Pion-nucleon σ term in lattice QCD

Abstract

We calculate both connected and disconnected contribution to the π-N σ-term in quenched lattice QCD with Wilson quark action on a 12 3 × 20 lattice at β = 5.7. The latter is evaluated with the aid of the variant wall source method, which was previously applied successfully for extraction of π-π scattering lengths and η ′ meson mass. We found that the disconnected contribution is about twice larger than the connected one. The value for the full π-N σ term σ = 40 − 60 MeV is consistent with the experimental estimates. The nucleon matrix element of the strange quark densityss is fairly large in our result.

Pion-nucleon σ term with dynamical Wilson fermions

“…Furthermore, ref. [4] estimates y = 0.66 (15). Given the value of 2 : 1 for the ratio of disconnected to connected contributions, this is exactly the value one would expect from the assumption of flavour symmetry of the disconnected contributions.…”

“…This corresponds to a lattice cutoff a −1 ρ ≃ 2.3GeV and a spatial length L ≃ 1.4fm. We have generated 200 statistically independent vacuum configurations at each of our 4 values of the sea quark mass, which correspond to m π /m ρ = 0.833(3), 0.809(15), 0.758(11) and 0.686 (11). Details of the simulation as well as the analysis of the light hadron spectrum can be found in [8].…”

Gaugino mass nonuniversality and dark matter in supergravity, strings, and D-brane models

“…The various determinations of σ πN , σ 0 and x using analyses of Ref. [33,34,35,36,37,28] are summarized in Table2. For σ πN one finds an average value of 48 ± 9 MeV, and for σ 0 an average value of 35.5 ± 6 MeV.…”

“…In recording the result of x for Ref. [37] we have reduced the y value by 35% as discussed in Ref. [36].…”

“…These give x = 0.74 ± 0.25. Further, there are two independent lattice gauge determinations [36,37] of y = 1 − x which we list in Table2. In recording the result of x for Ref.…”