Mitra, A. N. (2002) Minimum of QCD effective action as test of QCD confinement parameter Arxiv-eprints . pp. 1-12.
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Official URL: http://arxiv.org/pdf/hep-ph/0207258v2.pdf
Abstract
A new approach to the non-perturbative regime of QCD is proposed by introducing a (non-hermitian) field B related to the usual gluon field A by Bμ = (1+σ∂m)Aμ where m goes to zero after differentiation, and σ is a parameter which 'runs' with momentum |(k). An exact treatment yields a structure [1/k2 + 2μ2/k4] for the gluon propagator, where |σ2 = πk4/9μ2s, showing linear confinement in the instantaneous limit. This propagator was recently employed to evaluate some basic condensates and their temperature dependence (in the cosmological context), which were all reproduced for μ = 1GeV (termed the 'confinement scale parameter'), in association with the QCD scale parameter Λqcd = 200MeV [hep-ph/0109278]. This paper seeks to provide a formal basis for the ratio Λqcd/μ by employing the minimality condition for the integrated effective action, up to the 2-loop level, using the Cornwall-Jackiw formalism for composite operators. To that end the mass function m(p), determined via the Schwinger-Dyson equation (as a zero of the functional derivative of Γ w.r.t S'F), acts as a feeder, and the stationarity condition on Γ as function of μ and αs(μ) gives the ratio Λ/μ = 0.246, in fair accord with the value 0.20 given above. Inclusion of a two-loop is crucial for the agreement.
Item Type: | Article |
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Source: | Copyright of this article belongs to Arxiv Publications. |
Keywords: | Confinement Scale; QCD Effective Action; Minimality Condition; B-field |
ID Code: | 90193 |
Deposited On: | 07 May 2012 13:20 |
Last Modified: | 19 May 2016 04:29 |
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