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Prog. Theor. Phys. Vol. 73 No. 1 (1985) pp. 143-157

A Local Duality Scheme and a Uniquely Determined π-π Born Amplitude

Taketoshi Ino, Yasuo Munakata and Jiro Sakamoto

Physics Department, Shimane University, Matsue 690

(Received August 1, 1984)

Abstract:

We apply a local duality scheme to a construction of a new Born amplitude for π^--π⁺ scattering. We start with the most general Veneziano-type amplitude, which contains an infinite number of parameters, and restrict it by the two conditions: 1) A local duality scheme, which includes the SU(6)⊗O(3)_L hadron spectrum of the quark model. 2) An symptotic convergence condition. The infinite number of parameters reduces to only four by condition 1) and further to three by 2). Apart from the overall multiplying factor the amplitude has only two parameters: the Regge slope times the square of the pion mass and the zero-intercept of the trajectory. In this parameter space we determine the region which is ghost-free for all resonant states and find that the physical values are included in this region. The overall multiplying factor is adjusted by ρ→2π width. The predicted partial widths of low-lying resonances are in good agreement with available experiments. It also turns out that the amplitude satisfies Adler's PCAC condition in the limit of zero pion-mass. The amplitude takes two simple forms for certain values of the parameters; one is the same as the Neveu-Schwarz-Ramond amplitude and the other is quite a new one.

URL : http://ptp.ipap.jp/link?PTP/73/143/
DOI : 10.1143/PTP.73.143

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Citing Article(s) :

1. Progress of Theoretical Physics Vol. 74 No. 1 (1985) pp. 185-188 :

   Resonance Families and PCAC

   Taketoshi Ino

2. Progress of Theoretical Physics Vol. 74 No. 2 (1985) pp. 409-412 :

   High-Energy Behaviours of a Uniquely Determined π-π Dual Born Amplitude

   Taketoshi Ino

3. Progress of Theoretical Physics Vol. 82 No. 5 (1989) pp. 988-1001 :

   Resonance Families and Local Duality Relations int the Meson-Baryon Scattering

   Taketoshi Ino

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