Next-to-next-to-leading QCD corrections to the $\mathbf{B^+}$-$\mathbf{B_d^0}$, $\mathbf{D^+}$-$\mathbf{D^0}$, and $\mathbf{D_s^+}$-$\mathbf{D^0}$ lifetime ratios

TL;DR

This paper computes next-to-next-to-leading order QCD corrections to heavy meson lifetime ratios, improving theoretical predictions and matching experimental data through advanced perturbative calculations and hadronic matrix element evaluations.

Contribution

It provides the first three-loop order calculations of QCD corrections to meson lifetime ratios, incorporating new $ ext{alpha}_s^2/m_q^3$ terms and combining them with hadronic matrix elements from sum rules and lattice QCD.

Findings

Predicted $ au(B^+)/ au(B_d^0)=1.072 imes$ with 0.024 uncertainty.

Predicted $ au(D^+)/ au(D^0)=2.344 imes$ with 0.170 uncertainty.

Predicted $ au(D_s^+)/ au(D^0)=1.289 imes$ with 0.042 uncertainty.

Abstract

The total decay widths of heavy mesons can be systematically calculated in terms of an expansion in the two parameters $1/m_Q$ and $\alpha_s(m_Q)$, where $Q=c,b$ denotes the heavy quark. The dominant contributions to meson lifetime splittings stem from terms which are suppressed by $1/m_Q^3$ with respect to the leading universal contribution to the total decay width. We calculate three-loop contributions of order $\alpha_s^2/m_q^3$ to the lifetime ratios $\tau(B^+)/\tau(B_d^0)$, $\tau(D^+)/\tau(D^0)$, and $\tau(D_s^+)/\tau(D^0)$ in the limit of exact isospin and V-spin symmetry, respectively. Furthermore, we present new $\alpha_s/m_q^3$ corrections to the Cabibbo-suppressed terms in $\tau(B^+)/\tau(B_d^0)$. Combining our perturbative coefficients with hadronic matrix elements calculated from Heavy Quark Effective Theory sum rules, we find $\tau(B^+)/\tau(B_d^0)= {1.072 \pm 0.024 }$. Using hadronic matrix elements from a recent lattice QCD calculation we find $\tau(D^+)/\tau(D^0)={2.344 \pm 0.170} $ and $\tau(D_s^+)/\tau(D^0)={1.289 \pm 0.042}$. We find good agreement of our predictions with experimental data, which constitutes a successful probe of the calculations of hadronic matrix elements and permits estimates of the unknown $1/m_Q^4$ contributions as well as the V-spin breaking terms in $\tau(D_s^+)/\tau(D^0)$.