Pp Total Cross Section Rise with a Renormalized Romeron

Abstract

The single-loop Pomeron diagram connected through the generalized optical theorem to two-cluster production is used to construct an integral equation. The infinite class . of Pomeron loop diagrams taken into account by this equation effectively renormalizes the Pomeron singularity. A simple pole Pomeron·at IXo=l is renormalized by this procedure into a j-plane pole-doublet and leads to a rising pp total cross section. Single or double-particle diffrac:tive dissociation has been one of several mechanisms proposed to account for the observed proton-proton total cross section rise above PL=50 Ge V / c.u- 4> It is found, however, that quantitative predictions from either one are insufficient5'- 7' to explain this experimental feature, although numerical results vary according to the chosen functional form and strength at t=O of the triple Pomeron coupling.8'· 9' In this work we start from a bare Pomeron trajectory a ( t) = a 0 +a' t ex­ changed between two diffractively produced fireballs, and assumed to control the triple-Regge region. 10' An integral equ~tion is then constructed to sum the class of (bare) Pomeron loop-diagrams that correspond to diffractive production of an unrestricted number of fireballs. This equation is (approximately) solved and the contribution to the elastic amplitude of the resulting renormalized Pomeron is obtained and compared to pp total cross section data. One secondary term rvs- 1/ 2 is added to extend the description of data down to PL=10GeV/c. Proton-proton scattering may produce an event with at least one large repidity gap separating groups of particles. If the energy is larger than some certain threshold, a minimum separation in rapidity is ensured between the fireballs. The cross section for two fireballs with masses squared s1 and s2 is given in the Regge asymptotic limit by1n' 12'