# Study of hadrons using the Gaussian functional method in the O(4) linear σ model

• 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.
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CHEN Hua-Xing, Shotaro Imai, Hiroshi Toki and GENG Li-Sheng. Study of hadrons using the Gaussian functional method in the O(4) linear σ model[J]. Chinese Physics C, 2015, 39(6): 064103. doi: 10.1088/1674-1137/39/6/064103
CHEN Hua-Xing, Shotaro Imai, Hiroshi Toki and GENG Li-Sheng. Study of hadrons using the Gaussian functional method in the O(4) linear σ model[J]. Chinese Physics C, 2015, 39(6): 064103.
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沈阳化工大学材料科学与工程学院 沈阳 110142

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## Study of hadrons using the Gaussian functional method in the O(4) linear σ model

###### Corresponding author: GENG Li-Sheng,

Abstract: 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.

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