The width difference in the $B-\bar{B}$ system at next-to-next-to-leading order of QCD

Abstract

We extend the theoretical prediction for the width difference $\Delta {\Gamma }_q$ in the mixing of neutral $B$ mesons in the Standard Model to next-to-next-to-leading order in ${\alpha }_s$. To this aim we calculate three-loop diagrams with two $|\Delta B|=1$ current-current operators analytically. In the matching between $|\Delta B|=1$ and $|\Delta B|=2$ effective theories we regularize the infrared divergences dimensionally and take into account all relevant evanescent operators. Further elements of the calculation are the two-loop renormalization matrix $Z_{ij}$ for the $|\Delta B|=2$ operators and the $\mathcal{O}({\alpha }_s^2)$ corrections to the finite renormalization that ensures the $1/m_b$ suppression of the operator $R_0$ at two-loop order. Our theoretical prediction reads $\Delta {\Gamma }_s/\Delta M_s=(4.33\pm 0.93)\cdot 10^{-3}$ if expressed in terms of the bottom mass in the $\overline{\mathrm{MS}}$ scheme and $\Delta {\Gamma }_s/\Delta M_s=(4.20\pm 0.95)\cdot 10^{-3}$ for the use of the potential-subtracted mass. While the controversy on $|V_{cb}|$ affects both $\Delta {\Gamma }_s$ and $\Delta M_s$, the ratio $\Delta {\Gamma }_s/\Delta M_s$ is not affected by the uncertainty in $|V_{cb}|$ .

arXiv comment7 pages, 4 figures

References in corpus (46)

• New Developments in FeynCalc 9.0
• JaxoDraw: A graphical user interface for drawing Feynman diagrams
• FeynCalc 9.3: New features and improvements
• LiteRed 1.4: a powerful tool for the reduction of the multiloop integrals
• QCD Predictions for Lepton Spectra in Inclusive Heavy Flavour Decays
• Inclusive Semileptonic B and Polarized Lambda_b Decays from QCD
• Nonperturbative Corrections to Inclusive Beauty and Charm Decays: QCD versus Phenomenological Models
• Heavy Quark Effective Theory beyond Perturbation Theory: Renormalons, the Pole Mass and the Residual Mass Term
• FIRE6: Feynman Integral REduction with Modular Arithmetic
• The Pole Mass of The Heavy Quark. Perturbation Theory and Beyond
• Theoretical update of Bs-Bs-bar mixing
• Complete Corrections of O(αα_s) to the Decay of the Z Boson into Bottom Quarks
• Differential Distributions in Semileptonic Decays of the Heavy Flavors in QCD
• A quark mass definition adequate for threshold problems
• $B$- and $D$-meson leptonic decay constants from four-flavor lattice QCD
• Version 3 of {\tt RunDec} and {\tt CRunDec}
• PolyLogTools - Polylogs for the masses
• Effective Hamiltonian for Non-Leptonic |Delta F| = 1 Decays at NNLO in QCD
• Beta functions and anomalous dimensions up to three loops
• Anomalous Dimension Matrix for Radiative and Rare Semileptonic B Decays up to Three Loops
• Next-to-Leading Order QCD Corrections to the Lifetime Difference of $B_s$ Mesons
• 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
• Lifetime Differences and CP Violation Parameters of Neutral B Mesons at the Next-to-Leading Order in QCD
• |Delta F| = 1 Nonleptonic Effective Hamiltonian in a Simpler Scheme
• Measurement of the CP-violating phase ${\varphi }_s^{J/\psi \varphi }$ using the flavor-tagged decay $B_s^0\to J/\psi \varphi$ in 8 fb${}^{-1}$ of $p \barp$ collisions
• Three loop calculations and inclusive $V_{cb}$
• Baryogenesis and Dark Matter from $B$ Mesons
• Three-Loop Mixing of Dipole Operators
• Measurement of the Bottom-Strange Meson Mixing Phase in the Full CDF Data Set
• Dimension-six matrix elements for meson mixing and lifetimes from sum rules
• Measurement of the $CP$-violating phase ${\varphi }_s$ in $B_s^0\to J/\psi \varphi$ decays in ATLAS at 13 TeV
• Collider Signals of Baryogenesis and Dark Matter from $B$ Mesons: A Roadmap to Discovery
• Updated measurement of time-dependent $CP$-violating observables in $B_s^0\to J/\psi K^{+}{K}^{-}$ decays
• Measurement of the $CP$-violating phase ${\varphi }_{\mathrm{s}}$ in the B${}_{\mathrm{s}}^0$ $\to$ J$/\psi \varphi$(1020) $\to$ ${\mu }^{+}{\mu }^{-}$K${}^{+}$K${}^{-}$ channel in proton-proton collisions at $\sqrt{s}=$ 13 TeV
• 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 $(m_c/m_b{)}^1$
• Precise determination of the B0s-B0sbar oscillation frequency
• Next-to-Leading Order QCD Corrections to Spectator Effects in Lifetimes of Beauty Hadrons
• $SU(3)$ breaking effects in $B$ and $D$ meson lifetimes
• Pole mass renormalon and its ramifications
• Addendum to arXiv:0907.2110: "Charm and Bottom Quark Masses: An Update"
• Penguin contribution to width difference and CP asymmetry in $B_q$-${\bar{B}}_q$ mixing at order ${\alpha }_s^2{N}_f$
• Lattice QCD matrix elements for the $B_s^0-{\bar{B}}_s^0$ width difference beyond leading order
• Two-loop QCD penguin contribution to the width difference in $B_s-{\bar{B}}_s$ mixing
• 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 $({\mathbf{m}}_{\mathbf{c}}/{\mathbf{m}}_{\mathbf{b}}{)}^1$

Cited by in corpus (5)

• FeynCalc 10: Do multiloop integrals dream of computer codes?
• Dispersive analysis of neutral meson mixing
• ${\tau }_{B_s}/{\tau }_{B_d}$ and $\Delta {\Gamma }_s$ confront new physics in $b\to s\tau \tau$
• Complete next-to-next-to-leading order QCD corrections to the decay matrix in $\mathbf{B}$-meson mixing at leading power
• Decay matrix of B-\bar{B} mixing: Mixing of dimension-seven operators into dimension-six operators under renormalization