The magnetic mass of transverse gluon, the B-meson weak decay vertex and the triality symmetry of octonion

TL;DR

This paper explores the magnetic mass of transverse gluons, the B-meson weak decay vertex, and the triality symmetry of octonions, proposing a novel connection between these concepts within quantum chromodynamics.

Contribution

It introduces a new approach using octonion triality symmetry to calculate gluon magnetic mass and analyze corrections in B-meson decay processes.

Findings

Magnetic mass of gluons is approximately equal to the critical temperature at specific quark masses.

Derived a possible time-like magnetic gluon mass from self-dual gluon exchange.

Evaluated corrections to B-meson decay vertices due to self-dual gluon exchange.

Abstract

With an assumption that in the Yang-Mills Lagrangian, a left-handed fermion and a right-handed fermion both expressed as quaternion make an octonion which possesses the triality symmetry, I calculate the magnetic mass of the transverse self-dual gluon from three loop diagram, in which a heavy quark pair is created and two self-dual gluons are interchanged. The magnetic mass of the transverse gluon depends on the mass of the pair created quarks, and in the case of charmed quark pair creation, the magnetic mass $m_{mag}$ becomes approximately equal to $T_c$ at $T=T_c\sim 1.14\Lambda_{\bar{MS}}\sim 260$MeV. A possible time-like magnetic gluon mass from two self-dual gluon exchange is derived, and corrections in the B-meson weak decay vertices from the two self-dual gluon exchange are also evaluated.