Pion scattering in Wilson chiral perturbation theory

Abstract

We compute the scattering amplitude for pion scattering in Wilson chiral perturbation theory for two degenerate quark flavors. We consider two different regimes where the quark mass m is of order (i) aà 2 QCD and (ii) a 2 à 3 QCD . Analytic expressions for the scattering lengths in all three isospin channels are given. As a result of the Oða 2 Þ terms the I ¼ 0 and I ¼ 2 scattering lengths do not vanish in the chiral limit. Moreover, additional chiral logarithms proportional to a 2 lnM 2 are present in the one-loop results for regime (ii). These contributions significantly modify the familiar results from continuum chiral perturbation theory.

Nucleon toΔtransition form factors withNF=2+1domain wall fermions

“…Z A is required to renormalize the axial vector operator. This has been computed by the UKQCD-RBC and LHP collaborations for both ensembles [11,31,34]. The values provided in Table I confirm that Z V = Z A + O(a 2 ) in the chiral limit, as expected for the manifestly chiral DWF action.…”

“…We use the N f = 2 + 1 dynamical domain wall fermion (DWF) ensembles generated by the RBC and UKQCD collaborations [31,34,35] Details about the lattice parameters used in this study are provided in Table I, where for comparison the relevant values of the parameters used in our previous study using the mixed action [12,21,28] are also given. In order to create the proton and ∆ + states we use the standard interpolating operators…”

Continuum limit ofBKfrom2+1flavor domain wall QCD

“…Whilst this is correct asymptotically, i.e. when the p 2 i are sufficiently large for each choice of the quark masses, it was argued in References [28][29][30] that performing the renormalization using Green functions with no exceptional channels, i.e. with no channels in which the square of the momentum q 2 is small, suppresses the non-asymptotic chiral symmetry breaking effects more effectively.…”

“…p 1 + p 2 = 0) and in this paper we generalize the non-exceptional RI-SMOM schemes of References [28][29][30] to the four-quark operator. The choice of non-exceptional kinematics is not unique of course and in this paper we choose to study the Green function…”

Determination of low-energy constants of Wilson chiral perturbation theory

“…Lattice determinations of the pion scattering lengths have been used in refs. [41,42], an approach that was extended to a partially quenched setup in ref. [43].…”