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Soft and Hard Diffraction

Soft and Hard Diffraction. Konstantin Goulianos The Rockefeller University. Small x and Diffraction 2003 17-20 September 2003, FERMILAB. Contents. SOFT DIFFRACTION M 2 -scaling Triple-pomeron coupling  relate to color factors Derive full differential cross section from parton model

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Soft and Hard Diffraction

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  1. Soft and Hard Diffraction Konstantin Goulianos The Rockefeller University Small x and Diffraction 2003 17-20 September 2003, FERMILAB K. Goulianos, Small x and Diffraction, Fermilab

  2. Contents SOFT DIFFRACTION • M2-scaling • Triple-pomeron coupling  relate to color factors • Derive full differential cross section from parton model • Multi-gap diffraction HARD DIFFRACTION • Diffractive structure function  derive from proton PDFs • b and x dependence • Regge and QCD factorization • HERA versus TEVATRON • Normalization • b dependence K. Goulianos, Small x and Diffraction, Fermilab

  3. Classical Picture of Diffraction X Elastic Scattering and Diffraction Dissociation Diffraction dissociation coherence KG, Phys. Rep. 101 (1983) 171 K. Goulianos, Small x and Diffraction, Fermilab

  4. Non-diffractive interactions: Diffractive interactions: Diffraction and Rapidity Gaps • rapidity gaps are regions of pseudorapidity devoid of particles Rapidity gaps are formed by multiplicity fluctuations. Rapidity gaps are due to absence of radiation in “vacuum exchange” From Poisson statistics: (r=particle density in rapidity space) Gaps are exponentially suppressed • large rapidity gaps are signatures for diffraction K. Goulianos, Small x and Diffraction, Fermilab

  5. ? The Pomeron in QCD • Quark/gluon exchange across a rapidity gap: POMERON • No particles radiated in the gap: the exchange is COLOR-SINGLETwith quantum numbers of vacuum • Rapidity gap formation: NON-PERTURBATIVE • Diffraction probes the large distance aspects of QCD: POMERON CONFINEMENT • PARTONIC STRUCTURE • FACTORIZATION K. Goulianos, Small x and Diffraction, Fermilab

  6. Diffraction at CDF in Run I PRD 50 (1994) 5518 • Elastic scattering • Total cross section • Diffraction PRD 50 (1994) 5550 SOFT diffraction Control sample PRD PRL PRL PRL 50 (1994) 5535 87 (2001)141802 to be sub’d 91(2003)011802 HARD diffraction PRL reference with roman pots K. Goulianos, Small x and Diffraction, Fermilab

  7. SOFT DIFFRACTION HARD DIFFRACTION dN/dh dN/dh Dh=-lnx h t Single Diffraction x=DPL/PL fractional momentum loss of scattered hadron Additional variables: (x, Q2) Variables: (x, t) or (Dh, t) Questions:universality of gap formation and of diffractive PDF’s K. Goulianos, Small x and Diffraction, Fermilab

  8. Soft diffraction f parton model Factorization & (re)normalization Regge Pomeron trajectory COLOR FACTOR Renormalize to unity KG, PLB 358 (1995) 379 Gap probability K. Goulianos, Small x and Diffraction, Fermilab

  9. Soft Single Diffraction Data Total cross section KG, PLB 358 (1995) 379 Differential cross section KG&JM, PRD 59 (114017) 1999 REGGE RENORM s-independent • Differential shape agrees with Regge • Normalization is suppressed by factor • Renormalize Pomeron flux factor to unity M2 SCALING K. Goulianos, Small x and Diffraction, Fermilab

  10. The color factor k Experimentally: KG&JM, PRD 59 (114017) 1999 Theoretically: lg=0.20 lq=0.04 lR=-0.5 K. Goulianos, Small x and Diffraction, Fermilab

  11. Central and Double Gaps • Double diffraction • Plot #Events versus Dh • Double Pomeron Exchange • Measure • Plot #Events versus log(x) • SDD: single+double diffraction • Central gaps in SD events K. Goulianos, Small x and Diffraction, Fermilab

  12. Two-Gap Diffraction (hep-ph/0205141) 5 independent variables color factor Gap probability Sub-energy cross section (for regions with particles) Integral Renormalization removes the s-dependence SCALING K. Goulianos, Small x and Diffraction, Fermilab

  13. Central and Double-Gap CDF Results Differential shapes agree with Regge predictions DD SDD DPE • One-gap cross sections require renormalization • Two-gap/one-gap ratios are K. Goulianos, Small x and Diffraction, Fermilab

  14. Soft Double Pomeron Exchange • Roman Pot triggered events • 0.035 < x-pbar < 0.095 |t-pbar| < 1 GeV 2 • x-proton measured using • Data compared to MC based on Pomeron exchange with  Pomeron intercept e=0.1 • Good agreement over 4 orders of magnitude! K. Goulianos, Small x and Diffraction, Fermilab

  15. Soft Diffraction Summary Multigap variablesParton model amplitude rapidity gap regions color factor = 0.17 particle cluster regions also: t-across gap centers of floating gap/clusters Differential cross section Normalized gap probability Sub-energy cross section form factor for surviving nucleon color factor: one k for each gap K. Goulianos, Small x and Diffraction, Fermilab

  16. Hard diffraction at CDF in Run I BBC FCAL CDF Forward Detectors Rapidity gaps Antiproton tag BBC 3.2<h<5.9 FCAL 2.4<h<4.2 Diffractive dijets K. Goulianos, Small x and Diffraction, Fermilab

  17. SINGLE DIFFRACTION DOUBLE DIFFRACTION X CDF D0 W 1.15 (0.55) JJ 0.75 (0.10) 0.65 (0.04) b 0.62 (0.25) J/y 1.45 (0.25) Hard Diffraction w/Rapgaps SD/ND gap fraction (%) at 1800 GeV DD/ND gap fraction at 1800 GeV • All SD/ND fractions ~1% • Gluon fraction • Suppression by ~5 relative to HERA Just like in ND except for the suppression due to gap formation K. Goulianos, Small x and Diffraction, Fermilab

  18. (not detected) Diffractive Dijets with Leading Antiproton The diffractive structure function Bjorken-x of antiproton Nucleon structure function Diffractive structure function ISSUES:1) QCD factorization > is FSD universal? 2) Regge factorization > ? momentum fraction of parton in IP METHODof measuring FSD : measure ratio R(x,t) of SD/ND rates for given x,t set R(x,t)=FSD/FND evaluate FSD = R * FND K. Goulianos, Small x and Diffraction, Fermilab

  19. H1-2002 Regge factorization holds Dijets in Single Diffraction - Data Test Regge factorization Test QCD factorization suppressed at the Tevatron relative to extrapolations from HERA parton densities K. Goulianos, Small x and Diffraction, Fermilab

  20. Proton: RENORM F2 Tev HERA x DDIS vs DIS at HERA Pomeron: b K. Goulianos, Small x and Diffraction, Fermilab

  21. Dijets in Single Diffraction – R(x) K. Goulianos, Small x and Diffraction, Fermilab

  22. lg=0.5 lq=0.3 R(x) predicted from pronton PDFs eg=0.20 Power-law region xmax = 0.1 xmax = 0.1 b < 0.05x eq=0. 04 eR=-0.5 K. Goulianos, Small x and Diffraction, Fermilab

  23. RENORM prediction of R(x) vs data CDF data R(x) • Ratio of diffractive to non-diffractive structure functions is predicted from PDF’s and color factors with no free parameters. Fjj(b,x) correctly predicted • Test: processes sensitive to quarks will have more flat R(x) – diff W? RENORM predicion exp-syst-errors K. Goulianos, Small x and Diffraction, Fermilab

  24. RENORM PREDICTIONS HERATevatronTev/HERA (e+l)_effective -- 0.55 -- Normalization 0.76 0.042 0.06 R(x)=FD(x)/F(x) flat x-(e+l)_eff ~ x-0.5 e_eff = [e+l(Q2)]/2 ~ 0.2 -- -- HERA vs Tevatron normalized gap probability Pomeron flux K. Goulianos, Small x and Diffraction, Fermilab

  25. F2D(x,Q2) vs F2(x,Q2) at HERA At fixed xIP: F2D(x,Q2) evolves like F2(x,Q2) independent of the value of x K. Goulianos, Small x and Diffraction, Fermilab

  26. RENORM Pomeron Intercept in DDIS 1+l K. Goulianos, Small x and Diffraction, Fermilab

  27. Dijets in Double Pomeron Exchange Test of factorization R(SD/ND) equal? R(DPE/SD) (not detected) The second gap is less suppressed!!! Factorization breaks down, but… see next slide(Hatakeyama’s talk) K. Goulianos, Small x and Diffraction, Fermilab

  28. DSF: Tevatron double-gaps vs HERA The diffractive structure function derived from double-gap events approximately agrees with expectations from HERA K. Goulianos, Small x and Diffraction, Fermilab

  29. SUMMARY • Soft Diffraction Use reduced energy cross section • Pay a color factor kfor each gap • Hard Diffraction Get gap size from renormalized Pgap Soft and hard conclusions Hard SOFT Diffraction is an interaction between low-x partons subject to color constraints K. Goulianos, Small x and Diffraction, Fermilab

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