On the decoupling solution for pinch technique gluon propagator
Jun, 2009Citations per year
Abstract: (arXiv)
Within a simple Ansatz for gluon propagator and using perturbatively gauge invariant pinch-technique for Schwinger-Dyson equation, the upper limit on the effective gluon mass is derived. We calculated scheme invariant running coupling, which in order to be well defined, gives the upper limit on the gluon mass. The gluon mass cannot be larger then fraction of the QCD mass scale , it is bounded by maximal the possible value . For larger mass we get singular running coupling with Landau singularity situated bellow threshold , for between and it is located in the timelike regime, for larger , the singularity is gradually moving into the spacelike regime. Corresponding infrared value can be adjusted to settle chiral symmetry breaking when quarks are considered. For larger possible , the corresponding value is and it is non-monotonous in the timelike low . The model we use here is the same as considered in \cite{cornwall2009}, however we have arrived to a completely different conclusion, e.g we argue that there is no lower but upper limit on the gluon mass. The analyticity required by Kallen-Lehmann representation is not achieved for any value of since this is actually the inverse of the coupling and not the coupling itself which satisfies certain form of dispersion relation.- gluon: mass
- upper limit
- gluon: propagator
- coupling constant: energy dependence
- symmetry breaking: chiral
- invariance: gauge
- vertex function
- singularity
- Dyson-Schwinger equation
- quantum chromodynamics
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