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The Structure of the Pomeron

The Structure of the Pomeron. I. Y. Pomeranchuk ( 1913 -1966 ). SM. Quantumchromodynamics 8 gluons. Electroweak g, Z 0 , W + , W -. Precision measurements and test of higher order corrections Excellent experimental confirmation. Main assumptions experimentally

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The Structure of the Pomeron

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  1. The Structure of the Pomeron I. Y. Pomeranchuk ( 1913 -1966 )

  2. SM Quantumchromodynamics 8 gluons Electroweak g, Z0, W+, W- Precision measurements and test of higher order corrections Excellent experimental confirmation Main assumptions experimentally verified Predictions so far are limited: QCD is too complicated for our present theoretical and mathematical methods --> limited areas of application Very much work is spendt to enlarge the areas where QCD can be applied.

  3. as as as Elements of QCD All particles with color charge participate: Quarks Antiquarks Gluons Gluons carry color charge. They interact with each other This is all the difference to QED!! Experimental Status: • Gluons exist and carry spin 1 • Gluons carry color charge: ‚tripel gluon vertex‘ exists • There are 8 gluons (the gauge group is SU(3)C)

  4. fragmentation coupling rises strongly for large distances (≥ . 2 fm)‚soft processes‘ p r y coupling small for short distances (large scales) ‚hard processes‘ Color dipoles • no free quarks and gluons • at large distances color string r ~ 1/m V(r) k*r as r[fm] 1 0.4 ~1/r m2 [GeV2] 1 10 100 Perturbation theory works only for small distances, large scales (>1 GeV2)

  5. 1. bound state: proton is complicated state of three valence quarks, bound by gluon field (99.9% of mass!). QCD description: lattice theory 2. Parton-Parton scattering ‚hard processes with large scale‘: production of W‘s,Z0,Top, Jets 3. p-p scattering at high energies: total X-section and elastic scattering stot ~ Im [ Ael (t=0)] p p p Very active new working area! None of the established methods works! Successful description by perturbative QCD: aS << 1 p needs parton distributions Protons and Predictions of QCD

  6. Experimental facts of p-p scattering at high energies We observe a rather simple and universal picture! ds/dt 2. differential X-section shows ‘diffraction’ picture ECM ds/dt ~ s2le-bt t[GeV2] 1. total cross sections rise at high energy with s=Ecm2 stot = a s-a + b sl stot • l = 0.0808 determines the rise at high energy Ecm [GeV] 1. Proton has diffuse edge (Gauß profile) 2. it becomes larger with s 3. it is grey!

  7. The Pomeron p X p r,f2, -trajectory (Reggeon) Pomeron C=P=+1 X p p No exhange particle is known for sure which could explain the rise of p-p scattering at high energy! It would carry the quantum numbers of the vacuum P=C = +1and is colorless! artificial name : POMERON 1.0808 QCD: ´Pomeron´ must be composed of qq or gluon-gluon states! high energy scattering is dominated by the exchange of ‚particles‘: ‚Regge trajectories = hadons and their rotational exitations‘ stot s[a(0)-1]= s-0.45for ´Reggeon´ describes fall of X-section at low energies ECM < 20 GeV ds/dt ~ s 2[a (t) –1] trajectory a (t) = a (0) + a´ t J

  8. The best experimental surrounding to study these questions are not offered by the Tevatron (as might be expected) but by the Electron-Proton Storage Ring HERA (DESY)

  9. 30 GeV 820 (920) GeV HERA e p √s =320 GeV construction cost HERA ~ 1.2 billion DM 2 experiments ~200 MDM Start of construction 1984 Data taking: start 1992 end 30.06.2007 ca. 800 physicists at both e-p experiments p e H1 ZEUS DESY in HH….

  10. Deep Inelastic e-p Scattering: Measurement of Parton Structure Evidence for Scattering from pointlike partoncs ( colored quarks) • Electron is scattered by large • angle ~1/sin4(θ/2) Spectators color string • ‚Jets‘ in final state e • Hadrons in proton direction: a • colored parton was scattered and • left the proton p e color string Scattering event at HERA (H1)

  11. e e Q2 g x pp p Hard scattering process th ~ 1/Q << 1 fm F2 = Σei2x[qi(x)+qi(x)] fragmentation tF > 1 fm Snapshot of Parton Distribution with time resolution of ~1/Q << 1 fm

  12. Q2-Evolution of Strukturfunktionen • Electrons scatter only from Quarks • F2changes with Q2, because resolution improves: the rise of F2 at small x depends on the gluon density F2ep(x,Q2) = Sef2 x[ qf(x,Q2)+qf(x,Q2) ] dominant +

  13. Quark densities are directly • measured: 50% of proton momentum! • Gluon density is determined from • the observed scaling violations or • directly from 2-jet cross sections gluon Quark und Gluon Densities in the Proton F2(x) ~ x –l at small x huge Gluon- Momentum distribution ~ x –lg x

  14. Universality of Parton distributions: a triumph of QCD  LHC • QCD universality: the parton densities are valid for all hard scattering processes, • (after corrections for higher order effects in aS) • Example: 2 -Jet cross section in pp collisions is predicted! Tevatron x~0.3 x~0.03

  15. Proton rest frame *p rT L ~ 1/x rT~2/Q ( size of dipole) ~ 50 fm! ~ 1 .01 fm At low x a color dipole of variable size 2/Q interacts with the proton at high CM energy s=W2(p)≈ Q2/x ≈ 1000 ÷ 90000 GeV2 Low x = high energy scattering! Q2 steers the transition from hard collisions ( perturbative QCD) to soft hadron physics. We can ‘engineer’ our hadron! F2(x, Q2) = F2(W2 , Q2) ≈4π2Q2 * σ*p (W2,Q2) Hadron-Hadron Scattering at HERA? Infinite momentum frame e Q2 x p x= Q2/y*s (momentum fraction of parton) Electrons as probes for quark Structure -- parton densities, scaling violations ..

  16. the g* p cross section at high energies l soft Pomeron (p-p) intercept slope depends on Q ~ 1/r: there can be no universal Pomeron! Another look at deep inelastic scattering: proton rest system l=0.08 l=0.35 W2 low x • g*p(W2)~ F2(W2,Q2)/Q2 ~ W2l

  17. diffractive scattering 1. elastically scattered Proton! (would be best ) 2. no ‚forward energy‘ (rapidity gap event ) ca. 10% of all events q b xP Rapidity gap DIS gap e Large Q2 p Events first seen by ZEUS

  18. Electron Scattering from the Pomeron • we measure the diffractive structure function F2D(b, Q2, xP) • in inclusive scattering: Quark structure of the Pomeron Experimental Facts: 1. F2D(b, Q2, xP) = xP-2[a(t)-1]*F2D(b,Q2) Pomeron flux * Quark distribution of Pomeron 2. a(0) = 1.16±.03 = 1.08 ! (not soft Pomeron) 2. We scatter from pointlike partons - scaling - Jets e q b xP Rapidity gap Resolved Pomeron Model: -The wave function of the Protons contains a ‚Pomeron‘ component. -The electron scatters from the quarks in the ‚Pomeron‘. -The Pomeron flux factor is not described by the soft Pomeron!

  19. Diffractive Parton Distributions b • QCD analysis of scaling violations: • The Pomeron is dominated by • Gluons (~75 % of Pomeron momentum ) • Gluons have high average momenta b • but badly known at high b • Quark distribution is directly • measured b b • approximate scaling F2D(b,Q2) b

  20. -jet -jet Direct Measurement of the Pomeron Gluon Distribution 2-Jetevents measure gluons in the Pomeron! Factorisation? Are diffractive parton distributions universal for all diffractive processes? Do we get the same gluon distribution?

  21. 222-Jet cross section in diffractive DIS • 2-Jet cross section shows same • Pomeron flux with a(0)=1.2 and • agrees with resoved Pomeron • model. • Gluon density is in agreement with • F2D but only with Fit B 2-jets • discriminate between solutions • Pomeron is dominated by gluons • qqg fluctuationen in the Photon • dominate ß QCD factorisation is valid for Diffractive Deep Inelastic Scattering this is required by QCD -> Collins ß NLO QCD prediciton based on factorisation

  22. 22Diffractive Parton Distributions (best set) Combinded QCD analysis of F2D and 2-jet X-cross sections assuming factorisation z =b can we use them?

  23. Diffractive Parton Densities in p-p Collisions (Tevatron) p jet jet p p Diffractive X-sections in pp do not factorise! ??????? • Several models on the market to explain this fact: • Multiple interactions including ‚spectator partons • destroy the rapidity gap • or • color neutralisation by soft gluons • depends on parton final state and CM energy Diffractive processes in hadron reactions are more difficult to describe. What destroys factorisation?  study HERA gp (controversial..) p Predicted cross section using diffractive parton Densities from HERA gap ? Faktor 10

  24. Central diffractive particle production at pp Colliders • CDF Central Higgs production at LHC? Test at Tevatron: central 2-jet

  25. Main experimental results • ‚Pomeron‘ is (dominantly) a gluon state • rise of γ*p cross section is not universal but depends on Q2 • The diffractive gluon density is universal for DIS • It cannot be applied directly to Hadron-Hadron scattering These facts must be reproduced by any theoretical description! Next: Theoretical models which try to describe more aspects of diffractive scattering - flux factors - parton densities resp. σγ*p

  26. (98): Use 2 Pomeron trajectories hard Pomeron: aH(t) = 1.44 + 0.10 * t sgp(W2,Q2) at high Q2 Model describes data rather well and is economic! Phenomenological description of total X-sections by Pomeron trajectory Could Pomeron be a Regge trajectory which is exchanged in diffractiven processes? The bound states on this trajectory could be glueballs! Model of Donnachie und Landshoff soft Pomeron: aS(t) = 1.008 + 0.25 * t E xperiment: intercept a(0) of the ‚trajectory‘ changes with Q2 resp. the size of the hadrons. There can be no universal Pomeron trajectory! glueball candidates J=2 Soft Pomeron

  27. from hard to soft physics: do we see saturation? • We measure high energy scattering • of a color dipole with the proton • We can choose the transverse size • of the dipole via Q2 r~1/Q σ*p (x,Q2)~ F2(x,Q2)/Q2 • The only unknown in • principle is the dipole-p cross section which depends on: • x ~ 1/t • the transverse size of the • dipole • the distribution profile of • the gluons in the proton • can it be calculated? F2 dipole WF in the photon (calc.) dipole-p cross- section σT,Ldiffr B diffraction (F2D)

  28. R0(x) r~2/Q s g*p diffractive Ψ production describable by 2-gluon exchange (LO only so far) Ψ perturbative QCD predicition for small dipole sizes ~r2 confront to data: Fits to F2 at x<10 -2 to determine free parameters:  x0 = 3 10-4, λ= 0.15 , describes transition to soft physics! the dipole –p cross section: the saturation model ~r2(perturbative) saturation qq simplest version: Golec-Biernat , Wüsthoff 99 : R0(x)= (x/x0)λ*1 GeV2 improvements: + Bartels, Kowalski Ψ R0(x) ~ (1/x)λ: average gluon distance at which saturation sets in. Depends also on transverse gluon profile T(b). proton

  29. successes of dipole saturation model 1. describes F2 at small x and moderate Q2 2. predicts ‘geometric scaling’ of F2 at small x F2(x,Q2) = F2 ( Q2* R02(x) ) eqiv. σ*p = σ*p(Q2*R02(x) ) 3. predicts the ratio DIS diffractive/ DIS = constant vs. energy  this was one of the simple messages of the data which are not easily explained 4. detailed predictions concerning diffractive processes (needs more theoretical work) τ = Q2* R02(x) This is of course no proof of saturation but several disconnected effects are successfully predicted…  very appealing though not compelling

  30. soft color interaction: ,calculation‘ of dipole cross section in ‘semiclassical model’ The qq color dipole is scattered from the color field of the Proton and is neutralized statistically. How does the gluon field look like in the proton ?

  31. Free parameters (few) are determined by a fit of the predictions to F2(x,Q2)  Diffractive distributions are predicted. description of F2D is ‘acceptable’

  32. Diffractive 2-Jet events Models with color neutralisation by soft gluons (non pertubative) Color dipole models: 2gluon-exchange and ‚saturation‘ 2gluon Res. Pomeron saturation • Models exhibit approximate • factorisationof Pomeron flux • Normalisation off by factors 2 • BUT: only leading order • (no progress recently)

  33. how does the proton look like at high energy? b_ could be consolidated much better by HERA measurements and their theoretical interpretation edge area increases due to the evolution of soft gluons which become visible (active) at high energy S= Ecm2 proton gets blacker and inceases its size with increasing CM energy Profile function HERA energy ‚ black‘ LHC example: model of Pirner, Shoshi, Steffen ‚2002

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