%ASugaware, M.
%ANambu, Y.
%BOther Information: Orig. Receipt Date: 31-DEC-63
%D1963%KPHYSICS; ANGULAR DISTRIBUTION; CROSS SECTIONS; ELEMENTARY PARTICLES; FIELD THEORY; MANDELSTAM REPRESENTATION; MATHEMATICS; MOMENTUM; REGGE POLES; SCATTERING
%MOSTI ID: 4664549
%PMedium: ED; Size: Pages: 35
%TDOUBLE-PHASE REPRESENTATION OF ANALYTIC FUNCTIONS
%Uhttp://www.osti.gov/scitech//servlets/purl/4664549-EMNJGW/
%XThe 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, 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)
%ZOther Information: Orig. Receipt Date: 31-DEC-63
%0Technical Report
%@TID-19142
United States10.2172/4664549Thu Dec 18 07:00:10 EST 2008CHO; NSA-17-034737English