Extracting hadron masses from fixed topology simulations

Abstract

Lattice QCD simulations tend to become stuck in a single topological sector at fine lattice spacing or when using chirally symmetric overlap quarks. In such cases physical observables differ from their full QCD counterparts by finite volume corrections. These systematic errors need to be understood on a quantitative level and possibly be removed. In this paper we extend an existing relation from the literature between two-point correlation functions at fixed and the corresponding hadron masses at unfixed topology by calculating all terms proportional to $1/V^2$ and $1/V^3$, where $V$ is the spacetime volume. Since parity is not a symmetry at fixed topology, parity mixing is comprehensively discussed. In the second part of this work we apply our equations to a simple model, quantum mechanics on a circle both for a free particle and for a square-well potential, where we demonstrate in detail, how to extract physically meaningful masses from computations or simulations at fixed topology.

38 pages, 7 figures, addition of a discussion on parity mixing and correction of typos

References in corpus (10)

• Finite volume QCD at fixed topological charge
• Computing K and D meson masses with N_f = 2+1+1 twisted mass lattice QCD
• Two-flavor QCD simulation with exact chiral symmetry
• Topological susceptibility in two-flavor lattice QCD with exact chiral symmetry
• The static-light meson spectrum from twisted mass lattice QCD
• Overlap valence quarks on a twisted mass sea: a case study for mixed action Lattice QCD
• Hadron spectrum, quark masses and decay constants from light overlap fermions on large lattices
• Continuum Limit of Overlap Valence Quarks on a Twisted Mass Sea
• Status and challenges of simulations with dynamical fermions
• Studying and removing effects of fixed topology

Cited by in corpus (2)

• ${\Lambda }_{\overline{\text{MS}}}^{(n_f=2)}$ from a momentum space analysis of the quark-antiquark static potential
• Hadron masses from fixed topology simulations: parity partners and SU(2) Yang-Mills results