Soft diffraction at the LHC and properties of the Pomeron †

We briefly describe a model for soft diffraction. The model description of ISR, Spp̄S and Tevatron data, and the predictions of the total, elastic, single and double diffractive cross sections at the LHC can be found in the original paper. Here we address issues raised at Diffraction 2000, in particular concerning the nature of the resulting Pomeron trajectory. †Based on a talk by M.G. Ryskin at Diffraction 2000, Cetraro, Italy, September 2000 1 Model for soft diffraction Here we discuss a recent description [1] of soft diffraction in high energy pp (or pp̄) collisions which embodies (i) pion-loop insertions in the bare Pomeron pole, which represent the nearest singularity generated by t-channel unitarity, (ii) a two-channel eikonal which incorporates the Pomeron cuts generated by elastic and quasi-elastic (with N∗ intermediate states) s-channel unitarity, (iii) high-mass diffractive dissociation. To implement (i), we follow Anselm and Gribov [2] and write the Pomeron trajectory αIP (t) = α(0) + α ′t + β πm 2 π 32π3 h(t), (1) where α(0) + α′t is the bare trajectory and where the pion-loop insertions are given by h(t) = − τ F 2 π (t) [ 2τ − (1 + τ) ln (√ 1 + τ + 1 √ 1 + τ − 1 ) + ln μ mπ ] , (2) with τ = 4mπ/|t| and μ = 1 GeV. The coefficient β π specifies the ππ total cross section and Fπ(t) is the form factor of the pion-Pomeron vertex. The coefficient of h(t) in (1) is small but, due to the tiny scale mπ, the t dependence of h(t) is steep and non-linear. In this way we correctly reproduce the behaviour of the diffractive amplitude in the peripheral region. Note that h(t) of (2) has been renormalized [2] such that h(t) = hπ(t) − hπ(t = 0), (3) where hπ(t) denotes the full pion-loop contribution. The value of hπ(0) is determined by large virtualities of the pion, which are controlled by the scale μ. For this reason the contribution, β πm 2 π hπ(0)/32π 3 ∼ 0.1, (4) has been included in α(0), which describes the small size (∼ 1/μ) component of the Pomeron.