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$π$-$K$ scattering lengths at finite temperature in the Nambu--Jona-Lasinio model

P. Piwnicki·S. P. Klevansky·P. Rehberg
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Abstract

The transition amplitude for $πK$ scattering is evaluated within the SU(3) Nambu--Jona-Lasinio model. Ordering terms according to the expansion in $1/N_c$ leads to a box-like diagram, $t$ channel diagrams that admit scalar isoscalar $(σ,σ')$ exchanges, and a $u$ channel exchange of a scalar isodoublet $σ_K$ that has quantum numbers corresponding to the $K_0^*(1430)$. Both the Pauli-Villars and O(3) regularization procedures are used to evaluate the T=0 values of the $l=0$ scattering lengths $a_0^{3/2}$ and $a_0^{1/2}$. The finite temperature dependence is studied. We find that the variation in the $t$ channel in the calculation of $a_0^{3/2}$ leads to a change in $a_0^{3/2}$ of a factor of about two over the temperature range of T=150 MeV.

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P. Piwnicki, S. P. Klevansky, P. Rehberg. 1998-04-14. $π$-$K$ scattering lengths at finite temperature in the Nambu--Jona-Lasinio model. https://doi.org/10.1103/physrevc.58.502

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