Hadron Scattering Lengths in Lattice QCD

TL;DR

This paper presents lattice QCD calculations of s-wave hadron scattering lengths across multiple channels, introducing a more efficient wall source method that reduces computational costs and extends to disconnected quark contributions.

Contribution

Developed a novel wall source method for lattice QCD that reduces computational time and allows calculation of disconnected quark loops, improving efficiency and scope of hadron scattering studies.

Findings

Results agree with current algebra and PCAC predictions within errors for  and    scattering lengths.

 and  nucleon-nucleon forces are attractive, with larger scattering lengths than - and - cases.

Method reduces computational cost by a factor of L^3 and avoids Fierz mixing issues.

Abstract

Lattice QCD calculation of s-wave hadron scattering lengths in the channels \pi-\pi, \pi-N, K-N, {\bar K}-N and N-N is carried out in the quenched QCD at $\beta=6/g^2=5.7$. A variant of the method of wall sourceis developed for this purpose, which reduces the computer time by a factor L^3 on an L^3xT lattice compared to the conventional point source method and avoids the Fierz mixing problem. A version of the method in which gauge configurations are not fixed to any gauge can be extended to calculate disconnected quark loop con- tributions in hadron two- and three-point functions. An analytical estimate of statistical errors for this method is worked out, and the magnitude of errors without and with gauge fixing is compared for the case of \pi-\pi four-point functions calculated with the KS quark action. For \pi-\pi scattering both I=0 and 2 scattering lengths are evaluated using the KS and Wilson quark actions on a 12^3x20 lattice. For the same size of lattice, \pi-N, K-N and {\bar K}-N scattering lenghts are calculated with the Wilson quark action. For the \pi-\pi and \pi-N cases simulation results are consistent with the predictions of current algebra and PCAC within one to two standard deviations up to quite heavy quark masses corresponding to $m_\pi/m_\rho\approx 0.74$, while for the K-N and {\bar K}-N cases the agreement is within a factor of two. For N-N scat- tering simulations with the Wilson action on a 20^4 lattice with heavy quarks with $m_\pi/m_\rho\approx 0.74-0.95$, where the deuteron is expected to become unbound from a phenomenological study with one-boson exchange potentials, show that the nucleon-nucleon force is attractive for both spin triplet and singlet channels, and that the scattering lengths are substantially larger compared to those for the \pi-\pi and \pi-N cases even for such heavy quarks.