The authors show that SRG evolution makes a fitted pi-pi potential band-diagonal, but they do not verify that the evolved potential reproduces the original phase shifts.
The pi pi S-wave scattering lengths
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abstract
We match the known chiral perturbation theory representation of the pi pi scattering amplitude to two loops with a phenomenological description that relies on the Roy equations. On this basis, the corrections to Weinberg's low energy theorems for the S-wave scattering lengths are worked out to second order in the expansion in powers of the quark masses. The resulting predictions, a00=0.220 \pm 0.005, a20=-0.0444 \pm 0.0010, contain remarkably small uncertainties and thus allow a very sensitive experimental test of the hypothesis that the quark condensate is the leading order parameter of the spontaneously broken chiral symmetry.
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$\pi\pi$ scattering from a similarity renormalization group perspective
The authors show that SRG evolution makes a fitted pi-pi potential band-diagonal, but they do not verify that the evolved potential reproduces the original phase shifts.