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Article Dans Une Revue Physical Review D Année : 2022

S-wave pion-pion scattering lengths from nucleon-meson fluctuations

Résumé

We present calculations of the S-wave isospin-zero and isospin-two pion-pion scattering lengths within a nucleon-meson model with parity doubling. Both scattering lengths are computed in various approximations, ranging from a mean-field (MF) calculation toward the inclusion of loop corrections by means of the functional renormalization group (FRG). The bosonic part of the investigated nucleon-meson model is formulated in terms of stereographic projections as a “natural” set of coordinates on the respective vacuum manifold. We thereby elucidate subtleties concerning the truncation of the effective action with respect to higher-derivative pion interactions and the “successful” computation of the scattering lengths. As the main result, we find simultaneous agreement for the isospin-zero and isospin-two scattering lengths with experimental data within the LPA truncation of the FRG, together with chiral-symmetry breaking (roughly) occurring at the characteristic scale of 4πfπ. The isoscalar σ mass is dynamically generated by the FRG integration of momentum modes and is a prediction of the model. It ends being of the order of 500 MeV, i.e., much lower than the value (>1GeV) found in MF or one-loop treatment of this or related models. Finally, the convergence of the corresponding low-energy expansion of the quantum effective action in terms of pion momenta is discussed.

Dates et versions

hal-03520937 , version 1 (11-01-2022)

Identifiants

Citer

Jürgen Eser, Jean-Paul Blaizot. S-wave pion-pion scattering lengths from nucleon-meson fluctuations. Physical Review D, 2022, 105 (7), pp.074031. ⟨10.1103/PhysRevD.105.074031⟩. ⟨hal-03520937⟩
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