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

Aug 8 – 13, 2022
Hörsaalzentrum Poppelsdorf
Europe/Berlin timezone

## Investigating Unitarity Violation With Chiral Perturbation Theory

Aug 12, 2022, 2:30 PM
20m
CP1-HSZ/1st-1.004 - HS7 (CP1-HSZ)

### CP1-HSZ/1st-1.004 - HS7

#### CP1-HSZ

70
Oral Presentation 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 $\sim 100\%$ 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 $\sim 25\%$ and will be difficult to reduce in practice.

### Primary authors

Zachary Draper (University of Washington) Stephen Sharpe (University of Washington)