Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dispersion Relation Bounds for pi pi Scattering   Axiomatic principles such as analyticity, unitarity and crossing symmetry
constrain the second derivative of the pi pi scattering amplitudes in some
channels to be positive in a region of the Mandelstam plane. Since this region
lies in the domain of validity of chiral perturbation theory, we can use these
positivity conditions to bound linear combinations of \bar{l}_1 and \bar{l}_2.
We compare our predictions with those derived previously in the literature
using similar methods. We compute the one-loop pi pi scattering amplitude in
the linear sigma model (LSM) using the MS-bar scheme, a result hitherto absent
in the literature. The LSM values for \bar{l}_1 and \bar{l}_2 violate the
bounds for small values of m_sigma/m_pi. We show how this can occur, while
still being consistent with the axiomatic principles.

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The categories of this paper are: math-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: q-alg
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The categories of this paper are: solv-int
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The categories of this paper are: quant-ph
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The categories of this paper are: eess
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The categories of this paper are: supr-con
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The categories of this paper are: dg-ga
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The categories of this paper are: chem-ph
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The categories of this paper are: funct-an
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The categories of this paper are: astro-ph
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The categories of this paper are: q-fin
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The categories of this paper are: nlin
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The categories of this paper are: hep-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: math