Bounds on the Asymptotic Behavior of an Elastic Scattering Amplitude near the Forward Direction

概要

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Upper and lower bounds on the asymptotic behavior of Im F(s,t)-^^-^^-A(s,ν) and its higher derivatives on ν for large s with ν fixed to small non-positive values are derived using the results from axiomatic quantum field theory. Here, F(s,t) is a certain elastic scattering amplitude, s and t are the usual Mandelstam variables, ν-^^-^^-t(ln(s/S_0))^2 and s_0 is an unknown scaling factor. The rough forms of the results are: [numerical formula] [numerical formula] for υ_1/^<υ/^<0 and n=1,2,3<<{sσ_⁢tot>(s)/16_π}^1/2 , where A^^-(s,υ)-^^-^^-A(s,υ)/A(s, o),A^^-^<(n)>(s,υ)-^^-^^-d^n/dυ^n)/A(s, o), c_1, C_2, C_3, C_4, , and -υ_1 are positive constants. In connection with these bounds, it is proved that A(s,υ) and its higher derivatives on υ can be expanded into a power series of υ for large s and the higher order terms can be neglected even when s goes to infinity if υ is fixed to a sufficiently small value. An upper bound on the position of the zero of A(s,υ) as a function of υ(for large s) is derived and is compared with the result of Bessis.
理論物理学刊行会の論文
1971-08-25