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High Energy Physics - Theory

arXiv:1605.01841 (hep-th)
[Submitted on 6 May 2016 (v1), last revised 21 Apr 2017 (this version, v3)]

Title:Gluon bound state and asymptotic freedom derived from the Bethe--Salpeter equation

Authors:Hitoshi Fukamachi, Kei-Ichi Kondo, Shogo Nishino, Toru Shinohara
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Abstract: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 in the cases of the standing and running gauge coupling constant. 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 $\beta$ function.
Comments: Introduction has been a bit modified and Section 7 has been completely revised. This is the version accepted for publication in PTEP
Subjects: High Energy Physics - Theory (hep-th); High Energy Physics - Phenomenology (hep-ph)
Report number: CHIBA-EP-218-v3
Cite as: arXiv:1605.01841 [hep-th]
  (or arXiv:1605.01841v3 [hep-th] for this version)
  https://doi.org/10.48550/arXiv.1605.01841
Journal reference: Prog Theor Exp Phys (2017)
Related DOI: https://doi.org/10.1093/ptep/ptx059

Submission history

From: Shogo Nishino [view email]
[v1] Fri, 6 May 2016 07:03:56 UTC (1,661 KB)
[v2] Thu, 29 Dec 2016 12:23:39 UTC (1,764 KB)
[v3] Fri, 21 Apr 2017 04:45:29 UTC (1,510 KB)
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