Direct Channel Dominance in Goldstone Boson Scattering in the Resonance Region

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dc.creatorBeane, Silas R.
dc.creatorChiu, Charles B.
dc.date1993-03-13
dc.date.accessioned2026-07-07T03:55:59Z
dc.date.available2026-07-07T03:55:59Z
dc.descriptionWe consider the scattering of Goldstone bosons in the range of intermediate energies, and in particular focus our attention on the scattering of pions in the $ρ$-resonance region. The chiral perturbation series is obtained to order $E^4$ from a chiral $SU(2)\times SU(2)$ invariant effective Lagrangian. At order $E^4$, we isolate the low-energy manifestation of heavy particle exchange in the s-channel. We find that the contributions of this type to the I=1 and I=2 amplitudes have a one parameter dependence. This observation provides a symmetry rationale for Chanowitz's recent observation that in a chiral model with an explicitly coupled $ρ$, the I=1 and I=2 channels are strongly correlated. In order to realize, in a quantitative way, the fact that in the resonance region the direct-channel dominates, we make use of a simple and intuitive unitarization scheme. This allows us to derive a renormalization constant-independent relation for the I=1 and I=2 phase shifts. With the assumption of a $ρ$-resonance, this relation determines the position of a pole at euclidean momentum in the I=2 channel. Through an analysis based on the theory of redundant poles and the Adler sum rule we show that this ``tachyon'' pole actually represents a physical contribution to the unitary amplitude which accounts for $ρ$ and $ε$ exchange in the u-channel.
dc.description20,DOE-306-CPP-75
dc.identifierhttps://arxiv.org/abs/hep-ph/9303254
dc.identifierhttp://arxiv.org/abs/hep-ph/9303254
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/44768
dc.subjectHigh Energy Physics - Phenomenology
dc.titleDirect Channel Dominance in Goldstone Boson Scattering in the Resonance Region
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