Chirally Constraining the $\pi \pi$ Interaction in Nuclear Matter

Abstract

A general prescription for the construction of $\pi \pi$ interaction potentials which preserve scattering length constraints from chiral symmetry when iterated in scattering equations is derived. The prescription involves only minor modifications of typical meson-exchange models, so that coupling constants and cut-off masses in the models are not greatly affected. Calculations of $s$-wave $\pi \pi$ scattering amplitudes in nuclear matter for two models are compared with those for similar models which violate the chiral constraint. While the prescription tends to suppress the accumulation of the near sub-threshold strength of the $\pi \pi$ interaction, an earlier conjecture that amplitudes which satisfy chiral constraints will not exhibit an instability towards $\pi \pi s-$wave pair condensation appears to be incorrect. At the same time, however, conventional $\pi \pi$ interaction models which fit scattering data well can readily be adjusted to avoid the instability in nuclear matter without recourse to exotic mechanisms.

20 pages RevTeX and 5 figures (uuencoded .ps-files)

References in corpus (1)

• S-Wave Pion-Pion Correlations in Dense Nuclear Matter

Cited by in corpus (21)

• Chiral Unitary approach to meson-meson and meson-baryon interactions and nuclear applications
• A Precursor of Chiral Symmetry Restoration in the Nuclear Medium
• The $\sigma$ meson in a nuclear medium through two pion photoproduction
• Chiral nonperturvative approach to the isoscalar s-wave pion-pion interaction in a nuclear medium
• Role of medium modifications for neutrino-pair processes from nucleon-nucleon bremsstrahlung - Impact on the protoneutron star deleptonization
• Pi+ Pi- Emission in High-Energy Nuclear Collisions
• Scalar Isoscalar pion pairs in nuclei and the A(pi,pipi)X reaction
• Enhancement of $\pi A\to \pi \pi A$ Threshold Cross Sections by In-Medium $\pi \pi$ Final State Interactions
• Nuclear Saturation with in-Medium Meson Exchange Interactions
• Evaluation of the $\pi \pi$ scattering amplitude in the $\sigma$-channel at finite density
• Equation of State of an Interacting Pion Gas with Realistic $\pi$--$\pi$ Interactions
• Renormalization of the f0(980) and a0(980) scalar resonances in a nuclear medium
• The Two-Pion Exchange NN-Potential in Nuclear Matter and Nuclear Stability
• Two pion mediated scalar isoscalar NN interaction in the nuclear medium
• Nonequilibrium pion distribution within the Zubarev approach
• Electric conductivity of hot pion matter
• The $({\pi }^{-},\gamma \gamma )$ reaction in nuclei and the $\sigma$ meson in the medium
• Kaon-antikaon nuclear optical potentials and the kappa meson in the nuclear medium
• Final State Interactions in Pion Production from Nuclei
• Pre-critical Chiral Fluctuations in Nuclear Medium -- precursors of chiral restoration at $ρ_{B}\not=0 --
• Chiral unitary theory: application to nuclear problems