Stephen R. Cotanch, Ignacio J. General, Ping Wang, Felipe J. Llanes-Estrada
The Coulomb gauge model, involving an effective QCD Hamiltonian in the Coulomb gauge, is applied to scalar hadrons. Mass predictions are presented for both conventional q-qbar meson and q-qbar-q-qbar tetra-quark states. Mixing matrix elements between these states were also computed and diagonalized to provide a reasonable description of the scalar spectrum below 2 GeV.
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The Coulomb-hadron interference effects are examined at small and large $t$. The methods for the definition of spin-dependent parts of hadron scattering amplitude are presented. The additional contributions to analyzing power $A_N$ and the double spin correlation parameter $A_{NN}$ owing to the electromagnetic-hadron interference are determined in the diffraction dip domain of high-energy elastic hadron scattering.
The analysing power $A_N$ is examined in the range of the Coulomb-hadron interferenceon on the basis of the experimental data from p_L = 6 GeV/c up to 200 GeV/c taking account of a phenomenological analysis at p_L = 6 GeV/c and a dynamic high-energy spin model. The results are compared with the new RHIC data at p_L = 100 GeV/c. The new experimental data obtained at RHIC indicate the small contributions of the hadrons spin-flip amplitude.
We study the interplay of hadronic and Coulomb interactions for $pp$ scattering at LHC energies on the basis of the previous determination of the real part of the amplitude [{\it V.V. Anisovich, V.A. Nikonov, J. Nyiri}, Int. J. Mod. Phys. A{\bf 30}, 1550188 (2015)]. The interference of hadron and Coulomb interactions is discussed in terms of the $K$-matrix function technique. Supposing the black disk mode for the asymptotic interaction of hadrons, we calculate interference effects for the energies right up to $\sqrt{s}= 10^6$ TeV. It turns out that the real part of the amplitude is concentrate…
Comparative analysis of the interplay of hadron and Coulomb interactions in $pp^\pm$ scattering amplitudes is performed in a broad energy interval, $\sqrt{s}=1-10^6$ TeV, for two extreme cases: for the asymptotic interactions of hadrons in black disk and resonant disk modes. The interactions are discussed in terms of the $K$-matrix function technique. In the asymptotic regime the real part of the hadronic amplitude is concentrated in both cases on the boundary of the disks in the impact parameter space but the LHC energy region is not asymptotic for the resonant disk mode that lead to a specif…
On the basis of requirements of unitarity and analyticity we analyze the real and imaginary parts of the $pp^\pm$ scattering amplitudes at recent ultrahigh energies, 1-100 TeV. The predictions for the region $\sqrt s > 100$ TeV and ${\bf q}^2<0.4$ GeV$^2$ are given supposing the black disk asymptotic regime. It turns out that the real part of the amplitude is concentrated in the impact parameter space at the border of the black disk. The interplay of hadron and Coulomb interactions is discussed in terms of the $K$-matrix function. The $pp$ diffractive scattering cross section at 7 TeV is calcu…
We discuss progress in understanding the light and heavy quark excited hadron spectrum from Coulomb gauge QCD. For light quark systems we highlight the insensitivity to spontaneous chiral symmetry breaking, which predicts Wigner parity-degeneracy in the highly excited hadron spectrum and allows the quark mass momentum dependence to be experimentally probed. For heavy quark meson decays we invoke the Franck-Condon principle, a consequence of small velocity changes for heavy quarks, to extract qualitative, but model independent, structure insight from the momentum distribution of the decay produ…
The electromagnetic (e.m.) current conservation and renormalizability of QCD are used to calculate the amplitude of energetic hadron(photon) diffraction into several jets with large relative transverse momenta off the nucleon(nucleus) Coulomb field. Numerical estimates of the ratio of e.m. and strong amplitudes show that within the kinematic range where the leading twist approximation for the strong amplitude is applicable, the e.m. contribution can be neglected. In pA scattering at LHC and in the fragmentation of a photon into two jets in ultraperipheral AA collisions in the black limit (whic…
This brief note is devoted to reconcile the conclusions from a recent analysis of the IR solutions for the ghost propagator Dyson-Schwinger equations in Coulomb gauge with previous studies in Landau gauge.
In the framework of Coulomb Gauge QCD we explore dynamical breaking of chiral symmetry and screening of the confinement potential at finite density. The screened potential is applied in study of charmonium dissociation.
The Coulomb gauge Hamiltonian model is used to calculate masses for selected J^{PC} states consisting of exotic combinations of quarks and gluons: ggg glueballs (oddballs), q bar{q} g hybrid mesons and q bar{q} q bar{q} tetraquark systems. An odderon Regge trajectory is computed for the J^{--} glueballs with intercept much smaller than the pomeron, explaining its nonobservation. The lowest 1^{-+} hybrid meson mass is found to be just above 2.2 GeV while the lightest tetraquark state mass with these exotic quantum numbers is predicted around 1.4 GeV consistent with the observed pi(1400).
We study the abelian Higgs model out-of-equilibrium in two different approaches, a gauge invariant formulation, proposed by Boyanovsky et al. \cite{Boyanovsky:1996dc} and in the Coulomb gauge. We show that both approaches become equivalent in a consistent one loop approximation. Furthermore, we carry out a proper renormalization for the model in order to prepare the equations for a numerical implementation. The additional degrees of freedom, which arise in gauge theories, influence the behavior of the system dramatically. A comparison with results in the 't Hooft-Feynman background gauge found…
Using the non-relativisitc reduction of Coulomb gauge QCD we compute spectrum of the low mass hybrid mesons containing a heavy quark-antiquark pair. The gluon degrees of freedom are treated in the mean field approximation calibrated to the gluelump spectrum. We discuss the role of the non-abelian nature of the QCD Coulomb interaction in the ordering of the spin-parity levels.
We compute the energy spectrum of low-lying gluonic excitations in the presence of static quark-antiquark sources using Coulomb gauge and the quasi-particle representation. Within the valence sector of the Fock space we reproduce both, the overall normalization and the ordering of the spin-parity multiplets. We discus how the interactions induced by the non-abelian Coulomb kernel are central in to fine structure of the spectrum.
We consider the effects of the Faddeev-Popov determinant in the Coulomb gauge on the confinement properties of the QCD vacuum. We show that the the determinant is needed to regularize the otherwise divergent functional integrals near the Gribov horizon but still enables large field configurations to generate IR enhanced running coupling. The physical gluon propagator is found to be strongly suppressed in the IR consistent with expectations from lattice gauge calculations.
I demonstrate how confinement in Coulomb-gauge QCD makes quark-quark states of the color anti-triplet (diquarks) move out of the physical spectrum. Mesons as color singlet quark-antiquark states, on the other hand have finite masses and for highly excited states in the meson spectra effective restoration of chiral symmetry can be observed.
We investigate the infrared critical exponents of Coulomb gauge Yang-Mills theory in the limit of very high temperature. This allows us to focus on one scale (the spatial momentum) since all but the lowest Matsubara frequency decouple from the deep infrared. From the first-order Dyson-Schwinger equations in a bare-vertex truncation we obtain infrared exponents which correspond to confining or overconfining (yet mathematically well-defined) solutions. For three spatial dimensions the exponents are close to what is expected for a linearly rising color-Coulomb potential.
We compute the energy spectrum of gluelumps defined as gluonic excitations bound to a localized, static octet source. We are able to reproduce the nontrivial ordering of the spin-parity levels and show how this is related to the non-abelian part of the Coulomb interaction between color charges.
We calculate the ghost two-point function in Coulomb gauge QCD with a simple model vacuum gluon wavefunction using Monte Carlo integration. This approach extends the previous analytic studies of the ghost propagator with this ansatz, where a ladder-rainbow expansion was unavoidable for calculating the path integral over gluon field configurations. The new approach allows us to study the possible critical behavior of the coupling constant, as well as the Coulomb potential derived from the ghost dressing function. We demonstrate that IR enhancement of the ghost correlator or Coulomb form factor …
Calculations of observables in quantum chromodynamics can be performed using a method in which all of the integrations, including integrations over virtual loop momenta, are performed numerically. We use the flexibility inherent in this method in order to perform next-to-leading order calculations for event shape variables in electron-positron annihilation in Coulomb gauge. The use of Coulomb gauge provides the potential to go beyond a purely order alpha_s^2 calculation by including, for instance, renormalon or parton showering effects. We expect that the approximations needed to include such …
A model of mesons which is based on the QCD Hamiltonian in Coulomb gauge is presented. The model relies on a novel quasiparticle basis to improve the reliability of the Fock space expansion. It is also relativistic, yields chiral pions, and is tightly constrained by QCD (quark masses are the only parameters). Applications to hidden flavor mesons yield results which are comparable to phenomenological constituent quark models while revealing the limitations of such models.
The $S$-matrix pinch technique is used to derive an effective gluon self-energy to one-loop order, when the theory is quantized in the Coulomb gauge (CG) and in the temporal axial gauge (TAG). When the pinch contributions are added, the gluon self-energies calculated in CG and TAG turn out to be identical and coincide with the result previously obtained with covariant gauges. The issue of gauge independence of several quantities in hot QCD is discussed from the pinch technique point of view. It is also pointed out that the spurious singularities which appear in TAG calculations cancel out once…
We compare the use of the Coulomb gauge in finite temperature QED with a recently proposed prescription for covariant gauges, in which only the transverse photon degrees of freedom are thermalized. Using the Landau rule as a guide, we clarify the relation between the retarded electron self-energy and the elements of the self-energy matrix in the real-time formulation of . The general results are illustrated by means of the one-loop expressions for the electron self-energy in a QED plasma.
Quark confinement and the genesis of the constituent quark model are examined in nonperturbative QCD in Coulomb gauge. We employ a self-consistent method to construct a quasiparticle basis and to determine the quasiparticle interaction. The results agree remarkably well with lattice computations. They also illustrate the mechanism by which confinement and constituent quarks emerge, provide support for the Gribov-Zwanziger confinement scenario, clarify several perplexing issues in the constituent quark model, and permit the construction of an improved model of low energy QCD.
In the present paper we discuss various aspects of the 't Hooft model for two-dimensional QCD in the limit of infinite number of colours in the Coulomb gauge. The properties of mesonic excitations are addressed, with special attention paid to the pionic one. The twofold role of the pion is discussed: being a genuine quark-antiquark state it is also a Goldstone boson of two-dimensional QCD. In particular, it is demonstrated explicitly how the soft-pion theorems are satisfied. It is pointed out that the Coulomb-gauge choice seems to be indispensable in studies of hadronic observables with the pi…
A structured mixed phase consisting of quark and hadron phases is numerically studied with the Coulomb screening effect and the surface effect. We carefully introduced the Coulomb potential, so that a geometrical structure becomes mechanically unstable when the surface tension is large. Charge densities are largely rearranged by the screening effect, and thereby the equation of state shows the similar behavior to that given by the Maxwell construction. Therefore, although bulk calculations with the Gibbs conditions show that the mixed phase may exist in a wide density region, we can see it is …
With relation to the RHIC spin program we research the polarization effects in elastic proton-proton scattering at small momentum transfer and in the diffraction dip region. The calculations take into account the Coulomb-hadron interference effects including the additional Coulomb-hadron phase. In particular we show the impact of the form of the hadron potential at large distances on the behavior of the hadron spin-flip amplitude at small angles. The $t$-dependence of the spin-flip amplitude of high energy hadron elastic scattering is analyzed under different assumptions on the hadron interact…
Femtoscopy correlation functions and hadron-hadron scattering amplitudes in presence of Coulomb potential
本研究将库仑效应纳入费米子关联函数，提出近似修正方法，无需数值求解薛定谔方程即可精确提取强子散射振幅，并与ALICE实验数据吻合。
We study the long-range behavior of the heavy quark potential in Coulomb gauge using a quenched SU(3) lattice gauge simulation with partial-length Polyakov line correlators. We show that the Coulomb heavy quark potential associated with the instantaneous part of gluon propagators in Coulomb gauge, presents a linearly rising behavior at large distances, and the resulting Coulomb string tension is greater than the Wilson loop string tension, which can be explained by Zwanziger's inequality. The linearly rising behavior of the Coulomb heavy quark potential persists even in the deconfinement phase…
Coulomb gauge quantum chromodynamics within the first order functional formalism is considered. The quark contributions to the Dyson-Schwinger equations are derived and one-loop perturbative results for the two-point functions are presented.
Recent results obtained within the Hamiltonian approach to continuum Yang-Mills theory in Coulomb gauge are reviewed.
We propose a new method for the Coulomb wave function correction including the momentum resolution for charged hadron pairs and apply it to the precise data on $π^+π^-$ correlations obtained in $p + \mbox{Ta}$ reaction at 70 GeV/c. It is found that interaction regions of this reaction (assuming Gaussian source function) are $5.6 \pm 3.0$ and $4.4 \pm 2.6$ fm for the thicknesses of the target $8$ and $1.4$ microns, respectively. The physical picture of the source size obtained in this way is discussed.
Compositeness of near-threshold exotic hadrons in systems with Coulomb and short-range interactions
本文通过非相对论有效场论，研究库仑加短程相互作用系统中近阈值s波态的复合性，发现弱库仑时保留短程低能普适性导致复合态主导，强库仑时该普适性消失。
The Yang-Mills Schrödinger equation is variationally solved in Coulomb gauge for the vacuum sector using a trial wave functional, which is strongly peaked at the Gribov horizon. We find the absence of gluons in the infrared and also a confining quark potential.
We study renormalization of Coulomb-gauge QCD within the Lagrangian second-order formalism. We derive a Ward identity and the Zinn-Justin equation, and, with the help of the latter, we give a proof of algebraic renormalizability of the theory. Through diagrammatic analyses, we show that, in the strict Coulomb gauge, g^2D^{00} is invariant under renormalization. (D^{00} is the time-time component of the gluon propagator.)
We discuss the essential role of the low-lying eigenmodes of the Faddeev-Popov (FP) ghost operator on the confining color-Coulomb potential using SU(3) quenched lattice simulations in the Coulomb gauge. The color-Coulomb potential is expressed as a spectral sum of the FP ghost operator and has been explored by partially summing the FP eigenmodes. We take into account the Gribov copy effects that have a great impact on the FP eigenvalues and the color-Coulomb potential. We observe that the lowest eigenvalue vanishes in the thermodynamic limit much faster than that in the Landau gauge. The color…
Using SU(3) lattice QCD, we investigate role of spatial gluons for hadron masses in the Coulomb gauge, considering the relation between QCD and the quark model. From the Coulomb-gauge configurations at the quenched level on a $16^3 \times 32$ lattice at $β$ = 6.0, we consider the $\vec{A} = 0$ projection, where all the spatial gluon fields are set to zero. In this projection, the inter-quark potential is unchanged. We investigate light hadron masses and find that nucleon and delta baryon masses are almost degenerate. This result suggests that the N-$Δ$ mass difference arises from the color-mag…
Force potential exerting between two classical static sources of pure non-abelian gauge theory in the Coulomb gauge is reconsidered at a periodic/twisted box of size $L^3$. Its perturbative behavior is examined by the short-distance expansion as well as by the derivative expansion. The latter expansion to one-loop order confirms the well-known change in the effective coupling constant at the Coulomb part as well as the Uehling potential while the former is given by the convolution of two Coulomb Green functions being non-singular at $\bm{x}=\bm{y}$. The effect of the twist comes in through its…
We study the static gluon and quark propagator of the Hamiltonian approach to Quantum Chromodynamics in Coulomb gauge in one-loop Rayleigh--Schrödinger perturbation theory. We show that the results agree with the equal-time limit of the four-dimensional propagators evaluated in the functional integral (Lagrangian) approach.
In Coulomb gauge QCD in the Lagrangian formalism, energy divergences arise in individual diagrams. We give a proof on cancellation of these divergences to all orders of perturbation theory without obstructing the algebraic renormalizability of the theory.
The Slavnov-Taylor identities of Coulomb gauge Yang-Mills theory are derived from the (standard, second order) functional formalism. It is shown how these identities form closed sets from which one can in principle fully determine the Green's functions involving the temporal component of the gauge field without approximation, given appropriate input.
We give the results for all the one-loop propagators, including finite parts, in the Coulomb gauge. In finite parts we find new non-rational functions in addition to the single logarithms of the Feynman gauge. Of course, the two gauges must agree for any gauge invariant function. We revise the manuscript hep-th/0311118v2 and Eur.Phys.J.C37, 307-313(2004) in accordance with the notation and correct Feynman rules for the Coulomb gauge in Minkowski space found in [16]. The high-energy behaviour of the proper two-point functions is added in Appendix C.
The infrared behaviour of gluon and ghost propagators, ghost-gluon vertex and three-gluon vertex is investigated for both the covariant Landau and the non-covariant Coulomb gauge. Assuming infrared ghost dominance, we find a unique infrared exponent in the d=4 Landau gauge, while in the d=3+1 Coulomb gauge we find two different infrared exponents. We also show that a finite dressing of the ghost-gluon vertex has no influence on the infrared exponents. Finally, we determine the infrared behaviour of the three-gluon vertex analytically and calculate it numerically at the symmetric point in the C…
We study the static quantum potential for a gauge theory which includes the mixing between the familiar photon $U(1)_{QED}$ and a second massive gauge field living in the so-called hidden-sector $U(1)_h$. Our discussion is carried out using the gauge-invariant but path-dependent variables formalism, which is alternative to the Wilson loop approach. Our results show that the static potential is a Yukawa correction to the usual static Coulomb potential. Interestingly, when this calculation is done inside a superconducting box, the Coulombic piece disappears leading to a screening phase.
A generalized gauge fixing which interpolates among the Landau, Coulomb and maximal Abelian gauges is constructed.
Electromagnetic field produced in high-energy heavy-ion collisions contains much useful information, because the field can be directly related to the motion of the matter in the whole stage of the reaction. One can divide the total electromagnetic field into three parts, i.e., the contributions from the incident nuclei, non-participating nucleons and charged fluid, the latter consisting of strongly interacting hadrons or quarks. Parametrizing the space-time evolution of the charged fluid based on hydrodynamic model, we study the development of the electromagnetic field which accompanies the hi…
I will review results obtained recently within the Hamilton approach to QCD in Coulomb gauge. The focus will be on finite-temperature Yang--Mills theory and chiral symmetry breaking in QCD.
It is argued that within the continuum functional formalism, there is no need to supply a further (spatially independent) gauge constraint to complete the Coulomb gauge of Yang-Mills theory. It is shown explicitly that a natural completion of the gauge-fixing leads to a contradiction with the perturbative renormalizability of the theory.
In the Coulomb gauge of nonabelian gauge theories there are in general, in individual graphs, 'energy-divergences' on integrating over the loop energy variable for fixed loop momentum. These divergences are avoided in the Hamiltonian, phase-space formulation. But, even in this formulation, energy-divergences re-appear at 2-loop order. We show in an example how these cancel between graphs as a consequence of Ward identities.
We discuss the Coulomb propagator in the formalism developed recently in which we construct the Coulomb gauge path-integral by correlating it with the well-defined Lorentz gauge path-integrals through a finite field-dependent BRS transformation. We discover several features of the Coulomb gauge from it. We find that the singular Coulomb gauge HAS to be treated as the gauge parameter lambda --> 0 limit. We further find that the propagator so obtained has good high energy behavior (k_0^{-2}) for lambda and epsilon nonzero. We further find that the behavior of the propagator so obtained is sensit…
We calculate the eigenvalue distribution of the Faddeev-Popov operator in Coulomb gauge QCD using quenched SU(3) lattice simulation. In the confinement phase, the density of the low-lying eigenvalues increases with lattice volume, and the confinement criterion is satisfied. Moreover, even in the deconfinement phase, the behavior of the FP eigenvalue density is qualitatively the same as in the confinement phase. This is consistent with the fact that the color-Coulomb potential is not screened in the deconfined phase.
The functional approach to Coulomb gauge Yang-Mills theory is considered within the standard, second order, formalism. The Dyson-Schwinger equations and Slavnov-Taylor identities concerning the two-point functions are derived explicitly and one-loop perturbative results are presented.
If the color Coulomb potential is confining, then the Coulomb field energy of an isolated color charge is infinite on an infinite lattice, even if the usual UV divergence is lattice regulated. A simple criterion for Coulomb confinement is that the expectation value of timelike link variables vanishes in Coulomb gauge, but it is unclear how this criterion is related to the spectrum of the corresponding Faddeev-Popov operator, which can be used to formulate a quite different criterion for Coulomb confinement. The purpose of this article is to connect the two seemingly different Coulomb confineme…
The Weyl-gauge ($A_0^a=0)$ QCD Hamiltonian is unitarily transformed to a representation in which it is expressed entirely in terms of gauge-invariant quark and gluon fields. In a subspace of gauge-invariant states we have constructed that implement the non-Abelian Gauss's law, this unitarily transformed Weyl-gauge Hamiltonian can be further transformed and, under appropriate circumstances, can be identified with the QCD Hamiltonian in the Coulomb gauge. We demonstrate an isomorphism that materially facilitates the application of this Hamiltonian to a variety of physical processes, including th…
The Yang-Mills Schrödinger equation is solved in Coulomb gauge for the vacuum by the variational principle using an ansatz for the wave functional, which is strongly peaked at the Gribov horizon. A coupled set of Schwinger-Dyson equations for the gluon and ghost propagators in the Yang-Mills vacuum as well as for the curvature of gauge orbit space is derived and solved in one-loop approximation. We find an infrared suppressed gluon propagator, an infrared singular ghost propagator and a almost linearly rising confinement potential.
Perturbative Coulomb gauge Yang-Mills theory within the first order formalism is considered. Using a differential equation technique and dimensional regularization, analytic results for both the ultraviolet divergent and finite parts of the two-point functions at one-loop order are derived. It is shown how the non-ultraviolet divergent parts of the results are finite at spacelike momenta with kinematical singularities on the light-cone and subsequent branch cuts extending into the timelike region.
The topological susceptibility is calculated within the Hamiltonian approach to Yang-Mills theory in Coulomb gauge, using the vacuum wave functional previously determined by a variational solution of the Yang-Mills Schroedinger equation. The numerical result agrees qualitatively with the predictions of lattice simulations.
We investigate the equal-time (static) quark propagator in Coulomb gauge within the Hamiltonian approach to QCD in $d=2$ spatial dimensions. Although the underlying Clifford algebra is very different from its counterpart in $d=3$, the gap equation for the dynamical mass function has the same form. The additional vector kernel which was introduced in $d=3$ to cancel the linear divergence of the gap equation and to preserve multiplicative renormalizability of the quark propagator makes the gap equation free of divergences also in $d=2$.
The chirally symmetric Overlap quark propagator is explored in Coulomb gauge. This gauge is well suited for studying the relation between confinement and chiral symmetry breaking, since confinement can be attributed to the infrared divergent Lorentz-vector dressing function. Using quenched gauge field configurations on a $20^4$ lattice, the quark propagator dressing functions are evaluated, the dynamical quark mass is extracted and the chiral limit of these quantities is discussed. By removing the low-lying modes of the Dirac operator, chiral symmetry is artificially restored. Its effect on th…
The Bethe-Salpeter equation and leptonic decay constants for pseudoscalar and vector quark-antiquark mesons with arbitrary quark masses are studied in Coulomb gauge, under a leading order truncation. As input, we use a pure linear rising potential, supplemented by a contact term arising from the conservation of total color charge. It is shown how the equations can be written in terms of manifestly finite functions, despite the infrared singular interaction. The resulting equations are solved numerically. Both the pattern of dynamical chiral symmetry breaking and the leading order heavy quark l…
We report results on the Coulomb-gauge ghost propagator and the color-Coulomb potential computed in two lattice gauge-field ensembles: (1) configurations derived from our recently proposed Yang-Mills vacuum wave functional in 2+1 dimensions, and (2) lattices generated by Monte Carlo simulations of the three-dimensional Euclidean SU(2) lattice gauge theory with the Wilson action. We observe remarkable agreement between the ghost propagators in both ensembles, but some differences in the potentials. Those originate from rare configurations with very small values of the lowest eigenvalue of the C…
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