Relativistic corrections to $\psi(nS)\to\rho\pi$ exclusive decays and their role in the understanding of the $\rho\pi$-puzzle

TL;DR

This paper investigates relativistic corrections to charmonium decays into rho pi and gamma pi, finding that these corrections are significant and may help resolve the rho pi puzzle by combining with radiative QCD effects.

Contribution

It provides a detailed calculation of relativistic corrections in NRQCD and collinear factorization, highlighting their importance in understanding the rho pi puzzle.

Findings

Relativistic corrections of order v^2 are dominant among higher order effects.

Numerical contributions of relativistic corrections are comparable to leading-order terms.

Results suggest combined relativistic and radiative corrections could explain the rho pi puzzle.

Abstract

We study relativistic corrections to exclusive $S$-wave charmonium decays into $\rho\pi$ and $\gamma\pi$ final states. The contribution of relative order $v^2$ and the set of associated higher order corrections are calculated using NRQCD and collinear factorisation framework. Numerical estimates show that the dominant effect is provided by the corrections of relative order $v^2$. The numerical values of these contributions are of the same order as the leading-order ones. These results suggest a scenario where the sum of relativistic and radiative QCD corrections could explain the $\rho\pi$-puzzle.