Evolution equation for soft physics at high energy

P Brogueira (1) , J Dias de Deus (1)

1 Departamento de Física

Based on the non-linear logistic equation we study, in a qualitative and semi-quantitative way, the evolution with energy and saturation of the elastic differential cross-section in pp(¯ pp) collisions at high energy. Geometrical scaling occurs at the black disk limit, and scaling develops first for small values of the scaling variable |t|σ tot.. Our prediction for dσ/ dt at LHC, with two zeros and a minimum at large |t| differs, as far as we know, from all existing ones. Evolution equation for soft physics at high energy 2 Saturation phenomena are expected to dominate QCD physics at high energy and high matter density [ 1, 2 ], as it may happen at LHC and cosmic rays at ultra high energies. This is in fact an old problem related to unitarization and the need to reduce particle multiplicity and lowering total cross sections (see, for instance, [ 3]). Non linear differential equations include, in a natural way, saturation effects. This happens with the well known logistic equation[4 ]. See[5 ] and [ 6 ] for discussions on evolution and saturation. We shall concentrate here in the evolution of the imaginary part of the impact parameter elastic amplitude, or the profile function Γ(b, R) ≡ Im B(b, R), where b is the impact parameter, related to angular momentum.

Mots clés: Physical Sciences

P Brogueira, J Dias de Deus. Evolution equation for soft physics at high energy. Journal of Physics G: Nuclear and Particle Physics, 2010, 37 (7), pp.75006. ⟨10.1088/0954-3899/37/7/075006⟩. ⟨hal-00630017⟩