Pomeron Intercept and Slope: are they related?

Transcription

1 Pomeron Intercept and Slope: are they related? K. Goulianos The Rockefeller University intercept slope Small-x and Diffraction, FERMILAB, 7-3 March 007

2 Contents Introduction Diffraction in QCD Pomeron intercept and slope Cross sections with /no free parameters Conclusion Fermilab, 7-3 March 007 Pomeron Intercept and Slope: are they related? K. Goulianos

3 The Pomeron Trajectory REGGE THEORY α(t) = t T(s,t) = β ( t ) s resonances S β ( t ) S α (t) φ _a(t) β ( t ) t β ( t ) σ T = β( 0) S α (0)- ε ~ s Slope=0.5 Intercept=. -large- -smallπ α (t) ~ Regge trajectories f,a ρ,ω f4,[a4] ρ3,ω3 π t=m (GeV ) [f6] ρ5 REGGEON α(t)= t PION α (t)=0+0.7t POMERON α(t)=.+0.5t Fermilab, 7-3 March 007 Pomeron Intercept and Slope: are they related? K. Goulianos 3

4 Historical perspective α(t) = α 0 + α ' time t ~994: α =0.5, α ο =. ~970: α =0.5, α ο = first guess: a ~ (as for other trajectories) In this talk: are α and α o related? A toy estimate of the ratio α /α o Fermilab, 7-3 March 007 Pomeron Intercept and Slope: are they related? K. Goulianos 4

5 A clue from Diffraction Dissociation KG, Phys. Rep. 0, 69 (983) M d σ dt dm t= 0.05 ξ< 0. dσ dσ ~ ~ dm M dξ ξ Why /M? Fermilab, 7-3 March 007 Pomeron Intercept and Slope: are they related? K. Goulianos 5

6 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 Fermilab, 7-3 March 007 Pomeron Intercept and Slope: are they related? K. Goulianos 6

7 Diffractive Rapidity Gaps X dn/dη η φ p X dσ dδη t= 0 ξp Particle production ln M X ln s constant dσ dm ~ M p Rapidity gap -ln ξ p dσ dξ ~ ξ η Fermilab, 7-3 March 007 Pomeron Intercept and Slope: are they related? K. Goulianos 7

8 Single Diffraction and Unitarity: more clues d σ dtdξ SD = f IP/p (t, ξ) σ IP p (sξ ) σ SD ~ s ε Unitarity problem: Using factorization and std pomeron flux σ SD exceeds σ T at s TeV. Renormalization: Normalize the Pomeron flux to unity KG, PLB 358 (995) 379 ξ 0. min 0 t= f IP/p (t,ξ) dξ dt = Fermilab, 7-3 March 007 Pomeron Intercept and Slope: are they related? K. Goulianos 8

9 M -scaling KG&JM, PRD 59 (999) 407 renormalization dσ dm s (M ε + ε ) Independent of S over 6 orders of magnitude in M! std. and renorm. flux fits Δ ε Δ = 0.05 Δ = 0.5 renorm. flux prediction... 4 GeV (0.0 < ξ < 0.03) 0 GeV (0.0 < ξ < 0.03) 546 GeV (0.005 < ξ < 0.03) 800 GeV (0.003 < ξ < 0.03) (M ) +Δ 546 GeV std. flux prediction 800 GeV std. flux prediction Factorization breaks down so as to ensure M -scaling! Fermilab, 7-3 March 007 Pomeron Intercept and Slope: are they related? K. Goulianos 9

10 PHENOMENOLOGY 450 BC? 869 Plato ( B.C) Aristotle Demokritos Mendeleyev 007 platonic love earth water air fire atom periodic table candidates superimposed Fermilab, 7-3 March 007 Pomeron Intercept and Slope: are they related? K. Goulianos 0

11 The QCD Connection σ φ ε Δy T ( s) = σ o e = Δy = ln s σ o s ε y /α s Emission spacing controlled by α-strong σ Τ : power law rise with energy (see E. Levin, An Introduction to Pomerons,Preprint DESY 98-0) α reflects the size of the emitted cluster, which is controlled by /α s and thereby is related to ε Im f el φ ( s, t) Δy = ln s e ( ε + α t ) Δy y assume linear t-dependence Forward elastic scattering amplitude Fermilab, 7-3 March 007 Pomeron Intercept and Slope: are they related? K. Goulianos

12 Single Diffraction in QCD t Δy Δy independent variables: d dt t, Δy σ = C Fp ( t) dδy gap probability color factor κ = g IP IP IP ( t) β (0) IP p p { ( ε + α t ) Δy} { ε Δy e κ σ e } o sub-energy x-section 0.7 Gap probability MUST be normalized to unity! Fermilab, 7-3 March 007 Pomeron Intercept and Slope: are they related? K. Goulianos

13 Single diffraction (re)normalized d dt σ = N gap C Fp ( t) dδy N gap ( s) = d σ dt dδy Δy, t P gap = C P gap ( Δy, t) ( Δy, t) { ( ε + α t ) Δy} { ε Δy e κ σ e } ε s s dδy dt C ln s [ ] ε ( Δy ln s) ( b0 + α Δy) t e ln s e o Grows slower than s ε The Pumplin bound is obeyed at all impact parameters Fermilab, 7-3 March 007 Pomeron Intercept and Slope: are they related? K. Goulianos 3

14 The Factors κ and ε g IP IP IP Experimentally: κ = = 0.7 ± 0.0, ε = 0.04 β IP p KG&JM, PRD 59 (407) 999 Q Color factor: κ = f + f = g = 0.8 q Nc Nc 8 3 Pomeron intercept: ε = λ g w g + λq w q = 0. λ HERA CTEQ5L x f(x) = x λ f g =gluon fraction f q =quark fraction x = /s f ( x) dx ~ s λ x f (x) 0 λ g =0.0 λ q =0.04 λ R =-0.5 Q = GeV gluon valence quarks sea quarks x Fermilab, 7-3 March 007 Pomeron Intercept and Slope: are they related? K. Goulianos 4

15 α versus ε α' Constant set to σ o pp Pp κσ pp 0 0 σ = α' = ε 4 el b o ln(κ ) = 0.04 exp ε sd b κ o = ' α 9. = 4 ln( 0.7) 0.3 GeV Fermilab, 7-3 March 007 Pomeron Intercept and Slope: are they related? K. Goulianos 5

16 Multigap Diffraction (KG, hep-ph/0054) Δy Δ Δy y Δy φ y y y Fermilab, 7-3 March 007 Pomeron Intercept and Slope: are they related? K. Goulianos 6

17 Multigap Cross Sections d 5 i= 5 5 independent variables σ dv i = C Fp ( t) i= - Gap probability Δ y, t ~ Δ y Δ Δ y { ( ε + α t ) } i Δyi ε ( Δy +Δy ) e κ σ e ε s / ln s Same suppression as for single gap! y y y t Δ y = Δ y + Δ y t { } o Δ y color factor Sub-energy cross section (for regions with particles) Fermilab, 7-3 March 007 Pomeron Intercept and Slope: are they related? K. Goulianos 7

18 Diffractive CDF Elastic scattering σ T =Im f el (t=0) Total cross section φ GAP η OPTICAL THEOREM φ η SD DD DPE SDD=SD+DD Fermilab, 7-3 March 007 Pomeron Intercept and Slope: are they related? K. Goulianos 8

19 Central and Two-Gap CDF Results events σ DD (mb) for Δη > CDF UA5 (adjusted) Regge Renormalized gap Agreement with renormalized Regge predictions CDF Preliminary M X s=800 GeV DATA DD + non-dd MC non-dd MC 0 s = 800 GeV ξ- p t- p.0 GeV DD SDD 0 DP Δη 0 =η max -η min events One-gap cross sections are suppressed Two-gap/one-gap ratios are κ = 0. 7 gap fraction Δη > s=800 GeV DATA SDD + SD MC SD MC Δη 0 exp =η max -η min CDF: one-gap/no-gap CDF: two-gap/one-gap Regge prediction Renorm-gap prediction -gap -gap Number of Events per Δlogξ = 0. Fraction of Events with ξ p < ( GeV ) Data DPE MC SD MC DPE+SD MC ξ E X p CDF Data: DPE/SD ratio (Preliminary) Regge + Factorization Gap Probability Renorm. Pomeron Flux Renom s (GeV) sub-energy s --, (GeV) s (GeV) Fermilab, 7-3 March 007 Pomeron Intercept and Slope: are they related? K. Goulianos 9

20 Gap Survival Probability gap fraction Δη > 3.0 CDF: one-gap/no-gap CDF: two-gap/one-gap Regge prediction Renorm-gap prediction -gap S = gap/0 gap S gap/ gap(800 GeV) gap gap/0 gap S gap/ gap(630 GeV) sub-energy s --, (GeV) Results similar to predictions by: Gotsman-Levin-Maor Kaidalov-Khoze-Martin-Ryskin Soft color interactions Fermilab, 7-3 March 007 Pomeron Intercept and Slope: are they related? K. Goulianos 0

21 Conclusion Use: M scaling Non-suppressed -gap to -gap ratios Renormalization phenomenology Build: QCD theory of diffraction Fermilab, 7-3 March 007 Pomeron Intercept and Slope: are they related? K. Goulianos