Speaker
Description
Roy-equation analyses on lattice data of ππ scattering phase shifts at mπ = 391MeV reveals
that the lowest f0 meson becomes a bound state under this condition. In addition, there is a pair
of complex poles below threshold generated by crossing symmetry [1]. We use the N/D method
to partially recover crossing symmetry of the O(N ) σ model amplitude at leading order of 1/N
expansion, and qualitatively reproduce the pole structure and pole trajectories with varying pion
masses as revealed by Roy-equation analyses. The σ pole trajectory with varying temperature is also
discussed and found to be similar to its properties when varying mπ . As the temperature increases,
the complex σ poles firstly move from the second Riemann sheet to the real axis becoming two
virtual state poles, and then one virtual state pole moves to the first sheet turning into a bound
state pole and finally tends to the pion pole position at high temperature which is as expected
from the chiral symmetry restoration. Our results provide further evidences that the lowest f0 state
extracted from experiments and lattice data plays the role of σ meson in the spontaneous breaking
of chiral symmetry. Finally, we also briefly discuss the problems of the effective potential in the
situation when mπ and temperature get large.
