Axial amplitudes for Δ excitation in chiral quark models (original) (raw)
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Pion scattering and electro-production on nucleons in the resonance region in chiral quark models
2011
Pion scattering and electro-production amplitudes have been computed in a coupled-channel framework incorporating quasi-bound quark-model states, based on the Cloudy Bag model. All relevant low-lying nucleon resonances in the P33, P11, and S11 partial waves have been covered, including the Delta(1232), the N*(1440), N*(1535), and N*(1650). Consistent results have been obtained for elastic and inelastic scattering (two-pion, eta-N, and K-Lambda
Pion transitions and models of chiral symmetry
Physical Review D, 1989
We describe a set of pion-decay and scattering amplitudes which are described by only two lowenergy parameters in the effective chiral Lagrangian of QCD. After a phenomenological analysis of the data, we demonstrate how the effective-Lagrangian framework correlates the many predictions of these reactions which have been made in the literature using a variety of models with chiral symmetry. A comparison with the data then also determines which model represents @CD. Not surprisingly, the winner is a form of vector dominance.
Pion amplitudes in a nonchiral world
Annals of Physics, 1970
The popular strong PCAC (i.e., pion pole dominance of all Green's funcitons involving the divergence D of the axial vector current) and good chiral SU(2) x SU(2) symmetry framework has led to many successful predictions. It also, however, leads to some difficulties since, for example, it predicts the approximate vanishing of the Kz form factor ratio 5 = f-if+, of the x0 + yy decay amplitude F, (except in models witi anamolous PCAC), and of the 7-+ 3a decay amplitude A,. We therefore propose an alternate framework based on weak PCAC (i.e., pion pole dominance of physical matrix elements of D) and good SU(3). We show that a precise formulation of these older ideas can reproduce all of the good results of the chiral scheme and none of the bad ones. We assume the usual Gell-Mann current algebra and the (3, 3) + (3, 3) symmetry breaking Hamiltonian H' = cz,,SO + Q@. We make, and motivate with reference to a composite picture of the hadrons, the following four assumptions: (1) approximate SU(3), (2) weak PCAC, (3) minimal subtractions, (4) Regge theory. In this framework, the dominance of a given Green's function T by the pion pole depends on the nature of the despersion relations it satisfies in variables for which the absorptive part is expressible in terms of physical matrix elements of D. An unsubtracted dispersion relation leads to pole dominance but a subtracted one introduces a constant (or worse) difference between T and the corresponding on-shell pion amplitude. From assumptions (2)-(4), we derive the following successful results of the chiral framework: the Adler consistency condition, the Adler-Weisberger relation, the Weinberg-Tomozawa pion-target scattering lengths, the Weinberg n-r scattering lengths, the Fubini one-pion production relations, the Weinberg-Callan-Treiman Klr form factors, and the K,,-KS,, relations. The extra parameters (subtraction constants) encountered in applying weak PCAC, as determined by Regge theory, turn out not to contribute to these relations. Adding assumption (I), we obtain the further results: (~,,/v'Za,) N-0.17, 6 N-1, and an excellent simultaneous fit to the s-wave and P-wave hyperon decays. Here our extra parameters turn out to be present precisely in the places where they are required to insure the consistency of our approach. (For example, the g terms in our scheme need not be small.) None of these results are common to the chiral framework. We show further that F, and A,, need not approximately vanish in our framework. We therefore conclude that our theory seems to provide a better description of the present empirical situation than does the chiral theory.
Unitarized pion-nucleon scattering within heavy baryon chiral perturbation theory
Physical Review D, 2000
By means of the Inverse Amplitude Method we unitarize the elastic pion-nucleon scattering amplitudes obtained from Heavy Baryon Chiral Perturbation Theory to O(q 3). Within this approach we can enlarge their applicability range and generate the ∆(1232) resonance. We can find a reasonable description of the pion nucleon phase shifts with O(q 2) parameters in agreement with the resonance saturation hypothesis. However, the uncertainties in the analysis of the low energy data as well as the large number of chiral parameters, which can have strong correlations, allow us to obtain very good fits with rather different sets of chiral constants.
Lower excitation spectrum of the nucleon and delta in a relativistic chiral quark model
Journal of Physics G: Nuclear and Particle Physics, 2005
The lower excitation spectrum of the nucleon and ∆ is calculated in a relativistic chiral quark model. Contributions of the second order self-energy and exchange diagrams due-to pion fields to the mass spectrum of the SU (2) baryons are estimated. A splitting between N (939) and positive parity nucleon resonance (Roper resonance) N * (1440) is reproduced with a reasonable accuracy. The obtained structure of one-meson exchange interaction confirms a prediction of the large Nc limit approach stating that the mass splitting between various baryon states receive contributions from operators which simultaneously couple spin, isospin and orbital momentum. It is shown that onemeson exchange interaction generates a splitting between negative parity N * (1/2 −) and N * (3/2 −) states, and also between ∆ * (3/2 −) and ∆ * (1/2 −) states in contrast to the non-relativistic Goldstone-Boson Exchange based quark models. This splitting is due-to a relativistic operator which couples the lower and upper orbital momentum of two interacting valence quarks.
Annals of Physics, 2013
We present a novel analysis of the πN scattering amplitude in covariant baryon chiral perturbation theory up to O(p 3) within the extended-on-mass-shell renormalization scheme and including the ∆(1232) explicitly in the δ-counting. We take the hadronic phase shifts provided by partial wave analyses as basic experimental information to fix the low-energy constants. Subsequently, we study in detail the various observables and low-energy theorems related to the πN scattering amplitude. In particular, we discuss the results and chiral expansion of the phase shifts, the threshold coefficients, the Goldberger-Treiman relation, the pion-nucleon sigma term and the extrapolation onto the subthreshold region. The chiral representation of the amplitude in the theory with the ∆ presents a good convergence from very low energies in the subthreshold region up to energies well above threshold, leading also to a phenomenological description perfectly consistent with the one reported by the respective partial wave analyses and independent determinations. We conclude that a model-independent and systematic framework to analyze πN-scattering observables using directly experimental data shall be possible in covariant baryon chiral perturbation theory.
Sigma-term physics in the perturbative chiral quark model
Physical Review D, 2001
We apply the perturbative chiral quark model (PCQM) at one loop to analyse meson-baryon sigma-terms. Analytic expressions for these quantities are obtained in terms of fundamental parameters of low-energy pion-nucleon physics (weak pion decay constant, axial nucleon coupling, strong pion-nucleon form factor) and of only one model parameter (radius of the nucleonic three-quark core). Our result for the πN sigma term σ πN ≈ 45 MeV is in good agreement with the value deduced by Gasser, Leutwyler and Sainio using dispersionrelation techniques and exploiting the chiral symmetry constraints.
Chiral effective-field theory in the Delta(1232) region: Pion electroproduction on the nucleon
Physical Review D, 2006
We develop an extension of chiral perturbation theory to the Delta\DeltaDelta(1232)-resonance energy region and apply it to investigate the pion electroproduction off the nucleon ($e^- N \to e^- N\pi$). We present a complete calculation of this process, in the Delta\DeltaDelta-resonance region, up to next-to-leading order in the {\it delta\deltadelta-expansion}. At this order, the only free parameters are the three low-energy constants corresponding to the magnetic (M1), electric (E2), and Coulomb (C2) gammaNtoDelta\gamma N \to \Delta gammaNtoDelta transition strength. After fitting these parameters to a few well-known data, our calculation provides a prediction for observables and multipole amplitudes of pion electroproduction. These results compare favorably with the phenomenological multipole solutions and recent experimental results from MIT-Bates and MAMI. Our prediction for the pion-mass dependence of the gammaNDelta\gamma N\DeltagammaNDelta form factors offers an explanation for the discrepancy between the recent lattice-QCD results and the experimental value for the "C2/M1 ratio" at low Q2Q^2Q2.
Threshold pion photoproduction of nucleons in the chiral quark model
Physical review D: Particles and fields, 1994
In this paper, we show that the low energy theorem (LET) of the threshold pion-photoproduction can be fully recovered in the quark model. An essential result of this investigation is that the quark-pion operators are obtained from the effective chiral Lagrangian, and the low energy theorem does not require the constraints on the internal structures of the nucleon. The pseudoscalar quark-pion coupling generates an additional term at order µ = m π /M only in the isospin amplitude A (−). The role of the transitions between the nucleon and the resonance P 33 (1232) and P-wave baryons are also discussed, we find that the leading contributions to the isospin amplitudes at O(µ 2) are from the transition between the P-wave baryons and the nucleon and the charge radius of the nucleon. The leading contribution from the Pwave baryons only affects the neutral pion production, and improve the agreement with data significantly. The transition between the resonance P 33 (1232) and the nucleon only gives an order µ 3 corrections to A (−) .
Δ(1232) Electroproduction Amplitudes in Chiral Soliton Models of the Nucleon
Physical Review C, 2000
The multipole amplitudes for the N-∆(1232) electromagnetic transition are computed in the framework of the linear σ model and the chiral chromodielectric model for small and moderate photon virtualities. The models include quark and meson degrees of freedom and the nucleon and the delta are clusters of three valence hedgehog quarks surrounded by meson clouds described by coherent states. Angular momentum and isospin projections are performed to endow model states representing the nucleon and the delta with proper quantum numbers. Recoil corrections involved in the process γ v N → ∆ are taken into account by performing linear momentum projection of the initial and final baryon states. The ratios E2/M 1 and C2/M 1 are in good agreement with the data in the two models, but the magnetic amplitude is better reproduced in the Linear Sigma Model. The ratios show little dependence with the model parameters. Both in the Linear Sigma Model and in the Chromodielectric Model the charged pions are responsible for the non-vanishing quadrupoleelectric and-coulomb amplitudes. The recoil corrections enhance the results obtained for the amplitudes without linear momentum projection, improving the comparison with experimental data. The dependence of the theoretical amplitudes with the choice of the reference frame is also studied.