Impact of warped extra dimensions on the dipole coefficients in b → sγ transitions

Abstract

Abstract:We calculate the electro-and chromomagnetic dipole coefficients C 7γ,8g and C 7γ,8g in the context of the minimal Randall-Sundrum (RS) model with a Higgs sector localized on the IR brane using the five-dimensional (5D) approach, where the coefficients are expressed in terms of integrals over 5D propagators. Since we keep the full dependence on the Yukawa matrices, the integral expressions are formally valid to all orders in v 2 /M 2 KK . In addition we relate our results to the expressions obtained in the Kaluza-Klein (KK) decomposed theory and show the consistency in both pictures analytically and numerically, which presents a non-trivial cross-check. In Feynman-'t Hooft gauge, the dominant corrections from virtual KK modes arise from the scalar parts of the W ± -boson penguin diagrams, including the contributions from the scalar component of the 5D gauge-boson field and from the charged Goldstone bosons in the Higgs sector. The size of the KK corrections depends on the parameter y * , which sets the upper bound for the anarchic 5D Yukawa matrices. We find that for y * 1 the KK corrections are proportional to y 2 * . We discuss the phenomenological implications of our results for the branching ratio Br(B → X s γ), the time-dependent CP asymmetry S K * γ , the direct CP asymmetry A b→sγ CP and the CP asymmetry difference ∆A b→sγ CP . We can derive a lower bound on the first KK gluon resonance of 3.8 TeV for y * = 3, requiring that at least 10% of the RS parameter space covers the experimental 2σ error margins. We further discuss the branching ratio Br(B → X s l + l − ) and compare our predictions for C 7γ,9,10 andC 7γ,9,10 with phenomenological results derived from model-independent analyses.

Measurements of isospin asymmetry and difference of directCPasymmetries in inclusiveB→Xsγdecays

“…Our result constrains ImðC 8 =C 7 Þ in the positive region better than the only previously available measurement from BABAR [32], and gives a strong constraint on NP models [36]. If we take the average value ofΛ 78 ¼ 89 MeV as a benchmark [35], the 2σ confidence intervals is −0.17 < ImðC 8 =C 7 Þ < 0.86.…”

“…where α s is the strong coupling constant,Λ 78 is the hadronic parameter denoting the interference between electromagnetic and chromomagnetic dipole diagrams, m b is the bottom quark mass, and C 7 and C 8 are the Wilson coefficients for electromagnetic and chromomagnetic dipole operators, respectively [34]. In the SM, C 7 and C 8 are both real, therefore ΔA CP is zero, but in several NP models ΔA CP can reach the level of 10% in magnitude [33,35,36]. BABAR measured Δ 0− and ΔA CP using data samples of 81.9 fb −1 and 429 fb −1 , respectively, as Δ 0− ¼ ð−0.6 AE 5.8 AE 0.9 AE 2.4Þ% [37] and ΔA CP ¼ ðþ5.0 AE 3.9 AE 1.5Þ% [32], where the first uncertainty is statistical, the second is systematic, and the last one for Δ 0− is due to the uncertainty on the fraction of B þ B − to B 0B0 production in ϒð4SÞ decays.…”

Gluino-mediated electroweak penguin with flavor-violating trilinear couplings

“…where the right-handed contributions are taken into account [75]. The hadronic parameter Λ 78 introduces an uncertainty to the analysis and is estimated to be 12 MeV < Λ 78 < 190 MeV [68]. We take an average value, Λ 78 = 89 MeV, in the analysis.…”

Radiative $B$ Decays at Belle

“…One of the largest theoretical uncertainties is a resolved photon contribution which can be constrained from the measurement of isospin asymmetry in B → X s γ [11,12,13]. A newly proposed CP violation observable is a difference of the direct CP asymmetries between the charged and neutral B mesons, which is proportional to a ratio of Wilson coefficients Im(C 8 /C 7 ), is null in the SM while in some NP models, this value could be as large as 10% [8,14,15].…”