September 17-20, 2003.Kenichi Hatakeyama1 Soft Double Pomeron Exchange in CDF Run I Kenichi Hatakeyama The Rockefeller University for the CDF Collaboration.

September 17-20, 2003. Kenichi Hatakeyama 1

Soft Double Pomeron Exchange in CDF Run I

Kenichi HatakeyamaThe Rockefeller Universityfor the CDF Collaboration

Small-x and Diffraction 2003Fermilab, Illinois, USA


Introduction

Shaded Area :Region of Particle

Production


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, 5043-5048 (2000).


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, 4215-4220 (2000).

The formation of the 2ndgap is not as suppressed

as the 1st gap.

Extract diffractive structure function fromR[DPE/SD] and compare it with expectations from HERA results.


Diffractive Structure Functionmeasured using DPE dijet events

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

Factorizationholds?

SDDPE

R from

NDSD

R from


1/ σσ totSD 2TeV.s at

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 (fIP/p) to unity yields the correct √s-dependence of σSD.

Is the formation of the second gap suppressed?

Tevatrondata

StudyDPE

Similar results were obtainedfor double diffraction as well.

ξs).(s'σξ)(t,fdtdξ

σdpIPIP/p

SD2

Renormalization


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).

GeV. 1800s at 0.21σ

σ

SD

DPE

GeV. 1800s at 0.041σ

σ

SD

DPE

GeV. 1800s at 0.36σ

σ

SD

DPE

,s'(0)βκeπ4)β(t

dtdtdξdξ

σd ε22

P

2

p,pi

Δy1)α(ti

pppp

DPE4

gap

ii

,s'(0)βκ)t,(ξ)ft,(ξfdtdtdξdξ

σd ε22ppIP/ppppIP/

pppp

DPE4

=

tly.independen edrenormaliz are f and f Both pIP/IP/p

κ=g/β(0).

g:triple-Pomeron coupling,

coupling, )pp(IP:β(t)

flux, Pomeron:f )pIP/p(

momentum fractional:ξ )pp(

),pp( of loss

pp t,ξ

pp t,ξ


Analysis Strategy Use events triggered on a leading

antiproton.

ξpbar is measured by Roman Pots : ξpbar

RPS.

Measure ξp (ξpbar) from BBC and calorimeters : ξp

X (ξpbarX).

Calibrate ξX by comparing ξpbarRPS

and ξpbarX.

Plot ξpX distribution and look for a

DPE signal expected in the small ξp

X region.


Reconstruction of ξpX

Calorimeters : use ET and η of towers above noise level.

BBC : use hits in BBC scintillation arrays. pT is chosen to follow the

“known” pT spectrum :

Use calorimeter towers andBBC hits to reconstruct ξp :

.s

)ηexp(Eξ i iiT,X

p

./1.27)p(1pdpdσ 0.3)]35.8/ln(M/[4

TTT

Calorimeters

BBC


Calibration of ξX

.)P2

P1ξexp(

P2P1ξ

0.5P3exp)f(

ξX distribution in every ξRPS bin is fitted toP1 : PeakP2 : Width

P2/P1 = 0.57(ξX resolution is ~60%.)

ξX = ξRPS,(ξX is calibrated so that

ξX = ξRPS.)


ξpX Distribution

The input ξp distribution in DPE MC is 1/ξp

1+ε (ε = 0.104 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 ξpX

distribution is in agreement with the DPE+SD MC distribution.


DPE Fraction in SD Events0.095,ξ0.035 p 0.02ξp

)0.011(syst)0.001(stat0.195SD(incl)

DPER

GeV. 1800s at

GeV. 630s at )0.012(syst)0.001(stat0.168

SD(incl)DPE

R

R[DPE/SD(incl)]Source @ 1800 GeV @ 630 GeV

Data 0.195±0.001±0.011

0.168±0.001±0.012

Regge + factorization 0.36 0.25

Flux Renormalization 0.041 0.041

Pgap Renormalization 0.21 0.17In agreement with the renormalized gap predictions!


Soft Diffraction :Summary

σ (

mb

)G

ap

Fr

act

ion

Good Agreement withRenormalized Gap Predictions!

(GeV) s (GeV) s

(GeV) s (GeV) s'

SD DD

DPESDD


Conclusions The measured ξp

X distribution exhibits ~1/ξ1+ε behavior (ε = 0.104).

The measured DPE fraction in SD is :

for 0.035 <ξpbar< 0.095 and ξp< 0.02 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”!

)0.011(syst)0.001(stat0.195SD(incl)

DPER

September 17-20, 2003.Kenichi Hatakeyama1 Soft Double Pomeron Exchange in CDF Run I Kenichi Hatakeyama The Rockefeller University for the CDF Collaboration.

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