Topological Charge Density Correlator Research Articles

Fate of the η′ in the quark gluon plasma

In this paper we study the η′ in Nf=2+1+1 lattice QCD simulations at finite temperature. Results are obtained from the analysis of the gluonic defined topological charge density correlator after gradient flow. Our results indicate the growth of the η′ mass above the pseudocritical temperature, associated with the chiral symmetry restoration. In the vicinity of the pseudocritical temperature the results are consistent with a small dip in the η′ mass. The magnitude of the dip is compatible with the reduction of the η′ mass obtained by experimental analysis and suggests that η′ mass comes close to zero temperature non-anomalous contribution.

Localization of topological charge density near Tc in quenched QCD with Wilson flow

We smear quenched lattice QCD ensembles with lattice volume $32^3\times 8$ by using Wilson flow. Six ensembles at temperature near the critical temperature $T_c$ corresponding to the critical inverse coupling $\beta_c=6.06173(49)$ are used to investigate the localization of topological charge density. If the effective smearing radius of Wilson flow is large enough, the density, size and peak of Harrington-Shepard (HS) caloron-like topological lumps of ensembles are stable when $\beta\leq 6.050$, but start to change significantly when $\beta\geq6.055$. The inverse participation ratio (IPR) of topological charge density shows similar results, it begins to increase when $\beta\geq 6.055$ and is stable when $\beta\leq 6.050$. The pseudoscalar glueball mass is extracted from the topological charge density correlator (TCDC) of ensembles at $T=1.19T_c,~\textrm{and }1.36T_c$, the masses are $1.915(98)\textrm{ GeV}$ and $1.829(123)\textrm{ GeV}$ respectively, they are consistent with results from conventional methods.

Correlation and localization properties of topological charge density and the pseudoscalar glueball mass in SU(3) lattice Yang-Mills theory

Towards the goal of extracting the continuum properties, we have studied the Topological Charge Density Correlator (TCDC) and the Inverse Participation Ratio (IPR) for the topological charge density ($q(x)$) in SU(3) Lattice Yang-Mills theory for relatively small lattice spacings including some smaller than those explored before. With the help of recently proposed open boundary condition, it is possible to compute observables at a smaller lattice spacing since {\em trapping problem} is absent. On the other hand, the reference energy scale provided by Wilson flow allows us to study their scaling behavior in contrast to previously proposed smearing techniques. The behavior of TCDC for different lattice spacings at a fixed HYP smearing level shows apparent scaling violations. In contrast, at a particular Wilson flow time $t$ for all the lattice spacings investigated (except the largest one), the TCDC data show universal behavior within our statistical uncertainties. The continuum properties of TCDC are studied by investigating the small flow time behavior. We have also extracted the pseudoscalar glueball mass from TCDC, which appears to be insensitive to the lattice spacings (0.0345 fm $\leq a\leq$ 0.0667 fm) and agrees with the value extracted using anisotropic lattices, within statistical errors. Further, we have studied the localization property of $q(x)$ through IPR whose continuum behavior can be probed through the small values of Wilson flow time and observed the decrease of IPR with decreasing Wilson flow time. A detailed study of $q(x)$ under Wilson flow time revealed that as Wilson flow time decreases, the proximity of the regions of positive and negative charge densities of large magnitudes increases, and the charge density appears to be more delocalized resulting in the observed behavior of IPR.

Magnetic field-induced gluonic (inverse) catalysis and pressure (an)isotropy in QCD

We study the influence of strong external magnetic fields on gluonic and fermionic observables in the QCD vacuum at zero and nonzero temperatures, via lattice simulations with N_f=1+1+1 staggered quarks of physical masses. The gluonic action density is found to undergo magnetic catalysis at low temperatures and inverse magnetic catalysis near and above the transition temperature, similar to the quark condensate. Moreover, the gluonic action develops an anisotropy: the chromo-magnetic field parallel to the external field is enhanced, while the chromo-electric field in this direction is suppressed. We demonstrate that the same hierarchy is obtained using the Euler-Heisenberg effective action. Conversely, the topological charge density correlator does not reveal a significant anisotropy up to magnetic fields eB~1 GeV^2. Furthermore, we show that the pressure remains isotropic even for nonzero magnetic fields, if it is defined through a compression of the system at fixed external field. In contrast, if the flux of the field is kept fixed during the compression -- which is the situation realized in the lattice simulation -- the pressure develops an anisotropy. We estimate the quark and gluonic contributions to this anisotropy, and relate them to the magnetization of the QCD vacuum. After performing electric charge renormalization, we obtain an estimate for the magnetization, which indicates that QCD is paramagnetic.

Exploring autocorrelations in two-flavor Wilson Lattice QCD using DD-HMC algorithm

We perform an extensive study of the autocorrelation of several observables in lattice QCD with two degenerate flavors of unimproved Wilson fermions and Wilson gauge action using the DD-HMC algorithm. We show that (1) at a given lattice spacing, autocorrelation of topological susceptibility and unsmeared plaquette show indication of a decrease with decreasing quark mass, (2) autocorrelation of topological susceptibility and topological charge density correlator increase with decreasing lattice spacing but the effect is milder in the latter case and (3) increasing the size and the smear level increase the autocorrelation of smeared Wilson loop.

Topological charge density correlator in Lattice QCD with two flavours of unimproved Wilson fermions

We study the two-point Topological Charge Density Correlator (TCDC) in lattice QCD with two degenerate flavours of unimproved Wilson fermions and Wilson gauge action at two values of lattice spacings and different volumes, for a range of quark masses. Configurations are generated with DDHMC algorithm and smoothed with HYP smearing. In order to shed light on the mechanisms leading to the observed suppression of topological susceptibility with respect to the decreasing quark mass and decreasing volume, in this work, we carry out a detailed study of the two-point TCDC. We have shown that, (1) the TCDC is negative beyond a positive core and radius of the core shrinks as lattice spacing decreases, (2) as the volume decreases, the magnitude of the contact term and the radius of the positive core decrease and the magnitude of the negative peak increases resulting in the suppression of the topological susceptibility as the volume decreases, (3) the contact term and radius of the positive core decrease with decreasing quark mass at a given lattice spacing and the negative peak increases with decreasing quark mass resulting in the suppression of the topological susceptibility with decreasing quark mass, (4) increasing levels of smearing suppresses the contact term and the negative peak keeping the susceptibility intact and (5) both the contact term and the negative peak diverge in nonintegrable fashion as lattice spacing decreases. It is gratifying to note that observations similar to 1 and 5 have been made using topological charge density operator based on chiral fermion. The observations 2 and 3 may be confirmed more precisely by using formulations based on chiral fermions.

The negativity of the overlap-based topological charge density correlator in pure-glue QCD and the non-integrable nature of its contact part

We calculate the lattice two-point function of topological charge density in pure-glue QCD using the discretization of the operator based on the overlap Dirac matrix. Utilizing data at three lattice spacings it is shown that the continuum limit of the correlator complies with the requirement of non-positivity at non-zero distances. For our choice of the overlap operator and the Iwasaki gauge action we find that the size of the positive core is ≈2a (with a being the lattice spacing) sufficiently close to the continuum limit. This result confirms that the overlap-based topological charge density is a valid local operator over realistic backgrounds contributing to the QCD path integral, and is important for the consistency of recent results indicating the existence of a low-dimensional global brane-like topological structure in the QCD vacuum. We also confirm the divergent short-distance behavior of the correlator, and the non-integrable nature of the associated contact part.