Soft models and survival probability

1. Soft models and survival probability Low x meeting, Ischia Island,Italy September 8th – 13th 2009 Alan Martin, IPPP, Durham

2. “soft” scatt. destroys gaps in exclusive prod. e.g. pp  p+H+p gap • ~ S2 fg MggH fg H gap soft-hard factorizn conserved broken gap survival prob. S2 to “soft”… eikonal rescatt: between protons enhanced rescatt: involving intermediate partons

3. Model for “soft” high-energy interactions needed to ---- understand asymptotics, intrinsic interest ---- describe “underlying” events for LHC jet algorms ---- calc. rap.gap survival S2 for exclusive prodn “Soft” model should: • be self-consistent theoretically --- satisfy unitarity •  importance of absorptive corrections •  importance of multi-Pomeron interactions • 2. agree with available soft data • CERN-ISR to Tevatron range • 3. include Pomeron compts of different size---to study effects of • soft-hard factn breaking

4. at high energy use Regge Optical theorems but screening important so stotal suppressed gN2 High mass diffractive dissociation 2 M2 triple-Pomeron diag but screening important gN3g3P so (g3P)bare increased

5. Must include unitarity diagonal in b ~ l/p elastic unitarity  e-W is the probability of no inelastic interaction

6. given by data DL parametrization: Effective Pomeron pole aP(t) = 1.08+0.25t KMR parametrization includes absorption via multi-Pomeron effects

7. Elastic amp. Tel(s,b) bare amp. Im (-20%) multichannel eikonal Low-mass diffractive dissociation introduce diffve estates fi, fk (combns of p,p*,..) which only undergo “elastic” scattering (Good-Walker) (-40%) Im (SD -80%) include high-mass diffractive dissociation g3P ?

8. triple-Regge analysis of ds/dtdx, including screening (includes compilation of SD data by Goulianos and Montanha) fit: c2 = 171 / 206 d.o.f. CERN-ISR Tevatron PPP PPR PPP PPR RRR RRP RRP ppP ppP x x g3P=l gNl~0.2 g3P large, need to include multi-Pomeron effects LKMR see also Poghosan, Kaidalov,..

9. g3P=l gNl~0.2  large ? 2 gN M2 g3P M2dsSD/dM2 ~ gN3 g3P ~lsel ln s so at collider energies sSD ~ sel

10. Multi-compt. s- and t-ch analysis of soft data KMR 2008 model: 3-channel eikonal, fi with i=1,3 include multi-Pomeron diagrams ansatz  attempt to mimic BFKL diffusion in log qt by including three components to approximate qt distribution – possibility of seeing “soft  hard” Pomeron transition lgN nm 2

11. Use four exchanges in the t channel 3 to mimic BFKL diffusion in ln qt sec. Reggeon a = Plarge, Pintermediate, Psmall, R soft pQCD average qt1~0.5, qt2~1.5, qt3~5 GeV VRP1 ~ gPPR,gRRP VPiPj ~ BFKL evolve up from y=0 bare pole absorptive effects evolve down from y’=Y-y=0 solve for Waik(y,b) by iteration (arXiv:0812.2407)

12. Parameters multi-Pomeron coupling l from xdsSD/dxdt data ( x~0.01) diffractive eigenstates from sSD(low M)=2mb at sqrt(s)=31 GeV, -- equi-spread in R2, and t dep. from dsel/dt Results All soft data well described g3P=lgN with l=0.25 DPi = 0.3 (close to the BFKL NLL resummed value) a’P1 = 0.05 GeV-2 These values of the bare Pomeron trajectory yield, after screening, the expected soft Pomeron behaviour --- “soft-hard” matching (since P1 heavily screened,….P3~bare) DR = -0.4 (as expected for secondary Reggeon) D = a(0) - 1

13. elastic differential ds/dt f1*f1 LHC (x0.1) ~ g, sea f3*f3 f1: “large” f3: “small” more valence

14. Description of CDF dissociation data no ppP no ppP

15. Predictions for LHC stotal (mb) stotal = 91.7 mb* sel = 21.5 mb sSD = 19.0 mb *see also Sapeta, Golec-Biernat; Gotsman et al. All Pom. compts have Dbare=0.3 parton multiplicity pppX “soft”, screened, little growth, partons saturated “hard” ~ no screening much growth, s0.3

16. HERA data smooth in transition region Q2 ~ 0.3 – 2 GeV2 slope of bare trajectory a’ < 0.1 GeV-2, so typical kt in Pom. amp relatively large (a’~1/kt2) bare aP(0) - 1 ~ 0.3, close to BFKL, after NLL are resummed “soft” Pomeron “hard” Pomeron

17. Calculation of S2eik for pp  p + H +p prob. of proton to be in diffractive estate i survival factor w.r.t. soft i-k interaction hard m.e. i k  H over b average over diff. estates i,k S2eik ~ 0.02 for 120 GeV SM Higgs at the LHC  s ~ 2 - 3 fb at LHC

18. Calculation of S2enhanced for pp  p + H +p gap H gap Main enhanced rescatt. occurs at beginning of evolution. Evolution of “beam” affected by enhanced intn with “target”. Senh changes (b, kt) distribn of active partons: breaks factn Inclusion of Pomeron qt structure enables S2enh to be calculated

19. enh. abs. changes P3 distribn model has 4 t-ch. exchanges P1 y1 P3 3 to mimic BFKL diffusion in ln qt y2 a = Plarge, Pintermediate, Psmall, R soft pQCD average qt1~0.5, qt2~1.5, qt3~5 GeV VRP1 ~ gPPR,gRRP VPiPj ~ BFKL evolve up to y2 bare pole absorptive effects evolve down to y1 ~ solve with and without abs. effects

20. Two subtlities gap H gap • fg’s from HERA data already include rescatt. • of intermediate partons with parent proton • Usually take pt=0 and integrate with exp(-Bpt2). • S2/B2 enters (where 1/B = <pt2>). But enh. abs. • changes pt2 behaviour from exp., so quote S2<pt2>2 <S2tot>=<S2eikS2enh> ~ 0.015 (for B=4 GeV-2) see arXiv:0812.2413 <S2tot><pt2>2 = 0.0015

21. Satn scale Qs2<0.3 GeV2 for x~10-6 from g pJ/y p Watt, Kowalski <Seik>2 ~ 0.02 0.6 fm parton only survives eik. rescatt. on periphery, where parton density is small and prob. of enh. abs. small

22. Comments on GLM(2008) GLM include some 3P effects, but get <Senh2> = 0.063 <Stot2> = 0.0235 x 0.063 = 0.0015 Calculation should be extended to obtain reliable Senh • Need to calc. b, kt dep., Senh comes mainly from periphery • (after Seik suppression) where parton density is small. • So Senh (GLM) is much too small. • 2. First 3P diagram is missing, so sSD much too small. • 3. Four or more multi-Pomeron vertices neglected, so stot • asymptotically decreases (but GLM have stot asym. const.). • Model should specify energy interval where it is valid. • 4. Need to consider threshold suppression. • 5. Should compare predictions with observed CDF data.

23. Comments on Strikman et al. also predict a v.small Senh ! They use LO gluon with steep 1/x behaviour. Obtain black disc regime at LHC energy, with low x gluon so large that only on the periphery of the proton will gap have chance to survive. However, empricially the low x, low Q2 gluon is flat – the steep 1/x LO behaviour is an artefact of the neglect of large NLO corrections. Again should compare to CDF exclusive data.

24. Conclusions – soft processes at the LHC -- screening/unitarity/absorptive corrections are vital -- Triple-Regge analysis with screening  g3P increased by ~3  importance of multi-Pomeron diagrams (include, not just 3P vertices, but mn vertices, otherwise stotal decreases asymptotically) -- Latest analysis of all available “soft” data: multi-ch eikonal + multi-Regge + compts of Pom. to mimic BFKL (showed some LHC predictions … stotal ~ 90 mb, sSD~ 20 mb) --soft-hard Pomeron transition emerges “soft” compt. --- heavily screened --- little growth with s, s0.08 “intermediate” compt. --- some screening “hard” compt. --- little screening --- large growth (~pQCD), s0.3

25. Conclusions – on gap survival probabilities -- There is consensus for survival prob. of gaps to eik. rescatt. e.g. S2=0.02 for pp  p+H+p at LHC for 120 GeV SM Higgs -- A reliable calcn. of survival to enhanced rescatt. requires a soft model which includes the kt dep. of Pomeron exchange (soft-hard factorization breaking). Calcn has subtlities. e.g. S2 reduced by about 30% (conservative). -- Largest unknown is low x, low Q2 gluon -- CDF exclusive data are encouraging. Exclusive dijet at LHC should be informative.