scholarly journals Taylor's Series and Dispersion Relation Analyses of the Vector Pion Form Factor and their Comparison with Perturbative and Non Perturbative Calculations

2015 ◽  
Vol 25 (1) ◽  
pp. 21
Author(s):  
Truong Nguyen Tran
Keyword(s):  
Experimental Data ◽  
Perturbation Theory ◽  
Form Factor ◽  
Dispersion Relation ◽  
Momentum Transfer ◽  
Chiral Perturbation Theory ◽  
Pion Form Factor ◽  
P Wave ◽  
Chiral Perturbation ◽  
Taylor’S Series

The first three coefficients of the Taylor's series expansion of the vevtor pion form factor as a function of the momentum transfer are evaluated using the experimental data on the pion form factor and the P-wave \(\pi\pi\) phase shifts. The real part of the form factor as a function of energy is also calculated by dispersion relation. Comparisons there results with Chiral Perturbation Theory and unitarized models are given.

Resonant and non-resonant contributions of B → K∗(p1,𝜖1){Kπ,ππ,KK} decay modes

2019 ◽  
Vol 34 (06) ◽  
pp. 1950043
Author(s):  
Mahboobeh Sayahi
Keyword(s):  
Experimental Data ◽  
Perturbation Theory ◽  
Chiral Perturbation Theory ◽  
Branching Ratio ◽  
Heavy Meson ◽  
Chiral Perturbation ◽  
Decay Modes ◽  
Qcd Factorization ◽  
Three Body ◽  
Good Agreement

In this paper, the non-leptonic three-body decays [Formula: see text], [Formula: see text], [Formula: see text] are studied by introducing two-meson distribution amplitude for the [Formula: see text], [Formula: see text] and [Formula: see text] pairs in naive and QCD factorization (QCDF) approaches, such that the analysis is simplified into quasi-two body decays. By considering that the vector meson is being ejected in factorization, the resonant and non-resonant contributions are analyzed by using intermediate mesons in Breit–Wigner resonance formalism and the heavy meson chiral perturbation theory (HMChPT), respectively. The calculated values of the resonant and non-resonant branching ratio of [Formula: see text], [Formula: see text] and [Formula: see text] decay modes are compared with the experimental data. For [Formula: see text] and [Formula: see text], the non-resonant contributions are about 70–80% of experimental data, for which the total results by considering resonant contributions are in good agreement with the experiment.

Convergence issues in baryon chiral perturbation theory for the reaction π + N → 2π + N

2007 ◽  
Vol 85 (6) ◽  
pp. 663-669
Author(s):  
N Mobed ◽  
J Zhang ◽  
D Singh
Keyword(s):  
Experimental Data ◽  
Perturbation Theory ◽  
Chiral Perturbation Theory ◽  
Essential Role ◽  
Heavy Baryon ◽  
Transverse Polarization ◽  
Proton Target ◽  
Chiral Perturbation ◽  
Target Asymmetry ◽  
Chiral Order

We study the reaction π + N → 2π + N within the framework of heavy-baryon chiral perturbation theory of chiral order three. We find that contributions from amplitudes of chiral order three are large and play an essential role in reproducing the experimental data. In addition, we evaluate a polarization observable (target asymmetry) for the transverse polarization of the proton target and find that the asymmetry is generally small for the reaction under consideration. PACS Nos.: 25.80.Hp, 13.75.Gx, 11.30.Rd, 11.10.Ef

CHIRAL PERTURBATION THEORY AT THE QUARK LEVEL AND NEW NONPERTURBATIVE FORMULAE FOR THE PION DECAY CONSTANT IN QCD

1994 ◽  
Vol 09 (04) ◽  
pp. 605-634 ◽  
Author(s):  
V. SH. GOGOHIA
Keyword(s):  
Perturbation Theory ◽  
Momentum Transfer ◽  
Chiral Perturbation Theory ◽  
Decay Constant ◽  
Axial Vector ◽  
Bound State ◽  
Pion Decay ◽  
Pion Decay Constant ◽  
Chiral Perturbation ◽  
Quark Level

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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