Light Stop and the b → sγ Process

A constraint from b → sγ process to the minimal supersymmetric standard model is derived in the light stop region where the coupling between the lighter stop and the Z boson vanishes due to the left-right mixing of the stop states. It is pointed out that although some region in the parameter space is excluded from this process there remains a large parameter space where the amplitude of the b → sγ is suppressed due to partial cancellation between different diagrams. Stop as light as 20 GeV is still viable from the b → sγ constraint. Although supersymmetry (SUSY) has attracted much attention as a promising candidate of physics beyond the standard model of the elementary particle physics we do not have any direct evidence of superpartners which are predicted to exist in the supersymmetric theory. It is therefore very important to search for any direct and indirect information on superpartners in order to test the idea of supersymmetry. In this respect the flavor changing neutral current (FCNC) process deserves a special attention. In the supersymmetric standard model the FCNC is induced by loop effects just as in the case of the standard model. The origin of the flavor mixing is present not only in the quark mass matrices but also in those of its superpartner, i.e. squark. Therefore, FCNC process is sensitive to the masses and mixings of the squark sector. In fact it is well known that the squark masses are severely constrained from the K − K̄ mixing for general class of supersymmetric standard models at least for the first two generations[1]. This is one of motivations to consider so called minimal supergravity model where the constraint from the K − K̄ mixing can be avoided because all the scalars have a common SUSY soft breaking mass at the GUT scale [2, 3]. Another important FCNC process in the supersymmetric model is the b → sγ process. It is well known that in the standard model the inclusive branching ratio of this process is about 3x10 after taking account of the QCD correction[4, 5]. This is compared with the recent improved upper bound 5.4x10 from the CLEO collaboration[6]. In the supersymmetric theory we have four new contributions due to loops of (i) charged Higgs and up-type quark, (ii) chargino and up-type squark, (iii) gluino and down-type squark, (iv) neutralino and down-type squark. In the context of the minimal supergravity model it is known that the charged Higgs contribution as well as the chargino and gluino contribution is sizable and, for some choice of 1 parameters, can be comparable to the standard model contribution although the neutralino loop contribution (iv) is very small [7]-[12]. In this paper we study contribution to the b → sγ process from the light stop loop effect in the context of the minimal supersymmetric standard model. Since the stop sector can have a sizable left-right mixing it is possible that one of the two stop states becomes much lighter than other squarks. In fact it was pointed out in Ref. [13] that a stop lighter than 45 GeV is still allowed since we can arrange the squark mixing so that the lighter stop does not couple to the Z boson. In such case the experimental lower bound of the stop mass is given from the TRISTAN experiments. The bound is about 27 GeV provided that the photino mass is not close to the stop mass [15]. It is also possible that such a light stop can escape detection at the Fermilab Tevatron as discussed in Ref. [16]. If we assume that the stop exists in such a low mass region we can expect that the b → sγ amplitude becomes in principle very large because the stop and chargino loop contribution can dominate this process, therefore the improved measurement can put a useful constraint to the relevant parameter space. This is especially important if we assume the GUT relations among the gaugino masses, since not only one of the stops but also at least one of the charginos is necessarily light. We investigate the contribution from (ii) in the light stop region taking account of the experimental constraints in the gaugino and higgsino parameter space. We will see that although some parameter space is excluded from the b → sγ measurement there still remain an region where a stop as light as 20 GeV is not constrained. This is due to a partial cancellation between two graphs involving the top Yukawa and the SU(2) gauge coupling constants. We consider here the usual minimal supersymmetric standard model with three families of quarks and leptons and their supersymmetric partners. For the parameters of the gaugino and higgsino sector we assume the GUT con2 dition for the Majorana mass terms of the gauginos, then three gaugino mass parameters are related to each other in terms of gauge coupling constants. For FCNC processes the squark mass matrices are especially important. We take here that the following simplified form for the up-type squark mass matrix [8]: Lu−squark = (ũL ũR) ∗ 