Taste non-Goldstone pion decay constants in staggered chiral perturbation theory

Introducing the most general expression for the corresponding axial-vector vertex, the flavor nonsinglet, chiral axial-vector Ward-Takahashi (WT) identity is investigated in the framework of dynamical chiral symmetry breaking (DCSB). A chiral perturbation theory at the quark level (CHPTq) is proposed in terms of a Taylor series expansions in powers of the external momenta q (momentum of a massless pion) for the direct solution of the above identity at small momentum transfer q (momentum of a massless pion). Correct treatment of initial dynamical singularities at q=0 within the CHPTq approach in accordance with the Ball and Chiu procedure makes it possible to decompose the axial-vector vertex into pole and regular parts in a self-consistent way. The Bethe-Salpeter (BS) bound-state amplitude of a massless pion restored from the identity is shown to coincide with the residue at pole q2=0, which is proportional to the pion decay constant. We find exact solution for the regular piece of the corresponding vertex at zero momentum transfer in terms of the quark propagator dynamical variables alone. This solution automatically satisfies asymptotic freedom (it approaches the point-like vertex at infinity). Applying the proposed CHPTq approach to the matrix element of the axial-vector current determining the pion decay constant, we find “exact” (within the BS bound-state amplitude, restored fom the axial WT identity), nonperturbative expression for the pion decay constant in the current algebra (CA) representation. We show explicitly that the well-known formula of Pagels-Stokar-Cornwall for the pion decay constant is a particular case of the CHPTq approach. We find also new, nonperturbative formulae for the pion decay constant in the Jackiw-Johnson (JJ) representation as well. They now have full physical sense within the CHPTq approach. Renormalization of these expressions as well as their application in technicolor theories with slowly running couplings are briefly discussed. We also propose to distinguish between the scales of DCSB at the quark and hadronic levels (the scale of effective field theory) as well as advocate a simple relation between them based on naive counting arguments.

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Masses and decay constants of pions and kaons in mixed-action staggered chiral perturbation theory

Physical Review D ◽

10.1103/physrevd.96.034522 ◽

2017 ◽

Vol 96 (3) ◽

Cited By ~ 1

Author(s):

Jon A. Bailey ◽

Jongjeong Kim ◽

Weonjong Lee ◽

Hyung-Jin Kim ◽

Boram Yoon

Keyword(s):

Perturbation Theory ◽

Chiral Perturbation Theory ◽

Chiral Perturbation ◽

Decay Constants ◽

Mixed Action

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CURRENT PHYSICS RESULTS FROM STAGGERED CHIRAL PERTURBATION THEORY

Modern Physics Letters A ◽

10.1142/s0217732306022468 ◽

2006 ◽

Vol 21 (39) ◽

pp. 2913-2930 ◽

Cited By ~ 1

Author(s):

C. AUBIN

Keyword(s):

Perturbation Theory ◽

Chiral Perturbation Theory ◽

Quark Mass ◽

Continuum Limit ◽

Decay Constant ◽

Pion Mass ◽

Meson Decay ◽

Mass Limit ◽

Chiral Perturbation ◽

Decay Constants

We review several results that have been obtained using lattice QCD with the staggered quark formulation. Our focus is on the quantities that have been calculated numerically with low statistical errors and have been extrapolated to the physical quark mass limit and continuum limit using staggered chiral perturbation theory. We limit our discussion to a brief introduction to staggered quarks, and applications of staggered chiral perturbation theory to the pion mass, decay constant, and heavy–light meson decay constants.

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Nonequilibrium chiral perturbation theory and pion decay functions

Physics Letters B ◽

10.1016/s0370-2693(99)00067-2 ◽

1999 ◽

Vol 449 (3-4) ◽

pp. 288-298 ◽

Cited By ~ 1

Author(s):

A. Gómez Nicola ◽

V. Galán-González

Keyword(s):

Perturbation Theory ◽

Chiral Perturbation Theory ◽

Pion Decay ◽

Chiral Perturbation

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