Exploring the π + -π + Interaction in Lattice QCD

Abstract

An effective residual interaction for a meson-meson system is computed in lattice QCD. We describe the theoretical framework and present its application to the I = 2 channel S-wave interaction of the π-π system. Scattering phase shifts are also computed and compared to experimental results.

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].…”

K+K+scattering length from lattice QCD

“…These methods paved the way for pioneering quenched QCD calculations of two-particle interactions a little over a decade ago [30,31,32,33,34]. Since then, there have been a number of additional quenched calculations of the I = 2 ππ scattering length [35,36,37,38,39,40,41,42]. The first dynamical calculation of ππ interactions (including the phase-shift) was performed by the CP-PACS collaboration with two flavors (n f = 2) of improved Wilson fermions [43] and pion masses in the range 500 m π 1100 MeV.…”

Extracting scattering phase shifts in higher partial waves from lattice QCD calculations

“…Further, preliminary calculations of I = 0 ππ scattering, which contain disconnected diagrams, have been performed [20]. These calculations were preceded by quenched LQCD calculations [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39], and by early n f = 2 LQCD calculations [40]. Meson-baryon systems are starting to be explored in the channels for which disconnected diagrams are not required in the LQCD calculations [41].…”