Study of Hadron Scattering Using an Asymmetric Box

TL;DR

This paper introduces a method using an asymmetric lattice box in QCD simulations to access more low-momentum hadron scattering data, improving the precision and range of phase shift calculations compared to traditional symmetric boxes.

Contribution

It develops a modified Lüscher's formula for asymmetric boxes and demonstrates its effectiveness through pion-pion scattering phase shift calculations that align with experimental data.

Findings

Accurate phase shifts below 300MeV pion momentum.

Enhanced low-momentum data coverage with asymmetric volume.

Results consistent with experimental and previous theoretical data.

Abstract

We propose to study hadron-hadron scattering using lattice QCD in an asymmetric box which allows one to access more non-degenerate low-momentum modes for a given volume. The conventional L\"{u}scher's formula applicable in a symmetric box is modified accordingly. To illustrate the feasibility of this approach, pion-pion elastic scattering phase shifts in the I=2, J=0 channel are calculated within quenched approximation using improved gauge and Wilson fermion actions on anisotropic lattices in an asymmetric box. After the chiral and continuum extrapolation, we find that our quenched results for the scattering phase shifts in this channel are consistent with the experimental data when the three-momentum of the pion is below 300MeV. Agreement is also found when compared with previous theoretical results from lattice and other means. Moreover, with the usage of asymmetric volume, we are able to compute the scattering phases in the low-momentum range (pion three momentum less than about 350MeV in the center of mass frame) for over a dozen values of the pion three-momenta, much more than using the conventional symmetric box with comparable volume.