Can NRQCD explain the $\gamma\gamma^* \to \eta_c$ transition form factor data?

TL;DR

This paper investigates whether NRQCD can explain the  transition form factor data, including NNLO corrections, and finds that higher-order corrections significantly reduce agreement with experimental measurements, questioning NRQCD's applicability.

Contribution

First calculation of NNLO perturbative correction to  transition form factor within NRQCD, revealing large negative effects that challenge previous assumptions.

Findings

NNLO correction significantly reduces theoretical agreement with data.

Large negative _s^2 correction impacts NRQCD predictions.

Discrepancy questions NRQCD's validity for charmonium exclusive processes.

Abstract

Unlike the bewildering situation in the $\gamma\gamma^*\to \pi$ form factor, a widespread view is that perturbative QCD can decently account for the recent \textsc{BaBar} measurement of $\gamma\gamma^*\to \eta_c$ transition form factor. The next-to-next-to-leading order (NNLO) perturbative correction to the $\gamma\gamma^*\to \eta_{c,b}$ form factor, is investigated in the NRQCD factorization framework for the first time. As a byproduct, we obtain by far the most precise order-$\alpha_s^2$ NRQCD matching coefficient for the $\eta_{c,b}\to \gamma\gamma$ process. After including the substantial negative order-$\alpha_s^2$ correction, the good agreement between NRQCD prediction and the measured $\gamma\gamma^*\to \eta_c$ form factor is completely ruined over a wide range of momentum transfer squared. This eminent discrepancy casts some doubts on the applicability of NRQCD approach to hard exclusive reactions involving charmonium.