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.Comment: 38 pages, 7 figures, addition of a discussion on parity mixing and correction of typo

The Slab Method to Measure the Topological Susceptibility

“…This is the beginning of an expansion in 1/(V χ t ) = 1/ Q 2 , extensions are discussed in Refs. [9,10]. Once we have a set of results for O | Q , in different V and |Q|, a fit provides values for the unknown (intensive) quantities: O , χ t and the const.…”

Topological susceptibility from slabs

“…However, even at |Q| ≤ 1 the finite size effects are highly persistent. In fact, other methods and formulae show that these effects are only suppressed by a power series in 1/V for topologically fixed measurements [6][7][8][9][10][11][12].…”

“…Recently, several indirect methods to measure χ t nevertheless have been suggested and tested [6][7][8][9][10][11][12]. Here we address a different approach for this purpose, which was first sketched in ref.…”

Interpreting numerical measurements in fixed topological sectors

“…These terms are identified and discussed in detail in Refs. [15][16][17]. Here we mostly focus on the simplest form which captures the Q-dependence of O Q , and which involves only three parameters (though an incomplete second order),…”

“…Tests for a quantum rotor -more precisely a scalar particle on a circle with a potential -are reported in Refs. [15,16].…”