Fragmentation and energy conservation in the eikonal-Regge model

We have studied the effect of fragmentation and energy conservation in the eikonal-Regge model. A generalized eikonal representation involving multi-impact parameters is given for the elastic and inelastic amplitudes when fragmentation takes place. The generalized eikonal function which describes a many-body potential depends on more than one impact parameter. In the strong-absorption model and at high energy, however, the elastic amplitude can be approximated by a single-impact-parameter representation with an effective eikonal function. As a result of the fragmentation, we find that although ${\sigma }_E$ and ${\sigma }_T$ still increase as ${\ln }^{2}s$, their ratio is no longer ½. Instead, it is the sum of the elastic and diffractive cross sections which remains to be one half of the total cross section. To enforce the energy conservation, we propose a thermodynamic approach by introducing an impact-parameter-dependent temperature. Using well-known thermodynamics relations, we obtain various corrections to the naive eikonal-Regge model predictions due to energy conservation. Experimental consequences are discussed.