Diffraction at the LHC

1. Diffraction at the LHC A brief introduction to diffraction New model for high energy proton-proton “soft” interactions, based on a full set of multi-Pomeron interactions, as well as including multichannel eikonal scattering Ryskin, Martin, Khoze, arXiv:0710.2494 The model description of the total, elastic and (low and high mass) diffractive cross sections; and the predictions for the LHC Estimates of S2(Higgs): critique of recent models Alan Martin (Durham) Manchester Workshop December 2007

2. Optical theorems high energy stotal = s aP(0)-1 naïve---eff. pole High mass diffractive dissociation triple-Pomeron diagram t (M2)aP(0)-1 (s/M2)2aP(t)-1

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

4. Inelastic diffraction

6. includes low M dissociation High M dissociation

7. If you attempt to describe high mass diffraction in terms of a pure eikonal framework, then in the rapidity region where the parton showers overlap you are double counting c d • includes interaction of partons c and d • describes high M being considered separately • from each proton …..cannot avoid multi-Pomeron framework

8. Partonic evolution First, consider bare Pomeron contrib. to elastic amp. “splitting fn.” is prob. to emit parton c in dy so (Recall W=f) Multi-P contrib. corresponds to absorption of c during evolution is opacity of ck intern introduce l as ik = ck scatt. allows for many rescatt. (nm multi-P vertex: gnm ~ nm ln+m-2) 

9. gn1 Y y g1m 0 amplitude containing full sum of multi-P diagrams gnm y’=Y-y

10. Single dissociation sSD

11. amp. of c-i intn elastic s(c-k) prob. of c in dy’ no additional i-k scatt

12. Double dissociation sDD

13. low M dissoc. given eikonal --- y0=2.3 for y evoln (M>2.5GeV) use 3-channel eikonal (results similar for 2-ch.) fi-Pomeron vertex: bi • each compt. bi same trans. size / differs in parton density • compts. differ in trans. size / max. density same CERN-ISR expts: 2 – 3 mb l fixed by CDF dsSD/dxLdt data s0 = ( bi ) 2 Model fit to existing soft pp data

14. CERN-ISR measurements of single dissocn at low mass elastic scattering inelastic scatt

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

16. ~ g, sea ? f1: “large” f3: “small” ~ valence ?

17. 3-channel eikonal, multi-Pomeron analysis of available soft data

18. full multi-Pomeron contribn if give parameters unchanged full 3-P contribn only first 3-P diagram

20. SD growth due to Pomeron, i.e. D > 0, compensated by stronger absorption, i.e. decrease of S2 0.01 0.1 1-xL RP: 220 RP: 420

21. from the model actually directly related to elastic data

22. Discussion of Survival Probabilites …but, first, a comparison of the recent models used to estimate them: KMR arXiv:0710.2494 GLM model B(2) arXiv:0708.1506 Frankfurt, Hyde, Strikman, Weiss arXiv:0710.2942

23. KMR GLM FHSW Treatment of diffractive dissociation low M: 3-ch eikonal high M: multi-P 2-ch eik. for all SD, DD 1-ch eik estimated? but use DGLAP gluon at x~10-6 Enhanced diagrams for hard diffn No… show they are small No Diffractive eigenstates larger absorpn large RT compt. largest absn small RT SD, DD not studied ? stot, dsel/dt dsSD/dtdxL, sDD (Dy>3) stot, sel, Bel sSD, sDD (extrapol) hopefully stot, sel ? Data described v.close to 1  sSD,sDD~v.small felTevatron(b=0) ~0.9 ~0.6

24. GLM model LHC KMR models Tevatron

25. GLM model

26. Survival Probability survival factor w.r.t. soft i-k interaction hard m.e. i k  X average over diff. estates i,k over b If the outgoing protons are observed (with pT=0), then average amps

27. averaged over diff. estates at given b To get complete S2, average over b with weight with with

28. ggH naïve assumption

29. Estimate of S2 for exclusive Higgs production at the LHC using the naïve assumption KMR GLM(B(2)) FHSW 0.02 0.007 < 0.01 claim reduction of 4-5 from enhanced diagrams !! ~unchanged since KMR(2000) model does not describe dsel/dt DGLAP at v.small x ! v.few details in FHSW papers ? fi bizarre: in practice, include proton pT’s, proper propagators ~0.03 uncertainty factor 2.5 4mb 1400mb needed so sSD, sDD non-zero

30. enhanced eikonal BBKM. (first) corrn could be large and -ve,

31. BBKM  (first) corrn could be large and -ve,

32. BBKM (pQCD analysis) find first corrn could be large and –ve. BUT…need to sum complete set of diagrams. Terms alternate in sign. Amp 70% sum The new “soft” non-perturbative analysis finds that even at low QT, amp. is not completely suppressed QT~2GeV ln QT2 1st term corrn affects mainly small QT (large size dipoles)

33. Conclusions We presented a self-consistent multi-Pomeron, multi-ch eikonal model of soft pp interactions---basedon parton shower framework, so can be implemented in a Monte Carlo. 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 intn: s(total) ~ 90 mb at LHC To fix the model, crucial to measure t dep. of dsSD/dt in low M region, and the DPE cross section, at the LHC No reason to doubt the KMR estimate of S2(exclusive Higgs)