S-wave pion-pion scattering lengths from nucleon-meson fluctuations
| Autor: | Jürgen Eser, Jean-Paul Blaizot |
|---|---|
| Přispěvatelé: | Institut de Physique Théorique - UMR CNRS 3681 (IPHT), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS) |
| Rok vydání: | 2021 |
| Předmět: |
pi: momentum
Nuclear Theory [PHYS.NUCL]Physics [physics]/Nuclear Theory [nucl-th] pi pi: scattering length pi interaction FOS: Physical sciences momentum derivative: high GeV symmetry breaking Nuclear Theory (nucl-th) isospin High Energy Physics - Phenomenology (hep-ph) isoscalar derivative Nuclear Experiment pi: interaction pi pi fluctuation symmetry breaking: chiral high doubling chiral High Energy Physics - Phenomenology effective action parity scattering length [PHYS.HPHE]Physics [physics]/High Energy Physics - Phenomenology [hep-ph] parity: doubling renormalization group |
| Zdroj: | Phys.Rev.D Phys.Rev.D, 2022, 105 (7), pp.074031. ⟨10.1103/PhysRevD.105.074031⟩ Physical Review |
| DOI: | 10.48550/arxiv.2112.14579 |
| Popis: | International audience; 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 (>1 GeV) 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|