Gauge-invariant Gluon Mass Research Articles

Dyon in the SU(2) Yang\u2013Mills theory with a gauge-invariant gluon mass toward quark confinement

In the previous paper, we have shown the existence of magnetic monopoles in the pure SU(2) Yang–Mills theory with a gauge-invariant mass term for the gluon field being introduced. In this paper, we extend our previous construction of magnetic monopoles to obtain dyons with both magnetic and electric charges. In fact, we solve under the static and spherically symmetric ansatz the field equations of the SU(2) “complementary” gauge-scalar model, which is the SU(2) Yang–Mills theory coupled to a single adjoint scalar field whose radial degree of freedom is eliminated. We show that the novel dyon solution can be identified with the gauge field configuration of a dyon with a minimum magnetic charge in the massive Yang–Mills theory. Moreover, we compare the dyon of the massive Yang–Mills theory obtained in this way with the Julia–Zee dyon in the Georgi–Glashow gauge-Higgs scalar model and the dyonic extension of the Wu–Yang magnetic monopole in the pure Yang–Mills theory. Finally, we identify the novel dyon solution found in this paper with a dyon configuration on S^1 times {mathbb {R}}^3 space with nontrivial holonomy and propose to use it to understand the confinement/deconfinement phase transition in the Yang–Mills theory at finite temperature, instead of using the dyons constituting the Kraan–van Baal–Lee–Lu caloron.

Gauge-independent Brout\u2013Englert\u2013Higgs mechanism and Yang\u2013Mills theory with a gauge-invariant gluon mass term

For the Yang–Mills theory coupled to a single scalar field in the fundamental representation of the gauge group, we present a gauge-independent description of the Brout–Englert–Higgs mechanism by which massless gauge bosons acquire their mass. The new description should be compared with the conventional gauge-dependent description relying on the spontaneous gauge symmetry breaking due to a choice of the non-vanishing vacuum expectation value of the scalar field. In this paper we focus our consideration on the fundamental scalar field which extends the previous work done for the Yang–Mills theory with an adjoint scalar field. Moreover, we show that the Yang–Mills theory with a gauge-invariant mass term is obtained from the corresponding gauge-scalar model when the radial degree of freedom (length) of the scalar field is fixed. The result obtained in this paper is regarded as a continuum realization of the Fradkin–Shenker continuity and Osterwalder–Seiler theorem for the complementarity between Higgs regime and Confinement regime which was given in the gauge-invariant framework of the lattice gauge theory. Moreover, we discuss how confinement is investigated through the gauge-independent Brout–Englert–Higgs mechanism by starting with the complementary gauge-scalar model.

Exploring dynamical gluon mass generation in three dimensions

In the d=3 gluon mass problem in pure-glue non-Abelian $SU(N)$ gauge theory we pay particular attention to the observed (in Landau gauge) violation of positivity for the spectral function of the gluon propagator. This causes a large bulge in the propagator at small momentum. Mass is defined through $m^{-2}=\Delta (p=0)$, where $\Delta(p)$ is the scalar function for the gluon propagator in some chosen gauge, it is not a pole mass and is generally gauge-dependent, except in the gauge-invariant Pinch Technique (PT). We truncate the PT equations with a new method called the vertex paradigm that automatically satisfies the QED-like Ward identity relating the 3-gluon PT vertex function with the PT propagator. The mass is determined by a homogeneous Bethe-Salpeter equation involving this vertex and propagator. This gap equation also encapsulates the Bethe-Salpeter equation for the massless scalar excitations, essentially Nambu-Goldstone fields, that necessarily accompany gauge-invariant gluon mass. The problem is to find a good approximate value for $m$ and at the same time explain the bulge, which by itself leads, in the gap equation for the gluon mass, to excessively large values for the mass. Our point is not to give a high-accuracy determination of $m$ but to clarify the way in which the propagator bulge and a fairly accurate estimate of $m$ can co-exist, and we use various approximations that illustrate the underlying mechanisms. The most critical point is to satisfy the Ward identity. In the PT we estimate a gauge-invariant dynamical gluon mass of $m \approx Ng^2/(2.48 \pi)$. We translate these results to the Landau gauge using a background-quantum identity involving a dynamical quantity $\kappa$ such that $m=\kappa m_L$, where $m_L^{-2}\equiv \Delta_L(p=0)$. Given our estimates for $m,\kappa$ the relation is fortuitously well-satisfied for $SU(2)$ lattice data.

Glueball mass from quantized knot solitons and gauge-invariant gluon mass(Fundamental Problems and Applications of Quantum Field Theory-Topological Aspects of Quantum Field Theory-)

Glueball mass from quantized knot solitons and gauge-invariant gluon mass(Fundamental Problems and Applications of Quantum Field Theory-Topological Aspects of Quantum Field Theory-)

Gauge-invariant gluon mass, infrared Abelian dominance, and stability of magnetic vacuum

We give an argument for deriving analytically the infrared “Abelian” dominance in a gauge invariant way for the Wilson loop average in SU(2) Yang– Mills theory. In other words, we propose a possible mechanism for realizing the dynamical Abelian projection in the SU(2) gauge-invariant manner without breaking color symmetry. This supports validity of the dual superconductivity picture for quark confinement. We also discuss the stability of the vacuum with magnetic condensation as a by-product of this result.

Glueball mass from quantized knot solitons and gauge-invariant gluon mass

We propose an approach which enables one to obtain simultaneously the glueball mass and the gluon mass in the gauge-invariant way to shed new light on the mass gap problem in Yang-Mills theory. First, we point out that the Faddeev (Skyrme--Faddeev-Niemi) model can be induced through the gauge-invariant vacuum condensate of mass dimension two from SU(2) Yang-Mills theory. Second, we obtain the glueball mass spectrum by performing the collective coordinate quantization of the topological knot soliton in the Faddeev model. Third, we demonstrate that a relationship between the glueball mass and the gluon mass is obtained, since the gauge-invariant gluon mass is also induced from the relevant vacuum condensate. Finally, we determine physical values of two parameters in the Faddeev model and give an estimate of the relevant vacuum condensation in Yang-Mills theory. Our results indicate that the Faddeev model can play the role of a low-energy effective theory of the quantum SU(2) Yang-Mills theory.

Resummed loop expansion for high temperature QCD

A simple method is proposed to establish on-shell gauge independence in theso far ill-conditioned loop expansion of QCD at high temperature. We perform a partial resummation by choosing an appropriate bare lagrangian with a gauge invariant gluon mass. Taking this mass equal to the plasmon frequency, the plasmon damping constant is explicitly shown to be gauge independent at one loop. The wrong sign of this constant points to the relevance of higher-loop corrections in the remaining redefined perturbation series.