Hadron scattering lengths in lattice QCD

Abstract

Lattice QCD calculation of s-wave hadron scattering lengths in the channels π-π, π-N, K-N,K-N and N-N is carried out in the quenched approximation at β = 6/g 2 = 5.7. A variant of the method of wall source is developed for this purpose, which reduces the computer time by a factor L 3 on an L 3 × T lattice compared to the conventional point source method and avoids the Fierz mixing problem. A version of the method in which gauge configurations are not fixed to any gauge can be extended to calculate disconnected quark loop contributions in hadron two-and three-point functions. An analytical estimate of statistical errors for this method is worked out, and the magnitude of errors without and with gauge fixing is compared for the case of π-π four-point functions calculated with the Kogut-Susskind quark action. For π-π scattering both I = 0 and 2 scattering lengths are evaluated using the Kogut-Susskind and Wilson quark actions on a 12 3 ×20 lattice. For the same size of lattice, π-N, K-N andK-N scattering lenghts are calculated with the Wilson quark action. For the π-π and π-N cases simulation results are consistent with the predictions of current algebra and PCAC within one to two standard deviations up to quite heavy quark masses corresponding to m π /m ρ ≈ 0.74, while for the K-N andK-N cases the agreement is within a factor of two. For N-N scattering a phenomenological study with one-boson exchange potentials indicate that the deuteron becomes unbound if the quark mass is increased beyond 30-40% of the physical value. Simulations with the Wilson action on a 20 4 lattice with heavy quarks with m π /m ρ ≈ 0.74 − 0.95 show that the nucleon-nucleon force is attractive for both spin triplet and singlet channels, and that the scattering lengths are substantially larger compared to those for the π-π and π-N cases even for such heavy quarks. Problem of statistical errors which has to be overcome toward a more realistic calculation of hadron scattering lengths is discussed.

New developments in lattice QCD: Calculation of flavor singlet nucleon matrix elements and hadron scattering lengths

“…These are precisely the features found in a lattice calculation of N -N scattering lengths [8,9]. The results are shown in Fig.…”

“…In Fig. 3 results for the R ratio (1) obtained with the wall method [11,12] at β = 5.7 and K = 0.164 (m π /m ρ = 0.74) are plotted. We observe reasonable signals with a linear increase in t for the disconnected amplitude( Fig.…”

“…In Table 2 (b) we summarize recent results [12,14]. These values are obtained by extrapolating the valence quark mass to the chiral limit while keeping the strange quark mass fixed at the physical value.…”

“…Generalizing the well-known argument [24], it is possible to show that the magnitude of gauge-variant noise terms is smaller than the signal by a factor 1/ √ V N for a sufficiently large volume V and a number of configurations N . In practice O(100 − 200) configurations are employed to obtain reliable signals on a lattice such as 16 3 × 20 at β = 5.7 [12,13].…”

I=2 pion scattering length with the parametrized fixed point action

“…In the literature several attempts to compute the scattering length with Wilson fermions [1][2][3][4][5] and staggered fermions [1,2] can be found. However, calculations with a chiral Dirac operator which allows for a better control of the small mass region are still missing.…”