Momentum dependence of the topological susceptibility with overlap fermions

Abstract

Knowledge of the derivative of the topological susceptibility at zero momentum is important for assessing the validity of the Witten-Veneziano formula for the η ′ mass, and likewise for the resolution of the EMC proton spin problem. We investigate the momentum dependence of the topological susceptibility and its derivative at zero momentum using overlap fermions in quenched lattice QCD simulations. We expose the role of the low-lying Dirac eigenmodes for the topological charge density, and find a negative value for the derivative. While the sign of the derivative is consistent with the QCD sum rule for pure Yang-Mills theory, the absolute value is overestimated if the contribution from higher eigenmodes is ignored. The XXVIII International Symposium on Lattice Filed Theory

Evaluating topological charge density with symmetric multi-probing method

“…( 7) with Conjugated Gradient(CG) algorithm for one source is more than O (N L ) (in consideration of that M i is a large sparse matrix, and its conditional number grows as N L grows), and there are 12N L point sources. So the cost of evaluating Q = x q (x) by calculating the trace of D ov with point sources will be larger than O (N 2 L ), which is too expensive especially for large N L [16,17], although it's the exact measurement of topological charge density on lattice without any approximation.…”

The topological susceptibility slope χ′ of the pure-gauge SU(3) Yang-Mills theory

“…However, for what concerns the numerical studies of the susceptibility slope, the current state of the art is pretty different compared to other topological quantities like the topological susceptibility. As a matter of fact, while χ has been extensively studied from the lattice in full QCD [22][23][24][25][26][27][28][29][30][31][32], in SU(N ) pure Yang-Mills theories [4,27,, and in other lower-dimensional models [54][55][56][57][58][59][60][61][62][63][64][65], only few preliminary numerical lattice studies of the topological susceptibility slope in QCD and in the pure-gauge SU(3) can be retrieved in the literature [66][67][68][69][70].…”