The HQET/NRQCD Lagrangian to order alpha/m^3

TL;DR

Problem: establish the HQET/NRQCD Lagrangian to one-loop order and order 1/m^3 in a gauge-invariant framework. Approach: perform matching using dimensional regularization, relate nine EFT operators to heavy-quark form-factor data F1 and F2 and their derivatives, and enforce reparametrization invariance. Key results: explicit one-loop corrections to the operator coefficients c_F, c_D, c_S, c_W1, c_W2, c_p'p, and c_M are given in terms of alpha_s and Casimir factors, with all coefficients determined by three independent constants F2, F1', F2' and F1(0)=1; reparametrization invariance yields six linear relations among the coefficients. Significance: the work unifies HQET and NRQCD matching in a continuum framework, clarifies the structure of higher-order terms, and provides a practical route to extend the Lagrangian by continuing the form-factor expansions.

Abstract

The HQET/NRQCD Lagrangian is computed to order alpha/m^3. The computation is performed using dimensional regularization to regulate the ultraviolet and infrared divergences. The results are consistent with reparametrization invariance to order 1/m^3. Some subtleties in the matching conditions for NRQCD are discussed.

Figures (5)

• Figure 1: Non-abelian contribution to the one-loop vertex correction.
• Figure 2: One-loop wavefunction renormalization.
• Figure 3: Abelian one-loop vertex correction.
• Figure 4: Quark contribution to the vacuum polarization.
• Figure 5: Gluon contribution to the vacuum polarization.