Electromagnetic form factor of pion from N_f=2+1 dynamical flavor QCD

TL;DR

This study calculates the pion's electromagnetic form factor using $N_f=2+1$ lattice QCD, employing advanced techniques to reduce errors and estimate the pion charge radius, aligning with experimental data.

Contribution

It introduces improved lattice QCD methods for calculating the pion form factor at near-physical pion masses, including twisted boundary conditions and error reduction techniques.

Findings

Pion charge radius estimated as 0.441 ± 0.046 fm² at physical pion mass.

Form factor calculations become feasible on larger lattices near the physical point.

Results are consistent with experimental measurements within error margins.

Abstract

We present a calculation of the electromagnetic form factor of the pion in $N_f=2+1$ flavor lattice QCD. Calculations are made on the PACS-CS gauge field configurations generated using Iwasaki gauge action and Wilson-clover quark action on a $32^3\times64$ lattice volume with the lattice spacing estimated as $a=0.0907(13)$ fm at the physical point. Measurements of the form factor are made using the technique of partially twisted boundary condition to reach small momentum transfer as well as periodic boundary condition with integer momenta. Additional improvements including random wall source techniques and a judicious choice of momenta carried by the incoming and outgoing quarks are employed for error reduction. Analyzing the form factor data for the pion mass at $M_\pi \approx 411$ MeV and 296 MeV, we find that the NNLO SU(2) chiral perturbation theory fit yields $<r^2>=0.441 \pm 0.046 {\rm fm}^2$ for the pion charge radius at the physical pion mass. Albeit the error is quite large, this is consistent with the experimental value of $0.452\pm 0.011 {\rm fm}^2$. Below $M_\pi\approx 300$ MeV, we find that statistical fluctuations in the pion two- and three-point functions become too large to extract statistically meaningful averages on a $32^3$ spatial volume. We carry out a sample calculation on a $64^4$ lattice with the quark masses close to the physical point, which suggests that form factor calculations at the physical point become feasible by enlarging lattice sizes to $M_\pi L\approx 4$.