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Elastic $ππ$ scattering to two loops

J. Bijnens, G. Colangelo, G. Ecker, J. Gasser, M. E. Sainio

Abstract

We evaluate analytically the elastic $ππ$ scattering amplitude to two loops in chiral perturbation theory and give numerical values for the two $S$--wave scattering lengths and for the phase shift difference $δ_0^0-δ_1^1$.

Elastic $ππ$ scattering to two loops

Abstract

We evaluate analytically the elastic scattering amplitude to two loops in chiral perturbation theory and give numerical values for the two --wave scattering lengths and for the phase shift difference .

Paper Structure

This paper contains 2 sections, 20 equations, 1 figure.

Table of Contents

  1. Loop functions
  2. The coefficients $b_1,\ldots,b_6$

Figures (1)

  • Figure 1: The phase shift difference $\delta_0^0-\delta_1^1$ (in degrees) as a function of the center of mass energy of the two incoming pions. The dotted (dash--dotted) line displays the tree (one--loop) result, whereas the solid line denotes the two--loop approximation, evaluated with $r_i^r(1\;\hbox{GeV})=0$. The data are from Ref. rosselet.