Connection between fixed-angle and fixed-momentum-transfer scattering in the framework of the double phase representation

Journal Article · Mon Aug 01 00:00:00 EDT 1977 · Phys. Rev., D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.16.646· OSTI ID:7090588

Grunberg, G

The double phase representation of Sugawara and Nambu, which assumes some simple analytical properties with respect to momentum transfer for the phase of the amplitude, is applied to the discussion of large-angle scattering. From the assumptions of Regge behavior and finite asymptotic Regge trajectories, one derives the fixed-angle scaling laws F (s,theta) approx. = s/sup ..delta..//sup F/(theta), and the extrapolation to the large-angle region of the Regge formula; the high-momentum-transfer behavior of Regge residues is thereby obtained. As a byproduct, we get the general form of the amplitude (including its phase) in the large-angle region for given values of ..delta.. and of the three asymptotic leading Regge trajectories in the s, t, and u channels. The angular dependence of various scattering processes is determined, using as input the values of ..delta.. and of the asymptotic trajectories given by the constituent-interchange model. A strong correlation between the forward-backward asymmetry of the angular distribution in a given channel and the ratio of the 90/sup 0/ cross sections in the other two channels is shown to be present in a simple case. Applied to ..pi../sup 0/..pi../sup 0/ scattering the double phase representation shows, together with positivity and the Froissart bound, that the angular distribution can take only two possible forms for each choice of the fixed-angle power ..delta..; in this case one also finds, using the Kinoshita-Loeffel-Martin upper bound, that the asymptotic Pomeron trajectory is bounded from above either by 0 or by 2/3.

• Research Organization: Departement de Physique Mathematique
• OSTI ID: 7090588
• Journal Information: Phys. Rev., D; (United States), Vol. 16:3
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
MESON-BARYON INTERACTIONS
SCATTERING AMPLITUDES
PION-PION INTERACTIONS
REGGE TRAJECTORIES
SCALING LAWS
ANGULAR DISTRIBUTION
CROSS SECTIONS
LINEAR MOMENTUM TRANSFER
AMPLITUDES
DISTRIBUTION
HADRON-HADRON INTERACTIONS
INTERACTIONS
MESON-MESON INTERACTIONS
MOMENTUM TRANSFER
PARTICLE INTERACTIONS
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