Thermal Corrections to pi-pi scattering lengths in the linear sigma model (published May 2008)

In this article we address the problem of getting the temperature dependence of the pi-pi scattering lengths in the frame of the linear sigma model. Using the real time formalism, we calculate all the relevant one loop diagrams. The temperature corrections are only considered in the pion sector, due to the Boltzmann suppression for heavier fields like the sigma meson. From this analysis we obtain the thermal behavior of the s waves scattering lengths a_{0}^{0} and a_{2}^{0} associated to isospin I=0 and I=2, respectively. If we normalize with the zero temperature value it turns out that a_{0}^{0}(T)/a_{0}^{0} grows with temperature, whereas the opposite occurs with a_{0}^{2}(T)/a_{0}^{2} . Finally we compare our results with other determinations of the scattering lengths based on the Nambu-Jona-Lasinio model and chiral perturbation theory.

M. Loewe and C. Martinez-Villalobos, Phys. Rev. D 77, 106006. DOI: 10.1103/PhysRevD.77.105006

https://journals.aps.org/prd/abstract/10.1103/PhysRevD.77.105006

Fig3_2008_LM

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s