Dispersion Relation Bounds for pi pi Scattering
| dc.creator | Manohar, A. V. | |
| dc.creator | Mateu, V. | |
| dc.date | 2008-01-21 | |
| dc.date | 2008-05-26 | |
| dc.date.accessioned | 2026-07-07T11:55:24Z | |
| dc.date.available | 2026-07-07T11:55:24Z | |
| dc.description | 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. | |
| dc.description | 12 pages, 8 figures. Two references added, a few minor changes. Published version | |
| dc.identifier | https://arxiv.org/abs/0801.3222 | |
| dc.identifier | http://arxiv.org/abs/0801.3222 | |
| dc.identifier | Phys.Rev.D77:094019,2008 | |
| dc.identifier | doi:10.1103/PhysRevD.77.094019 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/205232 | |
| dc.subject | High Energy Physics - Phenomenology | |
| dc.title | Dispersion Relation Bounds for pi pi Scattering | |
| dc.type | text |