Towards next-to-next-to-leading-log accuracy for the width difference in the Bs−BˉsB_s-\bar{B}_s system: fermionic contributions to order (mc/mb)0(m_c/m_b)^0 and (mc/mb)1(m_c/m_b)^1

We calculate a class of three-loop Feynman diagrams which contribute to the next-to-next-to-leading logarithmic approximation for the width difference $\Delta\Gamma_{s}$ in the $B_s-\bar{B}_s$ system. The considered diagrams contain a closed fermion loop in a gluon propagator and constitute the order $\alpha_s^2 N_f$, where $N_f$ is the number of light quarks. Our results entail a considerable correction in that order, if $\Delta\Gamma_{s}$ is expressed in terms of the pole mass of the bottom quark. If the $\overline{MS}$ scheme is used instead, the correction is much smaller. As a result, we find a decrease of the scheme dependence. Our result also indicates that the usually quoted value of the NLO renormalization scale dependence underestimates the perturbative error.Comment: We corrected a typographical mistake in Eq. (4.18), made larger axis labels in Fig.2. Version accepted by JHE

B→K∗ℓ+ℓ−B\to K^*\ell^+\ell^- Forward-backward Asymmetry and New Physics

The forward-backward asymmetry ${\cal A}_{\rm FB}$ in $B\to K^*\ell^+\ell^-$ decay is a sensitive probe of New Physics. Previous studies have focused on the sensitivity in the position of the zero. However, the short distance effective couplings are in principle complex, as illustrated by $B\to \rho\ell^+\ell^-$ decay within the Standard Model. Allowing the effective couplings to be complex, but keeping the $B\to K^*\gamma$ and $K^*\ell^+\ell^-$ rate constraints, we find the landscape for ${\cal A}_{\rm FB}(B\to K^*\ell^+\ell^-)$ to be far richer than from entertaining just sign flips, which can be explored by future high statistics experiments.Comment: RevTex 4 pages including 5 eps figures; Minor changes made, references adde

Towards the NNLL Precision in the Decay Bˉ→Xsγ\bar B \rightarrow X_s \gamma

The present NLL prediction for the decay rate of the rare inclusive process {bar B} {yields} X{sub s}{gamma} has a large uncertainty due to the charm mass renormalization scheme ambiguity. We estimate that this uncertainty will be reduced by a factor of 2 at the NNLL level. This is a strong motivation for the on-going NNLL calculation, which will thus significantly increase the sensitivity of the observable {bar B} {yields} X{sub s}{gamma} to possible new degrees of freedom beyond the SM. We also give a brief status report of the NNLL calculation