Transition of $\rho \rightarrow \pi \gamma$ in Lattice QCD

TL;DR

This paper presents the first lattice QCD calculation of the $ ho ightarrow ext{pi} ext{gamma}$ transition form factor with dynamical quarks, exploring its quark mass dependence and comparing results with experimental data.

Contribution

It introduces a novel lattice QCD approach using variational methods to isolate eigenstates for the $ ho ightarrow ext{pi} ext{gamma}$ transition at near-physical pion masses.

Findings

Results agree with quark model for heavy quarks

Observed quark mass dependence differs from model expectations

Discrepancy with experimental data suggests sea-quark loop effects are important.

Abstract

With the ongoing experimental interest in exploring the excited hadron spectrum, evaluations of the matrix elements describing the formation and decay of such states via radiative processes provide us with an important connection between theory and experiment. In particular, determinations obtained via the lattice allow for a direct comparison of QCD-expectation with experimental observation. Here we present the first light quark determination of the $\rho \rightarrow \pi \gamma$ transition form factor from lattice QCD using dynamical quarks. Using the PACS-CS 2+1 flavour QCD ensembles we are able to obtain results across a range of masses, to the near physical value of $m_\pi = 157$ MeV. An important aspect of our approach is the use of variational methods to isolate the desired QCD eigenstate. For low-lying states, such techniques facilitate the removal of excited state contributions. In principle the method enables one to consider arbitrary eigenstates. We find our results are in accord with the non-relativistic quark model for heavy masses. In moving towards the light-quark regime we observe an interesting quark mass dependence, contrary to the quark model expectation. Comparison of our light-quark result with experimental determinations highlights a significant discrepancy suggesting that disconnected sea-quark loop contributions may play a significant role in fully describing this process.