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A path integral formula for quark condensate states in a modified PQCD

  • A. Cabo Montes de OcaEmail author
  • N. G. Cabo-Bizet
  • A. Cabo-Bizet
Regular Article - Theoretical Physics

Abstract

A modified version of PQCD considered in previous works is investigated here in the case of retaining only the quark condensate. The Green function generating functional is expressed in a form in which Dirac’s delta functions are now absent from the free propagators. The new expansion implements the dimensional transmutation effect through a single interaction vertex in addition to the standard ones in massless QCD. The new vertex suggest a way for constructing an alternative to the SM, in which the mass and CKM matrices could be generated by the instability of massless QCD under the production of the top quark and other fermions condensates, in a kind of generalized Nambu–Jona-Lasinio mechanism. The results of a two loop evaluation of the vacuum energy indicate that the quark condensate is dynamically generated. However, the energy as a function of the condensate parameter is again unbounded from below in this approximation. Assuming the existence of a minimum of the vacuum energy at the experimental value of the top quark mass m q =173 GeV, we evaluate the two particle propagator in the quark–anti-quark channel in zero order in the coupling and a ladder approximation in the condensate vertex. Adopting the notion from the former top quark models in which the Higgs field corresponds to the quark condensate, the results suggest that the Higgs particle could be represented by a meson which might appear at energies around twice the top quark mass.

PACS

12.38.Aw 12.38.Bx 12.38.Cy 14.65.Ha 

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Copyright information

© Springer-Verlag / Società Italiana di Fisica 2009

Authors and Affiliations

  • A. Cabo Montes de Oca
    • 1
    • 2
    Email author
  • N. G. Cabo-Bizet
    • 3
    • 4
  • A. Cabo-Bizet
    • 3
  1. 1.Perimeter Institute for Theoretical PhysicsWaterlooCanada
  2. 2.Grupo de Física TeóricaInstituto de Cibernética, Matemática y FísicaLa HabanaCuba
  3. 3.Departamento de FísicaCentro de Aplicaciones Tecnológicas y Desarrollo Nuclear (CEADEN)La HabanaCuba
  4. 4.Institute of PhysicsBonn UniversityBonnGermany

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