Soft physics at the LHC Alan Martin (Durham) October 2007 A brief survey of diffraction New model for high energy proton-proton interactions, based on a full set of multi-Pomeron interactions, as well as including multichannel eikonal scattering The model description of the total, elastic and (low and high mass) diffractive cross sections; and the predictions for the LHC Ryskin, Martin, Khoze arXiv:

Soft interactions Hard diffraction

elastic unitarity  e -  is the probability of no inelastic interaction.

Inelastic diffraction

includes low M dissociation High M dissociation

Evolution of elastic bare Pomeron amplitude Multi-Pomeron contrib n

amplitude containing full sum of multi-P diagrams g n m g1mg1m gn1gn1 0 y Y y’=Y-y

Single dissociation  SD

prob. of c in dy’ amp. of c-i int n no additional i-k scatt elastic  (c-k)

Double dissociation  DD

low M dissoc. given eikonal --- y 0 =2.3 for y evol n (M>2.5GeV) use 3-channel eikonal (results similar for 2-ch.)  i -Pomeron vertex:  i (A) each compt.  i same trans. size / differs in parton density (B) compts. differ in trans. size / max. density same CERN-ISR expts: 2 – 3 mb fixed by CDF d  SD /dx L dt data  0 = (  i ) 2 Model fit to existing soft pp data

elastic scattering inelastic scatt CERN-ISR measurements of single dissoc n at low mass

SD RP: 220 RP: 420 SD energy dep. SD t dep.

   “large”    “small”

full multi-Pomeron contrib n full 3-P contrib n only first 3-P diagram

in EPJC(2000)

SD RP: 420 RP: x L growth due to Pomeron interactions compensated by stronger absorption, i.e. decrease of S 2

from the model actually directly related to elastic data

assuming point-like production – we fold in hard matrix element in a moment

  H

Conclusions First, self-consistent multi-Pomeron, multi-ch eikonal of soft pp interactions g n m = All multi-P interactions collected in factors which describe absorption of intermediate partons during the evolution of the parton cascade Even with minimum no. of parameters, get satisfactory description of all available soft data --- model (B) favoured Inescapable consequence of absorption by low M in eikonal rescatt. and high M in multi-P int n :  (total) ~ 90 mb at LHC In principle, can predict all diffractive processes at LHC but important to measure low M SD etc. to constrain model

GLM model