Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Comments on some chiral-dispersive calculations of $\pi\pi$ scattering   We consider the $\pi\pi$ scattering amplitude obtained by Colangelo, Gasser
and Leutwyler (CGL), using dispersion relations and chiral perturbation theory
to two loops. We point out that the input used by CGL for energies above 1.42
GeV is incompatible with a number of experimental results. Moreover, the error
they adscribe to the $\delta_0^{(0)}$ phase at 0.8 GeV, an important part of
their input, is much underestimated, and its central value is probably
displaced. Then, we compare CGL results with direct fits to experimental
$\pi\pi$ data; the outcome of this test is mismatch of the CGL amplitude, for
several quantities by as much as 4 standard deviations. We also evaluate
forward dispersion relations with the CGL amplitudes. We find that these
dispersion relations are fulfilled less and less well as the energy increases
towards 0.8 GeV. Moreover, the size that the experimental results for $\pi\pi$
scattering indicates for the two loop corrections in a chiral perturbation
theory analysis is less than those required by CGL, which suggests that at
least some of the CGL corrections are so large to cover biases in their
$\pi\pi$ amplitude and in the evaluation of the scalar form factor of the pion.
  We conclude on the necessity of repeating the analysis of CGL with correct
high energy amplitudes and a more realistic input for the $\delta_0^{(0)}$
phase at 0.8 GeV.

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The categories of this paper are: cs
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The categories of this paper are: patt-sol
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The categories of this paper are: comp-gas
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The categories of this paper are: q-fin
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The categories of this paper are: dg-ga
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The categories of this paper are: bayes-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-th
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The categories of this paper are: econ
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The categories of this paper are: gr-qc
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The categories of this paper are: math
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The categories of this paper are: acc-phys
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The categories of this paper are: quant-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: alg-geom