Chasing the light - gluino scenario through b → sγ

We investigate the impact of a light gluino, which might have escaped detection at colliders, on inclusive radiative B-decays mediated through penguin-like diagrams. We find that the viability of the scenario depends largely on the magnitude of the flavour-violating c-parameter. Some previously allowed regions of parameter space are now ruled out. PACS Nos: 14.80.Ly, 11.30.Pb, 13.40.Hq CERN-TH. 7245/94 DAMTP 94-31 May 1994 ∗) [email protected] There has been a continued speculation that a light gluino (∼ 2 – 5 GeV) has escaped detection at the colliders [1]. This assertion had also been fueled by the observation that a light, coloured, neutral fermion improves the agreement between lowand high-energy αS measurements; the light gluino is a strong candidate to satisfy such a requirement. This possibility has been looked into by a number of experiments [2], but it is still very much open, crying out for verification. It is noteworthy the direct search limits on squark masses from the CDF collaboration at Fermilab [3] are evaded in the presence of a light gluino; the squarks need, in principle, to be heavier than only MZ/2, from non-observation at the CERN e e collider, LEP. However, it has been pointed out [4] that the precision LEP measurements disfavour squarks below 60 GeV associated with such a light gluino. Of late, a particularly interesting gateway to examine various varieties of new physics, including this speculative lightgluino scenario, has been provided by the inclusive B-decay measurement, setting a limit Br(b → sγ) < 5.4 × 10 [5]. It has already been pointed out [6,7] that this rare decay has a strong influence on restricting the parameter space of supersymmetry (SUSY). This motivates us to examine in this paper the present status of the light gluino through this ‘microscope’. SUSY contributions to the rare decay b → sγ have been examined in the literature [8] earlier. On top of these investigations, we adopt a timely specialization to the recently reheated issue of a light gluino, following the improved experimental measurement. The branching ratio of b → sγ is given in units of the semileptonic b-decay branching ratio, as Br(b → sγ) Br(b → ceν) = 6α πρλ ∣∣∣∣ KtbK ∗ ts Kbc ∣∣∣∣ 2 [ ηAγ + 8 3 (η − η)Ag + C ]2 , (1) where η = αS(MZ)/αS(mb) = 0.548, ρ = (1−8r2+8r6−r8−24r4lnr) with r = mc/mb, λ = 1− 1.61 αS(mb)/π, and C(= −0.1766) is a coefficient from a complete calculation of the leading-logarithmic QCD corrections [9]; K is the standard Cabibbo-KobayashiMaskawa matrix. It may be noted that the mb 5 dependence in the partial decay widths of the b quark cancels out in eq. (1). An O(ms/mb) part in the branching ratio is neglected. We take Br(b → ceν) = 0.107. Aγ and Ag are the coefficients of the effective operators for bs-photon and bs-gluon interactions [10] following from Leff = √ GF 8π3 KtbK ∗ ts s σ μν [√ αAγFμν + √ αSAgTaG a μν ] (mbPR +msPL) b. (2) The contributions to Aγ and Ag from W bosons, charged Higgs bosons and gauginos are listed in [7]. The core of the interaction under our investigation is contained in a particular subset of SUSY induced by the quark-squark-gluino Lagrangian. For the sake of making this note self-contained, we extract, in what follows, the essence of the formalism of