Quick Search:
Prog. Theor. Phys. Vol. 43 No. 4 (1970) pp. 986-1001
A Model for the Scattering Amplitudes and Its Application to ππ and πN Scattering
Sunao Sakai
Department of Physics, Tokyo University of Education, Tokyo
(Received September 18, 1969)
Abstract:
A new model for scattering amplitudes is proposed. This model satisfies the finite energy sum rule, unitarity at threshold, and other desirable physical properties of scattering amplitudes. In this model daughters are also contained and the duality in our sense is related to Regge pole and cut (scattering state) duality, which is different from the conventional duality relating only to Regge poles.
The ππ amplitudes are constructed in our model under the condition of exchange degeneracy of αρ and αf. Our model gives good results on scattering lenghts. Adler's self-consistency condition gives αρ (µ2) > ½, which is consistent with the experimental results of αρ (0) = 0.57 ±0.01 and is different from Lovelace's results. The high energy amplitudes obey the Gell-Mann mechanism.
The πN amplitudes are constructed in our model under the conditin of non-exchange degeneracies among αα, αδ and αγ trajectories. Our πN amplitudes satisfy isospin constraints both in low and in high energy regions, and Δα= 2. Adler's self-consistency relation is approximately satisfied. The determination of free parameters from low energy resonances predicts high energy amplitudes which are consistent with experimental analysis.
URL :
http://ptp.ipap.jp/link?PTP/43/986/
DOI : 10.1143/PTP.43.986
References:
- G. Veneziano, Nuovo Cim. A 57 (1968), 190.
- C. Lovelace, Phys. Lett. B 28 (1968), 265.
K. Kawarabayashi, S. Kitakado and H. Yabuki, Phys. Lett. B 28 (1968), 432[CrossRef].
-
S. Mandelstam, Phys. Rev. Lett. 21 (1968), 1724[APS].
-
H. Rosenfeld et al., Rev. Mod. Phys. 41 (1969), 109[APS].
-
K. Igi, Phys. Lett. B 28 (1968), 330[CrossRef].
-
S. L. Adler, Phys. Rev. B 137 (1965), 1022[APS].
-
G. Höhler, J. Baacke, H. Schaile and P. Sonderegger, Phys. Lett. 20 (1966), 79[CrossRef].
C. H. Chan and L. K. Chavda, Phys. Rev. Lett. 22 (1969), 1228[APS].
- C. Lovelace, “ππ, Kπ, KK Phase Shifts and Their Off-Shell Dependence from Unitarized Veneziano Formula” TH. 1041-CERN preprint.
- Erdery, Magnus, Oberhettinger and Tricomi, Higher Transcendental Functions (McGraw-Hill Book Company, Inc., New York, 1953), Vol. 1.
- M. Ademollo and E. Del Giudice, “Non-Strong Amplitudes in a Veneziano Type Model”, MIT preprint.
-
S. Weingerg, Phys. Rev. Lett. 17 (1966), 616[APS].
- G. Cohen-Tannoudji, A. Morel and H. Navelet, Nuovo Cim. A 48 (1968), 1075.
M. Biyajima, S. Sakai and T. Watanabe, “Regge Pole Model with Diffractive Correction. I” (charged pion photoproduction) TUEP-69-9.
-
V. Barger and D. Cline, Phys. Rev. Lett. 19 (1967), 1504[APS];
ibid. 21 (1968), 392[APS].
-
T. T. Chou and C. N. Yang, Phys. Rev. 170 (1968), 1591[APS].
Chan Hong-Mo, “Collisions at High Energy”, Proceedings of the 14th International Conferene on High Energy Physics, Vienna (1968).
-
J. D. Bjorken, Phys. Rev. 148 (1966), 1467[APS].
- S. Fubini, Nuovo Cim. 43 (1966), 475.
J. B. Bronzan, I. S. Gerstein, B. W. Lee and F. E. Low, Phys. Rev. 157 (1967), 1448[APS].
- H. Sugawara, “Reggeized Pole Approximation to Non-Hadronic Processes” TUEP-69-4.
-
P. D. B. Collins, R. C. Johnson and E. J. Squires, Phys. Lett. B 27 (1968), 23[CrossRef].
-
C. Schmid, Phys. Rev. Lett. 20 (1968), 689[APS].
Citing Article(s) :
-
Progress of Theoretical Physics Vol. 46 No. 3 (1971) pp. 938-967
:
-
Hadronic Scattering Amplitudes in the Quark Model. II
-
Tsunehiro Kobayashi
-
Progress of Theoretical Physics Vol. 47 No. 1 (1972) pp. 208-227
:
-
An Approach to Regge Behaviour and Duality Based on an Infinite Sum of One-Particle-Exchange Amplitudes
-
Kisei Kinoshita, Masanori Kobayashi and Kunio Shiga
