2-VARIABLE EXPANSION OF SCATTERING AMPLITUDE FOR ANY MASS AND CROSSING SYMMETRY FOR PARTIAL WAVES

A two-variable expansion of the scattering amplitude for the process a+b c+d is proposed, where a, b, c, and d are spinless particles of arbitrary mass. It is diagonal in angular momentum, displays the threshold and pseudothreshold behavior of partial waves, and leads to sum rules which contain a finite number of partial waves due to the crossing symmetry of the collision amplitude. The results of our previous work are recovered when the masses are equal. The reaction +N +N is treated with the inclusion of nucleon spin. The expansion is valid over the Dalitz plot for a decay amplitude. A simple method to derive sum rules which relate a finite number of partial waves without the use of the two-variable expansion is also outlined. © 1969 The American Physical Society.