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Exclusive Diffraction at HERA Henri Kowalski DESY Ringberg October 2005 γp σ tot 1 ImAel (W 2 , t 0) 2 W Q2 γ* P 2 F2 (x, Q ) σ tot (W, Q ) 2 4 π αem 2 Q2 x 2 W F2 is dominated by single ladder exchange ladder symbolizes the QCD evol. process ( DGLAP or others ) Gluon density Gluon density dominates F2 for x < 0.01 Diffractive Scattering Non-Diffractive Event ZEUS detector Diffractive Event MX - invariant mass of all particles seen in the central detector t - momentum transfer to the diffractively scattered proton t - conjugate variable to the impact parameter Diffractive Signature diff Nondiff ~ DY= log(W2/M2X) Non-Diffraction Diffraction - Rapidity uniform, uncorrelated particle emission along the rapidity axis => probability to see a gap DY is ~ exp(-<n>DY) <n> - average multipl. per unit of Y dN/dM2X ~ 1/M2X => dN/dlog M2X ~ const Observation of diffraction indicates that single ladder may not be sufficient (partons produced from a single chain produce exponentially suppressed rap. gaps) Diffractive Structure Function Dipole Model ______________ Initial Diff. SF Q20 ~ 4 GeV2 Study of exclusive diffractive states may clarify which pattern is right Only few final states present in DiMo: qq, qqg (aligned and as jets) VM Dipole description of DIS equivalent to Parton Picture in the perturbative region momentum space configuration space dipole preserves its size during interaction. qq ~ r2xg(x,m) for small r Optical T Tf 2 Lf 2 3 em 2 2 eq {[ z (1 z ) 2 ] 2 K12 (r ) mq2 K 02 (r )} 2 2 3 em2 eq2 {4Q 2 z 2 (1 z ) 2 K 02 (r )} 2 2 z (1 z )Q 2 mq2 r<<1 Q2~1/r2 Mueller, Nikolaev, Zakharov tot *p 1 d rˆ dz* qq ( x, r 2 ) 2 0 p d VM 1 * |t 0 | d 2 r dzVM (Q 2 , z, r ) qq ( x, r 2 )(Q 2 , z, r ) |2 dt 16 0 * 1 p d diff * dt 1 |t 0 16 1 * 2 2 d r dz qq ( x, r ) 2 0 Dipole description of DIS GBW – first Dipole Saturation Mode (rudimentary evolution) Golec-Biernat, Wuesthoff r2 qq ( x, r ) 0 (1 exp( 2 )); R0 1 x R GeV 2 x0 GBW 2 0 BGBK – DSM with DGLAP Bartels, Golec-Biernat, Kowalski 2 2 qq ( x, r ) 0 (1 exp( r s xg( x, m 2 C / r 2 m02 ))) 3 0 Iancu, Itakura, Munier - BFKL-CGC motivated ansatz Forshaw and Shaw - Regge ansatz with saturation Impact Parameter Dipole Saturation Model Kowalski Teaney b – impact parameter Glauber-Mueller, d qq ( x, r ) d 2b Levin, Capella, Kaidalov… 2 2 2 1 exp( r s ( m 2 ) xg( x, m 2 )T (b)) 23 T(b) - proton shape p d VM 1 2 2 ib D * | d r d be dzVM (Q 2 , z, r ) dt 16 0 * 1 2 2 r s xg( x, m 2 )T (b))(Q 2 , z, r ) |2 1 exp( 23 d diff ~ exp( B t ) T (b) ~ exp( b 2 / 2 B) dt Total *p cross-section *p ~ (W 2 )tot ~ (1/ x)tot universal rate of rise of all hadronic cross-sections x < 10-2 m2 C m 02 2 r g 1 xg( x, m ) Ag (1 x)5.6 x 2 0 Ratio of tot to diff from fit to tot predict diff GBW, BGBK … diff is not a square of tot ! _ Diffractive production of a qq pair ~ probability to find a Pomeron(2g) in p ~ probability for a Pomeron(2g) to couple to a quark spin 1/2 spin 1 ~ s1 => dN/dlog M2X ~ const Diffractive production of a qqg state Inclusive Diffraction LPS — BGBK Dipole Comparison with Data FS model with/without saturation and IIM CGC model hep-ph/0411337. Fit F2 and predict xIPF2D(3) FS(nosat) F2 CGC FS(sat) F2 x Dipole cross section determined by fit to F2 Simultaneous description of many reactions F2 C Gluon density test? IP-Dipole Model Teubner *p -> J/y p *p -> J/y p IP-Dipole Model VM ~ W VM ~ W Exclusive r production d diff ~ exp( BD t ) dt Modification by Bartels, Golec-Biernat, Peters, (first proposed by Nikolaev, Zakharov) e p d VM 1 2 2 ib D * | d r d be dzVM (Q 2 , z, r ) dt 16 0 * 1 ib D e i ( b (1 z ) r )D 2 2 2 2 2 1 exp( r xg ( x , m ) T ( b )) (Q , z, r ) | s 23 H. Kowalski, L. Motyka, G. Watt preliminary Diffractive Di-jets Q2 > 5 GeV2 -RapGap Satrap Diffractive Di-jets Q2 > 5 GeV2 Diffractive Di-jets Q2 > 5 GeV2 Diffractive Di-jets at the Tevatron Dijet cross section factor 3-10 lower than expected using HERA Diffractive Structure Functions suppression due to secondary interactions ? H1 and ZEUS: NLO overestimates data by factor 1.6. Kaidalov et al.: resolved part needs to be rescaled by 0.34 scaled by factor 0.34 Survival Probability S2 S2 Soft Elastic Opacity t – distributions at LHC 2 ( s ,b ) 2 M ( s , b ) e d b 2 2 M ( s , b ) d b 2 (t1 ) 2 (t2 ) 2 F ( p1t , p2t ) S ( p1t , p2t ) 2 2 2 < S / b0 Khoze Martin Ryskin Effects of soft proton absorption modulate the hard t – distributions t-measurement will allow to disentangle the effects of soft absorption from hard behavior Dipole form double eikonal single eikonal ZEUS-LPS H1 VFPS at HERA Conclusions Inclusive diffraction, exclusive diffractive VM and jet production can be successfully derived from the measured F2 (Dipole Model with u. gluon densities obtained from F2 ) Detailed VM-data from HERA should allow to pin down VM wave functions Diffractive Structure Function analysis describes well the inclusive diffractive processes and the exclusive diffractive jet production although it has some tendency to amplify small differences of the input distributions Exclusive diffractive processes give detailed insight into DIS dynamics Press Release: The 2005 Nobel Prize in Physics 4 October 2005 The Royal Swedish Academy of Sciences has decided to award the Nobel Prize in Physics for 2005 with one half to Roy J. Glauber Harvard University, Cambridge, MA, USA "for his contribution to the quantum theory of optical coherence" Glauber wrote his formula for heavy nuclei and for deuteron. He was the first who realized that his formula in the case of deuteron describes both the elastic cross section and the diffractive dissociation of the deuteron. Genya Levin Roy Glauber’s Harvard Webpage Roy Glauber's recent research has dealt with problems in a number of areas of quantum optics, a field which, broadly speaking, studies the quantum electrodynamical interactions of light and matter. He is also continuing work on several topics in high- energy collision theory, including the analysis of hadron collisions, and the statistical correlation of particles produced in high-energy reactions. Specific topics of his current research include: the quantum mechanical behavior of trapped wave packets; interactions of light with trapped ions; atom counting-the statistical properties of free atom beams and their measurement; algebraic methods for dealing with fermion statistics; coherence and correlations of bosonic atoms near the BoseEinstein condensation; the theory of continuously monitored photon counting-and its reaction on quantum sources; the fundamental nature of “quantum jumps”; resonant transport of particles produced multiply in high-energy collisions; the multiple diffraction model of proton-proton and proton-antiproton scattering Saturation and Absorptive corrections F2 ~ Single inclusive linear QCD evolution - Diffraction Example in Dipole Model d 2 2 ( 1 exp( / 2 )) / 4 .... 2 d b High density limit —> Color Glass Condensate coherent gluon state McLerran Venogopulan 2-Pomeron exchange in QCD 0-cut Final States (naïve picture) Diffraction 1-cut <n> 2-cut <2n> QCD diagrams d qq 2 1 exp( ) 2 d b 2 d k k exp( ) 2 d b k! 2 2 r s ( m 2 ) xg( x, m 2 )T (b) NC AGK rules in the Dipole Model d k k exp( ) 2 d b k! 2 2 r s ( m 2 ) xg( x, m 2 )T (b) NC Note: AGK rules underestimate the amount of diffraction in DIS GBW Model IP Dipole Model r2 qq ( x, r ) 0 [1 exp( )] 4 R02 1 R ( x) GeV 2 2 0 x x 0 strong saturation d qq ( x, r ) d 2b 2 2 2 1 exp( r s xg( x, C / r 2 Q02 )T (b)) 23 less saturation (due to IP and charm) Saturation scale (a measure of gluon density) 2 HERA QS2 rS2 N 9 (Q ) C (QS2 ) q (QS2 ) q CF 4 2 S g RHIC 4 2 s N C 1 dN Q N C2 1 R 2 dy 2 S dN 1000 dy R 7 fm QS2 1 GeV 2 QSRHIC ~ QSHERA Geometrical Scaling A. Stasto & Golec-Biernat J. Kwiecinski 1 x R02 ( x) 2 GeV x0 Q 2 R02 ( x) Dipole X-section —— ---- BGBK GBW Geometrical Scaling can be derived from traveling wave solutions of non-linear QCD evolution equations Velocity of the wave front gives the energy dependence of the saturation scale Munier, Peschanski L. McLerran +… Al Mueller + .. Question: Is GS an intrinsic (GBW) or effective (KT) property of HERA data? 2-Pomeron exchange in QCD 0-cut Final States (naïve picture) Diffraction 1-cut <n> 2-cut <2n> AGK rules in the Dipole Model d k k exp( ) 2 d b k! 2 2 r s ( m 2 ) xg( x, m 2 )T (b) NC Note: AGK rules underestimate the amount of diffraction in DIS d qq 2 1 exp( ) 2 d b 2 d k k exp( ) 2 d b k! 2 2 r s ( m 2 ) xg( x, m 2 )T (b) NC HERA Result Unintegrated Gluon Density Dipole Model Example from dipole model - BGBK Another approach (KMR) f g ( x, m 2 ) (t ) [ T (Qt , m ) xg( x, Qt2 )] 2 ln Qt m 2 S (kt2 ) dkt2 kt /(m kt ) T (Qt , m ) exp 2 zP ( z ) dz gg 2 0 Qt 2 k t f g ( x1 , t , Qt , m ) (t ) f g ( x1 , t 0, Qt , m ) b(t ) exp( Bt / 2) Active field of study at HERA: UGD in heavy quark production, new result expected from high luminosity running in 2005, 2006, 2007 Exclusive Double Diffractive Reactions at LHC xIP = Dp/p, pT xIP ~ 0.2-1.5% xIP = Dp/p, pT xIP ~ 0.2-1.5% 1 event/sec High momentum measurement precision Diff ˆ L L S 2O 2 yM 2 dQt2 exclusive O 2 f g ( x1 , Qt ) f g ( x2 , Qt ) 4 ( N 1 ) b Q t c M2 low x QCD reactions: pp => pp + gJet gJet pp => pp + Higgs ~ 1 nb for M(jj) ~ 50 GeV ~ 0.5 pb for M(jj) ~ 200 GeV hJET| < 1 O(3) fb SM O(100) fb MSSM t – distributions at LHC t – distributions at HERA with the cross-sections of the O(1) nb and L ~ 1 nb-1 s-1 => O(107) events/year are expected. For hard diffraction this allows to follow the t – distribution to tmax ~ 4 GeV2 For soft diffraction tmax ~ 2 GeV2 diff d hard ~ exp( 4 | t |) dt Non-Saturated gluons t-distribution of hard processes should be sensitive to the evolution and/or saturation effects see: Al Mueller dipole evolution, BK equation, and the impact parameter saturation model for HERA data Saturated gluons Survival Probability S2 S2 Soft Elastic Opacity t – distributions at LHC 2 ( s ,b ) 2 M ( s , b ) e d b 2 2 M ( s , b ) d b 2 (t1 ) 2 (t2 ) 2 F ( p1t , p2t ) S ( p1t , p2t ) 2 2 2 < S / b0 Khoze Martin Ryskin Effects of soft proton absorption modulate the hard t – distributions t-measurement will allow to disentangle the effects of soft absorption from hard behavior Dipole form double eikonal single eikonal F2 Dipole Model Gluon Luminosity Exclusive Double Diffraction L. Motyka, HK preliminary Diff ˆ L M2 L S 2O 2 yM QT2 (GeV2) dQt2 exclusive O 2 f ( x , x ' , t , Q , m ) f ( x , x ' , t , Q , m ) g 1 1 t g 2 2 t 4 ( N 1 ) b Q t c fg – unintegrated gluon densities 2 Conclusions We are developing a very good understanding of inclusive and diffractive g*p interactions: F2 , F2D(3) , F2c , Vector Mesons (J/Psi)…. Observation of diffraction indicates multi-gluon interaction effects at HERA HERA measurements suggests presence of Saturation phenomena Saturation scale determined at HERA agrees with RHIC HERA determined properties of the Gluon Cloud Diffractive LHC ~ pure Gluon Collider => investigations of properties of the gluon cloud in the new region Gluon Cloud is a fundamental QCD object - SOLVE QCD!!!! Precise measurement of the Higgs Mass J. Ellis, HERA-LHC Workshop Higher symmetries (e.g. Supersymmetry) lead to existence of several scalar, neutral, Higgs states, H, h, A . . . . Higgs Hunter Guide, Gunnion, Haber, Kane, Dawson 1990 In MSSM Higgs x-section are likely to be much enhanced as compared to Standard Model (tan large because MHiggs > 115 GeV) CP violation is highly probable in MSSM similar masses ~120 GeV all three neutral Higgs bosons have can ONLY be RESOLVED in DIFFRACTION Ellis, Lee, Pilaftisis Phys Rev D, 70, 075010, (2004) , hep-ph/0502251 Correlation between transverse momenta of the tagged protons give a handle on the CP-violation in the Higgs sector Khoze, Martin, Ryskin, hep-ph 040178 Gluon density Gluon density dominates F2 for x < 0.01 The behavior of the rise with Q2 p ~ (W 2 ) * tot ( Q 2 ) ~ (1 / x)tot (Q 2 ) xg( x, m ) ~ (1 / x) 2 eff ( m 2 ( r )) universal rate of rise of all hadronic cross-sections Smaller dipoles steeper rise Large spread of eff characteristic for IP Dipole Models GBW Model r2 qq ( x, r ) 0 [1 exp( )] 4 R02 strong saturation KT-IP Dipole Model d qq ( x, r ) d 2b 2 2 2 1 exp( r s xg( x, C / r 2 Q02 )T (b)) 23 less saturation (due to charm) Unintegrated Gluon Densities Dipole Model Exclusive Double Diffraction f g ( x, x' , t , Qt , m ) (t ) Rg [ T (Qt , m ) xg( x, Qt2 )] 2 ln Qt m 2 S (kt2 ) dkt2 kt /(m kt ) T (Qt , m ) exp 2 zP ( z ) dz gg 2 0 Qt 2 k t f g ( x1 , x1 ' , t , Qt , m ) (t ) f g ( x1 , x1 ' , t 0, Qt , m ) b(t ) exp( Bt / 2) Note: xg(x,.) and Pgg drive the rise of F2 at HERA and Gluon Luminosity decrease at LHC Saturation Model Predictions for Diffraction Absorptive correction to F2 Example in Dipole Model d 2(1 exp( / 2)) 2 / 4 .... 2 d b F2 ~ - Single inclusive pure DGLAP Diffraction Fit to diffractive data using MRST Structure Functions A. Martin M. Ryskin G. Watt A. Martin M. Ryskin G. Watt AGK Rules QCD Pomeron The cross-section for k-cut pomerons: Abramovski, Gribov, Kancheli Sov. ,J., Nucl. Phys. 18, p308 (1974) k (1) mk mk m! 2 F (m) k!(m k )! 1-cut m F (m) – amplitude for the exchange of m Pomerons 1-cut 2-cut 2-Pomeron exchange in QCD Final States (naïve picture) detector 0-cut Diffraction p DY * *p-CMS <n> 1-cut * p *p-CMS detector <2n> 2-cut p * *p-CMS Feynman diagrams QCD amplitudes 0-cut 1-cut 2-cut 3-cut J. Bartels A. Sabio-Vera H. K. Probability of k-cut in HERA data Dipole Model *p *p k d r d 2b dz *f (Q 2 , z, r ) 21 exp( ) f (Q 2 , z , r ) 2 f 0 1 2 2 k * 2 d r d b dz f (Q , z, r ) exp( ) f (Q 2 , z, r ) k! f 0 1 2 Problem of DGLAP QCD fits to F2 CTEQ, MRST, …., IP-Dipole Model xg( x, m02 ) ~ x , 0 at small x valence like gluon structure function ? Remedy: Absorptive corrections? MRW Different evolution? BFKL, CCSS, ABFT dg ( x, m 2 ) dz x 2 2 P ( z , m ) g ( ,m ) x z gg d ln m 2 z 1 from Gavin Salam at low x LO DGLAP --- BFKL ------ s (m 2 ) xPgg ~ 2C A 2 1 xPgg ~ x 4 ln 2 s NC Next to leading logs NLLx ----- - Paris2004 Ciafalloni, Colferai, Salam, Stasto Similar results by Altarelli, Ball Forte, Thorn from Gavin Salam - Paris 2004 Density profile 2 2 D s ( m 2 (r )) xg( x, m 2 (r ))T (b) 3 grows with diminishing x and r approaches a constant value Saturated State - Color Glass Condensate S – Matrix => interaction probability Saturated state = high interaction probability S2 => 0 multiple scattering r2 S exp D 2 2 S 2 e 1 rS - dipole size for which proton consists of one int. length QS2 Saturation scale = Density profile at the saturation radius rS S = 0.25 S = 0.15 QS2 2 rS2 Saturated state is partially perturbative cross-sectiom exhibits the universal rate of growth (QS2 ) g NC 2 9 (QS ) q (QS2 ) q CF 4 RHIC 4 2 s N C 1 dN Q N C2 1 R 2 dy 2 S dN 1000 dy R 7 fm QS2 1 (QS2 ) RHIC (QS2 ) HERA Conclusions We are developing a very good understanding of inclusive and diffractive *p interactions: F2 , F2D(3) , F2c , Vector Mesons (J/Psi)…. Observation of diffraction indicates multi-gluon interaction effects at HERA Open problems: valence-like gluon density? absorptive corrections low-x QCD-evolution HERA measurements suggests presence of Saturation phenomena Saturation scale determined at HERA agrees with the RHIC one HERA+NMC data => Saturation effects are considerably increased in nuclei Diffractive Scattering Non-Diffractive Event ZEUS detector Diffractive Event MX - invariant mass of all particles seen in the central detector t - momentum transfer to the diffractively scattered proton t - conjugate variable to the impact parameter Diffractive Signature diff Non-Diffraction Nondiff Diffraction - Rapidity uniform, uncorrelated particle emission along the rapidity axis => probability to see a gap DY is ~ exp(-<n>DY) <n> - average multiplicity per unit of rapidity dN/ dM 2X ~ 1/ M 2X => dN/dlog M 2X ~ const note : DY ~ log(W2 / M 2 X) Slow Proton Frame incoming virtual photon fluctuates into a quark-antiquark pair which in turn emits a cascade-like cloud of gluons qq 1 1 10 1000 fm DE m p x Transverse size of the quark-antiquark cloud is determined by r ~ 1/Q ~ 2 10-14cm/ Q (GeV) σ γp tot 1 2 ImAel (W 2 , t 0) W σ γ* P tot 4 π 2 αem (W, Q ) F2 (x, Q 2 ) 2 Q 2 Rise of ptot with W is a measure of radiation intensity Diffraction is similar to the elastic scattering: replace the outgoing photon by the diffractive final state r , J/ or X = two quarks