Strong coupling hadron masses in 1d expansion for Wilson fermions

Motivated by the weak-strong coupling expansion [B. Rosenstein, Phys. Lett. B 351 (1995) 284], we calculate the spectrum of hadrons using a systematic 1d (d-dimensionality of spacetime) in addition to a strong coupling expansion in β. The 1d expansion is pushed to the next to leading order in 1d for mesons and next to leading order for baryons. We do the calculation using Wilson fermions with arbitrary r and show that doublers decouple from the spectrum only when r is close to the Wilson value r = 1. For these r the spectrum is much closer to the lattice results and the phenomenological values than those obtained by using either the (nonsystematic) “random walk” approximation or the hopping parameter expansion. In particular, the value of the nucleon to ϱ-meson mass ratio is lowered to (3 log d − 14)/(2arccosh2) + O(1d) ≈ 1.48. The result holds even for β as large as 5, where the weak-strong coupling expansion is applicable and therefore these results are expected to be reasonable.