Strong Coupling Hadron Masses in $1/d$ Expansion for Wilson fermions

TL;DR

This paper calculates hadron masses using a combined $1/d$ and strong coupling expansion with Wilson fermions, improving agreement with lattice results and phenomenology, especially near the Wilson parameter r=1.

Contribution

It introduces a systematic $1/d$ expansion for hadron spectra with Wilson fermions, extending previous methods and showing better alignment with lattice and experimental data.

Findings

Decoupling of doublers occurs near Wilson's r=1.

Nucleon to rho meson mass ratio is approximately 1.48.

Results are valid even at $eta$ as large as 5.

Abstract

Motivated by the weak-strong coupling expansion \cite{Rosenstein}, we calculate the spectrum of hadrons using a systematic $1/d$ ($d$ - dimensionality of spacetime) in addition to a strong coupling expansion in $\beta$. The $1/d$ expansion is pushed to the next to leading order in ($1/d$) for mesons and next to 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's 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) "randomwalk" approximation or the hopping parameter expansion. In particular, the value of the nucleon to $\rho$ - meson mass ratio is lowered to $\frac {3 \log d -1/4}{2 {\rm arccosh} 2}+O(1/d)\approx 1.48$. The result holds even for $\beta$ as large as 5, where the weak-strong coupling expansion is applicable and therefore these results are expected to be reasonable.