1996/09/30 by Jean-Loı̈c Kneur, J. -L. Kneur · 1 citation
Physics and Astronomy · #High-Energy Particle Collisions Research #Particle physics theoretical and experimental studies #Quantum Chromodynamics and Particle Interactions #hep-ph
paper · pdf · doi:10.1103/physrevd.57.2785
published as Phys.Rev. D57 (1998) 2785-2805 · 40 pages, LaTex, 2 PS figures. Additions in section 2.2 to better explain the relation between the current mass and the dynamical mass ansatz. Minor misprints corrected. Version to appear in Phys. Rev. D
arxiv created 1997/11/12 · openalex publication_date 1998/03/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We investigate in some detail a ``variational mass'' expansion approach, generalized from a similar construction developed in the Gross-Neveu model, to evaluate the basic order parameters of the dynamical breaking of the SU(2)L\ifmmode×\else\texttimes\fiSU(2)R and SU(3)L\ifmmode×\else\texttimes\fiSU(3)R chiral symmetries in QCD. The method starts with a reorganization of the ordinary perturbation theory with the addition of an arbitrary quark mass m. The new perturbative series can be summed to all orders thanks to renormalization group properties, with specific boundary conditions, and advocated analytic continuation in m properties. In the approximation where the explicit breakdown of the chiral symmetries due to small current quark masses is neglected, we derive Ans"atze for the dynamical contribution to the ``constituent'' masses Mq of the u,d,s quarks, the pion decay constant F_\ensuremathπ, and the quark condensate 〈qq〉 in terms of the basic QCD scale MS. Those Ans"atze are then optimized, in a sense to be specified, and also explicit symmetry breaking mass terms can be consistently introduced in the framework. The values of F_\ensuremathπ and Mq obtained are roughly in agreement with what is expected from other nonperturbative methods. In contrast we obtain quite a small value of |〈qq〉| within our approach. The possible interpretation of the latter results is briefly discussed.