I=2 Two-Pion Wave Functions with Non-zero Total Momentum

TL;DR

This study computes the I=2 two-pion wave function at finite momentum to validate finite-volume scattering methods, finding consistent interaction ranges and improved phase shift accuracy over traditional methods.

Contribution

It provides the first detailed calculation of the two-pion wave function with non-zero total momentum, testing the finite-volume method's validity and offering enhanced phase shift measurements.

Findings

Interaction range is approximately 1.2-1.7 fm.

Finite-volume condition is satisfied for L≥32 within statistical errors.

Phase shift determination has smaller statistical errors than traditional methods.

Abstract

We calculate the two-pion wave function for the I=2 $S$-wave two-pion system with a finite scattering momentum and estimate the interaction range between two pions. It allows us to examine the validity of the necessary condition for the finite-volume method for the scattering phase shift. A calculation is carried out with a plaquette gauge action for gluons and a clover-improved Wilson action for quarks at $1/a=1.63 {\rm GeV}$ on $32^3\times 120$ lattice in the quenched approximation. We conclude that the necessary condition is satisfied within statistical errors for the lattice size $L\ge 32$, when the quark mass is in the range $m_\pi^2=0.176 - 0.345 {\rm GeV}^2$ and the scattering momentum in $k^2 < 0.026 {\rm GeV}^2$. We also find that the energy dependence of the interaction range is small and it takes $1.2-1.7 {\rm fm}$ for our simulation parameters. We obtain the phase shift from the two-pion wave function with a smaller statistical error than that from the conventional analysis with the two-pion time correlator.