Manchester Dec 2003 Diffraction from HERA and Tevatron to LHCK. Goulianos1 Konstantin Goulianos The Rockefeller University Workshop on physics with forward proton taggers at the Tevatron and LHC December 2003, Manchester, UK Diffraction from HERA and Tevatron to LHC  results  theory  predictions

Manchester Dec 2003 Diffraction from HERA and Tevatron to LHCK. Goulianos2 Soft diffraction Elastic and total cross sections M 2 -scaling Soft diffraction cross sections Multigap diffraction Diffractive DIS at HERA Derive F2D3 Explain flat ratio of F2D3 / F2 Explain rise of  ( or  IP ) with Q 2 Hard diffraction at the Tevatron Explain ratio of F jj (SD) / F jj (ND) – magnitude and shape! Double-gap hard diffraction Diffraction at the LHC Soft and hard single and multigap diffraction Topics Determine: triple-pomeron coupling pomeron intercept diffractive cross section using soft parton densities Predict from hard plus soft parton densities

Manchester Dec 2003 Diffraction from HERA and Tevatron to LHCK. Goulianos3  Elastic scattering  Total cross section  Diffraction PRD PRL PRL PRL 50 (1994) (2001) submitted 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 16 papers

Manchester Dec 2003 Diffraction from HERA and Tevatron to LHCK. Goulianos4 Two (most) important results KG&JM, PRD 59 (1999) M 2 SCALING POWER LAW CDF, PRL 84 (2000) 5043 Soft DiffractionHard Diffraction

Manchester Dec 2003 Diffraction from HERA and Tevatron to LHCK. Goulianos5 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!

Manchester Dec 2003 Diffraction from HERA and Tevatron to LHCK. Goulianos6 Total Cross Section   t exhibits universal rise with energy  the falling term at low energies has NOTHING to do with this rise!  POWER LAW behavior: t=0 elastic scattering amplitude Parton model: # of wee partons grows exponentially

Manchester Dec 2003 Diffraction from HERA and Tevatron to LHCK. Goulianos7 Single Diffraction Variables  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 

Manchester Dec 2003 Diffraction from HERA and Tevatron to LHC K. Goulianos8 Factorization & (re)normalization Soft Single Diffraction Phenomenology  COLOR FACTOR Gap probability: Normalize to unity KG, PLB 358 (1995) 379

Manchester Dec 2003 Diffraction from HERA and Tevatron to LHCK. Goulianos9 The factors  and  Experimentally: Theoretically: KG&JM, PRD 59 (114017) 1999 g =0.20 q =0.04 R =-0.5

Manchester Dec 2003 Diffraction from HERA and Tevatron to LHCK. Goulianos10 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 Regge

Manchester Dec 2003 Diffraction from HERA and Tevatron to LHCK. Goulianos11  Double Diffraction Dissociation  One central gap  Double Pomeron Exchange  Two forward gaps  SDD: Single+Double Diffraction  Forward + central gaps Central and Double Gaps

Manchester Dec 2003 Diffraction from HERA and Tevatron to LHCK. Goulianos12 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/ )

Manchester Dec 2003 Diffraction from HERA and Tevatron to LHCK. Goulianos13 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

Manchester Dec 2003 Diffraction from HERA and Tevatron to LHCK. Goulianos14 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

Manchester Dec 2003 Diffraction from HERA and Tevatron to LHCK. Goulianos15 F 2 (x,Q 2 ) = c x - F 2 from Compton analysis (H1) (Q 2 ) versus Q 2 [from the talk of E. Small-x and Diffraction 2003, Fermilab]

Manchester Dec 2003 Diffraction from HERA and Tevatron to LHCK. Goulianos16 Diffractive HERA 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

Manchester Dec 2003 Diffraction from HERA and Tevatron to LHCK. Goulianos17 F 2 D3 (x IP, x, Q 2 )/F 2 (x, Q 2 ) At fixed x IP : F 2 D3 (x IP,x,Q 2 ) evolves as F 2 (x,Q 2 ) independent of the value of x

Manchester Dec 2003 Diffraction from HERA and Tevatron to LHCK. Goulianos18 Pomeron Intercept in DDIS 1+(  )/2 1+

Manchester Dec 2003 Diffraction from HERA and Tevatron to LHCK. Goulianos19 Test Regge factorization Test QCD factorization suppressed at the Tevatron relative to extrapolations from HERA parton densities Regge factorization holds Diffractive H1-2002

Manchester Dec 2003 Diffraction from HERA and Tevatron to LHCK. Goulianos20 R jj

Manchester Dec 2003 Diffraction from HERA and Tevatron to LHCK. Goulianos21 R jj =F jj SD /F jj ND Power-law region  max = 0.1  < 0.05   g =0.20  q =0. 04  R =-0.5 g =0.5 q =0.3

Manchester Dec 2003 Diffraction from HERA and Tevatron to LHCK. Goulianos22 RENORM prediction of R(x) vs data CDF data RENORM prediction 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)

Manchester Dec 2003 Diffraction from HERA and Tevatron to LHCK. Goulianos23 HERA vs Tevatron (re)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 ~

Manchester Dec 2003 Diffraction from HERA and Tevatron to LHC K. Goulianos24 Another issue QCD evolution No appreciable E T 2 dependence observed within 100 < E T 2 < 1600 GeV 2 R jj (x Bj ) vs Q 2

Manchester Dec 2003 Diffraction from HERA and Tevatron to LHCK. Goulianos25 (not detected) R(SD/ND) R(DPE/SD) Test of factorization equal? Factorization breaks down, but see next slide! The second gap is less suppressed!!! Dijets in Double Pomeron Exchange

Manchester Dec 2003 Diffraction from HERA and Tevatron to LHCK. Goulianos26 DSF: Tevatron double-gaps vs HERA The diffractive structure function derived from double-gap events approximately agrees with expectations from HERA

Manchester Dec 2003 Diffraction from HERA and Tevatron to LHC K. Goulianos27 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

Manchester Dec 2003 Diffraction from HERA and Tevatron to LHCK. Goulianos28 Inclusive Diffractive Higgs at the LHC  D (LHC) ~  2 *  ND (Tevatron) => (0.17) 2 * 1 pb = 30 fb p+p  p-gap-(H+X)-gap-p