I=2pion scattering amplitude with Wilson fermions

Abstract

We present an exploratory calculation of the I = 2 scattering amplitude at threshold using Wilson fermions in the quenched approximation, including all the required contractions. We nd good agreement with the predictions of chiral perturbation theory even for pions of mass 560-700 MeV. Within the 10% errors, we do not see the onset of the bad chiral behavior expected for Wilson fermions. We also derive rigorous inequalities that apply to 2-particle correlators and as a consequence show that the interaction in the antisymmetric state of two pions has to be attractive.

Pion Scattering in Wilson Chiral Perturbation Theory

“…However, note that the coefficient A I 00 is of O(a 2 ) rather than of O(a). This holds even for unimproved Wilson fermions, in contrast to what has been expected earlier [14,15].…”

Generalized Lüscher’s formula in multichannel baryon-baryon scattering

“…For the study of hadron-hadron interactions at low energies, Lüscher has set up a formalism which relates the twoparticle elastic scattering S-matrix elements with the corresponding two-particle energies in a finite volume [2][3][4][5]. Since the advent of Lüscher's formula, various lattice studies, both quenched [6][7][8][9][10][11][12][13] and unquenched [14][15][16][17][18][19][20][21][22][23], have been performed over the years to investigate the scattering of hadrons.…”

Hadronic Interactions From Lattice QCD

“…[86]. The first lattice calculations of ππ scattering were performed in quenched QCD [93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113], and the first partially-quenched QCD calculation of ππ scattering (the scattering length and phase-shift) was carried through by the CP-PACS collaboration, who exploited the finitevolume strategy to study I = 2, s-wave scattering with two flavors (n f = 2) of improved Wilson fermions [114], with pion masses in the range m π 0.5 − 1.1 GeV. The first fullydynamical calculation of the I = 2 ππ scattering length with three flavors (n f = 2 + 1) of light quarks was performed by NPLQCD using domain-wall valence quarks on asqtadimproved staggered sea quarks at four pion masses in the range m π 0.3 − 0.5 GeV at a single lattice spacing, b ∼ 0.125 fm [78].…”