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Condensates in quantum chromodynamics

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Abstract

The paper presents a short review of our knowledge today on vacuum condensates in quantum chromodynamics (QCD). The condensates are defined as vacuum averages of the operators which arise due to nonperturbative effects. The important role of condensates in determining physical properties of hadrons and of their low-energy interactions in QCD is underlined. The special value of the quark condensate, connected to the existence of baryon masses, is mentioned. Vacuum condensates induced by external fields are discussed. QCD at low energy is checked on the basis of the data on hadronic τ decay. In theoretical analysis, the terms of perturbation theory (PT) up to α 3s are accounted for; in the operator product expansion (OPE), those up to dimension 8. The total probability of the decay τ → hadrons (with zero strangeness) and of the τ-decay structure functions are best described at α s (m 2τ )=0.330±0.025. It is shown that the Borel sum rules for τ-decay structure functions along the rays in the q 2-complex plane are in agreement with experiment, having an accuracy of ∼2% at the values of the Borel parameter |M 2|>0.8 GeV2. The magnitudes of dimension 6 and 8 condensates were found, and the limitations on gluon condensates were obtained. The sum rules for the charmed-quark vector-current polarization operator were analyzed in three loops (i.e., in order α 2s ). The value of the charmed-quark mass (in an \(\overline {MS} \) regularization scheme) was found to be \(\bar m_c (\bar m_c^2 ) = 1.275 \pm 0.015\) GeV, and the value of gluon condensate was estimated as 〈0|(α s/π)G 2|0〉=0.009±0.007 GeV4. The general conclusion is that the QCD described by PT + OPE is in good agreement with experiment at Q 2≳1 GeV2.

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  1. Institute of Theoretical and Experimental Physics, Bol'shaya Cheremushkinskaya ul. 25, Moscow, 117218, Russia

    B. L. Ioffe

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From Yadernaya Fizika, Vol. 66, No. 1, 2003, pp. 32–46.

Original English Text Copyright © 2003 by Ioffe.

This article was submitted by the author in English.

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Ioffe, B.L. Condensates in quantum chromodynamics. Phys. Atom. Nuclei 66, 30–43 (2003). https://doi.org/10.1134/1.1540654

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