Three-loop anomalous dimension of the heavy-light quark current in HQET

TL;DR

The paper computes the three-loop corrections to the heavy-quark self-energy in HQET and, crucially, the three-loop anomalous dimension $\tilde{\gamma}_j$ of the heavy-light current, enabling consistent NNLO running of heavy-light operators. It employs non-Abelian exponentiation for the heavy-quark propagator, automated diagram generation and reduction (Grinder), and explicit evaluation of the heavy-light current vertex in arbitrary covariant gauges, delivering a full $d$-dimensional result and its $\varepsilon$-expansion. The work provides the next-to-next-to-leading perturbative correction to $f_B/f_D$ and offers practical formulas for lattice HQET and sum-rule applications, with results cross-checked against existing literature (e.g., MR:00). Overall, the study delivers essential inputs for precision $B$-physics phenomenology by refining the matching and running of heavy-light currents.

Abstract

The anomalous dimension of the heavy-light quark current in HQET is calculated with three-loop accuracy, as well as the renormalized heavy-quark propagator. The NNL perturbative correction to f_B/f_D is obtained.

Figures (7)

• Figure 1: Topologies of three-loop propagator diagrams in HQET
• Figure 2: Basis integrals
• Figure 3: Two-loop integrals $I$ and $J$
• Figure 4: One- and two-loop diagrams for the HQET propagator
• Figure 5: Exponentiation theorem