Eur. Phys. J. C (2008) 55: 85-93
https://doi.org/10.1140/epjc/s10052-008-0565-y

Regular Article - Theoretical Physics

Renormalized Wick expansion for a modified PQCD

¹ Group of Theoretical Physics, Instituto de Cibernética, Matemática y Física, Calle E, No. 309, Vedado, La Habana, Cuba
² The Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, 34014, Trieste, Italy

^* e-mail: cabo@icmf.inf.cu

Received: 1 September 2007
Published online: 11 March 2008

Abstract

The renormalization scheme for the Wick expansion of a modified version of the perturbative QCD introduced in previous works is discussed. Massless QCD is considered by implementing the usual multiplicative scaling of the gluon and quark wave functions and vertices. However, also massive quark and gluon counterterms are allowed in this massless theory since the condensates are expected to generate masses. A natural set of expansion parameters of the physical quantities is introduced: the coupling itself and the two masses m_q and m_g associated to quarks and gluons, respectively. This procedure allows one to implement a dimensional transmutation effect through these new mass scales. A general expression for the new generating functional in terms of the mass parameters m_q and m_g is obtained in terms of integrals over arbitrary but constant gluon or quark fields in each case. Further, the one loop potential is evaluated in more detail in the case when only the quark condensate is retained. This lowest order result again indicates the dynamical generation of quark condensates in the vacuum.