Higgsboson coupling to charginos in the MSSM at linear colliders.
Abstract
We discuss the associated production of a light Higgs boson () and a light chargino () pair in the process in the Minimal Supersymmetric Standard Model (MSSM) at linear colliders (LC) with . This process gives direct informations about Higgsboson coupling to light charginos which cannot be analyzed in decay processes due to phasespace restriction. We compute total cross sections in the regions of the MSSM parameter space where the process cannot proceed via onshell production and subsequent decay of either heavier charginos or pseudoscalar Higgs bosons . Cross sections up to a few are allowed, making this process potentially detectable at highluminosity LC. We also compute analytically the final momentum distributions in the limit of heavy electronsneutrino masses, .
G. Ferrera\IIrefuniinfn\Acknowa, B. Mele\IIrefinfnuni\Acknowb
uniUniversità di Roma “La Sapienza”, Rome, Italy \AffiliationinfnINFN, Sezione di Roma, Rome, Italy \AcknowfootaTalk presented by G.Ferrera, email: \Acknowfootbemail:
1 Introduction
In this talk we present the main features of the work discussed more exhaustively in [1]. We know that linear colliders with would be a very powerful precision instrument for Higgsboson physics and physics beyond the standard model (SM) that could show up at the LHC. In fact, if supersymmetry (SUSY) exists with partners of known particles with masses not too far from present experimental limits, it will be necessary to study the details of new physics in order to understand which SUSY scenario is effectively realized. Nextgeneration linear colliders such as TESLA and NLC/JLC [2] would be able to measure (sometimes with excellent precision) a number of crucial parameters (such as masses, couplings and mixing angles), and eventually test the fine structure of a particular SUSY model.
We know that the Higgs couplings to particle are strictly related to the mass of particles. In the case of light particle the Higgs couplings are suppressed (as for the light fermions couplings to the Higgs bosons, where ) and the coupling can generally be determined through the corresponding Higgs decay branching ratio measurement.
On the other hand, the Higgs couplings to vector bosons are unsuppressed and the analysis of the main Higgsboson production cross section, that occurs through the couplings to vector bosons, can provide a good determination of such couplings.
There are a number of Higgsboson couplings to quite heavy particles, other than gauge bosons, that can not be investigated through Higgsboson decay channels due to phasespace restrictions. In this case, the associated production of a Higgs boson and a pair of the heavy particles, when allowed by phase space, can provide an alternative to measure the corresponding coupling, even if some reduction in the rate due to the possible phasespace saturation is expected.
For instance, the SM Higgsboson unsuppressed coupling to the top quark, , can be determined at linear colliders with TeV through the production rates for the Higgs radiated off a topquark pair in the channel [3].
Our purpose is to use the latter strategy in the context of the MSSM, that introduces an entire spectrum of relatively heavy partners, in many cases coupled to Higgs bosons via an unsuppressed coupling constant. A typical example is that of the light Higgsboson coupling to the light top squark , that can be naturally large. The continuum production has been studied in [4] as a means of determining this coupling (the corresponding channel at hadron colliders has been investigated also in [5]). The Higgs coupling to the slepton has been considered in [6].
Here, we discuss the possibility to measure the light Higgs coupling to light charginos through the Higgsboson production in association with a chargino pair at linear colliders through the process
(1) 
We will not include in our study the case where the considered process proceeds through the onshell production of either the heavier chargino or the pseudoscalar Higgs boson with a subsequent decay and , respectively. We will also assume a large value for the electron sneutrino mass (i.e., TeV). This suppresses the Feynman diagrams with a sneutrino exchange, involving predominantly the gaugino components of the charginos. Note that while heavy Higgs bosons couplings to SUSY partners can be mostly explored via Higgs decay rates. the light Higgsboson coupling to light charginos cannot be investigated through Higgs decay channels due to phasespace restrictions. Indeed, in the MSSM is expected to be lighter that about 130 GeV [7], and the present experimental limit on the chargino mass GeV (or even the milder one GeV, in case of almost degenerate chargino and lightest neutralino) [8] excludes the decay .
Note that the SM process (that can be connected by a SuSy transformation to ) has a total cross section of about 5.6 fb for GeV, at GeV [9].
1.0 \SetWidth0.7
2 Relevant MSSM Scenarios
In the MSSM, charginos are the mass eigenstates of the mass matrix that mixes charged gauginos and higgsinos (see [10], [1]). At tree level, the mass eigenvalues and and the mixing angles can be analytically written in terms of the parameters , and . The presence of a Higgs boson in the process requires a further parameter, that can be the pseudoscalar mass . On the other hand, the inclusion of the main radiative corrections to the Higgsboson mass and couplings involves all the basic parameters needed for setting the complete mass spectrum of the SuSy partners in the MSSM. We set GeV, this pushes the pseudoscalar field beyond the threshold for direct production, thus preventing resonant contribution to the final state. At the same time, this choice for sets a decouplinglimit scenario ().
Present experimental lower limits on [11] in the decouplinglimit MSSM are close to the ones derived from the SM Higgs boson direct search (i.e., GeV at 95% C.L. [12]).
The corrections to the light Higgs mass and coupling parameter have been computed according to the code FeynHiggsFast [13], with the following input parameters : TeV , either 0 or 2 TeV, , GeV, GeV, GeV, GeV, and renormalization scale at , in the most complete version of the code (varying the and parameters would affect the Higgs spectrum and couplings negligibly).
We assumed three different scenarios, and corresponding values for GeV:
a) , with maximal stop mixing (i.e., TeV), and GeV;
b) , with no stop mixing (i.e., ), and GeV;
c) , with maximal stop mixing (i.e., TeV), and GeV;
that are allowed by present experimental limits [11]. In this talk we focalize on the scenario a).
There are 13 Feynman diagrams involved in the process , 7 with the channel / exchange and 6 with the channel electronsneutrino exchange. In our crosssection evaluation, we include only the channel diagrams reported in Fig. 1, and disregard the 6 diagrams in Fig. 2. In fact the latter are expected to contribute moderately to the cross section in the case TeV, GeV. We discuss the accuracy of this assumption in [1]. In Fig. 3, we show (in grey), the area in the plane that is of relevance for the non resonant process. The solid lines correspond to the threshold energy contour level :
(2) 
while the dashed lines refer to the experimental limit on the light chargino mass ( GeV).
The straight dotdashed lines limit from above the region that allows the associated production of a light chargino and a resonant heavier chargino (that we are not interested in), and correspond to :
(3) 
A further region of interest (beyond the grey one) could be the one where, although , the heavier chargino is below the threshold for a direct decay . Then, again a resonant would not be allowed. The area where is the one inside the oblique stripes in Fig. 3. The intersection of these stripes with the area between the solid and dashed curves is a further (although quite restricted) region relevant to the non resonant process. In our analysis, we did not include this parameter region, since this would have required some further dedicated elaboration of the analytic form for the distributions.
3 Cross Sections and Distributions
As anticipated, our analysis concentrates on the set of 7 Feynman diagrams presented in Fig. 1. Our evaluation will then be particularly suitable in case of heavy electron sneutrinos.
All external momenta are defined in Fig. 1, as flowing from the left to the right, and different couplings in Eq. (4) are defined in [1]. The lower indices of the spinors refer to the particle spin.
We squared, averaged over the initial spin, and summed over the final spin the sum of the matrix elements in Eq. (4) with the help of FORM [14]. Then, we performed a double analytic integration over the phasespace variables. This allowed us to obtain an exact analytic expression for the Higgsboson momentum distribution
(5) 
where . The complete code, including the analytic result for (that is a quite lengthy expression), and the numerical integration routine that allows a fast evaluation of the total cross section, is available from the authors’ email addresses.
In Fig. 4, we show the total cross section for at . We obtained it by numerically integrating over the Higgsboson energy and angle the analytic distribution in Eq. (5). In Fig. 4, we scan the relevant parameter space for GeV, and GeV. Cross sections of a few are reached in a good portion of the allowed regions especially for positive . We checked that our results completely agree with the cross section evaluated by CompHEP [15] on the basis of the same set of Feynman diagrams of Fig. 1.
We studied quantitatively the consequence of disregarding the 6 diagrams in Fig. 2, involving either pseudoscalar or sneutrino exchange, by comparing our results with the cross section corresponding to the complete set of 13 diagrams, computed by CompHEP. While the pseudoscalarexchange diagram never contributes sizable for GeV, the influence of the 5 sneutrinoexchange diagrams depends critically on and also on the relative importance of the gauginohiggsino components in the chargino [1].
We also considered the cross sections at the higherenergy extension expected for a linearcollider project [2]. Going at TeV, our treatment of the cross section becomes less accurate. As far as production rates are concerned, for chargino and Higgsboson masses not much heavier than present experimental limits, and heavy sneutrinos, the phase of the linear collider could be the best option to study the process .
We finally studied the behavior of Higgsboson energy and angular distributions versus the MSSM parameters. In Figs. 5 and 6, we plot energy and angular distributions in the c.m. frame, as obtained by numerically integrating over one variable Eq. (5). Both the energy and angulardistribution shapes are considerably influences by the gaugino/higgsino composition of the light chargino, and by a possible saturation of the available phasespace [1].
4 Conclusions
We analyzed the associated production of a light Higgs boson and a lightchargino pair in the MSSM at linear colliders. The process was discussed in the region of the MSSM parameter space where there is no resonant production of either the heavier chargino or the pseudoscalar Higgs boson and in the limit of heavy sneutrino masses ( TeV). We computed analytically distributions in the Higgsboson momentum. We obtained cross sections up to a few (for ) for masses not much heavier than present experimental limits. These rates make this process potentially detectable at LC with an integrated luminosity of the order of . This could allow a first determination of the production rate with a statistical error of the order of , that, in absence of further systematics, could be extrapolated to a determination of the coupling with comparable accuracy. Future studies in this direction are requires for a more solid assessment of the potential of this process.
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