Renormalized Diffractive Parton Densities and Exclusive Production K

Renormalized Diffractive Parton Densities and Exclusive Production K. Goulianos The Rockefeller University Diffraction 2006 Milos island, Greece, 5 -10 September 2006 1

Contents Ø Ø Introduction Phenomenology Experiment confronts phenomenology Exclusive Production Diffraction 2006, Milos, Greece, Sep 05 -10 Renormalized Diffractive Parton Densities K. Goulianos 2

p-p Interactions Non-diffractive: Color-exchange Diffractive: Colorless exchange with vacuum quantum numbers rapidity gap Incident hadrons acquire color and break apart P O M E R O N Incident hadrons retain their quantum numbers remaining colorless Goal: develop a QCD based phenomenology for diffraction Diffraction 2006, Milos, Greece, Sep 05 -10 Renormalized Diffractive Parton Densities K. Goulianos 3

X Diffractive Rapidity Gaps p xp p X p ln s f Particle production ln MX 2 Rapidity gap -ln x h Diffraction 2006, Milos, Greece, Sep 05 -10 Renormalized Diffractive Parton Densities K. Goulianos 4

Diffraction Dissociation KG, Phys. Rep. 101, 169 (1983) x< 0. 1 Diffraction 2006, Milos, Greece, Sep 05 -10 Renormalized Diffractive Parton Densities K. Goulianos 5

Factorization and scaling in soft single diffraction § Total SD cross section factorization breakdown § M 2 -scaling controls level of breakdown d. N/dh h Diffraction 2006, Milos, Greece, Sep 05 -10 Renormalized Diffractive Parton Densities K. Goulianos 6

Total Single Diffractive Cross Section v Unitarity problem: Using factorization and std pomeron flux s. SD exceeds s. T at v Renormalization: Normalize the Pomeron flux to unity KG, PLB 358 (1995) 379 Diffraction 2006, Milos, Greece, Sep 05 -10 Renormalized Diffractive Parton Densities K. Goulianos 7

2 M -scaling KG&JM, PRD 59 (1999) 114017 renormalization 1 Independent of S over 6 orders of magnitude in M 2 ! Factorization breaks down so as to ensure M 2 -scaling! Diffraction 2006, Milos, Greece, Sep 05 -10 Renormalized Diffractive Parton Densities K. Goulianos 8

Double Diffraction Dissociation entral rapidity gaps How does one apply Pomeron flux renormalization in this case? Need generalized renormalization! Diffraction 2006, Milos, Greece, Sep 05 -10 Renormalized Diffractive Parton Densities K. Goulianos 9

PHENOMENOLOGY 450 BC 1869 Plato (427 -347 B. C) Aristotle Demokritos platonic love earth water air fire atom Mendeleyev periodic table 2006 Diffraction 2006, Milos, Greece, Sep 05 -10 Renormalized Diffractive Parton Densities K. Goulianos 10

Elastic and Total Cross Sections QCD expectations f y The exponential rise of s. T(Dy’) is due to the increase of wee partons with Dy’ Total cross section: power law rise with energy ~1/as (see E. Levin, An Introduction to Pomerons, Preprint DESY 98 -120) f Diffraction 2006, Milos, Greece, Sep 05 -10 y Elastic cross section: forward scattering amplitude Renormalized Diffractive Parton Densities K. Goulianos 11

Single Diffraction t color factor 2 independent variables: gap probability sub-energy x-section Gap probability MUST be normalized to unity! Diffraction 2006, Milos, Greece, Sep 05 -10 Renormalized Diffractive Parton Densities K. Goulianos 12

Single diffraction (re)normalized Grows slower than se The Pumplin bound is obeyed at all impact parameters Diffraction 2006, Milos, Greece, Sep 05 -10 Renormalized Diffractive Parton Densities K. Goulianos 13

The Factors k and e Experimentally: KG&JM, PRD 59 (114017) 1999 Color factor: Pomeron intercept: CTEQ 5 L lg =0 . 20 fg=gluon fraction fq=quark fraction lq=0. 04 5 0. = l. R Diffraction 2006, Milos, Greece, Sep 05 -10 Renormalized Diffractive Parton Densities K. Goulianos 14

Multigap Diffraction (KG, hep-ph/0205141) f y Diffraction 2006, Milos, Greece, Sep 05 -10 Renormalized Diffractive Parton Densities K. Goulianos 15

Multigap Cross Sections color factor 5 independent variables Gap probability Sub-energy cross section (for regions with particles) Same suppression as for single gap! Diffraction 2006, Milos, Greece, Sep 05 -10 Renormalized Diffractive Parton Densities K. Goulianos 16

Diffractive Studies @ CDF s. T=Im fel (t=0) Elastic scattering f h SD f OPTICAL THEOREM GAP DD Diffraction 2006, Milos, Greece, Sep 05 -10 Total cross section h DPE SDD=SD+DD Renormalized Diffractive Parton Densities K. Goulianos 17

Central and Two-Gap CDF Results Agreement with renormalized Regge predictions DD SDD DP E Ø One-gap cross sections are suppressed Ø Two-gap/one-gap ratios are Diffraction 2006, Milos, Greece, Sep 05 -10 Renormalized Diffractive Parton Densities K. Goulianos 18

Gap Survival Probability S= Results similar to predictions by: Gotsman-Levin-Maor Kaidalov-Khoze-Martin-Ryskin Soft color interactions Diffraction 2006, Milos, Greece, Sep 05 -10 Renormalized Diffractive Parton Densities K. Goulianos 19

Lessons from Soft Diffraction Ø M 2 – scaling renormalization Ø Non-suppressed 2 -gap to 1 -gap ratios Pomeron: composite object made up from underlying proton pdf’s subject to QCD color constraints Diffraction 2006, Milos, Greece, Sep 05 -10 Renormalized Diffractive Parton Densities K. Goulianos 20

HARD DIFFRACTION § Diffractive structure function factorization breakdown - how? § Restoring factorization § Diffractive fractions d. N/dh h Diffraction 2006, Milos, Greece, Sep 05 -10 JJ, W, b, J/y Renormalized Diffractive Parton Densities K. Goulianos 21

Diffractive Structure Function: Breakdown of QCD Factorization b = momentum fraction of parton in Pomeron The diffractive structure function at the Tevatron is suppressed by a factor of ~10 relative to expectation from pdf’s measured by H 1 at HERA H 1 CDF Using preliminary pdf’s from Diffraction 2006, Milos, Greece, Sep 05 -10 Similar suppression factor as in soft diffraction relative to expectations from Regge theory and factorization! Renormalized Diffractive Parton Densities K. Goulianos 22

Restoring Factorization @ Tevatron R(SD/ND) R(DPE/SD) DSF from two/one gap: factorization restored! Diffraction 2006, Milos, Greece, Sep 05 -10 Renormalized Diffractive Parton Densities K. Goulianos 23

FDJJ(b) from ZEUS-LPS Data From: M. Arneodo, HERA/LHC workshop, CERN, 11 -13 Oct 2004 H 1 Fit without charm data Flat after subtracting Reggeon contribution Diffraction 2006, Milos, Greece, Sep 05 -10 ZEUS Fit including charm data Renormalized Diffractive Parton Densities K. Goulianos 24

Hard Diffractive Fractions @ CDF d. N/dh h % Fraction (+/-) Fraction: SD/ND ratio at 1800 Ge. V W 1. 15 (0. 55) JJ 0. 75 (0. 10) b 0. 62 (0. 25) J/y 1. 45 (0. 25) Diffraction 2006, Milos, Greece, Sep 05 -10 All ratios ~ 1% ~ uniform suppression ~ FACTORIZATION ! Renormalized Diffractive Parton Densities K. Goulianos 25

Diffractive Structure Function: Q 2 dependence ETjet ~ 100 Ge. V ! Small Q 2 dependence in region 100 < Q 2 < 10, 000 Ge. V 2 ð Pomeron evolves as the proton! Diffraction 2006, Milos, Greece, Sep 05 -10 Renormalized Diffractive Parton Densities K. Goulianos 26

Diffractive Structure Function: t- dependence Fit ds/dt to a double exponential: Ø No diffraction dips Ø No Q 2 dependence in slope from inclusive to Q 2~104 Ge. V 2 Diffraction 2006, Milos, Greece, Sep 05 -10 Ø Same slope over entire region of 0 < Q 2 < 4, 500 Ge. V 2 across soft and hard diffraction! Renormalized Diffractive Parton Densities K. Goulianos 27

Diffractive DIS @ HERA J. Collins: factorization holds (but under what contitions? ) Pomeron exchange p IP e x, t g* Diffraction 2006, Milos, Greece, Sep 05 -10 Color reorganization jet x p e g* Q 2 reorganize Renormalized Diffractive Parton Densities K. Goulianos 28

Inclusive vs Diffractive DIS KG, “Diffraction: a New Approach, ” J. Phys. G 26: 716 -720, 2000 e-Print Archive: hep-ph/0001092 H 1, ICHEP 2006 F 2 ~ x-l total error (eq+l)/2 eq Diffraction 2006, Milos, Greece, Sep 05 -10 Renormalized Diffractive Parton Densities K. Goulianos 29

Diffractive Dijets @ Tevatron jet p jet reorganize Diffraction 2006, Milos, Greece, Sep 05 -10 Renormalized Diffractive Parton Densities K. Goulianos 30

FDJJ(x, b, Q 2) @ Tevatron Diffraction 2006, Milos, Greece, Sep 05 -10 Renormalized Diffractive Parton Densities K. Goulianos 31

SD/ND Dijet Ratio vs x. Bj@ CDF 0. 035 < Flat Diffraction 2006, Milos, Greece, Sep 05 -10 Renormalized Diffractive Parton Densities x < 0. 095 x dependence K. Goulianos 32

Gap Between Jets Diffraction 2006, Milos, Greece, Sep 05 -10 Renormalized Diffractive Parton Densities K. Goulianos 33

Hard Diffraction in QCD p p deep sea valence quarks Derive diffractive from inclusive PDFs and color factors antiproton x=x proton Diffraction 2006, Milos, Greece, Sep 05 -10 Renormalized Diffractive Parton Densities K. Goulianos 34

Diffractive Higgs @ LHC Back of the envelope calculation p p Inclusive production H p p Øs. D(LHC) ~ P(gap) x s. ND (Tevatron) p ~ 0. 1 x 1 pb = 100 fb p Exclusive production H p Øsexcl ~ sincl x 0. 02~ 2 fb p Fraction of 2/all particle multiplicity OTHER THEORETICAL PREDICTIONS Exclusive DPE Higgs production pp p H p : 3 -10 fb (KMR) Inclusive DPE Higgs production pp p+X+H+Y+p : 50 -200 fb (others) Diffraction 2006, Milos, Greece, Sep 05 -10 Renormalized Diffractive Parton Densities K. Goulianos 35

SUMMARY Diffraction is an interaction between low-x partons subject to color constraints Diffraction 2006, Milos, Greece, Sep 05 -10 Renormalized Diffractive Parton Densities K. Goulianos 36