Soft Physics at the LHC: gap survival and Monte Carlo Khoze-Martin-Ryskin + Krauss, Hoeth, Zapp --- IPPP, Durham Forward Physics at the LHC Manchester, December 2009 Importance of minimum-bias events (and rap. gap survival) Up to now no complete model (Monte Carlo) including all facets --- elastic scattering, diffractive events, hard jets, etc. --- on the same footing Intimate connection to underlying event First physics at the LHC More specific physics reasons – 2 examples from Higgs searches

1. Higgs search via vector-boson fusion Signature: two forward jets + rap.gap filled by Higgs decay Essential for S/B: survival rate of gap Typical manifestation of gap: central jet/hadron veto Folklore: requirement of central gap effectively suppresses QCD-driven background Gap survival depends on extra jets + underlying event (calculable) (need Monte C.)

2. pp  p+H+p Base value: s = 2.5 fb update SM MH=120 GeV LHC=14 TeV eikonal screening H Base value: s = 2.5 fb update -45% adjust c in upper limit 1 - kt/(cMH+kt) of z integration of Sudakov factor to reproduce one-loop result. Find c=1 (Coughlin, KMR09), and not 0.62 (KKMR04) -25% if enhanced screening included (KMR-0812.2413) +20% due to NLO unintegrated gluon (MRWatt-0909.5529) +20% connected with self-energy insertions in propagator of screening gluon (Ryskin et al.) see later PS Recall factor 3 uncertainty PPS Remember SUSY Higgs can be greatly enhanced

Model for “soft” high-energy interactions needed to ---- understand asymptotics, intrinsic interest ---- describe “min. bias/underlying” events ---- calc. rap.gap survival prob. S2 ---- devise “all-purpose” Monte Carlo 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 due to enhanced rescatt. 4. be suitable for “all-purpose” MC --- partonic approach

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

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

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

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 include high-mass diffractive dissociation (SD -80%) g3P “large”

Towards a partonic interpretation Structure of the Pomeron before QCD sum of ladder diagrams  sa behaviour cut: scalar particles contribn of cell (Y=ln s) kt limited. Impossible to obtain a(0)>1 for m<1.5 GeV, but for larger m we have larger kt  pQCD

Partonic QCD structure of the Pomeron gluon ladder – spin 1 gives extra s n-1 rungs recursion reln: BFKL kernel n rungs Random walk: current cell differs from previous by

Smooth transition from “hard” to “soft” Pomeron? No irregularity in HERA data in Q2 = 0.3 – 2 GeV2 region Global analysis of “soft” data (including absorptive effects) give “bare” slope a’ < 0.1 GeV-2 (a’ ~ 1/<kt2> --- kt in perturbative region) give “bare” intercept D = aP(0) - 1 ~ 0.3 The absorptive effects increase as we go to low kt: screening  aPeffective ~ 1.08 + 0.25 t (t in GeV2) (up to Tevatron energies) see later

Partonic QCD structure of the Pomeron gluon ladder – spin 1 gives extra s n-1 rungs recursion reln: BFKL kernel n rungs Random walk: current cell differs from previous by

Partonic interpretation “bare” Pomeron pole contribn to elastic amp D = splitting function = prob. of emission of parton c in dy evolution eq. Multi-Pomeron contribns e.g. triple-Pomeron diagram: parton c has extra scattering with “target” k

Multi-Pomeron contribns continued Many rescatt: different no. of ladders between c and k where lWk reflects the different opacity of “target” k felt by c, rather opacity Wk than felt by “beam” i l~0.25 Include rescatt of c with “beam” i evolve up from y=0 Y evolve down from y’=Y-y=0 y’ =Y-y y solve iteratively

Y Wi Wk i b2 c b b1 k

only y dep. of evolution shown. Need b and kt dep. to calc Senh2 pole: in mom. space  s1+D+a’ t BFKL diffusion in log kt2 rescatt. between low x, low kt partons and “target” distorts input distribn -- violates soft-hard factorizn P1 P3 large kt partons -- rescatt. negligible H Simplify the kt behaviour: sec. Reggeon 3 compts to mimic BFKL diffusion in ln kt full treatment in progress a = Plarge, Pintermediate, Psmall, R average kt1~0.5, kt2~1.5, kt3~5 GeV

Evolve and tune to all soft data: VRP1 ~ gPPR,gRRP with a = P1, P2, P3, R VPiPj ~ BFKL soft QCD Evolve and tune to all soft data: -- multi-Pomeron coupling l from xdsSD/dxdt data ( x~0.01) -- info on diffractive eigenstates from sSD(low M) = 2 mb at ISR -- info on form factors from dsel/dt Results l=0.25 “bare” Pomeron: DP = a(0)-1~ 0.3, a’P ~ 0.05 GeV-2 P1 heavily screened  effective DL Pomeron (up to Tevatron) s(tot) ~ 90 mb at LHC (suppressed by screening) DReggeon ~ -0.4 (as expected)

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

Description of CDF dissociation data no ppP no ppP

“soft” Pomeron: partons saturated little growth “hard” Pomeron: little screening much growth s0.3

Survival prob. for pp  p+H+p at LHC Eikonal rescattering ---- consensus Effect of enhanced rescattering ---- controversy

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

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

gap gap Two subtlities H 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 0812.2413 <S2tot><pt2>2 = 0.0010 GeV4

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 correln. GLM assume enh. abs. is the same at all b (so does not depend on parton density at given b). But 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. 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.ut

Comments on Strikman et al. also predict a v.small Senh ?! They use LO gluon with v.steep 1/x behaviour. Obtain black disc regime at LHC energy, with low x (10-6) gluon so large that only on the periphery of the proton will gap have chance to survive. However, empirically the low x, low Q2 gluon is flat for x < 10-3 – the steep 1/x LO behaviour is an artefact of the neglect of large NLO corrections. Again, should compare model with CDF exclusive data.

Monte Carlo based on simplified KMR model Existing “all purpose” Monte Carlos split eikonal W(s,b) = Wsoft + Whard(pQCD) We seek MC that describes all aspects of minimum bias -- total, differential elastic xsections, diffraction, jet prod...— in a unified framework; capable of modelling exclusive final states. Monte Carlo based on simplified KMR model Krauss, Hoeth, Zapp Status report: first, outline steps of producing the MC

step 1: solve evoln eqs and generate Wik(b) Y Wi Wk i b2 c b b1 k

step 2: generate ladders step 3: generating emissions

step 3: generating emissions contd 8 8 8 8 1 1 8 8 8 8

step 4 step 5 Select “beam” partons (xi,Qi2) from known PDFs Check energy conservation, step 2. step 5 Implement the “usual” parton shower + hadronisation + hadron decays + QED … Can such an “all purpose” Monte Carlo, based on a model tuned to describe elastic, diffractive processes, also really describe inelastic, single-particle production etc. (e.g. p+ pT distribution)?

First Monte Carlo results v. encouraging: -- total and elastic differential cross sections OK -- single jet and identified particles ~OK e.g. p+, jet,… xsections at STAR (pp 200 GeV) -- <pt> versus Nch, dNch/dh OK -- minimum bias CDF (1800 GeV): “Rick Fields” plots ~OK in “forward” and “away” Dj quadrants undershoot in “transverse” quadrants  need to extend simple model, particularly for large triggering scale, where inclusion of BFKL diffusion should help

p+ transverse momentum

Mean track pT vs multiplicity

Charge multiplicity

leading jet Nch in toward region Toward region Nch in away region

Nch in transverse region Improvement needed in the transverse region. Not enough particles, tho’ find the average pT per particle is OK

Conclusions -- Obtained a fully consistent description of all high-energy soft interactions; the model incorporates both a multi-channel eikonal and multi-Pomeron interactions -- screening/unitarity/absorptive corrections are appreciable at LHC energies. (stotal (14 TeV) ~ 90 mb) -- soft-hard Pomeron transition emerges “soft” compt. --- heavily screened --- little growth with s “hard” compt. --- little screening --- large growth (~pQCD) -- Model allows both eikonal and enhanced rescatt. corrections and gap survival prob. to be calculated for any diffractive proc. -- Model has partonic interpretation, so can form basis of “all purpose” Monte Carlo. Model tuned to describe elastic, diffractive processes, but MC also gives description of multiparticle production. Preliminary results v.encouraging.