**Lecturer:**Prof. Dr. Dirk H. Rischke （Institut für Theoretische Physik Johann Wolfgang Goethe-Universität ）

Time & Place: 2:30pm, Nov. 14 (Tuesday), 2017，Room 9409

Title： The extended Linear Sigma Model as a low-energy model for QCD

Abstract：The chiral symmetry of QCD is spontaneously broken in the vacuum by a non-vanishing quark condensate. At sufficiently high temperature and chemical potential, this symmetry is effectively restored. A signal of chiral symmetry restoration is the degeneracy of chiral partners in the hadronic mass spectrum. In order to study chiral symmetry restoration in a theoretical approach, a linear sigma model is particularly well suited, as it treats chiral partners on the same footing.

In this talk, I present such a model, termed “extended Linear Sigma Model” (eLSM), which features scalar and vector mesons as well as baryons (and their chiral partners) and respects the chiral and dilatation symmetries of QCD. A fit of the coupling constants of this model to hadronic vacuum properties reveals a surprisingly good agreement with experiment. A consequence of this fit is that the scalar-isoscalar resonances f_0(1370) and f_0(1500) are identified as chiral partners of the pions and the eta-meson. The f_0(1710) resonance is (predominantly) a glueball state. The light scalar-isoscalar resonances f_0(500) and f_0(980) are then resonances that are dynamically generated through the interaction of pseudoscalar mesons. Incorporating f_0(500) into the eLSM as an interpolating field, pion-pion as well as pion-nucleon scattering lengths can be reproduced as well. It can be shown that the low-energy limit of the eLSM agrees with chiral perturbation theory. Baryons are introduced as quark-diquark states with definite chiral transformation properties. This naturally leads to four spin-1/2 baryon multiplets with definite transformation properties under parity. A consequence is that N(939) and N(1535), as well as N(1440) and N(1650) are chiral partners. The anomalously large decay width of N(1535) into N(939) and eta can be interpreted as a consequence of the axial anomaly of QCD.