Complete analysis of pion–nucleon scattering in chiral perturbation theory to third order (original) (raw)
Related papers
Pion-nucleon scattering in chiral perturbation theory (I): Isospin-symmetric case
Nuclear Physics A, 1998
We construct the complete effective chiral pion-nucleon Lagrangian to third order in small momenta based on relativistic chiral perturbation theory. We then perform the so-called heavy baryon limit and construct all terms up-to-and-including order 1/m 2 with fixed and free coefficients. As an application, we discuss in detail pionnucleon scattering. In particular, we show that for this process and to third order, the 1/m expansion of the Born graphs calculated relativistically can be recovered exactly in the heavy baryon approach without any additional momentum-dependent wave function renormalization. We fit various empirical phase shifts for pion laboratory momenta between 50 and 100 MeV. This leads to a satisfactory description of the phase shifts up to momenta of about 200 MeV. We also predict the threshold parameters, which turn out to be in good agreement with the dispersive analysis. In particular, we can sharpen the prediction for the isovector S-wave scattering length, 0.083 M −1 π ≤ a − 0+ ≤ 0.093 M −1 π. We also consider the subthreshold parameters and give a short comparison to other calculations of πN scattering in chiral perturbation theory or modifications thereof.
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.
Pion-nucleon phase shifts in heavy baryon chiral perturbation theory
Physical Review D, 1997
We calculate the phase shifts in the pion-nucleon scattering using the heavy baryon formalism. We consider phase shifts for the pion energy range of 140 to 200 MeV. We employ two different methods for calculating the phase shifts -the first using the full third order calculation of the pion-nucleon scattering amplitude and the second by including the resonances ∆ and N * as explicit degrees of freedom in the Lagrangian. We compare the results of the two methods with phase shifts extracted from fits to the pion-nucleon scattering data. We find good to fair agreement between the calculations and the phase shifts from scattering data.
Pion-nucleon scattering and isospin violation
1998
I discuss low-energy pion-nucleon scattering in the framework of chiral perturbation theory. I argue that using this theoretical method one is able to match the in some cases impressive experimental accuracy (for the low partial waves). I then show how strong and electromagnetic isospin violation can be treated simultaneously. Some first results for neutral pion scattering and the σ-term are given.
Physical Review D, 2011
We calculate the pion-pion elastic scattering phase shifts for pion masses from the chiral limit to values of interest for lattice studies. At low energies, we use the standard Chiral Perturbation Theory expressions to one and two loops. In addition, we study the phase shifts mass dependence in the resonance region by means of dispersion theory in the form of unitarized Chiral Perturbation Theory and the Inverse Amplitude Method. We pay particular attention to the case when resonances are close to threshold, illustrating the different behavior between scalar and vector resonances. We also provide the estimation of uncertainties, which are dominated by those of the O(p 6) chiral parameters.
πN scattering in relativistic baryon chiral perturbation theory reexamined
Physical Review C, 2011
We have analyzed pion-nucleon scattering using the manifestly relativistic covariant framework of Infrared Regularization up to O(q 3) in the chiral expansion, where q is a generic small momentum. We describe the low-energy phase shifts with a similar quality as previously achieved with Heavy Baryon Chiral Perturbation Theory, √ s 1.14 GeV. New values are provided for the O(q 2) and O(q 3) low-energy constants, which are compared with previous determinations. This is also the case for the scattering lengths and volumes. Finally, we have unitarized the previous amplitudes and as a result the energy range where data are reproduced increases significantly.
Isospin violation in pion–nucleon scattering
Physics Letters B, 1998
We construct the complete effective chiral pion-nucleon Lagrangian in the presence of virtual photons to one loop. As an application, we consider strong and electromagnetic isospin violation for scattering of neutral pions off nucleons. We show that for the scattering lengths these isospin violating terms are of the same size as the purely hadronic ones. We also analyze isospin-violating effects for the σ-term. These can be as large as 10% for the absolute value but are negligible for the shift to the Cheng-Dashen point. #1 Work supported in part by funds provided by the Graduiertenkolleg "Die Erforschung subnuklearer Strukturen der Materie" at Bonn University.
Improved unitarized Heavy Baryon Chiral Perturbation Theory for πN scattering
Physics Letters B, 2000
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 ∆(1232) resonance, the convergence problems and the power counting of the chiral parameters.
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.