ππ interactions and the size of the σ meson

Miguel Albaladejo (Murcia)

We explore the nature of the σ meson by studying its size [1], that we determine from its quadratic scalar radius.  This is deduced from the scalar form factor, that we calculate from SU(2) O(p⁴) chiral lagrangians, without any ad-hoc free parameter, given the dynamically generated nature of the σ meson in the ππ interactions.  A small value for the size of the σ meson is found, which points to a four-quark nature of the latter, rather than to a pion molecule picture.  We also calculate the dependence of the σ meson pole and the quadratic scalar radius on the pion mass, in order to give further meaning to our results.  We also study ππ interactions in a finite volume within two different frameworks that implement chiral dynamics and unitarity, namely, the IAM and the N/D method [2].  We include in the chiral amplitudes the O(p⁴) terms, which are explicitly volume dependent, in order to quantify the contribution of these terms, that are exponentially suppressed in Lüscher’s formalism.

[1] M. Albaladejo and J. A. Oller, Phys. Rev. D 86, 034003 (2012).
[2] M. Albaladejo, J. A. Oller, E. Oset, G. Rios and L. Roca, JHEP 1208, 071 (2012).

(Besprechungsraum 2.003)