Upper Bounds on Susy Contributions to Transitions
From Mixing
Abstract
We study the constraints on supersymmetric contributions to transitions from the recent allowed range and measurement of mixing obtained by the D0 and CDF collaborations at the Tevatron. We compute the upper bounds on the relevant offdiagonal squark mass terms and compare them with the bounds coming from decays. We find that the constraints on chiralityflipping mass insertions are unaffected. Conversely, the measurement of mixing is effective in constraining chiralityconserving mass insertions, and it has striking effects in the case in which left and righthanded insertions have similar size. Finally, we discuss the phase of the mixing amplitude in the presence of SUSY contributions.
The study of Flavour Changing Neutral Currents (FCNC) and CP violation at low energies is a very powerful probe of New Physics (NP). In particular, the Unitarity Triangle (UT) analysis ckmfit ; utfitNP and the study of rare and decays lucaLP provide stringent constraints on additional sources of flavour and CP violation beyond the SM. The impact of these constraints on supersymmetry (SUSY) is impressive pellicani . Indeed, the Minimal Supersymmetric Standard Model (MSSM) contains about a hundred new sources of flavour and CP violation, mainly given by the sfermion mass matrices Hall . A closer look at the data from and physics reveals that, while new sources of flavour violation in and transitions are strongly constrained, the possibility of large NP contributions to transitions remains open utfitNP .
Interestingly, CP violation in nonleptonic penguin decays, such as , exhibits some hint of a departure from SM expectations bspenguinsexp . SUSY can account for such deviations while respecting all other available constraints from physics susybs . In addition, in SUSY Grand Unified Theories (GUTs) the large mixing angle observed in the neutrino sector can be connected to a large mixing between righthanded b and stype squarks bsneutrino . Therefore, SUSY models with large contributions to transitions have received a lot of interest recently susybsothers .
A crucial piece of information which has been missing until now is the amplitude and phase of mixing. Clearly, this would provide an independent source of information on transitions. While the mixing phase remains unknown, a preliminary measurement of the mixing amplitude has been presented very recently cdf . The aim of this paper is to assess the impact of this measurement on SUSY sources of transitions.
To fulfill our task in a modelindependent way we use the massinsertion approximation. Treating offdiagonal sfermion mass terms as interactions, we perform a perturbative expansion of FCNC amplitudes in terms of mass insertions. The lowest nonvanishing order of this expansion gives an excellent approximation to the full result, given the tight experimental constraints on flavour changing mass insertions. It is most convenient to work in the superCKM basis, in which all gauge interactions carry the same flavour dependence as SM ones. In this basis, we define the mass insertions as the offdiagonal mass terms connecting downtype squarks of flavour and and helicity and , divided by the average squark mass.
The constraints on have been studied in detail in ref. susybs , using as experimental input the branching ratios and CP asymmetries of and decays, and the lower bound on mixing previously available. An update using the summer 2005 data has been presented in ref. lucaLP . We perform the same analysis using, instead of the previously available lower bound, the following result for mixing:
(1) 
and refer the reader to susybs for the details of the procedure ^{1}^{1}1In a previous version of this Letter, we used the milder twosided C.L. bound from the D0 collaboration d0 ..
For definiteness, we choose an average squark mass of GeV, a gluino mass of GeV, GeV and ^{2}^{2}2The dependence on and on is induced by the presence of a chirality flipping, flavour conserving mass insertion proportional to .. In Fig. 1, we present the allowed range in the ReIm plane, using the previous lower bound (upper left) or the present measurement (upper right) of . We see that the effect of the measurement is to suppress the regions Im. For higher values of , the effect of becomes less important, since the constraints from processes become comparable for and then dominate, as can be seen looking at the lower part of Fig. 1, where the same analysis has been performed with .
In Fig. 2, we present the allowed range in the ReIm plane, using the previous lower bound (left) or the present value (right) of (the plots correspond to , but the dependence on is negligible here and in the following). The effect of the constraint from can clearly be seen, leading to an upper bound on Re around . The effect of the bound from is much more striking in the case of , as can be seen in Fig. 3. In this case, the upper bound obtained on is around . For the other mass insertions , the constraint from is irrelevant since the main effect comes from processes. This leaves open the possibility of sizable deviation from the SM prediction in the CP asymmetries in penguin decays lucaLP .
Finally, in Fig. 4 we present the p.d.f. for , where is the phase of the mixing amplitude, relevant for measurements of CP violation in physics. Comparing these results with the SM value utfitSM , it is evident that there is still plenty of room to observe nonstandard CP violation in the system.
This work has been supported in part by the EU network “The quest for unification” under the contract MRTNCT2004503369.
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