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Title: DOUBLE-PHASE REPRESENTATION OF ANALYTIC FUNCTIONS

DOUBLE-PHASE REPRESENTATION OF ANALYTIC FUNCTIONS The double phase representation for the elastic scattering amplitude A(s,t,u) as a function of the covariant Mandelstam variables s, t, and u is discussed. Conditions for the existence of the double representation, and their implications, are examined. The asymptotic forms of this double phase representation when some of s, t, and u become infinite are derived in the case when the phase approaches the limit at infinity not too slowly. This is the case when the elastic scattering anrplitude exhibits asymptotically a power behavior in energy (usually called the Regge behavior). In particular, the case when the forward peak of high-energy elastic scattering does not shrink is examined closely. No-shrinkage is found to be the case when the phase in the crossed channel does not diverge logarithmically at infinity in its momentum-transfer plane. If the forward peak shrinks, the above phase diverges logarithmically at infinity ln the case of no-shrinkage, the asymptotic shape of the forward peak is determined solely by the phase in the crossed channel. Furthermore, the above shape assumes a pure exponential function of the covariant momentum-transfer squared when momentum-transfer is small, more » and approaches a power behavior in the same variable for large momentumtransfer. Some of the specific predictions of the phase representation approach to high-energy elastic scattering are listed. (auth) « less
Authors: ;
Publication Date:
OSTI Identifier:OSTI ID: 4664549
Report Number(s):TID-19142
DOE Contract Number:AT(11-1)-264
Resource Type:Technical Report
Resource Relation:Other Information: Orig. Receipt Date: 31-DEC-63
Research Org:Purdue Univ., Lafayette, Ind.; Chicago. Univ. Enrico Fermi Inst. for Nuclear Studies; Chicago. Univ.
Sponsoring Org:USDOE
Country of Publication:United States
Language:English
Subject: PHYSICS; ANGULAR DISTRIBUTION; CROSS SECTIONS; ELEMENTARY PARTICLES; FIELD THEORY; MANDELSTAM REPRESENTATION; MATHEMATICS; MOMENTUM; REGGE POLES; SCATTERING