Abstract:
Pion-pion scattering amplitude obtained from one-loop Chiral Perturbation Theory (ChPT) is crossing symmetric, however the corresponding partial-wave amplitudes do not respect exact unitarity relation. There are different approaches to get unitarized results from ChPT. Here we consider the inverse amplitude method (IAM) and, using the Roskies relations, we measure the amount of crossing symmetry violation when IAM is used in order to fit pion-pion phase-shifts to experimental data in the resonance region. We also show the unitarity violation of the crossing symmetric ChPT amplitude with its parameters fixed in order to fit to experimental phase-shifts.

Abstract:
the slow convergence of chiral perturbation theory for heavy baryons (hbchpt) suggests that any attempt to unitarize the amplitude following from this method will fail to describe the experimental phase shifts. however, it was possible to obtain a chpt pion nucleon amplitudes respecting exact unitarity relation by using the inverse amplitude method (iam), but the resulting total amplitude violates the important property of crossing symmetry [1] . on the other hand, the use of a dispersive calculation, starting directly from a result at second order in the pion momentum, is an alternative approach to get unitarized scattering amplitude. by this method it was possible to fit, with two parameters, the p33 partial wave to the experimental low energy phase shifts, and to present the resulting s and p partial wave phase shifts [2]. this was done with a crossing symmetric amplitude, that respect approximate elastic unitarity relation. in the present exercise, we do not impose crossing symmetry for the amplitude obtained in the previous work, in order to verify the role played by crossing symmetry in the dispersive approach. as in the previous work, our strategy was to perform a fit of the p33 amplitude to the experimental phase shifts and then use the fixed parameters in the s and p partial waves to compare them with the corresponding experimental phase shifts. we conclude that, when we do not impose crossing symmetry for the total amplitude, more parameters are needed in the fitting procedure for p33, moreover the theoretical results for s11, s31, p11, p31 and p13 are quite far from the experimental points.

Abstract:
We extend our previous analysis of the unitarized pion-nucleon scattering amplitude including up to fourth order terms in Heavy Baryon Chiral Perturbation Theory. We pay special attention to the stability of the generated Delta(1232 resonance, the convergence problems and the power counting of the chiral parameters.

Abstract:
A crossing symmetric $\pi N$ scattering amplitude is constructed through a complete attachment of two external pions to the dressed nucleon propagator of an underlying $\pi N$ potential model. Our formulation automatically provides expressions also for the crossing symmetric and gauge invariant pion photoproduction and Compton scattering amplitudes. We show that our amplitudes are unitary if they coincide on-shell with the amplitudes obtained by attaching one pion to the dressed $\pi NN$ vertex of the same potential model.

Abstract:
We report on our present work, where by means of the Inverse Amplitude Method we unitarize the elastic pion nucleon scattering amplitudes of Heavy Barion Chiral Perturbation Theory at O(q^3). We reproduce the scattering up to the inelastic thresholds including the Delta(1232) resonance. The fitted chiral constants are rather different from those obtained by fitting the extrapolated threshold parameters for the non-unitarized theory.

Abstract:
The pion distribution amplitude (DA) can be related to the fundamental QCD Green's functions as a function of the quark self-energy and the quark-pion vertex, which in turn are associated with the pion wave function through the Bethe-Salpeter equation. Considering the extreme hard asymptotic behavior in momentum space allowed for a pseudoscalar wave function, which is limited by its normalization condition, we compute the pion DA and its second moment. From the resulting amplitude, representing the field theoretical upper limit on the DA behavior, we calculate the photon-pion transition form factor $F_{\pi\gamma\gamma^{\ast}}(Q^{2})$. The resulting upper limit on the pion transition form factor is compared with existing data published by CLEO, BaBar and Belle collaborations.

Abstract:
We examine the role of the elementary isoscalar pion--nucleon scattering amplitude in the description of the processes $pp \to pp\pi^0$ and $pp\to d\pi^+$ at threshold. We argue that the presently used tree level dimension two approximation used in chiral perturbation theory is insufficient as input by direct comparison with the $\pi$N scattering data. We also show that a successful semi--phenomenological boson--exchange model does better in the description of these data. The influence of the violation of crossing symmetry in the meson--exchange model has to be studied in more detail. We stress that further investigations of the process $pp\to d\pi^+$ can pave the way to a deeper understanding of the pion dominated part of the transition operator.

Abstract:
The Vector Pion form factor below 1 GeV is analyzed using experimental data on its modulus, the P-wave pion pion phase shifts and dispersion relation. It is found that causality is satisfied. Using dispersion relation, terms proportional to s squared and s cubed are calculated using the experimental data, where s is the momentum transfer. They are much larger than the one-loop and two-loop Chiral Perturbation Theory calculations. Unitarized model calculations agree very well with dispersion relation results.

Abstract:
We analyze amplitudes for the pion electroproduction on proton derived from Lagrangians based on the local chiral SU(2) x SU(2) symmetries. We show that such amplitudes do contain information on the nucleon axial form factor F_A in both soft and hard pion regimes. This result invalidates recent Haberzettl's claim that the pion electroproduction at threshold cannot be used to extract any information regarding F_A.

Abstract:
We discuss what can be learned about the shape of the pion distribution amplitude from the form factor for gamma* gamma(*) to pi transitions.