Loop corrections to sub-leading heavy quark currents in SCET

TL;DR

The paper extends SCET matching to sub-leading power by computing the one-loop hard corrections to heavy-to-light currents for arbitrary Dirac structures. It derives a complete set of coefficient functions for both two-body (A0,A1) and three-body (B1) currents, including their mu- and ν-dependences and inter-operator mixing. The results clarify how sub-leading currents contribute to heavy-to-light form factors in the large-recoil regime and provide the ingredients for higher-accuracy factorization, such as in B→π decays. The findings enable refined predictions for exclusive B decays and guide future work on sub-leading power factorization theorems.

Abstract

We compute the one-loop (hard) matching correction to heavy-to-light transition currents in soft-collinear effective theory (SCET) to sub-leading power in the SCET expansion parameter for an arbitrary Dirac structure of the QCD weak current.

Figures (2)

• Figure 1: One-loop contributions to $\langle q(p_1^\prime) g(p_2^\prime)|J_X|b(p)\rangle$. Counterterm diagrams are not shown.
• Figure 2: Graphical representation of (\ref{['top']}). The shaded circle denotes the current insertion times its short-distance coefficient.