17-20 September 2003K. Goulianos, Small x and Diffraction, Fermilab1 Konstantin Goulianos The Rockefeller University Small x and Diffraction September 2003, FERMILAB Soft and Hard Diffraction

17-20 September 2003K. Goulianos, Small x and Diffraction, Fermilab2 Contents SOFT DIFFRACTION M 2 -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   and  dependence  Regge and QCD factorization  HERA versus TEVATRON  Normalization   dependence

17-20 September 2003K. Goulianos, Small x and Diffraction, Fermilab3 Classical Picture of Diffraction Elastic Scattering and Diffraction Dissociation X Diffraction dissociation KG, Phys. Rep. 101 (1983) 171 coherence

17-20 September 2003K. Goulianos, Small x and Diffraction, Fermilab4  Non-diffractive interactions:  Diffractive interactions: rapidity gaps are regions of pseudorapidity devoid of particles Gaps are exponentially suppressed From Poisson statistics: ( r =particle density in rapidity space) large rapidity gaps are signatures for diffraction Rapidity gaps are formed by multiplicity fluctuations. Rapidity gaps are due to absence of radiation in “vacuum exchange” Diffraction and Rapidity Gaps

17-20 September 2003K. Goulianos, Small x and Diffraction, Fermilab5  Quark/gluon exchange across a rapidity gap: POMERON  No particles radiated in the gap: the exchange is COLOR-SINGLET with quantum numbers of vacuum  Rapidity gap formation: NON-PERTURBATIVE  Diffraction probes the large distance aspects of QCD: POMERON CONFINEMENT  PARTONIC STRUCTURE  FACTORIZATION ? The Pomeron in QCD

17-20 September 2003K. Goulianos, Small x and Diffraction, Fermilab6  Elastic scattering  Total cross section  Diffraction PRD PRL PRL PRL 50 (1994) (2001) to be sub’d 91(2003) SOFT diffraction HARD diffraction Control sample W 78 (1997) 2698JJ 74 (1995) 855JJ 85 (2000) 4217 JJ 79 (1997) 2636JJ 80 (1998) 1156 b-quark 84 (2000) 232JJ 81 (1998) 5278 J/  87 (2001) JJ 84 (2000) 5043 JJ 88 (2002) with roman pots PRL reference PRD 50 (1994) 5518 PRD 50 (1994) 5550 Diffraction at CDF in Run I

17-20 September 2003K. Goulianos, Small x and Diffraction, Fermilab7 Single Diffraction  SOFT DIFFRACTION  HARD DIFFRACTION  =  P L /P L fractional momentum loss of scattered hadron Variables: ( , t) or ( , t) Additional variables: (x, Q 2 )  dN/d   =-ln  t dN/d  Questions: universality of gap formation and of diffractive PDF’s

17-20 September 2003K. Goulianos, Small x and Diffraction, Fermilab8 Factorization & (re)normalization Soft diffraction Renormalize to unity KG, PLB 358 (1995) 379 Gap probability  COLOR FACTOR Pomeron trajectory parton model Regge

17-20 September 2003K. Goulianos, Small x and Diffraction, Fermilab9 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 M 2 SCALING Soft Single Diffraction Data

17-20 September 2003K. Goulianos, Small x and Diffraction, Fermilab10 The color factor  Experimentally: Theoretically: KG&JM, PRD 59 (114017) 1999 g =0.20 q =0.04 R =-0.5

17-20 September 2003K. Goulianos, Small x and Diffraction, Fermilab11  Double diffraction  Plot #Events versus   Double Pomeron Exchange  Measure  Plot #Events versus log(  )  SDD: single+double diffraction  Central gaps in SD events Central and Double Gaps

17-20 September 2003K. Goulianos, Small x and Diffraction, Fermilab12 color factor 5 independent variables Gap probabilitySub-energy cross section (for regions with particles) Integral Renormalization removes the s-dependence SCALING Two-Gap Diffraction (hep-ph/ )

17-20 September 2003K. Goulianos, Small x and Diffraction, Fermilab13 Differential shapes agree with Regge predictions  One-gap cross sections require renormalization DDSDDDPE  Two-gap/one-gap ratios are Central and Double-Gap CDF Results

17-20 September 2003K. Goulianos, Small x and Diffraction, Fermilab14 Soft Double Pomeron Exchange  Roman Pot triggered events  <  -pbar < |t-pbar| < 1 GeV 2   -proton measured using  Data compared to MC based on Pomeron exchange with  Pomeron intercept  =0.1  Good agreement over 4 orders of magnitude!

17-20 September 2003K. Goulianos, Small x and Diffraction, Fermilab15 Multigap variables Parton model amplitude rapidity gap regions color factor = 0.17 particle cluster regions also: t-across gap centers of floating gap/clusters Soft Diffraction Summary Differential cross section Sub-energy cross sectionNormalized gap probability form factor for surviving nucleon color factor: one  for each gap

17-20 September 2003K. Goulianos, Small x and Diffraction, Fermilab16 Hard diffraction at CDF in Run I BBC 3.2<  <5.9 FCAL 2.4<  <4.2 BBC FCAL Diffractive dijets CDF Forward Detectors

17-20 September 2003K. Goulianos, Small x and Diffraction, Fermilab17  SINGLE DIFFRACTION  DOUBLE DIFFRACTION 1.45 (0.25) J/  0.62 (0.25)b 0.65 (0.04)0.75 (0.10)JJ 1.15 (0.55)W D0CDFX SD/ND gap fraction (%) at 1800 GeVDD/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 Hard Diffraction w /Rapgaps

17-20 September 2003K. Goulianos, Small x and Diffraction, Fermilab18 ISSUES: 1) QCD factorization > is F SD universal? 2) Regge factorization > (not detected) Bjorken-x of antiproton Nucleon structure function Diffractive structure function ? momentum fraction of parton in IP METHOD of measuring F SD : measure ratio R( ,t) of SD/ND rates for given ,t set R( ,t)=F SD /F ND evaluate F SD = R * F ND Diffractive Dijets with Leading Antiproton The diffractive structure function

17-20 September 2003K. Goulianos, Small x and Diffraction, Fermilab19 Test Regge factorization Test QCD factorization suppressed at the Tevatron relative to extrapolations from HERA parton densities Regge factorization holds Dijets in Single Diffraction - Data H1-2002

17-20 September 2003K. Goulianos, Small x and Diffraction, Fermilab20 DDIS vs DIS at HERA Pomeron : Proton : x F2F2  RENORM HERA Tev

17-20 September 2003K. Goulianos, Small x and Diffraction, Fermilab21 Dijets in Single Diffraction – R(x)

17-20 September 2003K. Goulianos, Small x and Diffraction, Fermilab22 R(x) predicted from pronton PDFs Power-law region  max = 0.1 x max = 0.1  < 0.05   g =0.20  q =0. 04  R =-0.5 g =0.5 q =0.3

17-20 September 2003K. Goulianos, Small x and Diffraction, Fermilab23 RENORM prediction of R(x) vs data CDF data RENORM predicion exp-syst-errors  Ratio of diffractive to non-diffractive structure functions is predicted from PDF’s and color factors with no free parameters.  F jj (  ) correctly predicted  Test: processes sensitive to quarks will have more flat R(x) – diff W? R(x)

17-20 September 2003K. Goulianos, Small x and Diffraction, Fermilab24 HERA vs Tevatron normalized gap probability Pomeron flux RENORM PREDICTIONS HERA Tevatron Tev/HERA  effective Normalization R(x)=F D (x)/F(x) flat x - (  eff ~ x -0.5  _eff = [  (Q 2 ) ]/2 ~

17-20 September 2003K. Goulianos, Small x and Diffraction, Fermilab25 F 2 D (x, Q 2 ) vs F 2 (x, Q 2 ) at HERA At fixed x IP : F 2 D (x,Q 2 ) evolves like F 2 (x,Q 2 ) independent of the value of x

17-20 September 2003K. Goulianos, Small x and Diffraction, Fermilab26 Pomeron Intercept in DDIS RENORM 1+

17-20 September 2003K. Goulianos, Small x and Diffraction, Fermilab27 (not detected) R(SD/ND) R(DPE/SD) Test of factorization equal? Factorization breaks down, but… see next slide(Hatakeyama’s talk) The second gap is less suppressed!!! Dijets in Double Pomeron Exchange

17-20 September 2003K. Goulianos, Small x and Diffraction, Fermilab28 DSF: Tevatron double-gaps vs HERA The diffractive structure function derived from double-gap events approximately agrees with expectations from HERA

17-20 September 2003K. Goulianos, Small x and Diffraction, Fermilab29 SUMMARY Soft and hard conclusions b Soft Diffraction e Hard Diffraction  Pay a color factor  for each gap Use reduced energy cross section Get gap size from renormalized P gap Diffraction is an interaction between low-x partons subject to color constraints