hep-ph/9808412 Charged Higgs Mass Bounds from b → sγ in a Bilinear R-Parity Violating Model

The experimental measurement of B(b → sγ) imposes important constraints on the charged Higgs boson mass in the MSSM. If squarks are in the few TeV range, the charged Higgs boson mass in the MSSM must satisfy mH± ∼440 GeV. For lighter squarks, then light charged Higgs bosons can be reconciled with B(b → sγ) only if there is also a light chargino. In the MSSM if we impose m χ ± 1 > 90 GeV then we need mH± ∼ 110 GeV. We show that by adding bilinear R–Parity violation (BRpV) in the tau sector, these bounds are relaxed. The bound on mH± in the MSSM–BRpV model is ∼ 340 GeV for the the heavy squark case and mH± ∼ 75 GeV for the case of light squarks. In this case the charged Higgs bosons would be observable at LEP II. The relaxation of the bounds is due mainly to the fact that charged Higgs bosons mix with staus and they contribute importantly to B(b → sγ). 1. The first measurement of the inclusive rate for the radiative penguin decay b → sγ has opened an important window for physics beyond the Standard Model (SM). The CLEO Collaboration has reported B(b → sγ) = (2.32 ± 0.57 ± 0.35) × 10−4, where the first error is statistical and the second is systematic. Conservatively they find 1.0 × 10−4 < B(b → sγ) < 4.2 × 10−4 at 95% C.L. [1]. Recently new results have been presented, the new bounds are 2.0 × 10−4 < B(b → sγ) < 4.5 × 10−4 at 95% C.L. [2]. This measurement has established for the first time the existence of one–loop penguin diagrams. In addition, this inclusive branching ratio has been measured by the ALEPH Collaboration at LEP to be B(b → sγ) = (3.11±0.80± 0.72) × 10−4 [3], consistent with CLEO. In the SM, loops including the W gauge boson and the unphysical charged Goldstone boson G± contribute to the decay rate. The latest estimate of this decay rate in the SM is B(b → sγ) = (3.28 ± 0.33) × 10−4 [4]. This prediction is in agreement with the CLEO measurement at the 2σ level. In two Higgs doublet models (2HDM) the physical charged Higgs boson H± also contributes to the decay rate. In 2HDM of type I, one Higgs doublet gives mass to the fermions while the other Higgs doublet decouples from fermions. On the contrary, in 2HDM of type II, the Higgs doublet H1 gives mass to the down-quarks and the second Higgs doublet H2 gives mass to the up-quarks. Important constraints on the charged Higgs mass mH± are obtained in 2HDM type II because the charged Higgs contribution always adds to the SM contribution [5, 6]. Constraints on mH± are not important in 2HDM type I because charged Higgs contributions can have either sign. In supersymmetric models, loops containing charginos/squarks, neutralinos/squarks, and gluino/squarks have to be included [7]. In the limit of very heavy super-partners, the stringent bounds on mH± are valid in the Minimal Supersymmetric Standard Model (MSSM) because its Higgs sector is of type II [5]. Nevertheless, even in this case the bound is relaxed at large tan β due to two-loop effects [8]. It was shown also that by decreasing the squarks and chargino masses this bound disappears because the chargino contribution can be large and can have the opposite sign to the charged Higgs contribution, canceling it [9, 10]. Further studies have been made in the MSSM and in its Supergravity version [11, 12]. As a result, for example, most of the parameter space in MSSM-SUGRA is ruled out for μ < 0 especially for large tanβ. QCD corrections are very important and can be a substantial fraction of the decay rate. Recently, several groups have completed the Next–to–Leading order QCD corrections to B(b → sγ). Two–loop corrections to matrix elements were calculated in [13]. The two–loop boundary conditions were obtained in [14] (see also [15]). Bremsstrahlung corrections were obtained in [16]. Finally, three–loop anomalous dimensions in the effective theory used for resumation of large logarithms ln(mW /m 2 b) were found in [4, 17] (see also [18]). In this work we include all