Connected and disconnected contractions in pion–pion scattering

Neramballi Ripunjay Acharya,Feng-Kun Guo,Ulf-G Meißner,Chien-Yeah Seng

doi:10.1016/j.nuclphysb.2017.07.012

Abstract

We show that the interplay of chiral effective field theory and lattice QCD can be used in the evaluation of so-called disconnected diagrams, which appear in the study of the isoscalar and isovector channels of pion–pion scattering and have long been a major challenge for the lattice community. By means of partially-quenched chiral perturbation theory, we distinguish and analyze the effects from different types of contraction diagrams to the pion–pion scattering amplitude, including its scattering lengths and the energy-dependence of its imaginary part. Our results may be used to test the current degree of accuracy of lattice calculation in the handling of disconnected diagrams, as well as to set criteria for the future improvement of relevant lattice computational techniques that may play a critical role in the study of other interesting QCD matrix elements.

Highlights

Quantum Chromodynamics (QCD) is well-accepted as the fundamental field theory of the strong interaction
Chiral Perturbation Theory (ChPT) is an example of such kind, based on the fact that chiral symmetry is spontaneously broken at the hadronic scale and the lowest-lying pseudoscalar mesons play the role of Goldstone bosons
This work is arranged as follows: In Section 2 we review the basic setup of SU(4|2) partially-quenched QCD (PQQCD) and Partially-quenched chiral perturbation theory (PQChPT)

Summary

Introduction

Quantum Chromodynamics (QCD) is well-accepted as the fundamental field theory of the strong interaction. Contraction diagrams involving quark propagators starting from and ending at points with the same time coordinates appear to be extremely noisy, which makes the extraction of lattice signals very difficult. The outcome, has to be extrapolated to the region where the sea quark masses take their physical values This is made possible by PQQCD which first separates the usual fermionic quarks into “valence” and “sea” quarks, and introduces, for each valence quark, a degenerate bosonic quark (known as “ghost quark”) that cancels all the closed-loop contribution of the valence quark.. We demonstrate exactly how PQChPT can be applied to distinguish contributions from different Wick contractions to the ππ scattering amplitude This task has been carried out at the LO, i.e. O(p2), in Ref. The appendices contain analytic expressions of scattering lengths decomposed into contributions from different types of contractions, as well as PQChPT in a formulation slightly different from the one discussed in the main text

Basic setup

Classification of the contraction diagrams

Analytical results

D C R V Total

Summary