Heavy-to-light form factors for non-relativistic bound states

TL;DR

The paper addresses heavy-to-light form factors for non-relativistic bound states at large recoil energies. It applies non-relativistic QCD with Coulomb-like bound-state wave functions within a factorization framework analogous to SCET to compute soft-overlap contributions. It derives a tree-level spectator-scattering formula and performs a one-loop analysis across hard, soft, and collinear regions, including a careful treatment of endpoint divergences; it discusses limits of resummation for large logs in this NR setting. Numerical results at fixed order α_s show stabilized scale dependence (about 15%), with a dominant non-factorizable contribution, providing a controlled perturbative estimate and informing expected power corrections in heavy-to-light phenomenology.

Abstract

We investigate transition form factors between non-relativistic QCD bound states at large recoil energy. Assuming the decaying quark to be much heavier than its decay product, the relativistic dynamics can be treated according to the factorization formula for heavy-to-light form factors obtained from the heavy-quark expansion in QCD. The non-relativistic expansion determines the bound-state wave functions to be Coulomb-like. As a consequence, one can explicitly calculate the so-called ``soft-overlap'' contribution to the transition form factor.

Figures (4)

• Figure 1: Resummation of "potential" gluons into a non-relativistic Coulomb wave function.
• Figure 2: Tree-level exchange of one hard-collinear gluon. The thick line represents the heavy quark.
• Figure 3: Hard, hard-collinear, collinear and soft momentum regions for the pentagon diagram.
• Figure 4: Renormalization-scale dependence of $F_+(0)$ for $B_c \to \eta_c$ transitions at LO and NLO.