Determining low-energy constants in partially quenched Wilson chiral perturbation theory

Abstract

In the low energy effective theory describing the partially quenched extension of two light Wilson fermions, three low energy constants (LECs) appear in terms proportional to a^2 (a being the lattice spacing). We propose methods to separately calculate these LECs, typically called W'_6, W'_7 and W'_8. While only one linear combination of these constants enters into physical quantities, different combinations enter into the description of the spectral density and eigenvalue distributions of the lattice Dirac operator and its Hermitian counterpart. Thus it is useful to be able to determine the LECs separately. Our methods require studying certain correlation functions for either two or three pion scattering, which are accessible only in the partially quenched extension of the theory.

17 pages, 8 figures

References in corpus (4)

• Light hadrons from lattice QCD with light (u,d), strange and charm dynamical quarks
• Chiral symmetry breaking and the Banks--Casher relation in lattice QCD with Wilson quarks
• Discretization errors in the spectrum of the Hermitian Wilson-Dirac operator
• Pion scattering in Wilson ChPT

Cited by in corpus (13)

• Scattering lengths for two pseudoscalar meson systems
• Determination of Low-Energy Constants of Wilson Chiral Perturbation Theory
• Spectral Properties of the Wilson Dirac Operator and random matrix theory
• The Realization of the Sharpe-Singleton Scenario
• Mixing of orthogonal and skew-orthogonal polynomials and its relation to Wilson RMT
• New Ways to Determine Low-Energy Constants with Wilson Fermions
• Baryon chiral perturbation theory with Wilson fermions up to $\mathcal{O}(a^2)$ and discretization effects of latest $n_f=2+1$ LQCD octet baryon masses
• Applicability of the two-particle quantization condition to partially-quenched theories
• Partial-wave and helicity operators for the scattering of two hadrons in lattice QCD
• Chiral Dynamics With Wilson Fermions
• $\pi \pi$ scattering in partially-quenched twisted-mass chiral perturbation theory
• Wilson chiral perturbation theory, Wilson-Dirac operator eigenvalues and clover improvement
• Finite volume corrections to LECs in Wilson and staggered ChPT