Quark sector of Coulomb gauge Quantum Chromodynamics

Carina Popovici

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Quark sector of Coulomb gauge Quantum Chromodynamics

Carina Popovici

High Energy Physics - Phenomenology · Submitted 3 Jun 2011

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim It is shown that only color singlet of quark-antiquark (meson) and qqq (baryon) states are physically allowed.

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The quark sector of Coulomb gauge quantum chromodynamics is considered within the functional integral approach. The quark contributions to the Dyson-Schwinger equations are derived and one-loop perturbative results for the two-point functions are presented. The problem of confinement is addressed in the heavy quark limit, by rewriting the generating functional of quantum chromodynamics in terms of a heavy quark mass expansion. By restricting to leading order in this expansion and considering only the two-point functions of the Yang-Mills sector, the rainbow-ladder approximation to the gap and Bethe-Salpeter equations is shown to be exact. Analytic nonperturbative solutions to the Bethe-Salpeter equation for quark-antiquark bound states and Faddeev equation for three-quark bound states, in the case of equal quark separations, are presented. The quark-antiquark and three-quark confining potentials are derived and a direct connection between the temporal gluon propagator and the corresponding string tensions is found. It is shown that only color singlet of quark-antiquark (meson) and qqq (baryon) states are physically allowed. Moreover, the four-point Green's functions, in both quark-antiquark and diquark channels, are explicitly derived. It is found that the corresponding poles relate to the bound state energy of the heavy quark systems, and a natural separation between physical and unphysical poles in the Green's functions emerges.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	The quark sector of Coulomb gauge quantum chromodynamics is considered within the functional integral approach.	contribution 0.53	0.75	0.03	asserted 0.93
s1	The quark contributions to the Dyson-Schwinger equations are derived and one-loop perturbative results for the two-point functions are presented.	contribution 0.72	0.94	0.06	asserted 0.99
s2	The problem of confinement is addressed in the heavy quark limit, by rewriting the generating functional of quantum chromodynamics in terms of a heavy quark mass expansion.	contribution 0.52	0.90	0.09	asserted 0.96
s3	By restricting to leading order in this expansion and considering only the two-point functions of the Yang-Mills sector, the rainbow-ladder approximation to the gap and Bethe-Salpeter equations is shown to be exact.	result 0.75	0.88	0.14	asserted 1.00
s4	Analytic nonperturbative solutions to the Bethe-Salpeter equation for quark-antiquark bound states and Faddeev equation for three-quark bound states, in the case of equal quark separations, are presented.	result 0.73	0.92	0.11	asserted 1.00
s5	The quark-antiquark and three-quark confining potentials are derived and a direct connection between the temporal gluon propagator and the corresponding string tensions is found.	result 0.99	0.93	0.24	asserted 1.00
s6	It is shown that only color singlet of quark-antiquark (meson) and qqq (baryon) states are physically allowed.	result 0.94	0.86	0.35	asserted 1.00
s7	Moreover, the four-point Green's functions, in both quark-antiquark and diquark channels, are explicitly derived.	contribution 0.62	0.94	0.06	asserted 1.00
s8	It is found that the corresponding poles relate to the bound state energy of the heavy quark systems, and a natural separation between physical and unphysical poles in the Green's functions emerges.	result 0.94	0.93	0.19	asserted 1.00

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Original abstract

The quark sector of Coulomb gauge quantum chromodynamics is considered within the functional integral approach. The quark contributions to the Dyson-Schwinger equations are derived and one-loop perturbative results for the two-point functions are presented. The problem of confinement is addressed in the heavy quark limit, by rewriting the generating functional of quantum chromodynamics in terms of a heavy quark mass expansion. By restricting to leading order in this expansion and considering only the two-point functions of the Yang-Mills sector, the rainbow-ladder approximation to the gap and Bethe-Salpeter equations is shown to be exact. Analytic nonperturbative solutions to the Bethe-Salpeter equation for quark-antiquark bound states and Faddeev equation for three-quark bound states, in the case of equal quark separations, are presented. The quark-antiquark and three-quark confining potentials are derived and a direct connection between the temporal gluon propagator and the corresponding string tensions is found. It is shown that only color singlet of quark-antiquark (meson) and qqq (baryon) states are physically allowed. Moreover, the four-point Green's functions, in both quark-antiquark and diquark channels, are explicitly derived. It is found that the corresponding poles relate to the bound state energy of the heavy quark systems, and a natural separation between physical and unphysical poles in the Green's functions emerges.

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2 arXiv papers cite this in 2 sentences

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Papers whose main result relates to this one's

Found among the papers closest to this one by title and main claim. Pith's classifier compared each pair's main results and a second model family confirmed the relation; checked against two further families, shown conflicts agreed 118 times in 120 and shown same results 218 times in 239. The quoted sentence is the other paper's main claim.

States the same result 1 paper

Further, it is shown that for the 4-point quark correlation functions, only confined bound states of color-singlet quark-antiquark (meson) and quark-quark (baryon) pairs exist.

Coulomb gauge confinement in the heavy quark limit · 0.98

Papers citing it · 1 sentence without a confident label

Cites it as background 1 paper

For details, see [ref] and references therein.

Spectra of heavy quarkonia in a Bethe-Salpeter-equation approach · Introduction · 0.99

What it cites · 91 sentences without a confident label

Uses the method or tool of 3 papers

The presentation of the first order formalism, together with the reduction to the “physical” degrees of freedom, follows [ref] and is discussed in some detail.

Propagator Dyson-Schwinger Equations of Coulomb Gauge Yang-Mills Theory Within the First Order Formalism · Motivation and main idea · 0.93
To handle this type of divergences, Leibbrandt introduced a modified form of the dimensional regularization, the so-called split dimensional regularization [ref] , in which two complex parameters $$ and $$ are introduced, $d^3q⃗→d^2q⃗ and d q_0→d^2 q_0$ with the limits $→3/2$ and $→1/2$ to be taken after all the integrations have been completed.

Split Dimensional Regularization for the Coulomb Gauge · Motivation and main idea · 0.96
Applying similar reasoning as in Ref. [ref] , we come to the following parametric form of the integral (recall that $x=k_4^2$, $y=k⃗^2$): A_m=(x+y+m^2)^-1-/(4π)^2-(1+) ×∫_0^1 d∫_0^1- d/ (+)^1/2 [/(+) x/(x+y+m^2)+(1-)y+m^2/x+y+m^2] ^-1-.

Perturbation Theory of Coulomb Gauge Yang-Mills Theory Within the First Order Formalism · Heavy quarks · 0.96

Uses data or values from 3 papers

In the above, we have inserted the tree-level spatial quark-gluon vertex, eq:treelevelquarkvertex2, and the tree-level ghost two-point function from Ref. [ref] _c̅c^ad (0)(k)=^adk⃗^2.

Two-Point Functions of Coulomb Gauge Yang-Mills Theory · Perturbative analysis · 1.00
The (spatial and temporal) tree-level gluon propagators needed in this work have been derived in [ref] and are given by: W_A A ij^(0)ab(k)=^ab t_ij(k⃗)/k_0^2-k⃗^2, W_^(0)ab(k)=^ab/k⃗^2

Propagator Dyson-Schwinger Equations of Coulomb Gauge Yang-Mills Theory Within the First Order Formalism · Feynman rules · 0.88
together with the ghost two-point function (previously calculated in [ref] ) _c^ab(k)=-^abk⃗^24/3N_c/(4π)^21/ +finite terms.

Perturbation Theory of Coulomb Gauge Yang-Mills Theory Within the First Order Formalism · Perturbative analysis · 0.99

Compares with 3 papers

This expression is very similar to the one derived in Ref. [ref] for the case.

Slavnov-Taylor identities in Coulomb gauge Yang-Mills theory · Formal derivation · 0.97
By inspecting the relations eq:letransf, containing the quark contribution to the propagator $D_AA$ , and those obtained in Ref. [ref] for the part of the propagator $D_AA$ and the propagator $D_c$, we see that the same result is achieved in Coulomb gauge.

Perturbation Theory of Coulomb Gauge Yang-Mills Theory Within the First Order Formalism · Results in the limit epsilon 0 · 0.99
The relations eq:AsiST are similar to the identities for the part of the theory, derived in [ref] .

Two-Point Functions of Coulomb Gauge Yang-Mills Theory · Results in the limit epsilon 0 · 0.98

Cites as support 7 papers

As already mentioned, because the total color charge of the system is conserved and vanishing [ref] , neither the quark or antiquark can exist as an independent asymptotic physical state.

Resolving temporal Gribov copies in Coulomb gauge Yang-Mills theory · equation for mesons and diquarks · 0.98
Although this gauge does not have so many practical advantages as Landau gauge for example, there are several reasons motivating our choice: in Coulomb gauge there is a natural picture of confinement, Gauss law is naturally built in (such that in principle gauge invariance is fully accounted for) and the total color charge is conserved and vanishing [ref] .

Completing Continuum Coulomb Gauge in the Functional Formalism · First order functional formalism · 0.98
The conversion to the first order (or phase-space) formalism is motivated by the fact that within this formalism the famous Coulomb gauge energy divergence [ref] can be avoided.

Split Dimensional Regularization for the Coulomb Gauge · Motivation and main idea · 0.97

Cites as background 39 papers

All these will not be considered in this work (a complete derivation of the terms appearing in the Coulomb gauge gluon propagators can be found in Ref. [ref] ).] In contrast to covariant gauges, the various gluonic degrees of freedom (temporal and spatial) are being separated into three proper two-point functions, $_$, $_AA$ and $_A$.

Propagator Dyson-Schwinger Equations of Coulomb Gauge Yang-Mills Theory Within the First Order Formalism · Quark contributions to the gluon propagators · 0.92
Currently, the most popular continuum formalism to QCD in Coulomb gauge is the Hamiltonian formalism [ref] .[In Ref. [ref] , the results obtained within the Hamiltonian approach to theory are reviewed.] In this approach, one starts by imposing Weyl gauge $A_0^a(x)=0$, and subsequently, the Coulomb gauge is fixed with the help of the Faddeev-Popov method, whereas the Gauss law is imposed as constraint.

Subcritical solution of the Yang-Mills Schroedinger equation in the Coulomb gauge · Alternative methods · 0.97
Currently, the most popular continuum formalism to QCD in Coulomb gauge is the Hamiltonian formalism [ref] .[In Ref. [ref] , the results obtained within the Hamiltonian approach to theory are reviewed.] In this approach, one starts by imposing Weyl gauge $A_0^a(x)=0$, and subsequently, the Coulomb gauge is fixed with the help of the Faddeev-Popov method, whereas the Gauss law is imposed as constraint.

Coulomb Gauge QCD, Confinement, and the Constituent Representation · Alternative methods · 0.97

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