We study properties of hadrons in the O（4） linear σ model, where we take into account fluctuations of mesons around their mean field values using the Gaussian functional （GF） method. In the GF method we calculate...We study properties of hadrons in the O（4） linear σ model, where we take into account fluctuations of mesons around their mean field values using the Gaussian functional （GF） method. In the GF method we calculate dressed σ and π masses, where we include the effect of fluctuations of mesons to find a better ground state wave function than the mean field approximation. Then we solve the Bethe-Salpeter equations and calculate physical σ and π masses. We recover the Nambu-Goldstone theorem for the physical pion mass to be zero in the chiral limit. The σ meson is a strongly correlated meson-meson state, and seems to have a two meson composite structure. We calculate σ and π masses as functions of temperature for both the chiral limit and explicit chiral symmetry breaking case. We get similar behaviors for the physical σ and π masses as the case of the mean field approximation, but the coupling constants are much larger than the values of the case of the mean field approximation.展开更多
基金Supported by National Natural Science Foundation of China(11205011,11475015,11005007)Fundamental Research Funds for the Central Universities+1 种基金the Grant for Scientific Research from MEXT of Japan[Priority Areas"New Hadrons"(E01:21105006),(C)No.23540306]the JSPS Research(21540267)
文摘We study properties of hadrons in the O（4） linear σ model, where we take into account fluctuations of mesons around their mean field values using the Gaussian functional （GF） method. In the GF method we calculate dressed σ and π masses, where we include the effect of fluctuations of mesons to find a better ground state wave function than the mean field approximation. Then we solve the Bethe-Salpeter equations and calculate physical σ and π masses. We recover the Nambu-Goldstone theorem for the physical pion mass to be zero in the chiral limit. The σ meson is a strongly correlated meson-meson state, and seems to have a two meson composite structure. We calculate σ and π masses as functions of temperature for both the chiral limit and explicit chiral symmetry breaking case. We get similar behaviors for the physical σ and π masses as the case of the mean field approximation, but the coupling constants are much larger than the values of the case of the mean field approximation.
