IsoscalarS-WaveππPhase Shift from a Unitary Current-Algebra Model
- 15 September 1970
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review D
- Vol. 2 (6), 1140-1146
- https://doi.org/10.1103/physrevd.2.1140
Abstract
Using the equal-time commutation relations of chiral , we derive a Ward identity relating the vertex function to the propagator. Adopting a model for the primitive three-point function of two axial-vector currents and an isoscalar operator, we derive an integral equation for the vertex function by inserting elastic unitarity into the identity. In the approximation of neglecting inelastic effects, we solve the integral equation exactly. The solution contains three arbitrary constants which we fix from current-algebra and partially conserved axial-vector current considerations. We then obtain an isoscalar, -wave phase shift which is positive and rises to 180° at infinity. Moreover, it corresponds to a scattering length just 5% larger than Weinberg's and, together with the and contributions, saturates the Adler-Weisberger relation to within 10%. Finally, we predict MeV and MeV.
Keywords
This publication has 13 references indexed in Scilit:
- Construction of Three- and Four-Point Functions of Currents for Arbitrary Spin-One Spectral FunctionsPhysical Review D, 1970
- Unique Set ofI=0S-WaveππPhase ShiftsPhysical Review B, 1969
- Hard-Pion Effective-Range Formula for the Pion Form FactorPhysical Review Letters, 1969
- Model for PionS-Wave Phase Shifts from Current Algebra and Partial Conservation of Axial-Vector CurrentPhysical Review B, 1968
- Current Algebra and Ward Identities: Three- and Four-Point FunctionsPhysical Review B, 1968
- Hard-Pion Calculation ofπ−πScatteringPhysical Review Letters, 1968
- Current-Algebra Calculation of Hard-Pion Processes:andPhysical Review B, 1967
- New Consistency Conditions on Pion-Pion Amplitudes and Their Determination to Fourth Order in External MomentaPhysical Review B, 1967
- Pion Scattering LengthsPhysical Review Letters, 1966
- Sum Rules for the Axial-Vector Coupling-Constant Renormalization inDecayPhysical Review B, 1965