superpositions of p-p collisions (participant scaling). The distributions in Fig.~\ref{Figure1} are dominated by 1) a 1D quadrupole component $\propto \cos(2\phi_\Delta)$ conventionally attributed to elliptic flow; 2) a 1D dipole component $\propto \cos(\phi_\Delta)$ associated with transverse momentum conservation in a thermal system, and 3) a 2D `same-side' ($|\phi_\Delta| < \pi / 2$) peak.  The same-side peak is assumed to be associated with parton fragmentation to hadrons, albeit for fragments with much lower $p_t$s than are considered in a conventional jet analysis. Since no leading or trigger particle is invoked in this model-independent analysis we refer to the corresponding fragment systems as {\em minijets} (minimum-bias jets).

Momentum conservation in a thermal multiparticle system should result in a dipole $\cos(\phi_\Delta)$ angular correlation~\cite{fesh}. We also expect back-to-back or {\em away-side} ($\phi_\Delta \sim \pi$) azimuth correlations from momentum conservation in parton scattering (dijets). However, at low $p_t$ the away-side jet structure is broad, and indistinguishable from the dipole $cos(\phi_\Delta)$ component describing momentum conservation in the bulk system. We subtract dipole and quadrupole $cos(2\phi_\Delta)$ components from distributions in Fig.~\ref{Figure1} to obtain Fig.~\ref{Figure2} by minimizing $\eta_\Delta$-independent sinusoidal residuals on the away side region ($|\phi_\Delta| > \pi / 2$) and for $|\eta_\Delta| \sim 2$. The small excess in the (0,0) bins is due to conversion-electron pair contamination. The same-side 2D peaks in this figure are the main subject of this analysis. 

We observe that the away-side region in Fig.~\ref{Figure2} is featureless, even for the most peripheral collisions. If Lund-model strings~\cite{lund} remained dynamically relevant in the final stage of heavy ion collisions we would expect, in the accepted $p_t$ interval, significant correlation structure on the away side of Fig.~\ref{Figure2}: a prominent 1D gaussian on $\eta_\Delta$ approximately symmetric on azimuth and due to local charge conservation on $z$ (during longitudinal string fragmentation) and coupling of $z$ to $\eta$ due to longitudinal Hubble expansion, as observed in p-p collisions~\cite{isrpp,jeffpp}. The absence of such structure suggests that longitudinal strings play {\em no significant role} in the final stage of Au-Au collisions, even for the most peripheral collisions in this study. That trend is consistent with the centrality dependence of net-charge correlations in which structure characteristic of string fragmentation is strongly suppressed with increasing centrality of Au-Au collisions~\cite{cdpaper}. 

The same-side peak isolated in Au-Au collisions by the multipole subtraction varies strongly with centrality, transitioning from significant elongation on azimuth difference $\phi_\Delta$ for p-p collisions~\cite{jeffpp} to dramatic broadening along $\eta_\Delta$ for the more central Au-Au collisions (note the non-unit aspect ratio of these 2D plots). HBT and Coulomb pair cuts (see Sec.~\ref{SecData}) reduce the bins nearest (0,0) by 10\% or less. 1D projections of data and 2D model fits (discussed below) onto difference variables $\phi_{\Delta}$ and $\eta_{\Delta}$ are shown in Fig.~\ref{Figure3}. Solid dots and curves (open triangles and dashed curves) correspond to $\eta_{\Delta}$ $(\phi_{\Delta})$ projections. 

\section{Errors}

Statistical errors for joint autocorrelations approximately double as $|\eta_{\Delta}|$ increases from 0 to 2 because of the bounded $\eta$ acceptance, but are uniform on $\phi_{\Delta}$ because the azimuthal acceptance is continuous (periodic) in STAR.  Statistical errors for $\hat r$ at $|\eta_{\Delta}| = 0$ vary from $0.0001$ for central collisions to $0.001$ for peripheral collisions. Statistical errors for $\bar N(\hat r - 1)$ ($\sim 0.1$) are nearly independent of centrality. Systematic errors were estimated as in \cite{meanptprl}. Contamination from photon conversions to $e^{\pm}$ pairs is significant only within the bin defined by $|\eta_\Delta| < 0.1$, $|\phi_\Delta| < 0.1$ which was excluded from model fits. The dominant source of systematic error is non-primary background, mainly weak-decay daughters~\cite{spectra}, whose correlation with primary particles is unknown and is estimated by assuming those correlations vary from zero to the measured correlation amplitude for primary particles \cite{meanptprl}. Total systematic errors for data presented in Fig.~\ref{Figure1} are $\pm$7\% of signal, but increase to $\pm$8\% for $|\eta_\Delta| < 0.5$ and to $\pm$11\% for $|\phi_\Delta| < 0.05$. Correlations from resonance $(\rho^0 , \omega )$ decays are $\sim$3\% of the peaks at (0,0) in Fig.~\ref{Figure2} in $|\eta_{\Delta}| < 0.5$, $|\phi_{\Delta}| < 2$~\cite{mevsim}.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[h]
%\includegraphics[keepaspectratio,width=3.3in]{fig4-1008-1}
\includegraphics[width=1.65in,height=1.3in]{ciproj1}
\includegraphics[width=1.65in,height=1.3in]{ciproj2}
\includegraphics[width=1.65in,height=1.3in]{ciproj3}
\includegraphics[width=1.65in,height=1.3in]{ciproj4}
%\includegraphics[width=3.3in,height=1.3in]{ciprojtop}
%\includegraphics[width=3.3in,height=1.3in]{ciprojbot}
\caption{\label{Figure3} 
Projections of 2D CI joint autocorrelations $\bar N(\hat{r} - 1 )$
in Fig.~\ref{Figure2} onto difference variables $\eta_{\Delta}$ (solid dots) and $\phi_{\Delta}$ (open triangles). The solid (dashed) curves represent corresponding projections of 2D analytical model fits to the data. 2D peaks are substantially reduced in amplitude by 1D projections.}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\section{Model Fits}

Joint autocorrelations, as in Fig.~\ref{Figure1} but without factor $\bar N$, were fitted with a model function consisting of dipole and quadrupole terms on $\phi_\Delta$, a 1D gaussian on $\eta_{\Delta}$ and a 2D same-side gaussian on $(\eta_{\Delta},\phi_{\Delta})$, plus a constant offset 
%(motivated by similar structure in initial fit residuals). The complete model function for $\hat r_{ij} - 1$ in Fig.~\ref{Figure1} is 
\bea \label{Eq3}
F & = & A_{\phi_\Delta}\, \cos(\phi_\Delta) + A_{2\phi_\Delta}\, \cos(2\, \phi_\Delta) + A_0\, e^{- \left( \frac{\eta_{\Delta}}{\sqrt{2} \sigma_{0}} \right)^2 } \nonumber \\ 
&+&  A_1 \, e^{- \left\{ \left( \frac{\phi_{\Delta}}{\sqrt{2} \sigma_{\phi_{\Delta}}} \right)^2  + \left( \frac{\eta_{\Delta}}{\sqrt{2} \sigma_{\eta_{\Delta}}} \right)^2 \right\} } + A_2.
\eea
%Fig.~\ref{Figure2} shows an intermediate stage of the fitting procedure with $v_1$ and $v_2$ subtracted. 
Best-fit parameters for the model fits shown in Fig.~\ref{Figure3} are listed in Table~\ref{TableI}, including mean multiplicity factor $\bar N$ as in Figs.~\ref{Figure1}-\ref{Figure3} plus tracking efficiency correction factor ${\cal S}$~\cite{norm}. Those fit parameters confirm that with increasing centrality 2D peak structures exhibit 1) strong and non-monotonic amplitude variation, 2) strong $\eta_\Delta$ width increase and 3) significant $\phi_\Delta$ width {\em reduction}. 
%%%%%%%%%%%%%%%%%%%%
\begin{table}[h]
\caption{\label{TableI}
Parameters and fitting errors (only) for model fits [Eq.~(\ref{Eq3})] to
joint autocorrelation data in Fig.~\ref{Figure1} for centrality bins (a) - (d)
(central - peripheral). Total systematic error for efficiency-corrected amplitudes is 11\%~\cite{norm}.}
%Parameters and errors for model fits (Eq.~(\ref{Eq3})) to
%joint autocorrelation data in Fig.~\ref{Figure2} for centrality bins (a) - (d) (central - peripheral).  Errors represent fitting uncertainties only and are approximately constant with centrality; errors in the last column are averages except as noted. Total systematic error for normalized amplitudes is 11\%~\cite{norm}.}
\begin{tabular}{|c|c|c|c|c|c|} \hline  \vspace{-.13in} & & & & & \\
centrality  & (d) & (c)  & (b)  & (a)  & error\footnote{Range of fitting errors
in percent from peripheral to central.}(\%) \\
\hline \vspace{-.13in} & & & & & \\
${\cal S}$\cite{norm} &   1.19    &   1.22    &  1.25    &   1.27   & 8 (syst)
%\footnote{Systematic error.}
 \\
$\bar{N}$  &   115.5   &   424.9   &  790.2   &   983.0  &  \\
%\hline
%${\cal S} \bar{N} A_0$     & 0.86  &  1.09  & 0.88  &  0.84  &  0.05  \\
\hline  \vspace{-.12in} & & & & & \\
${\cal S} \bar{N} A_1$   & 1.93   & 3.23  &  3.72  &  3.10  &   5-2   \\
$\sigma_{\phi_{\Delta}}$ & 0.61  &  0.55  &  0.54  &  0.53  &   4-2   \\
$\sigma_{\eta_{\Delta}}$ & 0.58  &  1.05  &  1.34  &  1.36   &  5-2   \\
\hline \vspace{-.12in} & & & & & \\
${\cal S} \bar{N} A_0$   & 0.60   & 0.32  &  ---  &  ---  &  0.16-0.1\footnote{Magnitude of fitting errors.} \\
$\sigma_{0}$ & 1.11  &  0.24  &  ---  &  ---   &  28-22  \\
\hline \vspace{-.12in} & & & & & \\
${\cal S} \bar{N} A_{2}$     & -0.67 & -0.55  & -0.67  & -0.58 &  0\footnote{Fixed by normalization of $\hat r$}  \\
\hline \vspace{-.12in} & & & & & \\
${\cal S} \bar{N} A_{\phi_\Delta}$   & -0.31 & -0.76  & -0.97  & -0.74 &  22-5   \\
${\cal S} \bar{N} A_{2\phi_\Delta}$   & 1.05  &  2.72  &  1.30  &  0.32 &  2-17   \\
\hline  \vspace{-.12in} & & & & & \\
$\chi^2$/DoF & $\frac{439}{316}$ & $\frac{419}{316}$ & $\frac{675}{316}$ & $\frac{415}{316}$ &  \\
\hline
\end{tabular}
%\end{center}
%\end{minipage}
\end{table}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\section{Discussion}

In Fig.~\ref{Figure4}, the same-side peak amplitudes and widths from model fits are plotted $vs$ centrality measure $\nu$~\cite{nu} (mean participant path length in terms of the number of encountered nucleons, $\approx 2 N_{bin} / N_{part}$) along with measurements obtained from p-p collision data~\cite{jeffpp}. The same-side peaks in Fig.~\ref{Figure2} differ strongly from those for p-p collisions, where for the latter a 2D gaussian peak significantly elongated on {\em azimuth} dominates the same-side structure, widths on $\eta_\Delta$ and $\phi_\Delta$ being $\sim$ 0.5 and 0.7 respectively~\cite{jeffpp}. The similar same-side peak widths for mid-peripheral Au-Au collisions in this analysis (panel~(d), $\nu \sim 2.5$) are consistent with the p-p result. In central Au-Au collisions however, the widths of the same-side peak reverse the sense of the asymmetry: the peak is dramatically elongated on $\eta_\Delta$, the width ratio increasing to 2.6. 

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[h]
% \includegraphics[keepaspectratio,width=3.3in]{fig5-1114-1}
\includegraphics[width=1.6in,height=1.5in]{cicentralityamp}
\includegraphics[width=1.6in,height=1.5in]{cicentralitywid}
\caption{\label{Figure4}
Left: Fitted amplitudes and volumes for peaks in Fig.~\ref{Figure2} plotted {\em vs} mean participant path length $\nu$~\cite{nu}, from Table~\ref{TableI}. Right: Fitted widths $\sigma_{\eta_\Delta}$ (dots) and $ \sigma_{\phi_\Delta}$ (triangles).  Hatched regions show p-p values.  Curves guide the eye.}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

Same-side peak amplitudes ${\cal S}\bar N A_1$ (measuring correlations per final-state particle) in the left panel of Fig.~\ref{Figure4} increase nearly linearly with path-length as expected for {\em independent} binary collisions. However, peak {\em volume} $\equiv  {\cal S}\bar N A_1\, \sigma_{\eta_\Delta}\, \sigma_{\phi_\Delta}$ ($\propto$ minijet fragment number) has a more complex variation, strongly departing from linear $\nu$ scaling (dotted line) above $\nu = 2.5$. The dashed curve in the left panel is derived from the curves describing amplitude and peak widths. The volume excess beyond the linear extrapolation may indicate the onset of a strongly dissipative medium in which more correlated fragments with less $p_t$ result from each scattered parton. The latter increase is very likely a lower-$p_t$ manifestation of the observed suppression of the high-$p_t$ part of the $p_t$ spectrum measured by quantity $R_{AA}$~\cite{raa}. It is notable that the peak {\em amplitude} does not deviate from a linear trend, except for the most central point.

We speculate that the mechanism modifying the same-side peak in central Au-Au collisions is strong coupling of {\em minimum-bias} energetic partons (no high-$p_t$ trigger is imposed) to a {\em longitudinally-expanding} colored medium developed in the more central Au-Au collisions. Hadrons from fragmenting partons sample the {\em local velocity structure} of the pre-hadronic parton-medium coupled system. Growth of the colored medium and its coupling to the fragmenting parton with increasing collision centrality is then indicated by increased width on $\eta_\Delta$ of the same-side correlation peak.

%\section{Theory}

The perturbative QCD expectation for angular correlations about the jet  thrust axis in p-p collisions corresponds to a {\em nearly-symmetric} near-side peak on $(\eta_\Delta,\phi_\Delta)$. That `{\em in vacuo}\,' result is indeed observed in p-p collisions for higher-$p_t$ fragments ($> 2.5$ GeV/c). However, in a minimum-bias autocorrelation analysis of p-p data~\cite{jeffpp} {\em strong deviations} from expected pQCD angular symmetry about the jet thrust axis are observed. The Hijing Monte Carlo collision model~\cite{jetquench} includes a conventional pQCD model of jet production and quenching in A-A collisions. The default Hijing same-side peak is observed to be symmetric, and the widths on $\eta_\Delta$ {\em and} $\phi_\Delta$ both increase by only 10\% when jet quenching is imposed~\cite{ptscale}, {\em seriously underpredicting} the large width increase on $\eta_\Delta$ and contradicting the width {\em decrease} on $\phi_\Delta$ observed in the present analysis of Au-Au data. The pQCD jet-quenching mechanism in Hijing cannot produce an asymmetry on $(\eta_\Delta,\phi_\Delta)$, given the symmetry about the parton momentum of its perturbative bremsstrahlung quenching mechanism. Prominent low-$p_t$ longitudinal string-fragment correlations on $\eta_\Delta$ are observed for all Hijing centralities,  also contradicting results of the present analysis noted above.  RQMD~\cite{rqmd} CI correlations are featureless except for small flow-related correlations on $\phi_\Delta$.

Recently, effects of a flowing medium on parton energy loss and fragmentation have been explored theoretically~\cite{salgado}. The premise of that study is that gluon bremsstrahlung from energetic partons transiting a colored medium should be sensitive to the local structure of the velocity field on the medium. The model considered is uniform medium flow (`directed flow') transverse to the energetic parton momentum. A static medium is expected to broaden the bremsstrahlung angular distribution and hence the near-side peak (symmetric broadening from jet quenching is observed already with Hijing~\cite{ptscale}). Medium flow transverse to the parton direction was found in~\cite{salgado} to shift and distort the fragment-energy angular distribution relative to the thrust axis. In the LHC context, for 100 GeV jets with typical {\em energy} angular width $\sim 0.05$, the effect of the flowing medium on the angular distribution was found to be comparable to the width magnitudes (`marked medium-induced deviations'). However, the absolute angular changes were small.

In the RHIC context a comparison was made with a STAR leading-particle analysis of jet correlations~\cite{fuqiang}. The prediction of~\cite{salgado} for trigger particles with $p_t \in$ [4,6] GeV/c is width variation from peripheral to central 200 GeV Au-Au collisions of 0.35 (symmetric) to 0.4 on azimuth and to 0.56 on pseudorapidity. Those width increases are similar in magnitude to the symmetric Hijing width increases noted above. However, they differ qualitatively from the width {\em decrease} from 0.7 to 0.5 on azimuth and the dramatic width increase from 0.5 to 1.4 on pseudorapidity observed in the present minimum-bias jet study. The study of directed (vector) flow and parton bremsstrahlung in~\cite{salgado} does not address the issue of longitudinal Hubble (Bjorken) {\em expansion}, a tensor aspect of the velocity field. Coupling of parton fragmentation to the velocity field may be much stronger than what can be modelled perturbatively, requiring a nonperturbative treatment. The analysis in~\cite{salgado} also does not address the centrality dependence of angular deformation, which is strongly nonlinear on path length as demonstrated in Fig.~\ref{Figure4} (right panel).

Fluctuation analysis has been generally advocated as a probe of heavy ion collisions. It is important to note that charge-independent number fluctuations observed within a given detector acceptance integrate {\em over that acceptance} the CI joint autocorrelations presented in this paper (within a constant offset), as described in~\cite{inverse}. The constant offset in the joint autocorrelations, dominated by participant (`volume') fluctuations, is easily separated from the differential angular structure which reveals details of nuclear collision dynamics.  

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\section{Summary}

In conclusion, we have for the first time measured charge-independent joint autocorrelations on difference variables $\phi_{\Delta}$ {\em and} $\eta_{\Delta}$ for Au+Au collisions at $\sqrt{s_{NN}}$ = 130 GeV. Low-$p_t$ string-fragment correlations which appear prominently in p-p collisions are not observed for any centrality in this study: longitudinal string degrees of freedom are apparently strongly suppressed even for fairly peripheral Au-Au collisions. Other correlation structures are observed to have substantial amplitudes. In addition to azimuth structures associated with elliptic flow and transverse momentum conservation we observe a near-side peak structure varying from a nearly-symmetric shape on ($\eta_\Delta,\phi_\Delta$) in peripheral collisions to a shape strongly elongated on $\eta_\Delta$ in central collisions. We interpret the same-side peak as resulting from fragmentation of minimum-bias partons observed with no trigger condition (minijets). The trend of minijet angular deformation, observed in this first jet analysis with {\em low}-$p_t$ hadrons, can be interpreted as a transition from {\em in vacuo} jet fragmentation in p-p and peripheral Au-Au collisions to strong coupling of minimum-bias partons to a longitudinally-expanding colored medium in the more central collisions as part of a parton dissipation process. The concept of parton energy loss in heavy ion collisions is thereby extended to strongly {\em nonperturbative} aspects. Detailed comparisons between data and pQCD-based theory reveal several qualitative differences.
%Future high-statistics correlation measurements may quantify the centrality dependence of color medium development, minijet dissipation and resulting minijet angular deformation.

We thank the RHIC Operations Group and RCF at BNL, and the
NERSC Center at LBNL for their support. This work was supported
in part by the HENP Divisions of the Office of Science of the U.S.
DOE; the U.S. NSF; the BMBF of Germany; IN2P3, RA, RPL, and
EMN of France; EPSRC of the United Kingdom; FAPESP of Brazil;
the Russian Ministry of Science and Technology; the Ministry of
Education and the NNSFC of China; IRP and GA of the Czech Republic,
FOM of the Netherlands, DAE, DST, and CSIR of the Government
of India; Swiss NSF; the Polish State Committee for Scientific 
Research; STAA of Slovakia, and the Korea Sci. \& Eng. Foundation.

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\end{thebibliography}

\end{document}


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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

nucl-ex0411003.extracted_bib
\begin{thebibliography}{99}

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\bibitem{stock} % refs which motivate fluctuation analysis
R.~Stock, Nucl.\ Phys.\ {\bf A661}, 282c (1999);
H. Heiselberg, Phys. Rep. {\bf 351}, 161 (2001).

\bibitem{poly} A. Dumitru, R. Pisarski, Phys. Lett. {\bf B504}, 282 (2001).
%[hep-ph/0010083].

\bibitem{dcc}
L.\,M.~Bettencourt, K.~Rajagopal and J.~V.~Steele,
%``Langevin evolution of disoriented chiral condensate,''
Nucl.\ Phys.\ {\bf A693}, 825 (2001).
%[arXiv:hep-ph/0106257].

\bibitem{iss} M. Ga\'{z}dzicki, A. Leonidov, G. Roland, Eur. Phys. J. {\bf C6},
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\bibitem{jetquench} X.-N. Wang, M. Gyulassy, Phys. Rev. D {\bf 44}, 3501 (1991).

\bibitem{newref} Q. Liu and T. A. Trainor, Phys. Lett. {\bf B567}, 184 (2003).  

\bibitem{backjet} C.~Adler {\em et al.}, Phys. Rev. Lett. {\bf 90}, 082302 (2003).

\bibitem{salgado} 
  N.~Armesto, C.~A.~Salgado and U.~A.~Wiedemann,
  %``Measuring the collective flow with jets,''
  Phys.\ Rev.\ Lett.\  {\bf 93}, 242301 (2004)
%  [arXiv:hep-ph/0405301].

\bibitem{reco} R.\,Hwa and C.\,Yang, Phys. Rev. C {\bf 66}, 025205 (2002).

\bibitem{auto} An autocorrelation is a projection {\em by averaging} from subspace $(x_1,x_2)$ onto difference variable $x_\Delta \equiv x_1 - x_2$. A {\em joint} autocorrelation is a simultaneous projection onto two difference variables.

\bibitem{star}
K. H. Ackermann {\em et al.}, Nucl. Instrum. Meth. A {\bf 499}, 624 (2003);
see other STAR papers in volume A{\bf 499}.

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\bibitem{rqmd}
H. Sorge, H. St\"ocker, W. Greiner, Nucl. Phys. {\bf A498}, 567c (1989);
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\bibitem{mtxmt}
  J.~Adams {\it et al.}  (STAR Collaboration),
  %``Transverse momentum correlations and minijet dissipation in Au Au
  %collisions at s(NN)**(1/2) = 130-GeV,''
  nucl-ex/0408012.

\bibitem{cdpaper} J. Adams {\it et al.} (STAR Collaboration), nucl-ex/0406035.

\bibitem{inverse} 
   T.~A.~Trainor, R.~J.~Porter and D.~J.~Prindle,
  %``Autocorrelations from fluctuation scale dependence by inversion,''
  J.\ Phys.\ G {\bf 31}, 809 (2005).
 % (hep-ph/0410182).

\bibitem{mitmeths}
D.~J.~Prindle and T.~A.~Trainor,
  %``The equivalence of fluctuation scale dependence and autocorrelations,''
hep-ph/0506173, To appear in: Proceedings of the MIT Workshop on Correlations and Fluctuations in Relativistic Nuclear Collisions, Cambridge, Massachusetts, 21-23 April, 2005.

\bibitem{meanptprl} J.\,Adams\,{\it et\,al.}\,(STAR\,Collaboration), 
Phys. Rev. C {\bf 71} 064906 (2005).
%submitted to Phys. Rev. Lett. (2003); 
%nucl-ex/0308033.

\bibitem{spectra} C. Adler {\em et al.}, Phys. Rev. Lett. {\bf 87}, 112303
(2001); {\em ibid}. {\bf 89}, 202301 (2002).

\bibitem{trackcuts}
Track cuts required minimum track separations 5, 12 and 20~cm at radii 50, 127 and 200~cm from the TPC axis.  Crossing pairs with separations less than 10~cm ($z$) and 30~cm (azimuth) at mid-radius were also excluded.

\bibitem{starhbt} 
C. Adler {\em et al.} Phys. Rev. Lett. {\bf 87}, 082301 (2001).

\bibitem{endpoint}
$N_0$, the half-max point at the end of the minimum-bias
distribution plotted as $d\sigma / dN_{ch}^{1/4}$, is an estimator on multiplicity $N$ for the maximum number of participant nucleons; $N/N_0 \simeq N_{part}/N_{part,max}$ within 4\%.

%\bibitem{nu}
%Quantity $\nu \simeq 5.5\, (N_{part}/N_{part,max})^{1/3} \simeq 5.5 \, (N/N_0)^{1/3}$ estimates mean participant path length as a number of encountered nucleons.
%Quantity $\nu \equiv (N_{part}/2)^{1/3} \simeq 5.5(N/N_0)^{1/3}$ for Au 
%($N_{part}$ is participant number) estimates mean participant path 
%length in number of encountered nucleons.

%$\nu \equiv 5.5(N/N_0)^{1/3}$ for this analysis and $\simeq 2 N_{bin} / N_{part}$  ($N_{part}$ is participant number and $N_{bin}$ is number of binary collisions) estimates the mean participant path length in terms of number of encountered nucleons.

\bibitem{nu} $\nu$ estimates the mean participant path length as a number of encountered nucleons. For this analysis $\nu \equiv 5.5 \, (N/N_0)^{1/3} \simeq 5.5\, (N_{part}/N_{part,max})^{1/3} \simeq 2N_{bin}/N_{part}$, based on Glauber-model simulations. $N_{part}$ is the number of participants and $N_{bin}$ is the number of binary collisions. 
%and $N_0$ is the upper half-maximum endpoint of the minimum-bias data distribution plotted as $d\sigma/dN^{1/4}_{}$.

\bibitem{fesh} H. Feshbach, A. Gal and J. H\"ufner, Ann. Phys. (N.Y.) {\bf 66}, 20 (1971) (see Sec. 3.2).

\bibitem{lund}
B. Andersson, G. Gustafson, G. Ingelman and T. Sj\"{o}strand, Phys. Rep.
{\bf 97}, 31 (1983).

\bibitem{isrpp}
J. Whitmore, Phys. Rep. {\bf 27}, 187 (1976).

\bibitem{jeffpp} R.\,J.~Porter and T.\,A.~Trainor (STAR Collaboration), hep-ph/0406330.

\bibitem{mevsim} R. Ray and R. Longacre, nucl-ex/0008009.

\bibitem{norm} Extrapolation factors ${\cal S}$ for $\bar{N}(\hat{r} - 1)$~\cite{meanptprl} correct for contamination and inefficiency~\cite{spectra}. Systematic error in ${\cal S}$ was estimated to be $\pm$8\%.  Total systematic error for extrapolated quantities in Table~\ref{TableI} was 11\%.

\bibitem{raa}
J.~Adams {\it et al.,}
%(STAR Collaboration),
%``Transverse momentum and collision energy dependence of high p(T) hadron
%suppression in Au + Au collisions at ultrarelativistic energies,''
Phys.\ Rev.\ Lett.\  {\bf 91}, 172302 (2003).

\bibitem{ptscale}
 Q.~J.~Liu, D.~J.~Prindle and T.~A.~Trainor, to be published in Phys. Lett B (2005),
  %``Transverse-momentum p(t) correlations from mean-p(t) fluctuation scale
  %dependence in Hijing-1.37-simulated Au - Au collisions at s(NN)**(1/2) =
  %200-GeV,''
  hep-ph/0410180).

\bibitem{fuqiang} 
 F.~Wang  (STAR Collaboration),
  %``Measurement of jet modification at RHIC,''
  J.\ Phys.\ G {\bf 30}, S1299 (2004).
  %(Eprint nucl-ex/0404010).


%\bibitem{central} Centrality classes d) - a) for 300k events were defined by $N/N_0$~\cite{endpoint} cuts at $>0.03$, 0.21, 0.56 and $>0.79$. 

\end{thebibliography}