The 39th International Symposium on Lattice Field Theory (Lattice 2022)

Investigating Unitarity Violation With Chiral Perturbation Theory

12 Aug 2022, 14:30

20m

CP1-HSZ/1.004 (CP1-HSZ) - HS7 (CP1-HSZ)

Oral Presentation Hadron Spectroscopy and Interactions Hadron Spectroscopy and Interactions

Speaker

Zachary Draper (University of Washington)

Description

Partial quenching can be used to avoid isospin mixing in a theory incorporating a mass twist, but comes at the cost of introducing unitarity violation. This talk will examine pion-pion scattering in partially-quenched twisted-mass lattice QCD using chiral perturbation theory. The specific partially-quenched setup corresponds to that used in numerical lattice QCD calculations of the $I=0$ scattering length. We study previously unquantified discretization errors proportional to $a^2$, with $a$ the lattice spacing, and newly identified errors that arise due to the use of Lüscher’s two-particle quantization condition in a theory that is not unitary. The discretization errors may be as large as $\sim 100\mathrm{\%}$ but can be systematically subtracted using a calculation of the $I=2$ scattering amplitude in the same partially-quenched framework. The error from the violation of unitarity is $\sim 25\mathrm{\%}$ and will be difficult to reduce in practice.

Presentation materials

Draper Lattice22.pdf