Operator product expansion with analytic QCD in τ decay physics

Gorazd Cvetič, Cristián Villavicencio

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We apply a recently constructed model of analytic QCD in the operator product expansion (OPE) analysis of the τ lepton decay data in the V+A channel. The model has the running coupling A1(Q2) with no unphysical singularities, i.e., it is analytic. It differs from the corresponding perturbative QCD coupling a(Q2) at high squared momenta |Q2| by terms (1-Q2)5; hence it does not contradict the OPE philosophy of ITEP School (Institute of Theoretical and Experimental Physics) and can be consistently applied with OPE up to terms of dimension D=8. In evaluations for the Adler function we use a Padé-related renormalization-scale- independent resummation, applicable in any analytic QCD model. Applying the Borel sum rules in the Q2 plane along rays of the complex Borel scale and comparing with ALEPH data of 1998, we obtain the gluon condensate value (αsπ)G2=0.0055±0.0047GeV4. Consideration of the D=6 term gives us the result O6(V+A)=(-0.5±1.1)×10-3GeV6, not incompatible with positive values. The real Borel transform then gives us, for the central values of the two condensates, a good agreement with the experimental results in the entire considered interval of the Borel scales M2. In perturbative QCD in the minimal subtraction scheme we deduce similar results for the gluon condensate, 0.0059±0.0049GeV4, but the value of the D=6 condensate is negative, O6(V+A)=(-1.8±0.9)×10-3GeV6, and the resulting real Borel transform for the central values is close to the lower bound of the experimental band. © 2012 American Physical Society.
Original languageEnglish
JournalPhysical Review D - Particles, Fields, Gravitation and Cosmology
Publication statusPublished - 4 Dec 2012

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