Gauge bosons at zero and finite temperature

Abstract

Gauge theories of the Yang-Mills type are the single most important building block of the standard model of particle physics and beyond. They are an integral part of the strong and weak interactions, and in their Abelian version of electromagnetism. Since Yang-Mills theories are gauge theories their elementary particles, the gauge bosons, cannot be described without fixing a gauge. Therefore, to obtain their properties a quantized and gauge-fixed setting is necessary.Beyond perturbation theory, gauge-fixing in non-Abelian gauge theories is obstructed by the Gribov-Singer ambiguity, which requires the introduction of non-local constraints. The construction and implementation of a method-independent gauge-fixing prescription to resolve this ambiguity is the single most important first step to describe gauge bosons beyond perturbation theory. Proposals for such a procedure, generalizing the perturbative Landau gauge, are described here. Their implementation are discussed for two example methods, lattice gauge theory and the quantum equations of motion.After gauge-fixing, it is possible to study gauge bosons in detail. The most direct access is provided by their correlation functions. The corresponding two-and three-point correlation functions are presented at all energy scales. These give access to the properties of the gauge bosons, like their absence from the asymptotic physical state space, particle-like properties at high energies, and the running coupling. Furthermore, auxiliary degrees of freedom are introduced during gauge-fixing, and their properties are discussed as well. These results are presented for two, three, and four dimensions, and for various gauge algebras.Finally, the modifications of the properties of gauge bosons at finite temperature are presented. Evidence is provided that these reflect the phase structure of Yang-Mills theory. However, it is found that the phase transition is not deconfining the gauge bosons, although the bulk thermodynamical behavior is of a Stefan-Boltzmann type. The resolution of this apparent contradiction is also presented. In addition, this resolution provides an explicit and constructive solution to the Linde problem.Thus, the technical and conceptual framework presented here can be taken as a basis how to determine correlation functions in Yang-Mills theory, therefore opening up the avenue to investigate theories of direct practical relevance. The status of this effort will be briefly described, alongside with connections to other approaches to Yang-Mills theory beyond perturbation theory.

Exciting flavored bound states

“…Incidentally, this approximation bears similarity with common phenomenological Ansätze to the BSA for D mesons [76][77][78][79][80] and this is exactly what the values in Table III represent: masses and decay constants obtained with a model based on the lowest-order approximation for which the eigenvalues and BSA are real. The mass difference, ∆m [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30] MeV, between the D and D s mesons is smaller than experimentally observed, i.e. ∆m ∼ 100 MeV.…”

Baryons as relativistic three-quark bound states

“…Gauge fixing beyond perturbation theory is a very delicate (but highly interesting) issue which is reviewed e.g. in [149,150,196,197]. We note here only that, fortunately, it turns out that the associated 'Gribov copies' [198] are only relevant for momenta below ∼ 100 MeV [199,200], so their impact upon the calculation of observable quantities is in practice very small compared to other sources of errors, see e.g.…”

“…An approach that strengthens the evidence for confinement being related to the behaviour of Green's function in the extreme infrared only is based on the study of the gluon's quantum equation of motion and how its saturation in the infrared by physical or unphysical degrees of freedom distinguishes between the Coulomb, the Higgs and the confining phase of a gauge theory [148]. This investigation also further elucidates the role of the BRST symmetry of the gaugefixed theory for several types of confinement scenarios, see also the reviews [149,150] and references therein. Other related central questions are the one about the nature of the confining field configurations, the relation of confinement to dynamical chiral symmetry breaking and the axial anomaly, etc., see Refs.…”

Gribov-Zwanziger action in SU(2) maximally Abelian gauge withU(1)3Landau gauge

“…There are also accurate lattice studies recently which report the infrared behavior of the gluon propagator highly depends on the dimensionality [5,[8][9][10][11][12]. In both four and three dimensions, the gluon propagator would be finite at zero momentum [8,9], which seems to be contradict to the Gribov and Zwanziger scenario mentioned above.…”