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\title{The $h^0\rightarrow A^0 A^0\rightarrow b\overline{b}\tau^+\tau^-$ signal in Vector Boson Fusion production at the LHC}

\author{N. E. Adam$^1$, V. Halyo$^1$, M. Herquet$^2$, S. V. Gleyzer$^3$}
\institute{$^1$High Energy Experiment Group, Department of Physics, Princeton University, Princeton, NJ 08544, United States of America
\\$^2$Centre for Particle Physics an Phenomenology, Universit\'e catholique de Louvain, 2 Chemin du Cyclotron, 1348 Louvain-la-Neuve, Belgique
\\$^3$Florida State University TO BE COMPLETED}

\maketitle

\begin{abstract}
We examine the $h^0\rightarrow A^0 A^0\rightarrow
b\overline{b}\tau^+\tau^-$ signal after production of a Standard Model
(SM) like Higgs particle $h^0$ in Vector Boson Fusion (VBF) at the
LHC. This first analysis is restricted to a particular mass spectrum,
i.e. $m_{h^0}$=120 GeV and $m_{A^0}$=50 GeV, and assumes a reasonable
hypothesis for the involved branching ratios. + RESULTS
\end{abstract}

\section{MOTIVATION}
In the Minimal Supersymmetric extension of the Standard Model (MSSM), at least
one additionnal $SU(2)_L$ Higgs doublet is required compared to the SM in order to cancel
gauge anomalies of the superpartners and to allow Yukawa couplings for all fermions. In order to address the fine-tuning ``$\mu$-problem'' appearing in the MSSM, one can also add an extra complex singlet to these doublets. This last possibility, known in the literature as the Next-to-Minimal Supersymmetric Standard Model (NMSSM), has an interesting phenomenology (e.g. see \cite{Accomando:2006ga} and references therein for a recent review). 

In the NMSSM, one of the pseudoscalar states ($A^0$) is the Goldstone boson of either a global $U(1)$ R-symmetry or a $U(1)$ Peccei-Quinn symmetry in some limit of the model parameters. Since low-fine tuning scenarios predict a moderate breaking of these symmetries, the mass of $A^0$ is expected to be relatively small compare to the mass of the lightest scalar ($h^0$) such that the $h^0\rightarrow A^0 A^0$ decay is kinematically allowed. In \cite{Dermisek:2005ar}, two different types of scenarios are considered, depending if $m_{A^0}>2 m_b$ or $m_{A^0}<2 m_b$ . Scenarios with $m_{A^0}>2 m_b$ are disfavored when LEP data for $Z2b$ and $Z4b$ final states are taken into account. Indeed, the simultaneous analysis of both these channels excludes at better than 99\% the possibility for $h^0$ to be lighter than $\sim 108$ GeV, and an heavier $h^0$ in turns requires a higher fine-tuning of model parameters. At the contrary, scenarios with $m_{A^0}<2 m_b$ are favored by the same data and can even account for the $2\sigma$ excess observed in the $Z2b$ final state in the $m_{h^0}\sim 100$ GeV vicinity. As a consequence, many NMSSM related analysis focus on the $h^0\rightarrow A^0A^0\rightarrow \tau^+\tau^-\tau^+\tau^-$ decay which has the most favorable branching ratio if $m_{A^0}<2 m_b$ (REF OTHER LH STUDIES CMS+ATLAS).

Nevertheless, besides the particular context of the NMSSM, many other
possibilities remain open. If the MSSM scalar sector violates the $CP$ symmetry, standard mass relations do not hold anymore and the decay of $h^0$ into two lighter Higgs bosons may be allowed \cite{Carena:2002bb}. In \cite{Dobrescu:2000jt}, a
light $A^0$ (i.e., between 0.1 and a few tens of GeV)  decays predominantly into pairs of photons (or gluons) thanks to a vector-like quark loop.  Another possibility arises in the context of the generic two-Higgs-doublet model (2HDM). As shown in \cite{Gerard:2007kn}, a moderately light $A^0$ (i.e., between 10 and 100 GeV) can \textit{naturally} satisfy the $\rho$ parameter constraints thanks to a twisted realization of the custodial (or equivalently $CP$) symmetry. As emphasized in \cite{Krawczyk:2001pe}, a pseudoscalar in this mass range together with a moderate value of $\tan\beta$ can also account (in type II 2HDMs) for the observed discrepancy between the experimental measurement of the muon anomalous magnetic moment and the SM predictions.   

Assuming $m_{A^0}>2 m_b$, and that the coupling of $A^0$ to fermions is
proportional to the mass for down-type quarks and leptons (the up-type
quark couplings being negligible for $\tan\beta\gg 1$), the main decay
modes are $A^0\rightarrow b\overline{b}$ (BR $\sim$ 0.92) and
$A^0\rightarrow \tau^+\tau^-$ (BR $\sim$ 0.08).   Under the hypothesis
that BR($h^0\rightarrow A^0A^0$)$\sim1$ (which is a reasonable
approximation in many models), this gives a total branching ratio of
$\sim 0.85$ for $h^0\rightarrow A^0A^0\rightarrow 4b$, $\sim 0.15$ for
$h^0\rightarrow A^0A^0\rightarrow 2b2\tau$ and less than one percent for
$h^0\rightarrow A^0A^0\rightarrow 4\tau$. Since the four $\tau$ final state
signal is suppressed at least by a factor of a hundred compared to the
$m_{A^0}<2 m_b$ scenario studied in (REF SECTION 4TAU), the LHC discovery
of $h^0$ and $A^0$ in this channel is probably difficult. On the other
hand, the four $b$ final state has a large BR, but suffers from important QCD backgrounds. This final state has been investigated in direct production mode at the Tevatron (where it is overwhelmed by the backgrounds  \cite{Stelzer:2006sp})  and in $W/Z$ associated production \cite{Carena:2007jk}. At the LHC, a discovery significance may still be reached in this last  mode \cite{Carena:2007jk,Cheung:2007sva}. 

In the current work, we focus on the intermediate $2b2\tau$ final state,
which has a smaller (but still sizable) BR than the $4b$ final state, together with a much lower background. This final state has been considered in the framework of the associated production of $h^0$ with a $W/Z$ boson at the Tevatron in \cite{Carena:2007jk,Aglietti:2006ne}. However, in this case, only a few events could be observed  (at best) after a few fb$^{-1}$ due to the cuts and $b/\tau$ tagging necessary to remove the large reducible background. Similar difficulties with the reducible background are also expected at LHC \cite{Carena:2007jk}. In the present study, we concentrate on the Vector Boson Fusion (VBF) production mode for $h^0$, which has been shown to be a promising channel at the LHC for the SM decay $h^0\rightarrow \tau^+\tau^-$ both in parton-level analysis \cite{Rainwater:1998kj,Plehn:1999nw} and after full detector simulation \cite{Asai:2004ws,Cavalli:2002vs,Klute2002}.

\section{SIGNAL AND BACKGROUND}
The signal and background Monte-Carlo simulation has been carried out at tree level using \textsc{MadGraph/MadEvent v4} \cite{Alwall:2007st} for the parton-level event generation, \textsc{Pythia 6.4} \cite{Sjostrand:2006za} for parton showering and hadronization and \textsc{????} + REF for detector modeling.

In the framework of this preliminary analysis, some simplifying hypothesis are assumed. The SM-like Higgs $h^0$ shares all SM Higgs boson couplings plus an additional coupling to the pseudoscalar $A^0$ large enough to ensure BR($h^0\rightarrow A^0A^0$)$\sim1$. Its mass is fixed at 120 GeV, i.e. right above the best LEP limit to escape \textit{de facto} all possible direct constraints but light enough to ensure a sizable production cross section. The light pseudoscalar mass is fixed at 50 GeV to lie bellow the $m_{h^0}/2$ threshold, but is large enough to guarantee a good angular separation of decay products.

As mentioned in the previous section, the coupling of $A^0$ to fermions is assumed to be proportional to their mass for down-type quarks and charged leptons, giving a total branching ratio for $h^0\rightarrow A^0A^0\rightarrow 2b2\tau$ of about 0.15 to be compared to the SM expectation BR($h^0\rightarrow\tau^+\tau^-$)$\sim 0.08$. This is only true if the coupling to up-type quarks is strongly suppressed, for example due to an additional $\tan\beta$ factor in a type II 2HDM. If it is not the case, the considered total branching ratio can be reduced by up to a factor two. 

In order to improve efficiency, some production cuts have been applied already at the parton level. To ensure a good tagging/reconstruction efficiency, a minimal $p_T$ of 20 GeV is required for all (non $b$) jets and 10 GeV for $b$-jets and $\tau$'s. For the same reason, a maximal pseudorapidity of 5 is required for jets and of 2.5 for $b$-jets and $\tau$'s, and a minimal separation cut, i.e. $\Delta R>0.3$, is also imposed on all objects pairs. Furthermore, regarding the particular kinematic configuration of signal events, standard VBF cuts are applied, i.e. $|\Delta\eta|>4$ and $m_{jj}>700$ GeV for the two forward jets. Finally, a maximal invariant mass cut, i.e. $m_{\tau\tau}<80$ GeV, is imposed on all $\tau$ pairs to avoid the $Z$ peak and to force the background in the lower mass region where the signal stands.

The signal is characterized by a populated final state with two central $b$ jets, two central $\tau$'s and two forward jets. To avoid triggering issues, we focus on the leptonic decays of both $\tau$'s. The associated tree level cross section (after $\tau$'s decays and cuts) is 9 fb. The irreducible background where the $\tau$ pair is coming from an off shell photon or $Z$, and the $b$ pair from a gluon splitting is rather low, with a 1fb cross section. The same process with a $e$ or $\mu$ pair replacing the $\tau$ pair has a more sizable cross section, around 8.7 fb, due to the absence of the $\tau$ branching ratio. The most dangerous reducible background is the $t\overline{t}$ pairs produced by gluon fusion in the VBF kinematic configuration and fully leptonic top decays (through an intermediate $\tau$ or not). Even if the total cross section is almost three order of magnitude larger than the signal (3.2 pb), the associated distributions (in particular the invariant mass of $b$'s and $\tau$'s) and the total amount of missing transverse energy are very different.

\section{RESULTS}

\section{CONCLUSION}

\section*{ACKNOWLEDGEMENTS}
The work of MH was supported by the Institut Interuniversitaire des Sciences Nucl\'eaires and by the Belgian Federal Office for Scientific, Technical and Cultural Affairs through the Interuniversity Attraction Pole P6/11. 

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