Chromoelectric and chromomagnetic fields for the static gluon-quark-antiquark system
Marco Cardoso, Nuno Cardoso, Pedro Bicudo
备注：
8 pages, 14 figures, corrected a factor of 2 in the L geometry results, Presented at the XXVII International Symposium on Lattice Field Theory - LAT2009, July 26-31 2009, Peking University, Beijing, China
The chromoelectric and chromomagnetic fields, created by a static gluon-quark-antiquark system, are computed in the quenched approximation of lattice QCD, in a $24^3\times 48$ lattice at $β=6.2$. We study two geometries, one with a U shape and another with an L shape. The degenerate case of the two gluon glueball is also studied. This is relevant to understand the microscopic structure of hadrons, in particular of hybrids. This also contributes to understand confinement with flux tubes of the chromoelectric field, and to discriminate between the models of fundamental or adjoint tubes.
The heavy quark diffusion coefficient is encoded in the spectral functions of the chromoelectric and the chromomagnetic correlators that are calculable on the lattice. We study the chromoelectric and the chromomagnetic correlator in the deconfined phase of SU(3) gauge theory using Symanzik flow at two temperatures $1.5T_c$ and $10000 T_c$, with $T_c$ being the phase transition temperature. To control the lattice discretization errors and perform the continuum limit we use several temporal lattice extents $N_t=16,20,24$ and 28. We observe that the flow time dependence of the chromomagnetic corr…
Using lattice Monte Carlo simulations of SU(3) pure gauge theory, we determine the spatial distribution of all components of the color fields created by a static quark and antiquark. We identify the components of the measured chromoelectric field transverse to the line connecting the quark-antiquark pair with the transverse components of an effective Coulomb-like field $\vec{E}^C $ associated with the quark sources. Subtracting $\vec{E}^C$ from the total simulated chromoelectric field $\vec{E}$ yields a non-perturbative, primarily longitudinal chromoelectric field $\vec{E}^{NP}$, which we iden…
We study numerically the chromoelectric-chromomagnetic asymmetry of the dimension two $A^2$ gluon condensate as well as the infrared behavior of the gluon propagators at $T\simeq T_c$ in the Landau-gauge $SU(3)$ lattice gauge theory. We find that a very significant correlation of the real part of the Polyakov loop with the asymmetry as well as with the longitudinal propagator makes it possible to determine the critical behavior of these quantities. We obtain the screening masses in different Polyakov-loop sectors and discuss the dependence of chromoelectric and chromomagnetic interactions of s…
We report on the chromoelectric and chromomagnetic fields generated by a static quark-antiquark pair at zero temperature in pure gauge SU(3). From the spatial structure of chromoelectric field we extract its nonperturbative part and discuss its properties.
A characteristic signature of quark confinement is the concentration of the chromoelectric field between a static quark-antiquark pair in a flux tube. However, the structure of this flux tube, and hence of the confining force, has not been completely understood. Here we perform new lattice measurements of field distributions on smeared Monte Carlo ensembles in SU(3) gauge theory. On the basis of these simulations we demonstrate that the confining force can be understood using the analogy with the basic principles of electromagnetism as elucidated by Maxwell. We derive a chromomagnetic Lorentz …
Landau gauge longitudinal and transverse gluon propagators are studied in lattice QCD with gauge group $SU(2)$ at varying temperature and quark density. In particular, it is found that the longitudinal propagator decreases with increasing quark chemical potential at all temperatures under study, whereas the transverse propagator increases with increasing quark chemical potential at $T<200$ MeV and does not depend on it at higher temperatures. The relative strength of chromoelectric and chromomagnetic interactions is also discussed.
We study numerically the chromoelectric-chromomagnetic asymmetry of the dimension two gluon condensate as well as the longitudinal gluon propagator at $T\simeq T_c$ in the Landau-gauge $SU(2)$ lattice gauge theory. We show that substantial correlation between the asymmetry and the Polyakov loop as well as the correlation between the longitudinal propagator and the Polyakov loop pave the way to studies of the critical behavior of the asymmetry and the longitudinal propagator. The respective values of critical exponents and amplitudes are evaluated.
In this paper we study thermodynamic properties of dense cold $SU(2)$ QCD within lattice simulation with dynamical rooted staggered quarks which in the continuum limit correspond to $N_f=2$ quark flavours. We calculate baryon density, renormalized chiral and diquark condensates for various baryon chemical potentials in the region $μ\in (0,\,2000)$ MeV. It is found, that in the region $μ\in (0,\,540)$ MeV the system is well described by the ChPT predictions. In the region $μ> 540$ MeV the system becomes sufficiently dense and ChPT is no longer applicable to describe lattice data. For chemical p…
We use gradient flow to compute the static force based on a Wilson loop with a chromoelectric field insertion. The result can be compared on one hand to the static force from the numerical derivative of the lattice static energy, and on the other hand to the perturbative calculation, allowing a precise extraction of the $Λ_0$ parameter. This study may open the way to gradient flow calculations of correlators of chromoelectric and chromomagnetic fields, which typically arise in the nonrelativistic effective field theory factorization.
We report about an ongoing lattice field theory project concerned with the investigation of heavy hybrid mesons. In particular we discuss our computation of the structure of hybrid static potential flux tubes in SU(2) lattice Yang-Mills theory, which is based on the squares of the chromoelectric and chromomagnetic field strength components. Our flux tube results for hybrid static potential quantum numbers $Σ_g^-$, $Σ_u^+$, $Σ_u^-$, $Π_g$, $Π_u$, $Δ_g$, $Δ_u$ are significantly different compared to the flux tube of the ordinary static potential.
The static longitudinal and transverse gluon propagators in the Landau gauge are studied in $2+1$ lattice QCD with nonzero isospin chemical potential $μ_I$. Parameterization of the momentum dependence of the propagators is provided for all values of the chemical potential under study. We find that the longitudinal propagator is infrared suppressed at nonzero $μ_I$ with suppression increasing with increasing $μ_I$. It is found, respectively, that the electric screening mass is increasing with increasing $μ_I$. Additionally, we analyze the difference between two propagators as a function of the …
We study the structure of the hybrid static potential flux tube in the $Π_u$ sector in SU(2) lattice Yang-Mills theory. To this end, we compute the squares of the chromoelectric and chromomagnetic field strengths in the presence of a static quark-antiquark pair. We show clear evidence that the gluon distribution is significantly different compared to that of the ordinary static potential with quantum numbers $Σ_g^+$.
We explore a novel approach to compute the force between a static quark-antiquark pair with the gradient flow algorithm on the lattice. The approach is based on inserting a chromoelectric field in a Wilson loop. The renormalization issues, associated with the finite size of the chromoelectric field on the lattice, can be solved with the use of gradient flow. We compare numerical results for the flowed static potential to our previous measurement of the same observable without a gradient flow.
We measure the spatial distribution of all components of the color fields surrounding a static quark antiquark pair in QCD with (2+1) HISQ flavors. We isolate the nonperturbative component of the longitudinal chromoelectric color field responsible for the linear term in the confining potential.
We extend a previous numerical study of SU(3) Yang-Mills theory in which we measured the spatial distribution of all components of the color fields surrounding a static quark-antiquark pair for a wide range of quark-antiquark separations, and provided evidence that the simulated gauge invariant chromoelectric field can be separated into a Coulomb-like 'perturbative' field and a 'non-perturbative' field, identified as the confining part of the SU(3) flux tube field. In this paper we hypothesize that the fluctuating color fields not measured in our simulations do not contribute to the string ten…
We compute chromoelectric and chromomagnetic flux densities for hybrid static potentials in SU(2) and SU(3) lattice gauge theory. In addition to the ordinary static potential with quantum numbers $Λ_η^ε= Σ_g^+$, we present numerical results for seven hybrid static potentials corresponding to $Λ_η^{(ε)} = Σ_u^+, Σ_g^-, Σ_u^-, Π_g, Π_u, Δ_g, Δ_u$, where the flux densities of five of them are studied for the first time in this work. We observe hybrid static potential flux tubes, which are significantly different from that of the ordinary static potential. They are reminiscent of vibrating strings…
We investigate the type of dual superconductivity responsible for quark confinement. For this purpose, we solve the field equations of the $U(1)$ gauge-scalar model to obtain the static vortex solution in the whole range without restricting to the long-distance region. Then we use the resulting magnetic field of the vortex to fit the gauge-invariant chromoelectric field connecting a pair of quark and antiquark which was measured by numerical simulations for $SU(2)$ Yang--Mills theory on a lattice. This result improves the accuracy of the fitted value for the Ginzburg--Landau parameter to recon…
We investigate the type of dual superconductivity responsible for quark confinement. For this purpose, we solve the field equations of the $U(1)$ Abelian--Higgs model to obtain the static vortex solution in the whole range without restricting to the long-distance region. Then we use the resulting magnetic field of the vortex to fit the gauge-invariant chromoelectric field connecting a pair of quark and antiquark which was measured by numerical simulations for $SU(2)$ and $SU(3)$ Yang--Mills theories on a lattice. This result improves the accuracy of the fitted value for the Ginzburg--Landau pa…
The dual superconductivity is a promising mechanism of quark confinement. In the preceding works, we have given a non-Abelian dual superconductivity picture for quark confinement, and demonstrated the numerical evidences on the lattice. In this talk, we focus on the the confinement and deconfinement phase transition at finite temperature in view of the dual superconductivity. By using our new formulation of lattice Yang-Mills theory and numerical simulations on the lattice, we extract the dominant mode for confinement by decomposing the Yang-Mills field, and we investigate the Polyakov loop av…
We explore a novel approach to compute the force between a static quark and a static antiquark with lattice gauge theory directly. The approach is based on expectation values of Wilson loops or Polyakov loops with chromoelectric field insertions. We discuss theoretical and technical aspects in detail, in particular, how to compensate large discretization errors with a multiplicative renormalization factor and the evaluation using a multilevel algorithm. We also compare numerical results for the static force to corresponding results obtained in the traditional way, i.e., by computing first the …
