Penguin contribution to width difference and CP asymmetry in $B_q$-${\bar{B}}_q$ mixing at order ${\alpha }_s^2{N}_f$

Abstract

We present new contributions to the decay matrix element ${\Gamma }_{12}^q$ of the $B_q$-${\bar{B}}_q$ mixing complex, where $q=d$ or $s$. Our new results constitute the order ${\alpha }_s^2{N}_f$ corrections to the penguin contributions to the Wilson coefficients entering ${\Gamma }_{12}^q$ with full dependence on the charm quark mass. This is the first step towards the prediction of the CP asymmetry $a_{\mathrm{fs}}^q$ quantifying CP violation in mixing at next-to-next-to-leading logarithmic order (NNLO) in quantum chromodynamics (QCD) and further improves the prediction of the width difference $\Delta {\Gamma }_q$ between the two neutral-meson eigenstates. We find a sizable effect from the non-zero charm mass and our partial NNLO result decreases the NLO penguin corrections to $a_{\mathrm{fs}}^q$ by 37\% and those to $\Delta {\Gamma }_q$ by 16\%. We further update the Standard-Model NLO predictions for $a_{\mathrm{fs}}^q$ and the ratio of the width and mass differences of the $B_q$ eigenstates: If we express the results in terms of the pole mass of the bottom quark we find $a_{\mathrm{fs}}^s=(2.07\pm 0.10)\cdot 10^{-5}$, $a_{\mathrm{fs}}^d=(-4.71\pm 0.24)\cdot 10^{-4}$, $\Delta {\Gamma }_s/\Delta M_s=(4.33\pm 1.26)\cdot 10^{-3}$, and $\Delta {\Gamma }_d/\Delta M_d=(4.48\pm 1.19)\cdot 10^{-3}$. In the $\overline{\mathrm{MS}}$ scheme these numbers read $a_{\mathrm{fs}}^s=(2.04\pm 0.11)\cdot 10^{-5}$, $a_{\mathrm{fs}}^d=(-4.64\pm 0.25)\cdot 10^{-4}$, $\Delta {\Gamma }_s/\Delta M_s=(4.97\pm 1.02)\cdot 10^{-3}$, and $\Delta {\Gamma }_d/\Delta M_d=(5.07\pm 0.96)\cdot 10^{-3}$.

arXiv comment11 pages, 1 figure

References in corpus (33)

• Weak Decays Beyond Leading Logarithms
• Averages of $b$-hadron, $c$-hadron, and $\tau$-lepton properties as of summer 2016
• CP Violation and the CKM Matrix: Assessing the Impact of the Asymmetric B Factories
• FLAG Review 2019
• The Belle II Physics Book
• Theoretical update of Bs-Bs-bar mixing
• Observation of Bs-Bsbar Oscillations
• $B$- and $D$-meson leptonic decay constants from four-flavor lattice QCD
• Naive nonabelianization and resummation of fermion bubble chains
• Effective Hamiltonian for Non-Leptonic |Delta F| = 1 Decays at NNLO in QCD
• Next-to-Leading Order QCD Corrections to the Lifetime Difference of $B_s$ Mesons
• Heavy Quark Masses from Sum Rules in Four-Loop Approximation
• Charm Quark Contribution to K+ -> pi+ nu anti-nu at Next-to-Next-to-Leading Order
• Width Difference in the $B_s-\overline{B_s}$ System
• CP asymmetry in flavour-specific B decays beyond leading logarithms
• Neutral B-meson mixing from full lattice QCD at the physical point
• High-Precision Charm-Quark Mass and QCD Coupling from Current-Current Correlators in Lattice and Continuum QCD
• Precision measurement of $CP$ violation in $B_s^0\to J/\psi K^{+}{K}^{-}$ decays
• Lifetime Differences and CP Violation Parameters of Neutral B Mesons at the Next-to-Leading Order in QCD
• The B^+ B_d^0 Lifetime Difference Beyond Leading Logarithms
• Measurement of the Bottom-Strange Meson Mixing Phase in the Full CDF Data Set
• Precision measurement of the $B_s^0$-${\bar{B}}_s^0$ oscillation frequency with the decay $B^{0}_{s}\rightarrowD^{-}_{s}π^{+}$
• Model-independent bounds on new physics effects in non-leptonic tree-level decays of B-mesons
• On new physics in $\Delta {\Gamma }_d$
• Measurement of the CP-violating weak phase phi[s] and the decay width difference Delta Gamma[s] using the Bs to J/Psi phi(1020) decay channel in pp collisions at sqrt(s) = 8 TeV
• Charming new physics in rare B-decays and mixing?
• First study of the CP-violating phase and decay-width difference in $B_s^0\to \psi (2S)\varphi$ decays
• Measurement of the CP-violating phase ${\varphi }_s$ and the $B_s^0$ meson decay width difference with $B_s^0\to J/\psi \varphi$ decays in ATLAS
• Towards next-to-next-to-leading-log accuracy for the width difference in the $B_s-{\bar{B}}_s$ system: fermionic contributions to order $(m_c/m_b{)}^0$ and $(m_c/m_b{)}^1$
• Probing penguin coefficients with the lifetime ratio tau(B_s)/tau(B_d)
• Charming New $B$-Physics
• Lattice QCD matrix elements for the $B_s^0-{\bar{B}}_s^0$ width difference beyond leading order
• Constraining the CKM Parameters using CP Violation in semi-leptonic B Decays

Cited by in corpus (8)

• Mixing and $CP$ violation in the charm system
• Renormalisation scale setting for D-mixing
• The width difference in the $B-\bar{B}$ system at next-to-next-to-leading order of QCD
• Two-loop QCD penguin contribution to the width difference in $B_s-{\bar{B}}_s$ mixing
• Prospects on searches for baryonic Dark Matter produced in $b$-hadron decays at LHCb
• Quark-hadron duality for heavy meson mixings in the 't Hooft model
• Addendum: Towards next-to-next-to-leading-log accuracy for the width difference in the ${\mathbf{B}}_{\mathbf{s}}-{\bar{\mathbf{B}}}_{\mathbf{s}}$ system: fermionic contributions to order $({\mathbf{m}}_{\mathbf{c}}/{\mathbf{m}}_{\mathbf{b}}{)}^0$ and $({\mathbf{m}}_{\mathbf{c}}/{\mathbf{m}}_{\mathbf{b}}{)}^1$
• Three-loop topology analysis of neutral B-meson mixing with tapir