# Finite size effect on vector meson and baryon sectors in 2+1 flavor QCD at the physical point

## TL;DR

This study examines finite size effects on vector mesons and baryons in 2+1 flavor QCD at the physical point, finding minimal effects on stable octet baryons but notable effects on unstable vector mesons and decuplet baryons, with implications for resonance levels.

## Contribution

It provides a detailed comparison of finite size effects on various hadron sectors using large lattice volumes at the physical point, highlighting the behavior of unstable states and mixing phenomena.

## Key findings

- Octet baryons show negligible finite size effects within 0.5%.
- Vector mesons have masses below experimental resonance levels.
- Decuplet baryons exhibit similar finite size effects to vector mesons, possibly due to mixing with multihadron states.

## Abstract

We investigate the finite size effect on the vector meson and the baryon sectors using a subset of the "PACS10" configurations which are generated, keeping the space-time volumes over (10 fm$)^4$ in 2+1 flavor QCD at the physical point. Comparing the results on (5.5 fm$)^4$ and (10.9 fm$)^4$ lattices the ground states of octet baryons , which are stable on the lattice, show no finite size effect within less than 0.5% level of statistical errors. For those of vector mesons, which are unstable on the lattice, we observe that the effective masses are well below the experimental resonance levels both on (5.5 fm$)^4$ and (10.9 fm$)^4$ lattices. For the decuplet baryon sector we have found that the time dependence of the effective mass looks quite similar to that for the vector meson sector including the $\Omega$ baryon channel. We discuss its origin due to a possible mixing with the nearby multihadron states. Since the $\Xi$ baryon mass can be determined with the smallest ambiguity among the vector meson and the baryon masses, we use it together with the pion and kaon masses as the physical inputs to determine the physical point.