Speaker
Description
The mixing parameter $\Delta \Gamma_{12}^s$ is an important flavor observable that governs the lifetime difference $\Delta \Gamma_s$ of the neutral $B_s$ mesons. The state-of-the-art Standard Model prediction for $\Delta \Gamma_s$ is compatible with the HFLAV world average, yet the theoretical uncertainties due to uncalculated perturbative corrections are still large. In this talk I will report on our progress in reducing these uncertainties by calculating NNLO QCD corrections to the $B_s - \bar{B}_s$ mixing process. To this end we perform a fully analytic evaluation of the current-current correlators $P_{1,2}\otimes P_{1,2}$ at 3-loops, as well as the current-penguin $P_{1,2}\otimes P_{3,4,5,6}$ and current-chromomagnetic $P_{1,2}\otimes P_{8}$ correlators at 2-loops in the Chetyrkin-Misiak-M\"unz (CMM) basis. Some interesting aspects of this calculation to be addressed in my talk involve higher-order matching between two effective field theories ($\mathcal{H}_{\textrm{eff}}^{\Delta B = 1}$ and $\mathcal{H}_{\textrm{eff}}^{\Delta B = 2}$), dedicated treatment of evanescent operators in the presence of dimensionally regulated IR divergences, asymptotic expansion of the amplitudes in $m_c/m_b$ up to $\mathcal{O}(m_c^2)$ and the analytic evaluation of the resulting 3-loop on-shell integrals with one mass scale.
