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Register a new userMomentum dependence of the topological susceptibility with overlap fermions
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Knowledge of the derivative of the topological susceptibility at zero momentum is important for assessing the validity of the Witten-Veneziano formula for the eta 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.
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The chiral symmetry at finite lattice spacing of Ginsparg-Wilson fermionic actions constrains the renormalization of the lattice operators; in particular, the topological susceptibility does not require any renormalization, when using a fermionic estimator to define the topological charge. Therefore, the overlap formalism appears as an appealing candidate to study the continuum limit of the topological susceptibility while keeping the systematic errors under theoretical control. We present results for the SU(3) pure gauge theory using the index of the overlap Dirac operator to study the topology of the gauge configurations. The topological charge is obtained from the zero modes of the overlap and using a new algorithm for the spectral flow analysis. A detailed comparison with cooling techniques is presented. Particular care is taken in assessing the systematic errors. Relatively high statistics (500 to 1000 independent configurations) yield an extrapolated continuum limit with errors that are comparable with other methods. Our current value from the overlap is $chi^{1/4} = 188 pm 12 pm 5 MeV$.
HMC histories for light dynamical overlap fermions tend to stay in a fixed topological sector for many trajectories, so that the different sectors are not sampled properly. Therefore the suitable summation of observables, which have been measured in separate sectors, is a major challenge. We explore several techniques for this issue, based on data for the chiral condensate and the (analogue of the) pion mass in the 2-flavour Schwinger model with dynamical overlap-hypercube fermions.
Overlap fermions implement exact chiral symmetry on the lattice and are thus an appropriate tool for investigating the chiral and topological structure of the QCD vacuum. We study various chiral and topological aspects on Luescher-Weisz-type quenched gauge field configurations using overlap fermions as a probe. Particular emphasis is placed upon the analysis of the spectral density and the localisation properties of the eigenmodes as well as on the local structure of topological charge fluctuations.
We recently obtained an estimate of the axion mass based on the hypothesis that axions make up most of the dark matter in the universe. A key ingredient for this calculation was the temperature-dependence of the topological susceptibility of full QCD. Here we summarize the calculation of the susceptibility in a range of temperatures from well below the finite temperature cross-over to around 2 GeV. The two main difficulties of the calculation are the unexpectedly slow convergence of the susceptibility to its continuum limit and the poor sampling of nonzero topological sectors at high temperature. We discuss how these problems can be solved by two new techniques, the first one with reweighting using the quark zero modes and the second one with the integration method.
We determine the topological susceptibility chi_t in the topologically-trivial sector generated by lattice simulations of N_f = 2+1 QCD with overlap Dirac fermion, on a 16^3 x 48 lattice with lattice spacing ~ 0.11 fm, for five sea quark masses m_q ranging from m_s/6 to m_s (where m_s is the physical strange quark mass). The chi_t is extracted from the plateau (at large time separation) of the 2-point and 4-point time-correlation functions of the flavor-singlet pseudoscalar meson eta, which arises from the finite size effect due to fixed topology. In the small m_q regime, our result of chi_t agrees with the chiral effective theory. Using the formula chi_t = Sigma(m_u^{-1} + m_d^{-1} + m_s^{-1})^{-1} by Leutwyler-Smilga, we obtain the chiral condensate Sigma^{MSbar}(2 GeV) = [249(4)(2) MeV]^3.
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