Inclusive Double-Pomeron Exchange at the Fermilab Collider

1
Inclusive Double-Pomeron Exchange at the Fermilab
Collider
CDF Paper Seminar October 23, 2003.

• Authors M.E. Convery, K. Goulianos, K.
  Hatakeyama
• The Rockefeller University
• Godparents Andrey Korytov, Giorgio Bellettini,
  Mario Martinez-Perez
• PRL Draft CDF Note 6568

2
History of the Analysis

• Analysis blessed on May 2, 2002 and May 16,
  2003.
• 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
• http//www-cdf.fnal.gov/internal/people/links/Ken
  ichiHatakeyama/idpe.html

Many Thanks!
3
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.
4
Introduction
Diffraction in high energy hadron physics refers
to a reaction in which no quantum numbers are
exchanged between colliding particles.
5
CDF Publications on Diffraction in Run 1
Soft Diffraction
Single Diffractive (SD) Double Diffractive (DD) Double Pomeron Exchange (DPE) SingleDouble Diffractive (SDD)

PRD 50 (1994) 5535 PRL 87 (2001) 141802 This paper! PRL 91 (2003) 011802
Hard Diffraction (diffraction hard scattering)
Single Diffractive (SD) Single Diffractive (SD) Jet-Gap-Jet Double Pomeron Exchange (DPE)

W PRL 78 (1997) 2698 Dijet PRL 79 (1997) 2638 b-quark PRL 84 (2000) 232 J/? PRL 87 (2001) 241802 Dijets Roman Pots PRL 84 (2000) 5043 PRL 88 (2002) 151802 PRL 74 (1995) 855 PRL 80 (1998) 1156 PRL 81 (1998) 5278 Dijet PRL 85 (2000) 4217
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What did we learn from hard diffraction?
ND
For SD dijet production,

• 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.

SD
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Main Issue in Hadronic Diffraction Results from
single diffractive (SD) dijet production
CDF Collaboration, Phys. Rev. Lett. 84, 5043-5048
(2000).

• 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.

Factorization Breakdown
Next Q How is it broken?
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Dijet Production in DPE
CDF Collaboration, Phys. Rev. Lett. 85, 4215-4220
(2000).

• Dijet production by double pomeron exchange was
  studied by CDF.
• RDPE/SD is larger than RSD/ND by a factor of
  about 5.

The formation of the 2nd gap is not as
suppressed as the 1st gap.
Extract diffractive structure function
from RDPE/SD and compare it with expectations
from HERA results.
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Diffractive Structure Functionmeasured using DPE
dijet events
Factorization holds?
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Soft Diffraction Regge Theory
Single Diffractive Cross Section
Total Cross Section
stot (mb)
vs (GeV)
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Soft Diffraction Inclusive (Soft) SD Results
Unitarity problem

• 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
  (fIP/p) to unity yields the correct vs-dependence
  of sSD.

Tevatron data
Renormalization
K. Goulianos, PLB 353, 379 (1995).
Similar results were obtained for double
diffraction as well.
Study DPE
Is the formation of the second gap suppressed?
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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 (Pgap) renorm. model Pgap is
  renormalized.
• (only one gap is suppressed.) K. Goulianos, e.g.
  hep-ph/0110240 (2001).

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Analysis Strategy

• Use events triggered on a leading antiproton.
• ?pbar is measured by Roman Pots ?pbarRPS.
• Measure ?p (?pbar) from BBC and calorimeters
  ?pX (?pbarX).
• Calibrate ?X by comparing ?pbarRPS and ?pbarX.
• Plot ?pX distribution and look for a DPE signal
  expected in the small ?pX region.

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Roman PotSpectrometer
Roman Pots detect recoil antiprotons
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Reconstruction of ?pX
Calorimeters

• Cannot reconstruct ?p by RPS.
• Use calorimeter towers and
• BBC hits to reconstruct ?p

(J. Collins, hep-ex/9705393)
The CALBBC method allowed us to access all the
way down to the kinematic limit.

• Calorimeters use ET and ? of towers above noise
  level.
• BBC use hits in BBC scintillation arrays.
• pT is chosen to follow the known pT spectrum

BBC
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Data Sample and Event Selection

• Roman Pot triggered data collected in 1800 GeV
  low luminosity runs during Run 1C (ltLinstgt 0.2
  x 1030 cm-2s-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 Cut Number of Events
Total 1200779
Number of vertices 1 1123407
zvtx 60 cm (if there is one) 1058876
1 MIP in the RP trigger counters 971749
1 or 2 reconstructed tracks in RPS 763268
660240
West BBC multiplicity 6 568478
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Monte Carlo Event Generation MBR(CDF Note
0256, 0675, 5371. 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)
  141802.
• Detector simulation
• Calorimeters not well calibrated for low pT
  particles.
• Convert the generated particle pT to the
  calorimeter ET using calibrations determined
  specifically for low-pT particles.
• BBC assume that all charged particles will
  trigger the BBCs.

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Calibration of ?X
?X distribution in every ?RPS bin is fitted to
P1 Peak P2 Width
?X ?RPS, (?X is calibrated so that ?X ?RPS.)
P2/P1 0.57 (?X resolution is 60.)
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?pX Distribution

• The input ?p distribution in DPE MC is 1/?p1e (e
  0.104 is obtained from pp/pp/Kp total cross
  sections).
• The DPE and SD MC distributions are independently
  normalized to the data distribution.
• The measured ?pX distribution is in agreement
  with the DPESD MC distribution.

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?pX Distribution

• The ?p distribution on the previous page shows
  number of events per ?log?0.1
• Multiply each bin by 1/? to show dN/d?.
• A diffractive peak of 3 orders of magnitude is
  observed!

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• Corrections to RDPE/SD(incl)
• ?pX resolution
• According to MC, more events with ?pgt0.02 seem to
  fall into ?pXlt0.02 than events with ?plt0.02 fall
  into ?pXgt0.02.
• RDPE/SD(incl) is corrected by Fresol1.040.04
• Low ?pbarX enhancement
• 34 of events have very low ?pbarX values
  although those events have 0.035lt ?pbarRPS
  lt0.095.
• MC shows a similar effect, but not as pronounced
  as in data.
• Obtain RDPE/SD(incl) with/without ?pbarXlt0.003
  cut, and take the average.

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Systematic Uncertainties
Source Estimator Uncertainty
?pX calibration Change ?pX by 10 0.003 (2)
?pX resolution Whole correction 0.008 (4)
Low ?pbarX enhancement Half of the variation 0.008 (4)
Total 0.012 (6)
The measured fraction is in agreement with the
prediction from the renormalized gap probability
model (0.210.02)!
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Comparisons with phenomenological models
Source RDPE/SD(incl)
Data 0.1950.0010.010
Regge 0.360.04
Flux Renormalization 0.0410.004
Pgap Renormalization 0.210.02
In agreement with the renormalized gap
predictions!
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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 (MY2 lt8 GeV2) ?
  proton dissociation events.

• Particles in Y have rapidity up to y7.5.
• In 35 of events (A), east BBC covers up to
  ?5.9,
• MY2 lt e 7.5 - 5.9 5 GeV2.
• In 65 of events (B), east BBC covers up to
  ?5.2,
• MY2 lt e 7.5 - 5.2 10 GeV2.
• RDPE/SD(incl) is larger in B than in A by
  6.

Weighted average 8 GeV2
The contribution of proton dissociation
events with 1.5ltMY2lt8GeV2 to RDPE/SD(incl) is
15.
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Soft Diffraction Summary
SD
DD
s (mb)
DPE
SDD
Gap Fraction
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Summary

• We have observed double pomeron exchange events
  in an inclusive single diffractive event sample.
  
• The measured ?pX distribution exhibits 1/?1e
  behavior (e 0.104).
• The measured DPE fraction in SD is
• for 0.035 lt?pbarlt 0.095, tpbarlt1 GeV2, ?pXlt
  0.02 and MY2lt8GeV2at vs 1800 GeV,
• in agreement with the renormalized gap prediction.

Consistent with results from hard diffraction
Universality of the rapidity gap formation
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Summary

• 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.

The diffractive structure function measured using
DPE dijets is approximately equal to expectations
from HERA!
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• Backups

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Regge Theory Factorization
Single Diffractive Cross Section
Total EL Cross Sections
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Unitarity Problem
Single Diffractive Cross Section
Total Cross Section
e0.104 in PLB 389 (1996) 176
The ratio sDPE/sSD reaches unity at vs2 TeV.
In data, s2e in dsSD/dM2 ? 1
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Soft Single Diffraction Results
KGJM, PRD 59 (1999) 114017
KG, PLB 358 (1995)379
dsSD/dM2
sSDtot versus vs

• Differential cross section agrees with Regge
  predictions (left)
• Normalization is suppressed by flux factor
  integral (right)

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Renormalization
Single Diffractive Cross Section
In data, s2e ? 1
Renormalization
K. Goulianos, Phys. Lett. B 358 (1995) 379
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Soft Double Diffraction Results
CDF, Phys. Rev. Lett 87 (2001) 141802
dsDD/d??0
sDDtot versus vs

• Differential cross section agrees with Regge
  predictions (left)
• Normalization is suppressed by flux factor
  integral (right)

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Past Experimental Results UA8 CollaborationNLB
514 (1998) 3, PLB 481 (2000) 177, EPJC 25 (2002)
361.

• Extracted sIPIPtot using FIP/p(?,t) from their SD
  analysis.
• The extracted sIPIPtot shows an enhancement at
  low MX.
• They attributed it to the glueball
  production......
• Note If the standard e0.1 is used, the
  enhancement is reduced significantly. But, the
  extracted sIPIPtot is overall higher than the
  expectation.

? Consistent with our results
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Beam-Beam Counters
East BBC
West BBC

• In 35 of events
• (A),
• Red Dead Channels
• Light blue Channels used to reconstruct ?X
• In 65 of events (B),

East BBC
West BBC
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Reconstruction of ?pX BBC
Use calorimeter towers and BBC hits to
reconstruct ?X,

• BBC (?pBBC) use hits in BBC scintillation
  arrays
• use only inner 3 (shaded) layers (the most-outer
  layer overlaps with the forward cal).
• pT is chosen to follow the known pT spectrum
• ? is chosen randomly within the ? range of the
  BBC counter which has a hit.

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Reconstruction of ?pX Calorimeter

• Calorimeter (?pCAL) use ET and ? of towers
  above the noise level
• ?pCAL has to be corrected for
• Calorimeter non-linearity at low ET region
• Particles below the applied ET threshold
• The correction factor for ?CAL is obtained so
  that ?X(median)?RPS11.

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?X Calibration ?pbarX distributions in 9
?pbarRPS intervals
?X distribution in every ?RPS bin is fitted to
P1 Peak, P2 Width

• ?X(median) 0.94 ?RPS
• ?calibrated later to
• obtain ?X(median)?RPS
• P2/P1 0.57
• (?X resolution is 60.)

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?pbarX Distribution
We calibrated ?X so that ?X(median) ?RPS
becomes 1 1.
The choice of P1/median/mean does NOT make
a difference in RDPE/SD(incl), since the choice
is taken into account by the ?X resolution
correction, Fresol.
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BBC Multiplicities in MC
A
B

• The peak at EBBC0 in data distributions is due
  to DPE events.
• The MBR SD MC whose dN/d? 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, dont use the
  information of particles generated by MBR but
  simulate east BBC hits according to the data east
  BBC multiplicities.

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BBC Contribution to ?X
(A)
(B)
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?pX resolution correction

• Generate ? by using ds/d? from
• F. Abe et al., PRD 50 (1994) 5535.
• K. Goulianos J. Montanha, PRD 59 (1999)
  114017.
• Smear ? according to the form
• - P2/P1 0.57, P1 0.67?
• (P1 0.67xmedian when P2/P10.57)
• The number of events with ?lt0.02 increases about
  4 after the smearing.

Fresol1.040.04