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arXiv · 1605.01841

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

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.

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Hitoshi Fukamachi, Kei-Ichi Kondo, Shogo Nishino, Toru Shinohara. 2016-05-06. Gluon bound state and asymptotic freedom derived from the Bethe--Salpeter equation. https://doi.org/10.1093/ptep%2Fptx059

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