Operator Product Expansion with analytic QCD in tau decay physics

TL;DR

This paper employs an analytic QCD model with a well-behaved coupling to analyze tau decay data, extracting gluon and higher-dimension condensates consistent with experimental results and avoiding unphysical singularities.

Contribution

It introduces a model of analytic QCD with a coupling free of unphysical singularities, compatible with OPE, and applies it to tau decay data for precise condensate extraction.

Findings

Gluon condensate <(alpha_s/pi)G^2> = 0.0055 +- 0.0047 GeV^4

D=6 condensate <O6(V+A)> = (-0.5 +- 1.1) 10^{-3} GeV^6

Good agreement with experimental Borel transform results

Abstract

We apply a recently constructed model of analytic QCD in the Operator Product Expansion (OPE) analysis of the tau lepton decay data in the V+A channel. The model has the running coupling A(Q^2) with no unphysical singularities, i.e., it is analytic. It differs from the corresponding perturbative QCD coupling a(Q^2) at high squared momenta |Q^2| by terms ~ 1/(Q^2)^5, hence it does not contradict the ITEP OPE philosophy and can be consistently applied with OPE up to terms of dimension D=8. In evaluations for the Adler function we use a Pade-related renormalization-scale-independent resummation, applicable in any analytic QCD model. Applying the Borel sum rules in the Q^2 plane along rays of the complex Borel scale and comparing with ALEPH data of 1998, we obtain the gluon condensate value <(alpha_s/pi)G^2> = 0.0055 +- 0.0047 GeV^4. Consideration of the D=6 term gives us the result <O6(V+A)> = (-0.5 +- 1.1) 10^{-3} GeV^6, not incompatible with nonnegative values. The real Borel transform gives us then, for the central values of the two condensates, a good agreement with the experimental results in the entire considered interval of the Borel scales M^2. In perturbative QCD in MSbar scheme we deduce similar result for the gluon condensate, 0.0059 +- 0.0049 GeV^4, but the value of D=6 condensate is negative, <O6(V+A)> = (-1.8 +- 0.9) 10^{-3} GeV^6, and the resulting real Borel transform for the central values is close to the lower bound of the experimental band.