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Dispersion relation bounds for {pi}{pi} scattering

Journal Article · · Physical Review. D, Particles Fields
;  [1]
  1. Department of Physics, University of California at San Diego, La Jolla, California 92093 (United States)
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 l{sub 1} and l{sub 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 scheme, a result hitherto absent in the literature. The LSM values for l{sub 1} and l{sub 2} violate the bounds for small values of m{sub {sigma}}/m{sub {pi}}. We show how this can occur, while still being consistent with the axiomatic principles.
OSTI ID:
21250125
Journal Information:
Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 9 Vol. 77; ISSN PRVDAQ; ISSN 0556-2821
Country of Publication:
United States
Language:
English

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