Spin zero glueballs in the Bethe-Salpeter formalism

Meyers, Joseph; Swanson, Eric S.

doi:10.1103/physrevd.87.036009

Cited by 44 publications

(41 citation statements)

References 31 publications

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“…3 appears to be identical to the corresponding equation used in pure Yang-Mills theories to describe the formation of a glueball out of two gluons (see, e.g., [81,82]). This observation, together with the fact that massless solutions have indeed been found in our numerical treatment of the BSE, may raise the question of whether a massless glueball could also exist in the physical spectrum of the theory.…”

Section: Further Considerationsmentioning

confidence: 80%

“…This observation, together with the fact that massless solutions have indeed been found in our numerical treatment of the BSE, may raise the question of whether a massless glueball could also exist in the physical spectrum of the theory. However, no such state has ever been identified in any of the studies presented in the literature [81][82][83][84].…”

Section: Further Considerationsmentioning

confidence: 99%

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Schwinger mechanism in linear covariant gauges

2017

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In this work we explore the applicability of a special gluon mass generating mechanism in the context of the linear covariant gauges. In particular, the implementation of the Schwinger mechanism in pure Yang-Mills theories hinges crucially on the inclusion of massless bound-state excitations in the fundamental nonperturbative vertices of the theory. The dynamical formation of such excitations is controlled by a homogeneous linear Bethe-Salpeter equation, whose nontrivial solutions have been studied only in the Landau gauge. Here, the form of this integral equation is derived for general values of the gauge-fixing parameter, under a number of simplifying assumptions that reduce the degree of technical complexity. The kernel of this equation consists of fully-dressed gluon propagators, for which recent lattice data are used as input, and of three-gluon vertices dressed by a single form factor, which is modelled by means of certain physically motivated Ansätze. The gauge-dependent terms contributing to this kernel impose considerable restrictions on the infrared behavior of the vertex form factor; specifically, only infrared finite Ansätze are compatible with the existence of nontrivial solutions. When such Ansätze are employed, the numerical study of the integral equation reveals a continuity in the type of solutions as one varies the gauge-fixing parameter, indicating a smooth departure from the Landau gauge. Instead, the logarithmically divergent form factor displaying the characteristic "zero crossing", while perfectly consistent in the Landau gauge, has to undergo a dramatic qualitative transformation away from it, in order to yield acceptable solutions. The possible implications of these results are briefly discussed.

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Section: Further Considerationsmentioning

confidence: 80%

Section: Further Considerationsmentioning

confidence: 99%

Schwinger mechanism in linear covariant gauges

2017

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“…The explicit form of the kernel is given in Appendix A. This BS equation can be compared with that obtained by Meyers and Swanson [14]. Fig.…”

Section: The Homogeneous Bs Equation For the (Amputated) Bs Amplitudementioning

confidence: 96%

“…In obtaining such a solution, especially, we pay special attention to the aspect how our results for the bound state is consistent with the ultraviolet asymptotic freedom [13]. This is a feature that has not been discussed in the preceding works [14,15]. In their works, the precise determinations of the glueball spectrum have been the main purpose of investigations.…”

Section: Introductionmentioning

confidence: 95%

Gluon bound state and asymptotic freedom derived from the Bethe–Salpeter equation

Fukamachi¹,

Kondo

Nishino

et al. 2017

Progress of Theoretical and Experimental Physics

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In this paper we study the two-body bound states for gluons and ghosts in a massive Yang-Mills theory which is obtained by generalizing the ordinary massless Yang-Mills theory in a manifestly Lorentz covariant gauge. First, we give a systematic derivation of the coupled Bethe-Salpeter equations for gluons and ghosts by using the Cornwall-Jackiw-Tomboulis effective action of the composite operators within the framework of the path integral quantization. Then, we obtain the numerical solutions for the Bethe-Salpeter amplitude representing the simultaneous bound states of gluons and ghosts by solving the homogeneous Bethe-Salpeter equation in the ladder approximation. We study how the inclusion of ghosts affects the two-gluon bound states. Moreover, we show explicitly that the approximate solutions obtained for the gluon-gluon amplitude are consistent with the ultraviolet asymptotic freedom signaled by the negative β function.

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“…Complementary ongoing projects within the DSE framework concern the glueball spectrum [123,124] and the question whether states with exotic quantum numbers can be accounted for with relativistic quark-antiquark systems (in contrast to the non-relativistic quark model) [125].…”

Section: Develop the Dyson-schwinger Formalismmentioning

confidence: 99%

Issues and Opportunities in Exotic Hadrons

et al. 2016

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The last few years have been witness to a proliferation of new results concerning heavy exotic hadrons. Experimentally, many new signals have been discovered that could be pointing towards the existence of tetraquarks, pentaquarks, and other exotic configurations of quarks and gluons. Theoretically, advances in lattice field theory techniques place us at the cusp of understanding complex coupled-channel phenomena, modelling grows more sophisticated, and effective field theories are being applied to an ever greater range of situations. It is thus an opportune time to evaluate the status of the field. In the following, a series of high priority experimental and theoretical issues concerning heavy exotic hadrons is presented.

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Spin zero glueballs in the Bethe-Salpeter formalism

Cited by 44 publications

References 31 publications

Schwinger mechanism in linear covariant gauges

Schwinger mechanism in linear covariant gauges

Gluon bound state and asymptotic freedom derived from the Bethe–Salpeter equation

Issues and Opportunities in Exotic Hadrons

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