Loop Corrections to Heavy-to-Light Form Factors and Evanescent Operators in SCET

TL;DR

The paper computes complete one-loop matching corrections for heavy-to-light form factors within Soft-Collinear Effective Theory, addressing both QCD→SCET_I and SCET_I→SCET_II transitions. It provides explicit jet-function coefficients, analyzes evanescent operators and their scheme dependence, and demonstrates that soft-overlap contributions receive universal radiative corrections while hard-scattering terms depend sensitively on B-meson LCDAs. The results illuminate factorization properties at large recoil and clarify the renormalization schemes needed to interpret jet functions, with implications for related exclusive B-decays. Overall, the work quantifies radiative corrections and establishes a robust framework for precision predictions of heavy-to-light form factors in SCET.

Abstract

One-loop matching corrections are calculated for Soft-Collinear Effective Theory (SCET) operators relevant to the analysis of heavy-to-light meson form factors at large recoil. The numerical impact of radiative corrections on form factor predictions is assessed. Evanescent operators in the effective theory are studied and it is shown that even in problems of the Sudakov type, these operators can be renormalized to have vanishing matrix elements.

Figures (7)

• Figure 1: Two step matching from QCD to SCET$_{\rm I}$ to SCET$_{\rm II}$. The double line denotes the heavy quark; dashed lines denote hard-collinear fields in SCET$_{\rm I}$ and collinear fields in SCET$_{\rm II}$. The symbol "$\otimes$" indicates the convolution of the Wilson coefficient functions with the non-local operators.
• Figure 2: One-loop QCD diagrams contributing to the matching calculation for the subleading scalar current. The double line denotes the heavy quark.
• Figure 3: $\hbox{SCET}_{\rm I}$ graphs contributing to the matching of the currents $J_j^{B}$ (crossed circle) onto the $\hbox{SCET}_{\rm II}$ four-quark operators $O_i$. Full lines denote soft fields, dashed lines hard-collinear fields. Diagrams with soft gluons or scaleless loops are not shown.
• Figure 4: Abelian contribution to the anomalous dimension of the $B$-type $\hbox{SCET}_{\rm I}$ current operators. Full lines denote soft fields, dashed lines hard-collinear fields.
• Figure 5: One-loop graphs contributing to the difference between the matrix element of the original and the Fierz rearranged four-quark operators.