Glueball mass from quantized knot solitons and gauge-invariant gluon mass

Abstract

We propose an approach which enables one to obtain simultaneously the glueball mass and the gluon mass in the gauge-invariant way to shed new light on the mass gap problem in Yang-Mills theory. First, we point out that the Faddeev (Skyrme--Faddeev-Niemi) model can be induced through the gauge-invariant vacuum condensate of mass dimension two from SU(2) Yang-Mills theory. Second, we obtain the glueball mass spectrum by performing the collective coordinate quantization of the topological knot soliton in the Faddeev model. Third, we demonstrate that a relationship between the glueball mass and the gluon mass is obtained, since the gauge-invariant gluon mass is also induced from the relevant vacuum condensate. Finally, we determine physical values of two parameters in the Faddeev model and give an estimate of the relevant vacuum condensation in Yang-Mills theory. Our results indicate that the Faddeev model can play the role of a low-energy effective theory of the quantum SU(2) Yang-Mills theory.

17 pages, 2 figures, 3 tables; a version accepted for publication in J. Phys. A: Math. Gen.; Sect. 2 and sect. 5 (old sect. 4) are modified. Sect. 4, Tables 1 and Table 3 are added

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• Glueball scattering cross section in lattice SU(2) Yang-Mills theory
• Glueball phenomenology and the relativistic flux tube model
• Classically Isospinning Hopf Solitons
• Gravity assisted solution of the mass gap problem for pure Yang-Mills fields
• Hopfion canonical quantization
• Veneziano amplitudes, spin chains and Abelian reduction of QCD
• Collective coordinate quantization and spin statistics of the solitons in the $\mathbb{C}{P}^N$ Skyrme-Faddeev model
• Black magic session of concordance: Regge mass spectrum from Casson's invariant
• Composite operator and condensate in the $SU(N)$ Yang-Mills theory with $U(N-1)$ stability group
• Veneziano Amplitudes, Spin Chains and String Models
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