Bridging light-cone and NRQCD approaches: asymptotic behavior of $B_c$ electromagnetic form factor

TL;DR

This paper demonstrates that the light-cone approach, with refactorization, can reproduce NRQCD predictions for heavy quarkonium form factors at large momentum transfer, confirming their agreement at NLO and exploring asymptotic behaviors.

Contribution

It establishes a formal equivalence between light-cone and NRQCD approaches for heavy quarkonium form factors at NLO, and discusses obstacles for extending this to double charmonium production.

Findings

Light-cone and NRQCD approaches agree at NLO for $B_c$ form factor.

Refactorization of distribution amplitudes enables this equivalence.

Asymptotic behavior of heavy-light meson form factors is analyzed.

Abstract

This work aims at illustrating that, for a class of leading-twist hard exclusive reactions involving two heavy quarkonia, the light-cone approach, when equipped with the strategy of refactorization of the light-cone distribution amplitude of quarkonium, can be employed to elegantly reproduce the corresponding predictions made in the nonrelativistic QCD (NRQCD) factorization approach, order by order in perturbative expansion. Taking the electromagnetic form factor of the $B_c$ meson at large momentum transfer, $Q^2$, as a concrete example, we compare the results obtained from both NRQCD-based and light-cone-based calculations through the next-to-leading order (NLO) in $\alpha_s$, while at the leading order (LO) in both velocity and $1/Q^2$ expansion, and explicitly confirm their mutual agreement. As a byproduct, we apply our NLO result to explore certain features about the asymptotic behavior of the heavy-light meson form factor. We also address the major theoretical obstacles that prevent us from establishing an analogous equivalence between these two approaches for the double charmonium production process of phenomenological interest, $e^+e^-\to J/\psi+\eta_c$.