Diffraction saturation and pp cross sections Diffraction atsaturation

Diffraction, saturation, and pp cross sections Diffraction, atsaturation and the LHC pp cross sections at the LHC Moriond QCD and High Energy Interactions La Thuile, March 20 -27, 2011 Konstantin Goulianos The Rockefeller University (member of CDF and CMS) 1

CONTENTS q Introduction q Diffractive cross sections q The total, elastic, and inelastic cross sections q Monte Carlo strategy for the LHC q Conclusions K. Goulianos 2

Why study diffraction? Two reasons: one fundamental / one practical. q fundamental s. T measure s. T & r value at LHC: optical theorem Im fel(t=0) dispersion relations Re fel(t=0) check for violation of dispersion relations Diffraction sign for new physics Bourrely, C. , Khuri, N. N. , Martin, A. , Soffer, J. , Wu, T. T http: //en. scientificcommons. org/16731756 Ø saturation s. T q practical: underlying event (UE), triggers, calibrations the UE affects all physics studies at the LHC NEED ROBUST MC SIMULATION OF SOFT PHYSICS K. Goulianos 3

MC simulations: Pandora’s box was unlocked at the LHC! q Presently available MCs based on pre LHC data were found to be inadequate for LHC q MC tunes: the “evils of the world” were released from Pandora’s box at the LHC … but fortunately, hope remained in the box a good starting point for this talk Pandora's box is an artifact in Greek mythology, taken from the myth of Pandora's creation around line 60 of Hesiod's Works And Days. The "box" was actually a large jar (πιθος pithos) given to Pandora (Πανδώρα) ("all gifted"), which contained all the evils of the world. When Pandora opened the jar, the entire contents of the jar were released, but for one – hope. Nikipedia K. Goulianos 4

Diffractive gaps definition: gaps not exponentially suppressed X p p X p ln s f Particle production ln MX 2 Rapidity gap -ln x No ra di at io n h Moriond QCD 2011 Diffraction, saturation, and pp cross sections at the LHC K. Goulianos 5

Diffractive pbar p studies @ CDF s. T=Im fel (t=0) Elastic scattering f h SD Moriond QCD 2011 f OPTICAL THEOREM GAP DD Total cross section h DPE Diffraction, saturation, and pp cross sections at the LHC SDD=SD+DD K. Goulianos 6

Basic and combined diffractive processes gap DD SD a 4 gap diffractive process Moriond QCD 2011 Diffraction, saturation, and pp cross sections at the LHC K. Goulianos 7

Regge theory – values of so & g? KG 1995: PLB 358, 379 (1995) Parameters: q s 0, s 0' and g(t) q set s 0‘ = s 0 (universal IP ) q determine s 0 and g. PPP – how? Moriond QCD 2011 Diffraction, saturation, and pp cross sections at the LHC K. Goulianos 8

A complication … Unitarity! q ds/dt ssd grows faster than st as s increases unitarity violation at high s (similarly for partial x sections in impact parameter space) q the unitarity limit is already reached at √s ~ 2 Te. V Moriond QCD 2011 Diffraction, saturation, and pp cross sections at the LHC K. Goulianos 9

s. TSD vs s. T (pp & pp) p suppressed relative to Regge for √s>22 Ge. V p p’ x, t M s. T Factor of ~8 (~5) suppression at √s = 1800 (540) Ge. V RENORMALIZATION MODEL Moriond QCD 2011 1800 Ge. V √s=22 Ge. V 540 Ge. V KG, PLB 358, 379 (1995) CDF Run I results Diffraction, saturation, and pp cross sections at the LHC K. Goulianos 10

Single diffraction renormalized – (1) KG CORFU 2001: hep ph/0203141 KG EDS 2009: http: //arxiv. org/PS_cache/arxiv/pdf/1002. 3527 v 1. pdf t color factor 2 independent variables: gap probability sub-energy x-section Gap probability (re)normalize to unity Moriond QCD 2011 Diffraction, saturation, and pp cross sections at the LHC K. Goulianos 11

Single diffraction renormalized – (2) color factor Experimentally: KG&JM, PRD 59 (114017) 1999 QCD: Moriond QCD 2011 Diffraction, saturation, and pp cross sections at the LHC K. Goulianos 12

Single diffraction renormalized (3) set to unity determine so Moriond QCD 2011 Diffraction, saturation, and pp cross sections at the LHC K. Goulianos 13

Single diffraction renormalized – (4) grows slower than se Pumplin bound obeyed at all impact parameters Moriond QCD 2011 Diffraction, saturation, and pp cross sections at the LHC K. Goulianos 14

M 2 distribution: data ds/d. M 2|t=-0. 05 ~ independent of s over 6 orders of magnitude! KG&JM, PRD 59 (1999) 114017 Regge data 1 Independent of s over 6 orders of magnitude in M 2 scaling factorization breaks down to ensure M 2 scaling Moriond QCD 2011 Diffraction, saturation, and pp cross sections at the LHC K. Goulianos 15

Scale so and triple pom coupling Pomeron flux: interpret as gap probability set to unity: determines g. PPP and s 0 KG, PLB 358 (1995) 379 Pomeron proton x section q q Two free parameters: so and g. PPP Obtain product g. PPP • soe / 2 from s. SD Renormalized Pomeron flux determines so Get unique solution for g. PPP=0. 69 mb 1/2=1. 1 Ge. V 1 Moriond QCD 2011 So=3. 7± 1. 5 Ge. V 2 Diffraction, saturation, and pp cross sections at the LHC K. Goulianos 16

Saturation “glueball” at ISR? Giant glueball with f 0(980) and f 0(1500) superimposed, interfering destructively and manifesting as dips (? ? ? ) √so See M. G. Albrow, T. D. Goughlin, J. R. Forshaw, hep-ph>ar. Xiv: 1006. 1289 K. Goulianos 17

Multigap cross sections, e. g. SDD KG, hep ph/0203141 color factor 5 independent variables Gap probability Sub-energy cross section (for regions with particles) Same suppression as for single gap! Moriond QCD 2011 Diffraction, saturation, and pp cross sections at the LHC K. Goulianos 18

SDD in CDF: data vs NBR MC http: //physics. rockefeller. edu/publications. html § Excellent agreement between data and NBR (Min. Bias. Rockefeller) MC K. Goulianos 19

Multigaps: a 4 gap x section Moriond QCD 2011 Diffraction, saturation, and pp cross sections at the LHC K. Goulianos 20

The total x section http: //arxiv. org/ abs/1002. 3527 √s. F=22 Ge. V SUPERBALL MODEL 98 ± 8 mb at 7 Te. V 109 ± 12 mb at 14 Te. V Moriond QCD 2011 Diffraction, saturation, and pp cross sections at the LHC K. Goulianos 21

Total inelastic cross section Renormalization model ATLAS measurement of the total inelastic x section The sel is obtained from st and the ratio of el/tot Moriond QCD 2011 Diffraction, saturation, and pp cross sections at the LHC K. Goulianos 22

s. SD and ratio of a'/e Moriond QCD 2011 Diffraction, saturation, and pp cross sections at the LHC K. Goulianos 23

Diffraction in PYTHIA 1 some comments: § 1/M 2 dependence instead of (1/M 2)1+e § F factors put “by hand” – next slide § Bdd contains a term added by hand next slide K. Goulianos 24

Diffraction in PYTHIA 2 note: § 1/M 2 dependence § e 4 factor Fudge factors: § suppression at kinematic limit § kill overlapping diffractive systems in dd § enhance low mass region K. Goulianos 25

CMS: observation of Diffraction at 7 Te. V An example of a beautiful data analysis and of MC inadequacies • No single MC describes the data in their entirety K. Goulianos 26

Monte Carlo Strategy for the LHC MONTE CARLO STRATEGY q s. T from SUPERBALL model s. T optical theorem q optical theorem Im fel(t=0) q dispersion relations Re fel(t=0) Im fel(t=0) dispersion relations q sel Re fel(t=0) inel qs q differential s. SD from RENORM q use nesting of final states (FSs) for pp collisions at the IP p sub energy √s' Strategy similar to that employed in the MBR (Minimum Bias Rockefeller) MC 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 distributions “ Moriond QCD 2011 Diffraction, saturation, and pp cross sections at the LHC K. Goulianos 27

Monte Carlo algorithm nesting Profile of a pp inelastic collision gap no gap t h'c ln s' final state from MC w/no-gaps gap evolve every cluster similarly Dy‘ > Dy'min Dy‘ < Dy'min generate central gap EXIT repeat until Dy' < Dy'min Moriond QCD 2011 Diffraction, saturation, and pp cross sections at the LHC K. Goulianos 28

SUMMARY q Introduction q Diffractive cross sections Ø basic: SDp, DD, DPE Ø combined: multigap x sections derived from ND and QCD color factors Ø ND no gaps: final state from MC with no gaps v this is the only final state to be tuned q The total, elastic, and inelastic cross sections q Monte Carlo strategy for the LHC – use “nesting” Moriond QCD 2011 Diffraction, saturation, and pp cross sections at the LHC K. Goulianos 29

BACKUP Moriond QCD 2011 Diffraction, saturation, and pp cross sections at the LHC K. Goulianos 30

RISING X SECTIONS IN PARTON MODEL ~1/as f y Emission spacing controlled by a-strong s. T : power law rise with energy (see E. Levin, An Introduction to Pomerons, Preprint DESY 98 -120) a’ reflects the size of the emitted cluster, which is controlled by 1 /as and thereby is related to e f y assume linear t-dependence Forward elastic scattering amplitude K. Goulianos 31

Gap survival probability S= Moriond QCD 2011 Diffraction, saturation, and pp cross sections at the LHC K. Goulianos 32

Diffraction in MBR: dd in CDF http: //physics. rockefeller. edu/publications. html gap probability x section renormalized K. Goulianos 33

Diffraction in MBR: DPE in CDF http: //physics. rockefeller. edu/publications. html § Excellent agreement between data and MBR low and high masses are correctly implemented K. Goulianos 34

Dijets in gp at HERA from RENORM K. Goulianos, POS (DIFF 2006) 055 (p. 8) Factor of ~3 suppression expected at W~200 Ge. V (just as in pp collisions) for both direct and resolved components Moriond QCD 2011 Diffraction, saturation, and pp cross sections at the LHC K. Goulianos 35

Saturation at low Q 2 and small x figure from a talk by Edmond Iancu K. Goulianos 36

The end Moriond QCD 2011 Diffraction, saturation, and pp cross sections at the LHC K. Goulianos 37