Single topquark production by direct supersymmetric
flavorchanging neutralcurrent interactions at the LHC
Abstract
Production of (electrically neutral) heavyquark pairs, such as and , is extremely suppressed in the SM. In supersymmetric (SUSY) theories, such as the MSSM, the number of these events can be significantly enhanced thanks (mainly) to the FCNC couplings of gluinos. We compute the efficiency of this mechanism for FCNC production of heavy quarks at the LHC. We find that can reach , and therefore one can expect up to events per of integrated luminosity (with no counterpart in the SM). Their detection would be instant evidence of new physics, and could be a strong indication of underlying SUSY dynamics.
Single topquark production by direct supersymmetric FCNC interactions at the LHC \runauthorJ. Guasch, W. Hollik, S. Peñaranda, J. Solà
1 Introduction
Flavorchanging neutralcurrent (FCNC) interactions of top quarks are among the most promising processes to deal with as a probe of new physics. This is so because that kind of processes are (in contrast to lowenergy meson FCNC physics) extremely suppressed in the SM. For instance, while radiative meson decays have branching ratios of order , typical FCNC topquark decays, such as and , have SM branching ratios of order of at most and respectively [1], which in practice are impossible to measure. And among these FCNC processes the rarest ones in the SM are those involving the top quark and the Higgs boson, e.g. [2] and the crossed one  (depending on the Higgs mass)[3]. Fortunately, when one considers the impact of new physics (e.g. Supersymmetry or generalized Higgs sectors) the situation may change dramatically. Indeed, as first emphasized in the detailed work of [4], the FCNC processes involving top quarks and Higgs bosons may constitute a prominent door to SUSY physics in highluminosity colliders. In that work it was found that, in contradistinction to the SM case, the topquark decays into MSSM Higgs bosons [5] can be the most favored FCNC top decays of all, with branching ratios that can reach the level of . This is not possible (without finetuning) for the FCNC top quark decays into gauge bosons in the MSSM, which stay typically two orders of magnitude below [6]. Similarly, the maximal MSSM Higgs boson FCNC rates into topquark final states, e.g. , can be of order [7], which suggests that these decays could be a source of a sizeable number of FCNC events and in a highluminosity collider. Actually, a detailed calculation of the number of these events at the LHC has recently been reported in [8] and confirmed this expectation, to wit: a few thousand FCNC events per of integrated luminosity are possible. Furthermore, a number of works have stressed the importance of this kind of FCNC processes in more general twoHiggsdoublet models (2HDM) [3, 9], including some effects that could appear in multiple Higgs models [10]. Finally, let us also mention the possibility of enhanced FCNC topquark effects in topcolor assisted technicolor models [11]. A general, modelindependent, parametrization of new FCNC effects is presented in [12].
Interestingly enough, there also exists the possibility to produce and final states without Higgs bosons or any other intervening particle. In this work we will show that the FCNC gluino interactions in the MSSM can actually be the most efficient mechanism for direct FCNC production of top quarks.
2 FCNC interactions in the MSSM
The flavor structure of the MSSM involves fermion and sfermion mass matrices, and in general the diagonalization of the first flavor structure does not guarantee the diagonalization of the second. For example, the requirement of invariance means that the topleftsquark mass matrix cannot be simultaneously diagonal to the bottomleftsquark mass matrix, and therefore these two matrices cannot be in general simultaneously diagonal with the topquark and bottomquark mass matrices. Even if we would arrange this to be so, the radiative corrections (e.g. from the charged currents) would destroy this arrangement. This is a sign that one cannot consistently demand the absence of flavormixing interactions in the MSSM. Indeed, even if we would “align” the parameters at a high energy GUT scale, the RG running down the electroweak scale would missalign the mass matrices [13]. As a wellknown example, let us recall that the topsquark decay into charm quark and neutralino () is UVdivergent in the MSSM, unless we allow for FCNC interaction terms in the classical Lagrangian that can absorb these infinities [14]. Therefore, in general, in the MSSM we expect terms of the form gluino–quark–squark or neutralino–fermion–sfermion, with the quark and squark having the same charge but belonging to different flavors. In this work we will concentrate only on the first type of terms, which are expected to be dominant. A detailed Lagrangian describing these generalized SUSY–QCD interactions mediated by gluinos can be found, e.g. in [4]. The relevant parameters are the flavormixing coefficients . In contrast to previous studies [15], we will allow them only in the LL part of the sfermion mass matrices in flavorchirality space [4]. This assumption is not only for simplicity, but also because it is suggested by RG arguments [13]. Thus, if is the LL block of a sfermion mass matrix, we define () as follows: , where is the soft SUSYbreaking mass parameter corresponding to the LH squark of th flavor [4]. We will be mostly interested in the parameter , because it is the one relating the second and third generations (therefore involving the top quark physics). is the less restricted one from the phenomenological point of view. This is because the phenomenological bounds on the various (cf. [16]) are obtained from the lowenergy FCNC processes. These involve mainly the first and second generations. Thus is an essentially free parameter within, say, the natural interval . Actually we have two such parameters, and , for the uptype and downtype LL squark mass matrices respectively. The former enters the process under study whereas the latter enters . We will use this observable to restrict our predictions on production.


3 Single topquark production from gluino FCNC interactions in the MSSM
In Fig. 1 we show some of the diagrams involved in the direct production of the FCNC final states. We have performed the calculation of the full oneloop SUSY–QCD crosssection using standard algebraic and numerical packages for this kind of computations [17]. (Of course .) The complete formulae are very cumbersome, so to simplify the discussion it will be sufficient to quote the general form of the crosssection:
(1) 
Here is the trilinear topquark coupling, the higgsino mass parameter and stands for the overall scale of the squark masses – see (3) below. The gluino mass is denoted by . The superscript in is to emphasize that we consider only the contributions from the LL block of the (topsquark) mass matrix. We have performed the computation of the above crosssection together with the branching ratio in the MSSM, because only in this way can we be sure that the region of the parameter space that we employ to compute does respect the experimental bounds on . Specifically, we take  at the level [18]. Again, to ease the discussion, it suffices to quote the MSSM formula for the branching ratio as follows [8]:
(2) 
Notice that from the downquark mass matrix is related to the parameter in (1) (from the upquark mass matrix) because the two LL blocks of these matrices are precisely related by the CKM rotation matrix as follows: [16].
4 Numerical analysis
In Figs. 2 and 3 we present the main results of our numerical analysis. We see that is very sensitive to and that it decreases with , but mainly with . As expected, it increases with , but it does not reach the maximum range of this parameter. At the maximum of , it prefers , as we shall see below. The reason stems from the correlation of this maximum with the observable. At the maximum, the crosssection for production lies around , if we allow for relatively light gluino masses GeV (see Fig. 3). For higher the crosssection falls down fast; at GeV it is already times smaller. The total number of events per lies between  for this range of gluino masses. The fixed values of the parameters in these plots lie near the values that provide the maximum of the FCNC crosssection. The dependence on is not shown, but we note that decreases by in the allowed range  GeV. Values of GeV are forbidden by . Large negative is also excluded by the experimental bound we take for the lightest squark mass, GeV; too small GeV is ruled out by the chargino mass bound GeV. The approximate maximum of in parameter space has been computed using an analytical procedure.



Let us briefly summarize the method. Define , which is involved in (1). Then the lines of constant are hyperbolas in the plane. Next consider the uptype squark mass matrix in the following approximation (in particular, only the nd and rd squark families are considered):
(3) 
Upon diagonalization it is easy to see that the allowed squark masses should lie inside the circle whose radius is . Notice that increases with , but we impose the (approximate) constraint to avoid colorbreaking minima. This puts a bound on . Finally, looking for the point in the straight line where the outermost hyperbola is tangent to the circle of radius in the  plane, we find the approximate maximum at
(4) 
This is the result quoted before. The residual parameters of the maximum easily follow. A previous analysis of this process [15] did not make a systematic study of the parameter space and did not take into account the important restrictions imposed by for (cf. Fig. 2). That reference missed the bulk of the contribution and tended to emphasize that the main effects stem from the LR sector of the full mass matrix , namely from (). In contrast, we have proved that it suffices to consider the LL sector, which is the only one that is well motivated by renormalization group arguments [13].
Finally, we note that final states can also be produced at oneloop by the chargedcurrent interactions within the SM. We have computed this oneloop crosssection at the LHC, with the result It amounts to less than one event in the entire lifetime of the LHC. So it is pretty obvious that only the presence of new physics could be an explanation for these events, if they are ever detected.
5 Discussion and conclusions
We have computed the full oneloop SUSY–QCD crosssection for the production of single topquark states at the LHC. We have shown that this direct production mechanism is substantially more efficient (typically a factor of ) than the production and subsequent FCNC decay [8] of the heavy MSSM Higgs bosons (). It is important to emphasize that, if the mass generation mechanism is associated to a fundamental Higgs sector, then the detection of a significant number of states could be interpreted as a distinctive SUSY signature. The reason for this is that in an unconstrained 2HDM (types I and II), these FCNC events cannot be produced at comparable rates. There is no direct production mechanism in this case (at oneloop), and therefore a significant signature could only come from Higgsboson decays whose efficiency, though, was shown to be comparatively much smaller [3], namely only a few hundred events could be expected versus events that can be achieved by direct production in the MSSM. Given the robust signal carried by the single topquark in the final state, these FCNC processes could be a very helpful tool to complement the search for SUSY physics at the LHC collider. Before closing we point out that there are also direct SUSY–EW (electroweak) loop diagrams (complementing the SUSY–QCD ones in Fig. 1), which could be important in certain regions of the MSSM parameter space. The corresponding analysis of these SUSY–EW effects will be presented elsewhere.
Note added. After the present work was first submitted, we noticed the recent reference [19] which addresses the same subject.
Acknowledgements: JG has been supported by a Ramon y Cajal contract from MEC (Spain); JG and JS in part by MEC and FEDER under project 200404582C0201 and by DURSI Generalitat de Catalunya under project 2005SGR00564; SP by the European Union under contract No. MEIFCT2003500030.
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