Renormalization of the Mass Gap

Gogokhia, V.

doi:10.1007/s10773-009-0150-7

Cited by 4 publications

(16 citation statements)

References 51 publications

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“…[46] we have shown that the so-called INP gluon propagator is, by construction, purely transversal in a gauge invariant way.…”

Section: Confining Effective Chargementioning

confidence: 81%

“…It is for this reason that it is not uniquely separated from the PT gluon propagator, which effective charge that is always regular at origin. We distinguish between the INP and the PT effective charges not only by the presence of the mass gap, but by the character of the IR singularities as well [45,46]. So only after the replacement (13) the INP effective charge is uniquely and exactly separated from its PT counterpart, and the obtained expression for the bag constant (7) becomes now free of all the types of the PT contributions ("contaminations").…”

Section: Confining Effective Chargementioning

confidence: 99%

“…Unfortunately, one cannot perform analytically (i.e., exactly) the summation over the Matsubara frequencies in this integral, using the AF expression for α AF (ω 2 , ω 2 n ) [36,46]. At this stage the PT part (33) remains undetermined and will be numerically evaluated elsewhere.…”

Section: The Gluon Pressure At Non-zero Temperaturesmentioning

confidence: 99%

“…Both effective masses are due to the mass gap ∆ 2 , which is responsible for the largescale structure of the QCD ground state. It is dynamically generated by the nonlinear interaction of massless gluon modes [43,45,46]. The first massive excitations can be interpreted as the glueballs, since m ef f is comparable to the masses of scalar glueballs (though it is lighter than the pseudoscalar ones) [61].…”

Section: The Mass Gap and A "Fuzzy Bag" Termmentioning

confidence: 99%

See 3 more Smart Citations

The non-perturbative analytical equation of state for the gluon matter: I

Gogokhia¹,

Vasúth²

2010

J. Phys. G: Nucl. Part. Phys.

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HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés. Abstract. The effective potential approach for composite operators is generalized to non-zero temperatures in order to derive the equation of state for pure SU (3) Yang-Mills fields. In the absence of external sources, this is nothing but the vacuum energy density. The key element of this derivation is the introduction of a temperature dependence into the expression for the bag constant. The non-perturbative analytical equation of state for gluon matter does not depend on the coupling constant, but instead introduces a dependence on the mass gap. This is responsible for the largescale structure of the QCD ground state. The important thermodynamic quantities, such as the pressure, energy and entropy densities, etc., have been calculated. We show explicitly that the pressure may vary smoothly around T c = 266.5 MeV, whereas all other thermodynamic quantities undergo drastic changes at this point. The proposed analytical approach makes it possible to control for the first time the thermodynamics of gluon matter at low temperatures, below T c . We reproduce the properties of the socalled "fuzzy bag"-type models through the presence of the mass gap in our equation of state. An analytic calculation of the gluon condensate is obtained as a function of temperature.

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“…[46] we have shown that the so-called INP gluon propagator is, by construction, purely transversal in a gauge invariant way.…”

Section: Confining Effective Chargementioning

confidence: 81%

Section: Confining Effective Chargementioning

confidence: 99%

Section: The Gluon Pressure At Non-zero Temperaturesmentioning

confidence: 99%

Section: The Mass Gap and A "Fuzzy Bag" Termmentioning

confidence: 99%

See 2 more Smart Citations

The non-perturbative analytical equation of state for the gluon matter: I

Gogokhia¹,

Vasúth²

2010

J. Phys. G: Nucl. Part. Phys.

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“…In [46] we have shown that the so-called INP gluon propagator is, by construction, purely transversal in a gauge invariant way. It exactly converges to the gluon propagator, whose effective charge is Eq.…”

Section: Confining Effective Chargementioning

confidence: 99%

The Non-perturbative Analytical Equation of State for the Gluon Matter I

2013

The Mass Gap and Its Applications

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Abstract. The effective potential approach for composite operators is generalized to non-zero temperatures in order to derive the equation of state for pure SU (3) Yang-Mills fields. In the absence of external sources, this is nothing but the vacuum energy density. The key element of this derivation is the introduction of a temperature dependence into the expression for the bag constant. The non-perturbative analytical equation of state for gluon matter does not depend on the coupling constant, but instead introduces a dependence on the mass gap. This is responsible for the largescale structure of the QCD ground state. The important thermodynamic quantities, such as the pressure, energy and entropy densities, etc., have been calculated. We show explicitly that the pressure may vary continuously around T c = 266.5 MeV, whereas all other thermodynamic quantities undergo drastic changes at this point. The proposed analytical approach makes it possible to control for the first time the thermodynamics of gluon matter at low temperatures, below T c . We reproduce the properties of the socalled "fuzzy bag"-type models through the presence of the mass gap in our equation of state. An analytic calculation of the gluon condensate is obtained as a function of temperature.

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SU(3) Color Gauge Invariance and the Jaffe–Witten Mass Gap in QCD

Gogokhia¹

2014

J Math Sci

Self Cite

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The physical meaning of a mass gap introduced by Jaffe and Witten is to be responsible for the large-scale (low-energy/momentum), i.e., the non-perturbative structure of the true QCD vacuum. In order to make the existence of a mass gap perfectly clear it is defined as the difference between the regularized full gluon self-energy and its subtracted (also regularized) counterpart. The mass gap is mainly generated by the nonlinear interaction of massless gluon modes. A self-consistent violation of SU (3) color gauge invariance/symmetry is discussed in order to realize a mass gap in QCD. For this purpose, we propose not to impose the transversality condition on the full gluon self-energy, while restoring the transversality of the full gluon propagator relevant for the non-perturbative QCD at the final stage. At the same time, the Slavnov-Taylor identity for the full gluon propagator is always preserved. All this allows one to establish the general structure of the full gluon propagator in the presence of a mass gap. In this case, two independent types of formal solutions for the full gluon propagator have been established. The nonlinear iteration solution at which the gluons remain massless is explicitly present. The existence of the solution with an effective gluon mass is also demonstrated.

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Renormalization of the Mass Gap

Cited by 4 publications

References 51 publications

The non-perturbative analytical equation of state for the gluon matter: I

The non-perturbative analytical equation of state for the gluon matter: I

The Non-perturbative Analytical Equation of State for the Gluon Matter I

SU(3) Color Gauge Invariance and the Jaffe–Witten Mass Gap in QCD

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