Chiral Symmetry Breaking in QCD: A Variational Approach

Abstract

We develop a "variational mass" expansion approach, recently introduced in the Gross--Neveu model, to evaluate some of the order parameters of chiral symmetry breakdown in QCD. The method relies on a reorganization of the usual perturbation theory with the addition of an "arbitrary quark mass $m$, whose non-perturbative behaviour is inferred partly from renormalization group properties, and from analytic continuation in $m$ properties. The resulting ansatz can be optimized, and in the chiral limit $m\to 0$ we estimate the dynamical contribution to the "constituent" masses of the light quarks $M_{u,d,s}$; the pion decay constant $F_{\pi }$ and the quark condensate $<\bar{q}q>$.

10 pages, no figures, LaTex

References in corpus (10)

• A Precise Determination of the Running Coupling in the SU(3) Yang-Mills Theory
• $O(\alpha {\alpha }_s^2)$ correction to the electroweak $\rho$ parameter
• Nambu Jona-Lasinio Like Models and the Low Energy Effective Action of QCD
• Corrections of order ${\cal O}(G_F M_t^2 \as^2)$ to the $\rho$ parameter
• Comparison of the Pade Approximation Method to Perturbative QCD Calculations
• Convergence of Scaled Delta Expansion: Anharmonic Oscillator
• The QCD vacuum
• Convergence of the Optimized Delta Expansion for the Connected Vacuum Amplitude: Zero Dimensions
• Low--Energy Behavior of Two--Point Functions of Quark Currents
• Convergence of the Optimized Delta Expansion for the Connected Vacuum Amplitude -- Anharmonic Oscillator

Cited by in corpus (21)

• Virtual Photons in Low Energy pi-pi Scattering
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• Thermodynamics and Phase Structure of the Two-Flavor Nambu--Jona-Lasinio Model Beyond Large-N_c
• α_S from $F_{\pi }$ and Renormalization Group Optimized Perturbation
• The chiral condensate from renormalization group optimized perturbation
• Low-Energy QCD and Ultraviolet Renormalons
• Lambda^{QCD}_{MS} from Renormalization Group Optimized Perturbation
• Renormalization Group Improved Optimized Perturbation Theory: Revisiting the Mass Gap of the O(2N) Gross-Neveu Model
• A brief overview of hard-thermal-loop perturbation theory
• Renormalization Group Optimized Perturbation Theory at Finite Temperatures
• Variational Quark Mass Expansion and the Order Parameters of Chiral Symmetry Breaking
• Light quarks masses and condensates in QCD
• (Borel) convergence of the variationally improved mass expansion and the O(N) Gross-Neveu model mass gap
• Interplay Between Approximation Theory and Renormalization Group
• Low-energy photon-photon fusion into three pions in Generalized Chiral Perturbation Theory
• Mean field theory for collective motion of quantum meson fields
• Chiral Condensate and Spectral Density at full five-loop and partial six-loop orders of Renormalization Group Optimized Perturbation
• The Hadronic Gas Chiral Phase Transition within Generalized Chiral Perturbation Theory
• Theoretical and phenomenological aspects of G$\chi$PT
• Dynamical Chiral Symmetry Breaking from Variationally Improved Perturbative Expansion
• Variational Wave Functionals in Quantum Field Theory