1 Inclusive Double-Pomeron Exchange at the Fermilab Collider Authors : M.E. Convery, K. Goulianos, K. Hatakeyama The Rockefeller University Godparents : Andrey Korytov, Giorgio Bellettini, Mario Martinez-Perez PRL Draft : CDF Note 6568CDF Note 6568 CDF Paper Seminar October 23, 2003.

Kenichi Hatakeyama2 History of the Analysis  Analysis blessed on May 2, 2002 and May 16,  PRL Draft : CDF Note 6568 Comments from University of Toronto group UC Davis group University of Illinois group Universita di Padova group  Main Analysis Document : CDF Note 5865  Analysis Web Page : cdf.fnal.gov/internal/people/links/KenichiHatakeyama /idpe.html Many Thanks!

October 23, 2003.Kenichi Hatakeyama3 High Energy Particle Diffraction  Several of our collaborators have expressed an unfamiliarity with diffractive physics.  This talk will start with a brief introduction to diffraction at CDF.  Details may be found in textbooks such as this.  Also, “Diffractive interactions of hadrons at high energies”, K. Goulianos, Phys. Rep. 101, 169 (1983) would be helpful for understanding the basics of soft hadron-hadron diffraction. V. Barone, E. Predazzi, Springer Press, 2002.

October 23, 2003.Kenichi Hatakeyama4 Introduction Shaded Area : Region of Particle Production Diffraction in high energy hadron physics refers to a reaction in which no quantum numbers are exchanged between colliding particles.

October 23, 2003.Kenichi Hatakeyama5 CDF Publications on Diffraction in Run 1 Single Diffractive (SD) Double Diffractive (DD) Double Pomeron Exchange (DPE) Single+Double Diffractive (SDD) PRD 50 (1994) 5535 PRL 87 (2001) This paper! PRL 91 (2003) Single Diffractive (SD)Jet-Gap-JetDouble Pomeron Exchange (DPE) W : PRL 78 (1997) 2698 Dijet : PRL 79 (1997) 2638 b-quark: PRL 84 (2000) 232 J/ψ : PRL 87 (2001) Dijets + Roman Pots PRL 84 (2000) 5043 PRL 88 (2002) PRL 74 (1995) 855 PRL 80 (1998) 1156 PRL 81 (1998) 5278 Dijet : PRL 85 (2000) 4217 Soft Diffraction Hard Diffraction (diffraction +hard scattering)

October 23, 2003.Kenichi Hatakeyama6 What did we learn from hard diffraction? Main issue in hadronic diffraction :  Do hard diffraction processes obey QCD factorization? (Are the diffractive parton distribution functions universal?)  This question can be addressed by comparing the functions extracted from different processes. For SD dijet production, ND SD

October 23, 2003.Kenichi Hatakeyama7 Main Issue in Hadronic Diffraction : Results from single diffractive (SD) dijet production  The diffractive structure function measured using SD dijet events at the Tevatron is smaller than that at HERA by approximately an order of magnitude.  The discrepancy is generally attributed to additional color exchanges which spoil the “diffractive” rapidity gap. ~10 Factorization Breakdown CDF Collaboration, Phys. Rev. Lett. 84, (2000). Next Q : How is it broken?

October 23, 2003.Kenichi Hatakeyama8 Dijet Production in DPE  Dijet production by double pomeron exchange was studied by CDF.  R[DPE/SD] is larger than R[SD/ND] by a factor of about 5. CDF Collaboration, Phys. Rev. Lett. 85, (2000). The formation of the 2nd gap is not as suppressed as the 1st gap. Extract diffractive structure function from R[DPE/SD] and compare it with expectations from HERA results.

October 23, 2003.Kenichi Hatakeyama9 Diffractive Structure Function measured using DPE dijet events The diffractive structure function measured using DPE dijets is approximately equal to expectations from HERA! Factorization holds?

October 23, 2003.Kenichi Hatakeyama10 Soft Diffraction : Regge Theory Single Diffractive Cross SectionTotal Cross Section σ tot (mb) √s (GeV)

October 23, 2003.Kenichi Hatakeyama11 Unitarity problem : Soft Diffraction : Inclusive (Soft) SD Results  The measured SD cross section is smaller than the Regge theory prediction by approximately an order of magnitude at the Tevatron energy.  Normalizing the integral of the pomeron flux (f IP/p ) to unity yields the correct √s-dependence of σ SD. Is the formation of the second gap suppressed? Tevatron data Study DPE Similar results were obtained for double diffraction as well. Renormalization K. Goulianos, PLB 353, 379 (1995).

October 23, 2003.Kenichi Hatakeyama12 Inclusive (Soft) DPE Cross Section  Regge theory prediction + factorization :  Flux renorm. model : (both gaps are suppressed.) K. Goulianos, Phys. Lett. B 353, 379 (1995).  Gap probability (P gap ) renorm. model : P gap is renormalized. (only one gap is suppressed.) K. Goulianos, e.g. hep-ph/ (2001). = κ=g/β(0). g:triple-Pomeron coupling, pp t,ξ

October 23, 2003.Kenichi Hatakeyama13 Analysis Strategy  Use events triggered on a leading antiproton.  ξ pbar is measured by Roman Pots : ξ pbar RPS.  Measure ξ p (ξ pbar ) from BBC and calorimeters : ξ p X (ξ pbar X ).  Calibrate ξ X by comparing ξ pbar RPS and ξ pbar X.  Plot ξ p X distribution and look for a DPE signal expected in the small ξ p X region.

October 23, 2003.Kenichi Hatakeyama14 Roman Pot Spectrometer Roman Pots detect recoil antiprotons

October 23, 2003.Kenichi Hatakeyama15 Reconstruction of ξ p X Calorimeters : use E T and η of towers above noise level. BBC : use hits in BBC scintillation arrays. p T is chosen to follow the “known” p T spectrum : Cannot reconstruct ξ p by RPS. Use calorimeter towers and BBC hits to reconstruct ξ p : Calorimeters BBC (J. Collins, hep-ex/ ) The CAL+BBC method allowed us to access all the way down to the kinematic limit.

October 23, 2003.Kenichi Hatakeyama16 Data Sample and Event Selection  Roman Pot triggered data collected in 1800 GeV low luminosity runs during Run 1C ( ~ 0.2 x cm -2 s -1 ).  Overlap event (containing SD + additional ND collisions which kill the rapidity gap signal ) rate is low (~4%  ~0.5% after the cuts shown below). Selection CutNumber of Events Total Number of vertices ≤ |z vtx | ≤ 60 cm (if there is one) MIP in the RP trigger counters or 2 reconstructed tracks in RPS West BBC multiplicity ≤

October 23, 2003.Kenichi Hatakeyama17 Monte Carlo Event Generation : MBR (CDF Note 0256, 0675, PRD 50 (1994) 5535, 5550.) SD and DPE event generation MBR min-bias MC:  Specially designed to reproduce soft-interaction results from low-energy experiments  Used to determine CDF total, SD and DD cross sections [PRL 50 (1994) 5535, 5550, PRL 87 (2001) ] Detector simulation Calorimeters: not well calibrated for low p T particles.  Convert the generated particle p T to the calorimeter E T using calibrations determined specifically for low-p T particles. BBC: assume that all charged particles will trigger the BBCs.

October 23, 2003.Kenichi Hatakeyama18 Calibration of ξ X ξ X distribution in every ξ RPS bin is fitted to P1 : Peak P2 : Width P2/P1 = 0.57 (ξ X resolution is ~60%.) ξ X = ξ RPS, (ξ X is calibrated so that ξ X = ξ RPS.)

October 23, 2003.Kenichi Hatakeyama19 ξ p X Distribution  The input ξ p distribution in DPE MC is 1/ξ p 1+ε (ε = is obtained from p ± p/π ± p/K ± p total cross sections).  The DPE and SD MC distributions are independently normalized to the data distribution.  The measured ξ p X distribution is in agreement with the DPE+SD MC distribution.

October 23, 2003.Kenichi Hatakeyama20 ξ p X Distribution  The ξ p distribution on the previous page shows “number of events per Δlogξ=0.1”;  Multiply each bin by 1/ξ to show dN/dξ.  A diffractive peak of 3 orders of magnitude is observed!

October 23, 2003.Kenichi Hatakeyama21 Corrections to R[DPE/SD(incl)] :  ξ p X resolution : According to MC, more events with ξ p >0.02 seem to fall into ξ p X R[DPE/SD(incl)] is corrected by F resol =1.04±0.04  Low ξ pbar X enhancement: 3~4 % of events have very low ξ pbar X values although those events have 0.035< ξ pbar RPS < MC shows a similar effect, but not as pronounced as in data. Obtain R[DPE/SD(incl)] with/without ξ pbar X <0.003 cut, and take the average.

October 23, 2003.Kenichi Hatakeyama22 SourceEstimatorUncertainty ξ p X calibrationChange ξ p X by 10 %0.003 (2%) ξ p X resolutionWhole correction0.008 (4%) Low ξ pbar X enhancementHalf of the variation0.008 (4%) Total0.012 (6%) Systematic Uncertainties The measured fraction is in agreement with the prediction from the renormalized gap probability model (0.21±0.02)!

October 23, 2003.Kenichi Hatakeyama23 SourceR[DPE/SD(incl)] Data0.195±0.001±0.010 Regge0.36±0.04 Flux Renormalization0.041±0.004 P gap Renormalization0.21±0.02 In agreement with the renormalized gap predictions! Comparisons with phenomenological models

October 23, 2003.Kenichi Hatakeyama24 Proton Dissociation Events Our “DPE” signal actually consists of two classes of events;  Events in which both the proton and antiproton escape intact from the collision  typically called “DPE”.  Events in which the antiproton escapes intact from the collision, while the proton dissociates into a small mass cluster Y ( M Y 2 <~8 GeV 2 )  proton dissociation events.  Particles in Y have rapidity up to y=7.5.  In 35% of events (“A”), east BBC covers up to η=5.9, M Y 2 < e = 5 GeV 2.  In 65% of events (“B”), east BBC covers up to η=5.2, M Y 2 < e = 10 GeV 2.  R[DPE/SD(incl)] is larger in “B” than in “A” by 6%. Weighted average : 8 GeV 2 The contribution of proton dissociation events with 1.5<M Y 2 <8GeV 2 to R[DPE/SD(incl)] is ~15%. All the particles in Y go beyond BBC so that the event is indistinguishable from “DPE” events. DPE Proton dissociation event

October 23, 2003.Kenichi Hatakeyama25 Soft Diffraction : Summary σ (mb) Gap Fraction Good Agreement with Renormalized Gap Predictions! SDDD DPE SDD

October 23, 2003.Kenichi Hatakeyama26 Summary  We have observed double pomeron exchange events in an inclusive single diffractive event sample.  The measured ξ p X distribution exhibits ~1/ξ 1+ε behavior (ε = 0.104).  The measured DPE fraction in SD is : for <ξ pbar < 0.095, |t pbar |<1 GeV 2, ξ p X < 0.02 and M Y 2 <~8GeV 2 at √s = 1800 GeV,  in agreement with the renormalized gap prediction. In events with a rapidity gap, the formation of a second gap is “unsuppressed”! Consistent with results from hard diffraction Universality of the rapidity gap formation

October 23, 2003.Kenichi Hatakeyama27 Summary + The diffractive structure function measured using DPE dijets is approximately equal to expectations from HERA!  Universality of rapidity gap formation across soft and hard diffraction processes.  Events with multiple rapidity gaps can be used to eliminate the “suppression” factor…  Facilitate QCD calculation of hard diffraction.

October 23, 2003.Kenichi Hatakeyama28 Backups

October 23, 2003.Kenichi Hatakeyama29 Regge Theory & Factorization Single Diffractive Cross Section Total & EL Cross Sections

October 23, 2003.Kenichi Hatakeyama30 Unitarity Problem Single Diffractive Cross Section Total Cross Section [ε=0.104 in PLB 389 (1996) 176] The ratio σ DPE /σ SD reaches unity at √s~2 TeV. In data, s 2ε in dσ SD /dM 2  1

October 23, 2003.Kenichi Hatakeyama31 Soft Single Diffraction Results KG&JM, PRD 59 (1999) KG, PLB 358 (1995)379  Differential cross section agrees with Regge predictions (left)  Normalization is suppressed by flux factor integral (right) dσ SD /dM 2 σ SD tot versus √s

October 23, 2003.Kenichi Hatakeyama32 Renormalization Single Diffractive Cross Section In data, s 2ε  1 Renormalization K. Goulianos, Phys. Lett. B 358 (1995) 379

October 23, 2003.Kenichi Hatakeyama33 Soft Double Diffraction Results CDF, Phys. Rev. Lett 87 (2001)  Differential cross section agrees with Regge predictions (left)  Normalization is suppressed by flux factor integral (right) dσ DD /dΔη 0 σ DD tot versus √s

October 23, 2003.Kenichi Hatakeyama34 Past Experimental Results : UA8 Collaboration NLB 514 (1998) 3, PLB 481 (2000) 177, EPJC 25 (2002) 361. Extracted σ IPIP tot using F IP/p (ξ,t) from their SD analysis.  The extracted σ IPIP tot shows an enhancement at low M X.  They attributed it to the glueball production Note : If the standard ε~0.1 is used, the enhancement is reduced significantly. But, the extracted σ IPIP tot is overall higher than the expectation.  Consistent with our results

October 23, 2003.Kenichi Hatakeyama35 Beam-Beam Counters  In 35% of events (“A”), Red : Dead Channels Light blue : Channels used to reconstruct ξ X  In 65% of events (“B”), East BBC West BBC

October 23, 2003.Kenichi Hatakeyama36 Reconstruction of ξ p X : BBC BBC (ξ p BBC ) : use hits in BBC scintillation arrays  use only inner 3 (shaded) layers (the most-outer layer overlaps with the forward cal).  p T is chosen to follow the “known” p T spectrum  η is chosen randomly within the η range of the BBC counter which has a hit. Use calorimeter towers and BBC hits to reconstruct ξ X,

October 23, 2003.Kenichi Hatakeyama37 Reconstruction of ξ p X :Calorimeter Calorimeter (ξ p CAL ) : use E T and η of towers above the noise level ξ p CAL has to be corrected for  Calorimeter non-linearity at low E T region  Particles below the applied E T threshold The correction factor for ξ CAL is obtained so that ξ X (median):ξ RPS =1:1.

October 23, 2003.Kenichi Hatakeyama38 ξ X Calibration : ξ pbar X distributions in 9 ξ pbar RPS intervals ξ X distribution in every ξ RPS bin is fitted to P1 : Peak, P2 : Width ξ X (median) = 0.94 ξ RPS  calibrated later to obtain ξ X (median)=ξ RPS P2/P1 = 0.57 (ξ X resolution is ~60%.)

October 23, 2003.Kenichi Hatakeyama39 ξ pbar X Distribution We calibrated ξ X so that ξ X (median) : ξ RPS becomes 1 : 1. The choice of P1/median/mean does NOT make a difference in R[DPE/SD(incl)], since the choice is taken into account by the ξ X resolution correction, F resol.

October 23, 2003.Kenichi Hatakeyama40 BBC Multiplicities in MC  The peak at EBBC=0 in data distributions is due to DPE events.  The MBR SD MC whose dN/dη is already checked in PRD 50 (1994) 5535, shows much lower multiplicities in the east BBC.  The higher BBC multiplicities in data are presumably due to “splashes” which are hard to simulate.  In SD MBR, for east BBC hits, don’t use the information of particles generated by MBR but simulate east BBC hits according to the data east BBC multiplicities. “A”“B”

October 23, 2003.Kenichi Hatakeyama41 BBC Contribution to ξ X (A)(B)

October 23, 2003.Kenichi Hatakeyama42 ξ p X resolution correction  Generate ξ by using dσ/dξ from F. Abe et al., PRD 50 (1994) K. Goulianos & J. Montanha, PRD 59 (1999)  Smear ξ according to the form: - P2/P1 = 0.57, P1 = 0.67ξ (P1 = 0.67xmedian when P2/P1=0.57)  The number of events with ξ<0.02 increases about 4% after the smearing. F resol =1.04±0.04