scholarly journals CHIRAL PERTURBATION THEORY WITH NUCLEONS

1992 ◽  
Vol 01 (03) ◽  
pp. 561-601 ◽  
Author(s):  
Ulf-G. Meißner
Keyword(s):  
Perturbation Theory ◽  
Chiral Symmetry ◽  
Chiral Perturbation Theory ◽  
Chiral Limit ◽  
Nuclear Forces ◽  
Chiral Perturbation ◽  
Chiral Structure ◽  
Quark Masses ◽  
Alternative Approach ◽  
Working Out

I review the constraints posed on the interactions of pions, nucleons and photons by the spontaneously broken chiral symmetry of QCD. The framework to perform these calculations, chiral perturbation theory, is briefly discussed in the meson sector. The method is a simultaneous expansion of the Greens functions in powers of external momenta and quark masses around the massless case, the chiral limit. To perform this expansion, use is made of a phenomenological Lagrangian which encodes the Ward–identities and pertinent symmetries of QCD. The concept of chiral power counting is introduced. The main part of the lectures consists in describing how to include baryons (nucleons) and how the chiral structure is modified by the fact that the nucleon mass in the chiral limit does not vanish. Particular emphasis is put on working out applications to show the strengths and limitations of the method. Some processes which are discussed are threshold photopion production, low-energy Compton scattering off nucleons, πN scattering and the σ–term. The implications of the broken chiral symmetry on the nuclear forces are briefly described. An alternative approach, in which the baryons are treated as very heavy fields, is touched upon.

scholarly journals The Leutwyler–Smilga relation on the lattice

2019 ◽  
Vol 35 (01) ◽  
pp. 1950346 ◽  
Author(s):  
Gernot Münster ◽  
Raimar Wulkenhaar
Keyword(s):  
Perturbation Theory ◽  
Quantum Chromodynamics ◽  
Lattice Qcd ◽  
Chiral Perturbation Theory ◽  
Effective Action ◽  
Lattice Spacing ◽  
Chiral Perturbation ◽  
Quark Masses

According to the Leutwyler–Smilga relation, in Quantum Chromodynamics (QCD), the topological susceptibility vanishes linearly with the quark masses. Calculations of the topological susceptibility in the context of lattice QCD, extrapolated to zero quark masses, show a remnant nonzero value as a lattice artefact. Employing the Atiyah–Singer theorem in the framework of Symanzik’s effective action and chiral perturbation theory, we show the validity of the Leutwyler–Smilga relation in lattice QCD with lattice artefacts of order a2 in the lattice spacing a.

scholarly journals Hidden Local Symmetry and Effective Chiral Theory for Vector and Axial-vector Mesons

2007 ◽  
Vol 22 (07n10) ◽  
pp. 683-698 ◽  
Author(s):  
B. A. Li ◽  
Y. L. Wu
Keyword(s):  
Perturbation Theory ◽  
Chiral Symmetry ◽  
Chiral Perturbation Theory ◽  
Covariant Derivative ◽  
Local Symmetry ◽  
Low Energy ◽  
Chiral Perturbation ◽  
Chiral Theory ◽  
Basic Parameters ◽  
Chiral Lagrangian

We present the effective chiral Lagrangian of mesons (peusodoscalars, vectors and axial-vectors) obtained in the chiral limit by using two approaches. The first approach is based on symmetries: the explicit global chiral symmetry and hidden local chiral symmetry. In this approach, it is noticed that there are in general fourteen interacting terms up to the dimension-four of covariant derivative for meson fields rather than the usual eleven interacting terms given in literature from hidden local symmetry approach. Of particular, the additional terms are found to be very important for understanding the vector meson dominance and providing consistent predictions on the decay rates of a1 → γπ and a1 → ρπ as well as for resulting a consistent effective chiral Lagrangian with chiral perturbation theory. The second approach is motivated from the chiral symmetry of chiral quarks and the bound state solutions of nonperturbative QCD at low energy and large Nc. The second approach is more fundamental in the sense that it is based on the QCD Lagrangian of quarks and only relies on two basic parameters in addition to the ones in the standard model. As a consequence, it allows us to extract, in terms of only two basic parameters, all the fourteen parameters in the more general effective Lagrangian constructed from symmetries in the first approach. It is surprising to note that except the necessity of three additional new interacting terms introduced in this paper, the resulting values of the coupling constants for other three interacting terms at the dimension-four are also quite different from the ones given in the literature. It is likely that the structures of the effective chiral Lagrangian for the dimension-four given in the literatures by using hidden local symmetry are incomplete and consequently the resulting coulpings are not reliable. It is shown that the more general effective chiral Lagrangian given in the present paper shall provide a more consistent prediction for all the low energy phenomenology of ρ - a1 system and result in a more consistent description on the low energy behavior of light flavor mesons. Its fourteen parameters up to the dimension-four of covariant derivative may be uniquely determined from the effective chiral theory based on the second approach, which is consistent with the chiral perturbation theory.

THE $K_L^0\to \pi ^0 \gamma \gamma$ DECAY IN CHIRAL PERTURBATION THEORY BASED ON THE EXTENDED NAMBU-JONA-LASINIO MODEL

1992 ◽  
Vol 07 (21) ◽  
pp. 5115-5129 ◽  
Author(s):  
ANDREI N. IVANOV
Keyword(s):  
Perturbation Theory ◽  
Chiral Perturbation Theory ◽  
Chiral Limit ◽  
Decay Amplitude ◽  
Low Energy ◽  
Chiral Perturbation ◽  
Photon Exchange ◽  
Two Photon ◽  
Energy Approximation ◽  
Gamma Decay

The [Formula: see text] decay is analyzed within chiral perturbation theory based on the extended Nambu-Jona-Lasinio model, which is used as a low energy approximation of QCD. The two-photon spectrum of the [Formula: see text] decay and the value of the probability [Formula: see text] are obtained in good agreement with experimental data. It is shown that the CP-conserving two-photon exchange contribution to the [Formula: see text] decay mplitude is negligibly small compared to that of the CP-violating one-photon exchange. Also presented is the derivation of the low-energy theorem for the [Formula: see text] decay amplitude in the chiral limit.

scholarly journals Light- and strange-quark mass dependence of the ρ(770) meson revisited

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
R. Molina ◽  
J. Ruiz de Elvira
Keyword(s):  
Perturbation Theory ◽  
Chiral Perturbation Theory ◽  
Quark Mass ◽  
Strange Quark ◽  
Global Analysis ◽  
Mass Dependence ◽  
Chiral Perturbation ◽  
Quark Masses ◽  
Strange Quark Mass ◽  
Quark Mass Dependence

Abstract Recent lattice data on ππ-scattering phase shifts in the vector-isovector channel, pseudoscalar meson masses and decay constants for strange-quark masses smaller or equal to the physical value allow us to study the strangeness dependence of these observables for the first time. We perform a global analysis on two kind of lattice trajectories depending on whether the sum of quark masses or the strange-quark mass is kept fixed to the physical point. The quark mass dependence of these observables is extracted from unitarized coupled-channel one-loop Chiral Perturbation Theory. This analysis guides new predictions on the ρ(770) meson properties over trajectories where the strange-quark mass is lighter than the physical mass, as well as on the SU(3) symmetric line. As a result, the light- and strange-quark mass dependence of the ρ(770) meson parameters are discussed and precise values of the Low Energy Constants present in unitarized one-loop Chiral Perturbation Theory are given. Finally, the current discrepancy between two- and three-flavor lattice results for the ρ(770) meson is studied.

scholarly journals PHYSICAL RESULTS FROM PARTIALLY QUENCHED SIMULATIONS

2001 ◽  
Vol 16 (supp01c) ◽  
pp. 1219-1224 ◽  
Author(s):  
STEPHEN R. SHARPE ◽  
NOAM SHORESH
Keyword(s):  
Perturbation Theory ◽  
Chiral Perturbation Theory ◽  
Chiral Perturbation ◽  
Quark Masses ◽  
Physical Quantities

We describe how one can use chiral perturbation theory to obtain results for physical quantities, such as quark masses, using partially quenched simulations.

scholarly journals Nucleon-mass difference in chiral perturbation theory and nuclear forces

2004 ◽  
Vol 70 (4) ◽  
Author(s):  
J. L. Friar ◽  
U. van Kolck ◽  
M. C. M. Rentmeester ◽  
R. G. E. Timmermans
Keyword(s):  
Perturbation Theory ◽  
Chiral Perturbation Theory ◽  
Mass Difference ◽  
Nucleon Mass ◽  
Nuclear Forces ◽  
Chiral Perturbation
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