I=2ππscattering from fully-dynamical mixed-action lattice QCD

Abstract

We compute the I 2 scattering length at pion masses of m 294, 348, and 484 MeV in fullydynamical lattice QCD using Lüscher's finite-volume method. The calculation is performed with domainwall valence-quark propagators on asqtad-improved MILC configurations with staggered sea quarks at a single lattice spacing, b 0:125 fm. Chiral perturbation theory is used to perform the extrapolation of the scattering length from lattice quark masses down to the physical value, and we find m a 2 ÿ0:0426 0:0006 0:0003 0:0018, in good agreement with experiment. The I 2 scattering phase shift is calculated to be ÿ43 10 5 at jpj 544 MeV for m 484 MeV.

Two meson systems with Ginsparg-Wilson valence quarks

“…One can show that these terms are formally higher order in the SU 4j2 chiral expansion, but nevertheless we will see that they are not negligible. The NPLQCD Collaboration recently has computed m a I 2 and used the SU 2 extrapolation formula to determine l I 2 [19]. Adjusting for conventions and including their largest uncertainty, they determined l I 2 4 f ' ÿ10:9 1:8:…”

“…To do this, we must first convert the counterterm, l obtained by NPLQCD in Ref. [19], from the effective theory with two sea flavors to the theory with three sea flavors. For PQ and MA theories, there is an additional subtlety which arises in this matching.…”

“…(10), which is currently unknown. 19 Consequently we form the ratio, from Ref. [23], as their various fitting procedures produced little variation in the extraction of L 5 .…”

“…There have been a number of recent lattice computations [17][18][19][20][21][22][23][24][25] utilizing the scheme first developed by the LHP Collaboration [72,73] of employing domain wall valence quarks with the publicly available MILC configurations. In particular, the NPLQCD Collaboration has computed the I 2 scattering length [19], 17 f K =f [23] and determined both the I 3=2 and I 1=2 K scattering lengths through a direct determination of the I 3=2 K scattering length [25]. As we will demonstrate by explicit computation, the I 1 KK scattering length, together with the above three systems, share only two linearly independent sets of counterterms, which are the physical counterterms of interest.…”

“…the I 2 , I 3=2 K , and I 1 KK systems. 19 In Ref. [35], this quantity was recently estimated by comparing the MA form of the pion form factor to a MA simulation [17].…”