## Construction of Invariant Scalar Amplitudes

without Kinematical Singularities for

Arbitrary-Spin Nonzero-Mass

Two-Body Scattering Processes

### David N. Williams

#### September 9, 1967

Lawrence Radiation Laboratory

University of California, Berkeley
**Abstract:**
The relativistic transition amplitude for any two-body reaction
involving only particles of nonzero mass but arbitrary spin is
decomposed in terms of scalar amplitudes that are regular
functions in the space of scalar invariants at points
corresponding to regular points of the transition matrix
elements in momentum space, on the mass shell. Detailed
formulas for the scalar amplitudes in terms of the original
scattering matrix elements are given. The development is in the
framework of analytic S-matrix theory, and is based on a partial
generalization of the Hall-Wightman Theorem. The results hold
on the complete (multisheeted) domain of regularity of the
scattering amplitude.

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