$SU(3)$ breaking effects in $B$ and $D$ meson lifetimes

Abstract

In the heavy quark expansion (HQE) of the total decay rates of B s and D + s mesons non-perturbative matrix elements of four quark operators are arising as phase space enhanced contributions. We present the first determination of m s effects to the dimension six matrix elements of these four quark operators via a heavy quark effective theory (HQET) sum rule analysis. In addition we calculate for the first time eye contractions of the four quark operators as well as matrix elements of penguin operators. For the perturbative part we solve the 3-loop contribution to the sum rule and we evaluate condensate contributions. In this study we work in the strict HQET limit and our results can also be used to estimate the size of the matrix element of the Darwin operator via equations of motion.

Lifetimes of singly charmed hadrons

“…. Diagrammatic representation of "eye contractions", which serve as a further contribution relevant in the four-quark operators [39,82,83]. In particular, the quark running in the loop q need not match the valence quark in the hadron, q, leading to further non-valence contributions to the decay widths.…”

“…In particular, the quark running in the loop q need not match the valence quark in the hadron, q, leading to further non-valence contributions to the decay widths. Such contributions are numerically small [39,83], but allow, for example, for a PI contribution to the D 0 lifetime.…”

A lattice QCD perspective on weak decays of b and c quarks Snowmass 2022 White Paper

“…While the ratios τ (B + )/τ (B s ) and τ (B 0 )/τ (B s ) are in good agreement with the HFLAV average [201], the recent ATLAS measurement [222] deviates substantially from recent measurements by LHCb [223,224] and CMS [225]. To bolster confidence in the theory predictions, currently dominated by QCD sum-rule calculations [210,226], a state-of-the-art lattice calculation is desirable. Despite early attempts [227][228][229][230][231], no lattice calculation with a complete systematic error budget exists to date.…”

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

“…[33,34] have been calculated in an expansion in m c /m b to first and second order, respectively. ∆Γ s /∆M s further involves a well-computed ratio of two hadronic matrix elements [35][36][37]. The contribution to Γ s 12 being sub-leading in Λ QCD /m b is only known to LO of QCD [38] and the hadronic matrix elements still have large errors [39].…”

“…At each order Γ s is expressed as a sum of Wilson coefficients multiplying respective operator matrix elements. The latter has to be computed using lattice gauge theory [35] or QCD sum rules [36,37]. To leading order in the 1/m b expansion we have…”