Higher-order corrections to the kinetic mass definition for the bottom and the charm quarks

TL;DR

This paper explores higher-order perturbative QCD corrections to the relation between kinetic and on-shell mass schemes for bottom and charm quarks, crucial for precise quark mass determinations.

Contribution

It presents methods for calculating higher-order mass relations in QCD and provides a prediction for the bottom quark kinetic mass based on precise $ar{MS}$ mass measurements.

Findings

Predicted $m_b^{ ext{kin}}$ using higher-order corrections.

Enhanced understanding of mass scheme conversions.

Implications for $|V_{cb}|$ determinations.

Abstract

In these proceedings we discuss the relation between the kinetic and the on-shell schemes for the bottom and the charm quarks and present the methods for the calculation of the mass relation to higher orders in perturbative QCD. The bottom mass in the kinetic scheme is a pivotal input parameter in the inclusive determination of $|V_{cb}|$ from $B\to X_c \ell \nu_\ell$ decays. By combining the relation between the kinetic and the on-shell mass with well-know results for the $\overline{\mathrm{MS}}$-on-shell conversion, we obtain a prediction for $m_b^\mathrm{kin}$ based on precise determinations of $\overline{m}_b(\overline{m}_b)$.