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Pion-nucleon scattering in chiral perturbation theory I: Isospin-symmetric case
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abstract
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 pion-nucleon scattering. In particular, we show that 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, $0.083 M_\pi^{-1} \leq a_{0+}^- \leq 0.093 M_\pi^{-1}$. We also consider the subthreshold parameters and give a short comparison to other calculations of $\pi N$ scattering in chiral perturbation theory or modifications thereof.
Forward citations
Cited by 5 Pith papers
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Dispersive Analysis of $D$- and $B$-Meson Form Factors with Chiral and Heavy-Quark Constraints
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$S$-wave $KN$ scattering in a renormalizable chiral effective field theory
A renormalizable covariant chiral EFT calculation of s-wave KN scattering yields a good description of I=1 phase shifts with a negative effective range while the I=0 channel remains weakly constrained.
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Ab initio lattice study of neutron-alpha scattering with chiral forces at N3LO
A lattice calculation of neutron-helium-4 scattering with chiral forces at N3LO matches empirical phase shifts in the 2S1/2 and 2P3/2 channels but not the 2P1/2 channel, pointing to limitations in the three-nucleon force.
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Pion-Nucleon Scattering in Baryon Chiral Perturbation Theory combined with the ${ 1/N_c}$ Expansion
A one-loop chiral-plus-1/Nc effective field theory with the nucleon and Delta in a spin-flavor multiplet is fitted to SAID pion-nucleon scattering data up to 350 MeV.
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Constraint on ultralight Nelson-Barr dark matter from time-dependent nuclear decay
Non-observation of periodic modulation in tritium beta decay sets a new 95% CL exclusion on ultralight Nelson-Barr scalar dark matter: f below 7.0e9 to 1.4e7 GeV is ruled out for m_phi in 3.4e-23 to 1.7e-20 eV.
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