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Register a new userThe in-medium isovector pi N amplitude from low energy pion scattering
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E. Friedman
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Differential cross sections for elastic scattering of 21.5 MeV positive and negative pions by Si, Ca, Ni and Zr have been measured as part of a study of the pion-nucleus potential across threshold. The `anomalous repulsion in the s-wave term was observed, as is the case with pionic atoms. The extra repulsion can be accounted for by a chiral-motivated model where the pion decay constant is modified in the medium. Unlike in pionic atoms, the anomaly cannot be removed by merely introducing an empirical on-shell energy dependence.
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Measurements of elastic scattering of 21.5 MeV pi+ and pi- by Si, Ca, Ni and Zr were made using a single arm magnetic spectrometer. Absolute calibration was made by parallel measurements of Coulomb scattering of muons. Parameters of a pion-nucleus optical potential were obtained from fits to all eight angular distributions put together. The `anomalous s-wave repulsion known from pionic atoms is clearly observed and could be removed by introducing a chiral-motivated density dependence of the isovector scattering amplitude, which also greatly improved the fits to the data. The empirical energy dependence of the isoscalar amplitude also improves the fits to the data but, contrary to what is found with pionic atoms, on its own is incapable of removing the anomaly.
Focusing on three-pion states with maximal isospin ($pi^+pi^+pi^+$), we present the first non-perturbative determination of an energy-dependent three-hadron scattering amplitude from first-principles QCD. The calculation combines finite-volume three-hadron energies, extracted using numerical lattice QCD, with a relativistic finite-volume formalism, required to interpret the results. To fully implement the latter, we also solve integral equations that relate an intermediate three-body K matrix to the physical three-hadron scattering amplitude. The resulting amplitude shows rich analytic structure and a complicated dependence on the two-pion invariant masses, represented here via Dalitz-like plots of the scattering rate.
After a brief review of the quark-based model for nuclear matter, and some pion properties in medium presented in our previous works, we report new results for the pion valence wave function as well as the valence distribution amplitude in medium, which are presented in our recent article. We find that both the in-medium pion valence distribution and the in-medium pion valence wave function, are substantially modified at normal nuclear matter density, due to the reduction in the pion decay constant.
We report measurements of the $pi^- p to pi^o n$ differential cross sections at six momenta (104-143 MeV/c) and four angles (0-40 deg) by detection of $gamma$-ray pairs from $pi^o to gamma gamma$ decays using the TRIUMF RMC spectrometer. This region exhibits a vanishing zero-degree cross section from destructive interference between s-- and p--waves, thus yielding special sensitivity to pion-nucleon dynamics and isospin symmetry breaking. Our data and previous data do not agree, with important implications for earlier claims of large isospin violating effects in low energy pion-nucleon interactions.
We perform an expansion of the virtual Compton scattering amplitude for low energies and low momenta and show that this expansion covers the transition from the regime to be investigated in the scheduled photon electroproduction experiments to the real Compton scattering regime. We discuss the relation of the generalized polarizabilities of virtual Compton scattering to the polarizabilities of real Compton scattering.
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