The $\rho$-meson light-cone distribution amplitudes from lattice QCD

TL;DR

This lattice QCD study computes the light-cone distribution amplitudes of $ ho$ mesons, providing key parameters at a specific scale, with detailed renormalization and chiral extrapolation procedures.

Contribution

The paper presents the first non-perturbative determination of $ ho$ meson distribution amplitudes including conversion coefficients and systematic error estimates.

Findings

Ratio of tensor to vector coupling constants: 0.629(8)

Second Gegenbauer moments: a_2^∥=0.132(27), a_2^⊥=0.101(22)

Results obtained at μ=2 GeV with controlled systematics

Abstract

We present the results of a lattice study of the normalization constants and second moments of the light-cone distribution amplitudes of longitudinally and transversely polarized $\rho$ mesons. The calculation is performed using two flavors of dynamical clover fermions at lattice spacings between $0.060\,\text{fm}$ and $0.081\,\text{fm}$, different lattice volumes up to $m_\pi L = 6.7$ and pion masses down to $m_\pi=150\,\text{MeV}$. Bare lattice results are renormalized non-perturbatively using a variant of the RI'-MOM scheme and converted to the $\overline{\text{MS}}$ scheme. The necessary conversion coefficients, which are not available in the literature, are calculated. The chiral extrapolation for the relevant decay constants is worked out in detail. We obtain for the ratio of the tensor and vector coupling constants $f_\rho^T/f_\rho^{\vphantom{T}} = 0.629(8)$ and the values of the second Gegenbauer moments $a_2^\parallel = 0.132(27)$ and $a_2^\perp = 0.101(22)$ at the scale $\mu = 2\,\text{GeV}$ for the longitudinally and transversely polarized $\rho$ mesons, respectively. The errors include the statistical uncertainty and estimates of the systematics arising from renormalization. Discretization errors cannot be estimated reliably and are not included. In this calculation the possibility of $\rho\to\pi\pi$ decay at the smaller pion masses is not taken into account.