Predictions of Diffractive, Elastic, Total, and Total-Inelastic pp Cross Sections vs LHC Measurements Konstantin Goulianos The Rockefeller University DIS-2013, Marseille Diffractive X-Sections vs LHC Measurements K. Goulianos 1

CONTENTS DIS-2013, Marseille Diffractive X-Sections vs LHC Measurements K. Goulianos 2  The total pp cross section at LHC is predicted in a special fully unitarized parton model which does not employ eikonalization and does not depend on knowledge of the  -value.  The following diffractive cross sections are described in this model based on a LO QCD approach:  SD – SD1/SD2, single dissociation (one/the other proton dissociates).  DD - double dissociation (both protons dissociate).  CD – central dissociation (neither proton dissociates, but there is central production of particle).  This approach allows a unique determination of the Regge triple Pomeron coupling (PPP).  Details can be found in ICHEP 2012, 6 July 2012, arXiv: (talk by Robert Ciesielski and KG).

DIFFRACTION IN QCD Diffractive events  Colorless vacuum exchange   -gaps not exp’ly suppressed Non-diffractive events  color-exchange   -gaps exponentially suppressed POMERONPOMERON Goal : probe the QCD nature of the diffractive exchange rapidity gap p ppp p DIS-2013, Marseille Diffractive X-Sections vs LHC Measurements K. Goulianos 3

DEFINITIONS MXMX dN/d  ,t,t p’ rap-gap  =-ln  0 ln s ln Mx 2 ln s since no radiation  no price paid for increasing diffractive-gap width pp p MXMX p p’ SINGLE DIFFRACTION DIS-2013, Marseille Diffractive X-Sections vs LHC Measurements K. Goulianos 4 Forward momentum loss

DIFFRACTION AT CDF Single Diffraction or Single Dissociation Double Diffraction or Double Dissociation Double Pom. Exchange or Central Dissociation Single + Double Diffraction (SDD) SD DD DPE/CD SDD Elastic scatteringTotal cross section  T =Im f el (t=0) OPTICAL THEOREM   gap   JJ, b, J/   W p p JJ …ee…  exclusive DIS-2013, Marseille Diffractive X-Sections vs LHC Measurements K. Goulianos 5

Basic and combined diffractive processes 4-gap diffractive process-Snowmass gap SD DD DIS-2013, Marseille Diffractive X-Sections vs LHC Measurements K. Goulianos 6

KG-PLB 358, 379 (1995) Regge theory – values of s o & g PPP ? Parameters:  s 0, s 0 ' and g(t)  set s 0 ‘ = s 0 (universal IP )  determine s 0 and g PPP – how? DIS-2013, Marseille Diffractive X-Sections vs LHC Measurements K. Goulianos 7  (t)=  (0)+  ′t  (0)=1+ 

A complicatiion…  Unitarity! A complication …  Unitarity!   sd grows faster than  t as s increases *  unitarity violation at high s (similarly for partial x-sections in impact parameter space)  the unitarity limit is already reached at √s ~ 2 TeV !  need unitarization DIS-2013, Marseille Diffractive X-Sections vs LHC Measurements K. Goulianos 8 * similarly for (d  el /dt) t=0 w.r.t.  t  but this is handled differently in RENORM

Factor of ~8 (~5) suppression at √s = 1800 (540) GeV  diffractive x-section suppressed relative to Regge prediction as √s increases see KG, PLB 358, 379 (1995) 1800 GeV 540 GeV M ,t,t p p p’ √s=22 GeV RENORMALIZATION Regge FACTORIZATION BREAKING IN SOFT DIFFRACTION CDFCDF DIS-2013, Marseille Diffractive X-Sections vs LHC Measurements K. Goulianos 9 Interpret flux as gap formation probability that saturates when it reaches unity

Gap probability  (re)normalize to unity Single diffraction renormalized independent variables: t color factor gap probability subenergy x-section KG  CORFU-2001: DIS-2013, Marseille Diffractive X-Sections vs LHC Measurements K. Goulianos 10

Single diffraction renormalized - 2 color factor Experimentally: KG&JM, PRD 59 (114017) 1999 QCD: DIS-2013, Marseille Diffractive X-Sections vs LHC Measurements K. Goulianos 11

Single diffraction renormalized - 3 set to unity  determines s o DIS-2013, Marseille Diffractive X-Sections vs LHC Measurements K. Goulianos 12

M2 distribution: data KG&JM, PRD 59 (1999)  factorization breaks down to ensure M 2 scaling Regge 1 Independent of s over 6 orders of magnitude in M 2  M 2 scaling  d  dM 2 | t=-0.05 ~ independent of s over 6 orders of magnitude ! data DIS-2013, Marseille Diffractive X-Sections vs LHC Measurements K. Goulianos 13

Scale s 0 and PPP coupling DIS-2013, Marseille Diffractive X-Sections vs LHC Measurements K. Goulianos 14  Two free parameters: s o and g PPP  Obtain product g PPP s o  from  SD  Renormalized Pomeron flux determines s o  Get unique solution for g PPP Pomeron-proton x-section Pomeron flux: interpret as gap probability  set to unity: determines g PPP and s 0 KG, PLB 358 (1995) 379

Saturation at low Q 2 and small-x figure from a talk by Edmond Iancu DIS-2013, Marseille Diffractive X-Sections vs LHC Measurements K. Goulianos 15

DD at CDF renormalized gap probabilityx-section DIS-2013, Marseille Diffractive X-Sections vs LHC Measurements K. Goulianos 16

SDD at CDF  Excellent agreement between data and MBR (MinBiasRockefeller) MC DIS-2013, Marseille Diffractive X-Sections vs LHC Measurements K. Goulianos 17

CD/DPE at CDF  Excellent agreement between data and MBR  low and high masses are correctly implemented DIS-2013, Marseille Diffractive X-Sections vs LHC Measurements K. Goulianos 18

Difractive x-sections  1 =0.9,  2 =0.1, b 1 =4.6 GeV -2, b 2 =0.6 GeV -2, s′=s e -  y,  =0.17,  2 (0)=  0, s 0 =1 GeV 2,  0 =2.82 mb or 7.25 GeV -2 DIS-2013, Marseille Diffractive X-Sections vs LHC Measurements K. Goulianos 19

Total, elastic, and inelastic x-sections GeV 2 DIS-2013, Marseille Diffractive X-Sections vs LHC Measurements K. Goulianos 20 KG Moriond 2011, arXiv:  el p±p =  tot ×(  el  tot ), with  el  tot from CMG small extrapol. from 1.8 to 7 and up to 50 TeV ) CMG

The total x-section √s F =22 GeV 98 ± 8 mb at 7 TeV 109 ±12 mb at 14 TeV DIS-2013, Marseille Diffractive X-Sections vs LHC Measurements K. Goulianos 21 Main error from s 0

Reduce the uncertainty in s 0 DIS-2013, Marseille Diffractive X-Sections vs LHC Measurements K. Goulianos 22  glue-ball-like object  “superball”  mass  1.9 GeV  m s 2 = 3.7 GeV  agrees with RENORM s o =3.7  Error in s 0 can be reduced by factor ~4 from a fit to these data!  reduces error in  t.

TOTEM vs PYTHIA8-MBR DIS-2013, Marseille Diffractive X-Sections vs LHC Measurements K. Goulianos 23  inrl 7 TeV = 72.9 ±1.5 mb  inrl 8 TeV = 74.7 ±1.7 mb TOTEM, G. Latino talk at CERN 2012 MBR: 71.1±5 mb superball  ± 1.2 mb RENORM: 72.3±1.2 mb RENORM: 71.1±1.2 mb

CMS SD and DD x-sections vs ALICE: measurements and theory models DIS-2013, Marseille Diffractive X-Sections vs LHC Measurements K. Goulianos 24  KG*: after extrapolation into low  from measured CMS data using the MBR model: find details on data in Robert Ciesielski’s talk on Wed. at 15:30. Includes ND background KG*

DIS-2013, Marseille Diffractive X-Sections vs LHC Measurements K. Goulianos 25 Total-Inelastic Cross Sections vs model predictions

Monte Carlo Strategy for the LHC …   tot  from SUPERBALL model  optical theorem  Im f el ( t=0 )  dispersion relations  Re f el ( t=0 )   el  using global fit   inel =  tot -  el  differential  SD  from RENORM  use nesting of final states for pp collisions at the P­-p sub-energy √s' Strategy similar to that of MBR used in CDF based on multiplicities from: K. Goulianos, Phys. Lett. B 193 (1987) 151 pp “A new statistical description of hardonic and e + e − multiplicity distributios “  T optical theorem Im f el (t=0) dispersion relations Re f el (t=0) MONTE CARLO STRATEGY DIS-2013, Marseille Diffractive X-Sections vs LHC Measurements K. Goulianos 26

DIS-2013, Marseille Diffractive X-Sections vs LHC Measurements K. Goulianos 27 Monte Carlo algorithm - nesting y'cy'c Profile of a pp inelastic collision  y‘ <  y' min hadronize  y′ >  y' min generate central gap repeat until  y' <  y' min ln s′ =  y′ evolve every cluster similarly gap no gap final state of MC w /no-gaps t gap t t t1t1 t2t2

DIS-2013, Marseille Diffractive X-Sections vs LHC Measurements K. Goulianos 28 SUMMARY  Introduction  Diffractive cross sections:  basic: SD1,SD2, DD, CD (DPE)  combined: multigap x-sections  ND  no diffractive gaps:  this is the only final state to be tuned  Total, elastic, and total inelastic cross sections  Monte Carlo strategy for the LHC – “nesting” derived from ND and QCD color factors Thank you for your attention