Spacelike and timelike response of confined relativistic particles

Basic theoretical issues relating to the response of confined relativistic particles are considered including the scaling of the response in spacelike and timelike regions of momentum transfer and the role of final state interactions. A simple single particle potential model incorporating relativity and linear confinement is solved exactly and its response is calculated. The response is studied in common approximation schemes and it is found that final state interactions effects persist in the limit that the three-momentum transferred to the target is large. The fact that the particles are bound leads to a non-zero response in the timelike region of four-momentum transfer equal to about 10% of the total strength. The strength in the timelike region must be taken into account to fulfill the particle number sum rule. PACS. 13.60.Hb Total and inclusive cross sections (including deep-inelastic processes) – 12.39.Ki Relativistic quark model – 12.39.Pn Potential models