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

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Cited by in corpus (9)

• Topological susceptibility at high temperature on the lattice
• Hybrid static potentials in SU(3) lattice gauge theory at small quark-antiquark separations
• ${\Lambda }_{\overline{\text{MS}}}^{(n_f=2)}$ from a momentum space analysis of the quark-antiquark static potential
• Measuring the Topological Susceptibility in a Fixed Sector
• Interpreting Numerical Measurements in Fixed Topological Sectors
• Topological Susceptibility from Slabs
• Hadron Physics from Lattice QCD
• Hybrid static potentials in SU(2) lattice gauge theory at short quark-antiquark separations
• Hadron masses from fixed topology simulations: parity partners and SU(2) Yang-Mills results