Production of Neutral Higgs + Jet at the LHC in the SM and the MSSM\footnote{ \uppercase{T}alk presented by \uppercase{O.} \uppercase{B}rein at {\uppercase{SUSY} 2003: \uppercase{S}upersymmetry in the \uppercase{D}esert}\/, held at the \uppercase{U}niversity of \uppercase{A}rizona, \uppercase{T}ucson, \uppercase{AZ}, \uppercase{J}une 5-10, 2003. \uppercase{T}o appear in the \uppercase{P}roceedings.}
OLIVER BREIN
The cross section prediction for the production of the lightest neutral Higgs boson in association with a high-$p_T$ hadronic jet is presented in the framework of the minimal supersymmetric standard model (MSSM) and compared to the SM case. Prospects for the CERN Large Hadron Collider (LHC) are discussed.
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\begin{document}
\title{
Production of 
Neutral Higgs + Jet
at the LHC
in the SM and the MSSM\footnote{
\uppercase{T}alk presented by \uppercase{O.} \uppercase{B}rein
at {\it \uppercase{SUSY} 2003:
\uppercase{S}upersymmetry in the \uppercase{D}esert}\/, 
held at the \uppercase{U}niversity of \uppercase{A}rizona,
\uppercase{T}ucson, \uppercase{AZ}, \uppercase{J}une 5-10, 2003.
\uppercase{T}o appear in the \uppercase{P}roceedings.}}
%%  PLEASE USE THE ABOVE FOOTNOTE FOR ALL ARXIV POSTINGS,
%%   (SUBSTITUTING SPEAKER NAME, OF COURSE;  NO SPEAKER NAME NEEDED
%%      FOR SINGLE-AUTHOR CONTRIBUTIONS). 
%%  NOT NECESSARY TO HAVE FOOTNOTE FOR VERSIONS THAT ARE SENT TO 
%%  SUSY 2003 CONFERENCE FOR PUBLICATION

 
\author{OLIVER BREIN}

\address{Institut f\"ur Theoretische Physik E, RWTH Aachen\\ 
Aachen, D-52056 Germany, E-mail: brein@physik.rwth-aachen.de}


\author{WOLFGANG HOLLIK}

\address{Max--Planck--Institut f\"ur Physik (Werner--Heisenberg--Institut)\\
M\"unchen, D-80805 Germany, E-mail: hollik@mppmu.mpg.de}  


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\maketitle

\abstracts{
The cross section prediction for the production of the lightest 
neutral Higgs boson in association 
with a high-$p_T$ hadronic jet is presented in the framework of 
the minimal supersymmetric standard model (MSSM)
and compared to the SM case.
Prospects for
the CERN Large Hadron Collider (LHC)
are discussed. 
}

%%This Talk is divided in three sections.
%%%As an introduction 
%%First we recall the well-known SM process,
%%production of a Higgs boson associated with
%%a high-$p_T$ hadronic jet\cite{hjet-sm}, 
%%and draw attention to a recent physics
%%simulation with promising results.
%%%
%%Taking this as a Motivation,
%%Then we move on to the 
%%correspondig MSSM process with the lightest
%%neutral Higgs boson $h^0$, which is the topic
%%of our investigation\cite{hjet-paper}
%%and which has not been
%%studied theoretically up to now.
%%%
%%Finally, we present some results of our
%%calculation.



\section{Higgs + Jet in the Standard Model}

The production of SM Higgs bosons in hadron collisions at the 
LHC will proceed mainly via gluon fusion ($gg\to H$).
The detection of a SM Higgs boson
with a mass below 140$\,\gev$
at the LHC is rather difficult
because the predominant decay
into a $b\bar b$-pair is swamped by the large QCD two-jet 
background \cite{ATLASTDR}.
Therefore, only through observation of the
rare decay into two photons,
%($H\to \gamma\gamma$),
is the inclusive single Higgs boson production 
considered the best search channel 
in this mass range at the LHC.

Alternatively,  
and in order to fully explore the Higgs-detection capabilities 
of the LHC detectors, 
one can investigate more exclusive channels 
like e.g.~Higgs production in association with a high-$p_T$ hadronic jet.
The main advantage of this channel is the richer kinematical structure 
of the events
which 
allows for refined cuts increasing the 
signal-to-background 
ratio.
Recently, a detailed 
simulation\cite{ADIKSS-leshouchesHWG} of the SM reaction
$pp\to H+\text{jet}+X, H\to\gamma\gamma$
using the basic cuts $p_{T,\text{jet}} \geq 30\,\gev$, 
$|\eta_{\text{jet}}|\leq 4.5$
showed that this process is a promising alternative or 
supplement to the inclusive Higgs-boson production for 
$m_H < 140\,\gev$.

The partonic processes,
calculated at present to leading order\cite{hjet-sm},
contributing to the hadronic reaction 
$pp \to H + \text{jet} + X$ (see Fig.~\ref{SM_parton_processes}) 
are gluon fusion ($gg \to g H$, 50--70 \% of total rate), 
quark--gluon scattering 
($q(\bar q)g \to q(\bar q) H$, 30--50 \% of total rate)
and 
quark--antiquark annihilation ($q\bar q \to g H$, rate small).
The hadronic 
cross section is dominated by loop-induced processes, involving
effective $ggH$-- and $ggHZ$--couplings. If the $b$-quark is treated as a 
parton present in the proton, there are additional tree-level processes
for quark-gluon scattering and quark-antiquark annihilation
to consider. Yet, in the SM their contribution to the hadronic cross
section is small.
\begin{figure}[bt]
\begin{footnotesize}

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\end{footnotesize}

\caption{\label{SM_parton_processes}
Partonic processes contributing to 
$pp \to H + \text{jet} + X$ in the SM.
%($gg \to H g, q(\bar q)g \to H q(\bar q)$ and $q\bar q \to H g$). 
Hatched circles represent
loops of heavy quarks. The depicted tree-level $b$-quark processes
are much more important in the MSSM case.}
\end{figure}


\section{Higgs + Jet in the MSSM}

Motivated by the promising SM simulation\cite{ADIKSS-leshouchesHWG}
we investigated\cite{hjet-paper} the MSSM process $pp\to h^0+\text{jet}+X$,
involving the lightest MSSM Higgs boson.
Especially, as the process is essentially 
loop-induced, there are potentially large effects from virtual
superpartners to be expected.

In the MSSM, the contributing partonic processes are 
basically the same as in the SM,
{\it i.e.}~$gg\to gh^0, 
q(\bar q)\to q(\bar q)h^0, q\bar q\to g h^0$, 
but there are differences resulting from various sources: 
(i) different Yukawa couplings in the MSSM
%$g_{q\bar q H}^{\text{SM}} = e/(2 s_w) m_q/m_W \:\to\:g_{q\bar q
%h^0}^{\text{MSSM}} = e/(2 s_w) m_q/m_W f_q(\alpha,\beta)$
%with $f_u(\alpha,\beta) = \cos\alpha/\sin\beta$ and
%$= -\sin\alpha/\cos\beta$ for up- and down-type quarks respectively
involving the mixing angles $\alpha$ and $\beta$ of the MSSM Higgs sector.
Especially, 
the $b$-quark processes are enhanced for small 
values of the CP-odd Higgs boson mass $m_A$ ($< 150\,\gev$)
and large $\tan\beta$ in the MSSM.
(ii) Additional superpartner contributions
to the amplitudes, squark-loop insertions
for all SM-like topologies displayed in Fig.~\ref{SM_parton_processes}
and new Feynman graph topologies containing at least
one gluino line (Fig.~2). 
The calculation of the 
partonic processes was done with the help of FeynArts/FormCalc\cite{FAFC}.

\begin{figure}[bt]
\begin{footnotesize}
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\FAVert(10.,10.){-1}

\end{feynartspicture}
\end{picture}
\end{footnotesize}

\caption{\label{MSSM-xtra-tops}
Additional topologies for the loop-induced 
process $q g \to q h^0$ and $q\bar q\to g h^0$ in the MSSM. The hatched circles
represent loops containing at least one gluino line. 
}
\end{figure}


\section{Results}

The partonic cross sections $\hat\sigma_{n m}(\hat s)$ determine the 
hadronic cross section for $pp\to h^0+\text{jet}+X$ via the convolution
\begin{align*}
\sigma & =
\int_{\tau_0}^{1} d\tau 
\bigg(
\frac{ d{L}^{p p}_{g g} }{ d\tau }
\;\hat\sigma_{g h^0}(\tau S)
+\sum_{q} \frac{ d{L}^{p p}_{q g} }{ d\tau }
\;\hat\sigma_{q h^0}(\tau S)
+\sum_{q} \frac{ d{L}^{p p}_{q \bar q} }{ d\tau }
\;\hat\sigma_{g h^0}(\tau S)
\bigg)
\; ,
\end{align*}
with parton luminosities ${d{L}^{AB}_{nm}}/{d\tau}$,
and $\sqrt{S}=14\,\tev$ for the LHC. 
The cuts $p_{T,\text{jet}} \geq 30\,\gev$ and $|\eta_{\text{jet}}| \leq 4.5$
specify $\tau_0$ and the angular-integration limits;
they are chosen as in the SM analysis\cite{ADIKSS-leshouchesHWG}.
%This choice corresponds to the promising SM analysis\cite{hjet-sm}
%mentioned above.


Figs.~\ref{results}(a),(b) show results for the MSSM $m_h^{\text{max}}$ 
benchmark scenario\cite{improvedbm}
with a common squark-mass scale $\MSUSY=400\,\gev$.
For small values of the CP-odd Higgs boson mass $m_A$ ($< 150\,\gev$) and especially for large $\tan\beta$, 
the $b$-quark Yukawa coupling 
is strongly enhanced compared to the top-Higgs coupling.
Thus, in this parameter range, 
the $b$-quark processes dominate the hadronic cross section,
and also the loop-induced processes are dominated by the $b$-quark loops.
At large $m_A$ ($> 200\,\gev$), the coupling of the $b$--Higgs
coupling is much smaller than the top--Higgs coupling and therefore 
the loop-induced processes
dominate.
For $m_A = 400\,\gev$, and almost independently of $\tan\beta$,
the full result is reduced by 24\%
compared to the result with quark loops only. 
%
Fig.~\ref{results}(c) shows the $\MSUSY$--dependence of
the hadronic cross section with and without 
%inclusion of
superpartner contributions for the three benchmark
scenarios\cite{improvedbm}.
(The large-$\mu$ scenario had to be modified\cite{hjet-paper} in order to obey
the exclusion limit for the Higgs mass set by LEP data.)
For moderate, but allowed, squark masses the contribution of 
superpartners is significant.
%
In Fig.~\ref{results}(d) we display the relative difference
between the MSSM $m_h^{\text{max}}$ scenario and the 
SM prediction of the hadronic cross section 
plotted versus $m_A$ and $\tan\beta$.
The MSSM prediction 
is more than 20\% below the SM result 
(using the MSSM value of $m_{h^0}$ for the SM Higgs mass) 
in the 
whole area of the $m_A$--$\tan\beta$ plane displayed. 

In summary, Higgs + jet production 
is promising and deserves
a closer 
look in LHC physics simulations. 
To that end we provide the 
FORTRAN code 
for SM and MSSM predictions
for general use.

\begin{figure}[t]
{\setlength{\unitlength}{1cm}
\begin{picture}(4.5,6.)
\put(-1,0){\special{psfile=ma-plot.HJ.DRA.ps
hscale=80 vscale=80}}
\put(1.4,2.15){{\small (a)}}
\put(3,1.35){$\scriptstyle m_A [\gev]$}
\put(0.45,4){\footnotesize $\sigma [\pb]$}
\put(2.9,4.7){\footnotesize $m_h^{\text{max}}$ scenario}
\put(2.9,4.3){\footnotesize $\MSUSY=400\,\gev$}
\put(2.9,3.9){\footnotesize $\tan\beta=30$}
\end{picture}
\begin{picture}(4.5,6.)
\put(0,0){\special{psfile=tb-plot.HJ.DRA.ps
hscale=80 vscale=80}}
\put(2.3,2.15){{\small (b)}}
\put(4.,1.35){$\scriptstyle \tan\beta$}
\put(1.35,4){\footnotesize $\sigma [\pb]$}
\put(3.9,4.0){\footnotesize $m_h^{\text{max}}$ scenario}
\put(3.9,3.6){\footnotesize $\MSUSY=400\,\gev$}
\put(3.9,3.2){\footnotesize $m_A = 400\,\gev$}
\end{picture}\\
\begin{picture}(3.5,4.3)
\put(-.9,-.8){\special{psfile=Msquark-plot.HJ.1.ps 
hscale=80 vscale=80}}
\put(1.35,1.3){{\small (c)}}
\put(2.5,.3){$\scriptstyle M_{\text{SUSY}} [\gev]$}
\put(0.42,3.53){\footnotesize $\sigma [\pb]$}
\put(3.3,5.){\footnotesize $m_A = 200\,\gev$}
\put(3.3,4.6){\footnotesize $\tan\beta=6$}
\end{picture}
\begin{picture}(5,4.3)
\put(0,-2.45){\special{psfile=tb.ma.MSSM-SM-reldiff.ps 
hscale=80 vscale=80}}
\put(3.45,1.25){{\small (d)}}
\put(5,.3){$\scriptstyle m_A [\gev]$}
\put(7.8,2.7){$\scriptstyle \tan\beta$}
\put(4.15,3.6){\footnotesize $(\sigma_{\text{MSSM}}-\sigma_{\text{SM}})/\sigma_{\text{SM}}\; [\%]$}
\put(5.05,3.2){\footnotesize $m_h^{\text{max}}$ scenario}
\put(5.05,2.8){\footnotesize $\MSUSY=400\,\gev$}
\end{picture}
}
\caption{\label{results} 
Hadronic cross sections in picobarn
(a) as a function of $m_A$,  
(b) as a function of $\tan\beta$, 
both in the $m_h^{\text{max}}$ scenario,
(c) as function of $\MSUSY$ for the three benchmark scenarios.
(d) Relative difference of MSSM and SM prediction in the $m_h^{\text{max}}$
scenario.}
\end{figure}

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

\begin{thebibliography}{0}

\bibitem{ATLASTDR}
%`ATLAS detector and physics performance. Technical design report.  Vol. 2,''
ATLAS-TDR, Volume II, CERN-LHCC-99-15.

\bibitem{ADIKSS-leshouchesHWG}
S.~Abdullin {\it et al.}, 
%M.~Dubinin, V.~Ilyin, D.~Kovalenko, V.~Savrin and N.~Stepanov,
%``Higgs boson discovery potential of LHC in the channel p p $\to$ gamma
%gamma + jet,''
Phys.\ Lett.\ B {\bf 431}, 410 (1998);
%[hep-ph/9805341]
%%CITATION = HEP-PH 9805341;%%
%Higgs WG Reports
A.~Djouadi {\it et al.},
%``The Higgs working group: Summary report,''
hep-ph/0002258.
%%CITATION = HEP-PH 0002258;%%

% pp -> H + jet SM calculations
\bibitem{hjet-sm}
%R.~K.~Ellis, I.~Hinchliffe, M.~Soldate and J.~J.~van der Bij,
R.~K.~Ellis {\it et al.},
%``Higgs Decay To Tau+ Tau-: A Possible Signature Of Intermediate Mass Higgs
%Bosons At The Ssc,''
Nucl.\ Phys.\ B {\bf 297}, 221 (1988);
%%CITATION = NUPHA,B297,221;%%
%
%\bibitem{BaurGlover}
U.~Baur and E.~W.~Glover,
%``Higgs Boson Production At Large Transverse Momentum In Hadronic
%Collisions,''
Nucl.\ Phys.\ B {\bf 339}, 38 (1990);
%%CITATION = NUPHA,B339,38;%%
%
%\bibitem{CLLR}
%M.~Chaichian, I.~Liede, J.~Lindfors and D.~P.~Roy,
M.~Chaichian {\it et al.},
%``Associated Production Of Intermediate Mass Higgs Particle With A Large
%P(T) Jet At Ssc Energy,''
Phys.\ Lett.\ B {\bf 198}, 416 (1987)
[Erratum-ibid.\ B {\bf 205}, 595 (1987).
%%CITATION = PHLTA,B198,416;%%




\bibitem{hjet-paper}
O.~Brein and W.~Hollik,
%`MSSM Higgs bosons associated with high-p(T) jets at hadron colliders,''
Phys.\ Rev.\ D {\bf 68}, 095006 (2003).
%%CITATION = HEP-PH 0305321;%%


\bibitem{FAFC}
See: {\tt www.feynarts.de} .

\bibitem{improvedbm}
M.~Carena, S.~Heinemeyer, C.~E.~Wagner and G.~Weiglein,
%``Suggestions for improved benchmark scenarios for Higgs-boson searches  at
%LEP2,''
hep-ph/9912223.
%%CITATION = HEP-PH 9912223;%%

\end{thebibliography}

\end{document}


hep-ph0402058.extracted_bib
\begin{thebibliography}{0}

\bibitem{ATLASTDR}
%`ATLAS detector and physics performance. Technical design report.  Vol. 2,''
ATLAS-TDR, Volume II, CERN-LHCC-99-15.

\bibitem{ADIKSS-leshouchesHWG}
S.~Abdullin {\it et al.}, 
%M.~Dubinin, V.~Ilyin, D.~Kovalenko, V.~Savrin and N.~Stepanov,
%``Higgs boson discovery potential of LHC in the channel p p $\to$ gamma
%gamma + jet,''
Phys.\ Lett.\ B {\bf 431}, 410 (1998);
%[hep-ph/9805341]
%%CITATION = HEP-PH 9805341;%%
%Higgs WG Reports
A.~Djouadi {\it et al.},
%``The Higgs working group: Summary report,''
hep-ph/0002258.
%%CITATION = HEP-PH 0002258;%%

% pp -> H + jet SM calculations
\bibitem{hjet-sm}
%R.~K.~Ellis, I.~Hinchliffe, M.~Soldate and J.~J.~van der Bij,
R.~K.~Ellis {\it et al.},
%``Higgs Decay To Tau+ Tau-: A Possible Signature Of Intermediate Mass Higgs
%Bosons At The Ssc,''
Nucl.\ Phys.\ B {\bf 297}, 221 (1988);
%%CITATION = NUPHA,B297,221;%%
%
%\bibitem{BaurGlover}
U.~Baur and E.~W.~Glover,
%``Higgs Boson Production At Large Transverse Momentum In Hadronic
%Collisions,''
Nucl.\ Phys.\ B {\bf 339}, 38 (1990);
%%CITATION = NUPHA,B339,38;%%
%
%\bibitem{CLLR}
%M.~Chaichian, I.~Liede, J.~Lindfors and D.~P.~Roy,
M.~Chaichian {\it et al.},
%``Associated Production Of Intermediate Mass Higgs Particle With A Large
%P(T) Jet At Ssc Energy,''
Phys.\ Lett.\ B {\bf 198}, 416 (1987)
[Erratum-ibid.\ B {\bf 205}, 595 (1987).
%%CITATION = PHLTA,B198,416;%%




\bibitem{hjet-paper}
O.~Brein and W.~Hollik,
%`MSSM Higgs bosons associated with high-p(T) jets at hadron colliders,''
Phys.\ Rev.\ D {\bf 68}, 095006 (2003).
%%CITATION = HEP-PH 0305321;%%


\bibitem{FAFC}
See: {\tt www.feynarts.de} .

\bibitem{improvedbm}
M.~Carena, S.~Heinemeyer, C.~E.~Wagner and G.~Weiglein,
%``Suggestions for improved benchmark scenarios for Higgs-boson searches  at
%LEP2,''
hep-ph/9912223.
%%CITATION = HEP-PH 9912223;%%

\end{thebibliography}