Towards extracting the timelike pion form factor on CLS 2-flavour ensembles

TL;DR

This study explores the extraction of the timelike pion form factor using lattice QCD techniques, focusing on the $ ho$ resonance with an innovative correlator matrix approach on CLS ensembles.

Contribution

It introduces a novel application of the distillation method and GEVP analysis to determine the timelike pion form factor on CLS 2-flavour ensembles, advancing lattice QCD methods.

Findings

Successful extraction of energy levels in multiple frames

Initial results on the timelike pion form factor

Framework for future extension to physical pion masses

Abstract

Results are presented from an ongoing study of the $\rho$ resonance. We use the distillation approach in order to create correlator matrices involving $\rho$ and $\pi\pi$ interpolators. The study is done in a centre-of-mass frame and several moving frames. We are able to extract energy levels by solving the GEVP of those correlator matrices. The initial exploratory study is being done on a CLS 2-flavour lattice with a pion mass of $451$ $\mathrm{MeV}$ using $\mathcal{O}(a)$ improved Wilson fermions. One aim of this work is to extract the timelike pion form factor after applying the L\"uscher formalism. We also plan to integrate this study with the existing Mainz programme for the calculation of the hadronic vacuum polarization contribution to the muon $g-2$ and will extend our study to lower pion masses and larger lattices in the future, including ensembles with $2+1$ flavours.