# Hadron Spectrum with Wilson fermions

## TL;DR

This study uses Wilson fermions to analyze the hadron spectrum in quenched lattice QCD, revealing deviations from chiral theory, systematic errors in quark mass estimates, and assessing the quenched approximation's accuracy.

## Contribution

It provides high-statistics quenched spectrum results with Wilson fermions, including detailed baryon mass splittings and analysis of discretization errors, highlighting limitations of the quenched approximation.

## Key findings

- Significant deviations from lowest order chiral expansion.
- Approximate 20% systematic error in strange quark mass estimation.
- Quenched approximation is accurate within ~10-15%.

## Abstract

We present results of a high statistics study of the quenched spectrum using Wilson fermions at $\beta=6.0$ on $32^3 \times 64$ lattices. We calculate the masses of mesons and baryons composed of both degenerate and non-degenerate quarks. Using non-degenerate quark combinations allows us to study baryon mass splittings in detail. We find significant deviations from the lowest order chiral expansion, deviations that are consistent with the expectations of quenched chiral perturbation theory. We find that there is a $\sim 20%$ systematic error in the extracted value of $m_s$, depending on the meson mass ratio used to set its value. Using the largest estimate of $m_s$ we find that the extrapolated octet mass-splittings are in agreement with the experimental values, as is $M_\Delta - M_N$, while the decuplet splittings are 30% smaller than experiment. Combining our results with data from the GF11 collaboration we find considerable ambiguity in the extrapolation to the continuum limit. Our preferred values are $M_N / M_\rho = 1.38(7)$ and $M_\Delta / M_\rho = 1.73(10)$, suggesting that the quenched approximation is good to only $\sim 10-15%$. We also analyze the $O(ma)$ discretization errors in heavy quark masses.

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Source: https://tomesphere.com/paper/hep-lat/9512021