$B$-meson decay width up to $1/m_b^3$ corrections within and beyond the Standard Model

TL;DR

This paper provides a comprehensive calculation of B-meson decay widths up to order 1/m_b^3, including Standard Model and beyond effects, crucial for understanding B-meson lifetimes and resolving experimental-theoretical tensions.

Contribution

It offers the first complete analytic expressions for matching coefficients in the heavy quark expansion, including previously missing weak-annihilation contributions and beyond Standard Model effects.

Findings

Calculated matching coefficients for two-quark operators up to dimension-six.

Included weak-annihilation contributions in the HQE for the first time.

Reproduced known results and derived new coefficients for chromomagnetic and Darwin operators.

Abstract

Starting from the most general effective Hamiltonian describing non-leptonic $b$-quark decays $b\to q_1 \bar q_2 q_3$, we compute analytic expressions for all matching coefficients of the two-quark operator contributions in the heavy quark expansion~(HQE) of a $B$ meson, up to mass-dimension-six. In addition, we calculate the weak-annihilation contributions, which enter the matching of four-quark operators in the HQE at dimension-six and were previously missing. Our results complete the calculation of beyond Standard Model effects in non-leptonic, tree-level, $b$-quark decays relevant for $B$ meson lifetimes and lifetime ratios such as $\tau(B^0_s)/\tau(B^0_d)$. Such effects naturally arise in extensions of the Standard Model (SM) that aim to address the observed tensions between experimental measurements and theoretical predictions based on QCD factorisation in several colour-allowed non-leptonic $B$-meson decays. As a by-product of our calculation, we also determine the matching coefficients in the HQE induced by the QCD-penguin operators within the SM, including both the interference between current-current and penguin operators and the contributions quadratic in the penguin operators. Owing to the suppression of the QCD-penguin Wilson coefficients within the SM, these effects are typically regarded as corrections of order $\alpha_s$ and $\alpha_s^2$ in the strong coupling, respectively. Our results reproduce the known expressions at dimension-three and provide new results for the coefficients of the chromomagnetic operator at dimension-five and of the Darwin operator at dimension-six.