Inclusive Double-Pomeron Exchange at the Fermilab Collider

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 6568

CDF Paper SeminarOctober 23, 2003.

pp

October 23, 2003. Kenichi Hatakeyama 2

History of the Analysis Analysis blessed on May 2, 2002 and May 16,

2003.

PRL Draft : CDF Note 6568Comments 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/KenichiHatakeyama/idpe.html

Many Thanks!


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.


Introduction

Shaded Area :Region of Particle

Production

Diffraction in high energy hadron physics refers to a reaction in which no quantum numbers are exchanged betweencolliding particles.


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) 141802

This paper!PRL 91 (2003) 011802

Single Diffractive (SD) Jet-Gap-Jet Double Pomeron Exchange (DPE)

W : PRL 78 (1997) 2698Dijet : PRL 79 (1997) 2638b-quark: PRL 84 (2000) 232J/ψ : PRL 87 (2001) 241802

Dijets + Roman PotsPRL 84 (2000) 5043PRL 88 (2002) 151802

PRL 74 (1995) 855PRL 80 (1998) 1156PRL 81 (1998) 5278

Dijet : PRL 85 (2000) 4217

Soft Diffraction

Hard Diffraction (diffraction +hard scattering)


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,

.ˆ

),,()(ˆ ,

//td

dtxfxf

tdtdpddxdx

d jjab

bap

Dpbppa

pp

SD

ically.quasielast scattered is which antiproton the inpartons for ondistributi yprobabilit:/

Dpbf

ND

SD


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).

Next Q : How is it broken?


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


Soft Diffraction : Regge Theory

g(0)/β(0)κ

coupling IPtriple: g(t)

coupling )pp(IP: β(t)

trajectory Pomeron: (t)α

factor flux Pomeron:)(t,f

IP

IP/p

Single Diffractive Cross SectionΔy

2

es

)s'(Mp

Δpξ

)(s'

ε

0

ξ)(t,

(t)2α12

SD2

σ

ss'

β(0)g(t)

f

ξ16π

(t)βdtd

σd

totpIP

IP/p

IP

Total Cross Section1-(0)

0

2tot

IP

ss

(0)β)(σ

s

176 (1996) 389 PLB in 0.104ε

α'tε1(t)αIP

σto

t

(mb

)

√s (GeV)


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

RenormalizationK. Goulianos, PLB 353, 379 (1995).


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.


Roman PotSpectrometer

Roman Pots detectrecoil antiprotons


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 :

•Cannot reconstruct ξp by RPS.•Use calorimeter towers and BBC 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

(J. Collins, hep-ex/9705393)

The CAL+BBC method allowed us to accessall the way down to the kinematic limit.


Data Sample and Event Selection

Roman Pot triggered data collected in 1800 GeV low luminosity runs during Run 1C (<Linst> ~ 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 EventsTotal 1200779Number of vertices ≤ 1 1123407|zvtx| ≤ 60 cm (if there is one) 10588761 MIP in the RP trigger counters 9717491 or 2 reconstructed tracks in RPS 763268

660240West BBC multiplicity ≤ 6 568478

2pp GeV 1.0|t| .095,ξ.035


Monte Carlo Event Generation : MBR(CDF Note 0256, 0675, 5371. PRD 50 (1994) 5535, 5550.)

SD and DPE event generationMBR 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 simulationCalorimeters: 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.

)ss' at collisions pp as decayed are clusters mass (DPE Convery

M.E. by developed events DPE simulate to MBR for code New

pp


Calibration of ξX

.)exp(0.5P3exp)f(P2

P1ξ

P2

P1ξ

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.


ξpX Distribution

The ξp 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!

ξ.dξdN

dlnξdN

0.1Δlogξevents of#


SD(incl)

DPER Fraction Event DPE

)0.001(stat0.2020.04)1.04(/F568478119406

R resolSD(incl)

DPE

)0.001(stat0.194SD(incl)

DPER

Corrections to R[DPE/SD(incl)] : ξp

X resolution : According to MC, more events with

ξp>0.02 seem to fall into ξpX<0.02 than

events with ξp<0.02 fall into ξpX>0.02.

R[DPE/SD(incl)] is corrected by Fresol=1.04±0.04

Low ξpbarX enhancement:

3~4 % of events have very low ξpbarX

values although those events have 0.035< ξpbar

RPS <0.095. MC shows a similar effect, but not as

pronounced as in data. Obtain R[DPE/SD(incl)] with/without

ξpbarX<0.003 cut, and take the average.

0.02ξ ,GeV 1|t| 0.095,ξ0.035 for Xp

2pp


Source Estimator Uncertaintyξp

X calibration Change ξpX by 10 % 0.003 (2%)

ξpX resolution Whole correction 0.008 (4%)

Low ξpbarX

enhancementHalf of the variation 0.008 (4%)

Total 0.012 (6%)

0.02.ξ and GeV 1|t|0.095,ξ0.035 for

)0.012(syst)0.001(stat0.194SD(incl)

DPER

Xp

2pp

dcont'R Fraction Event DPE SD(incl)

DPE

Systematic Uncertainties

The measured fraction is in agreement with the predictionfrom the renormalized gap probability model (0.21±0.02)!


Source R[DPE/SD(incl)]

Data 0.195±0.001±0.010

Regge 0.36±0.04

Flux Renormalization 0.041±0.004

Pgap Renormalization 0.21±0.02

0.02ξ ,GeV 1|t| 0.095,ξ0.035 p2

pp

)0.012(syst)0.001(stat0.194RSD(incl)

DPE

In agreement with the renormalized gap predictions!

dcont'R Fraction Event DPE SD(incl)

DPE

Comparisons with phenomenological models


Proton Dissociation EventsOur “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 (MY

2 <~8 GeV2) 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,

MY2 < e 7.5 - 5.9 = 5 GeV2.

In 65% of events (“B”), east BBC covers up to η=5.2,

MY2 < e 7.5 - 5.2 = 10 GeV2.

R[DPE/SD(incl)] is larger in “B” than in “A” by 6%.

Weighted average : 8 GeV2

22minY,

2Y 1.5GeV~M const.,~Mln/ dd

The contribution of proton dissociation events

with 1.5<MY2<8GeV2 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


Soft Diffraction :Summary

σ (

mb)

Gap F

ract

ion

Good Agreement withRenormalized Gap Predictions!

(GeV) s (GeV) s

(GeV) s (GeV) s'

SD DD

DPESDD


Summary We have observed double pomeron exchange events

in an inclusive single diffractive event sample. 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, |tpbar|<1 GeV2, ξpX< 0.02 and MY

2<~8GeV2at √s = 1800 GeV,

in agreement with the renormalized gap prediction.In events with a rapidity gap,

the formation of a second gap is “unsuppressed”!

)0.012(syst)0.001(stat0.194RSD(incl)

DPE

Consistent with results from hard diffraction

Universality of the rapidity gap formation


SDDPE

R from

NDSD

R from

Summary +

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

Universality of rapidity gap formation across soft and harddiffraction processes.

Events with multiple rapidity gaps can be used to eliminatethe “suppression” factor… Facilitate QCD calculation of hard diffraction.


Backups


Regge Theory & Factorization

g(0)/β(0)κ

coupling IPtriple: g(t)

coupling )pp(IP: β(t)

trajectory Pomeron: (t)α

factor flux Pomeron:)(t,f

IP

IP/p

Single Diffractive Cross Section

Δy2

es

)s'(Mp

Δpξ

)(s'

ε

0

ξ)(t,

(t)2α12

SD2

σ

ss'

β(0)g(t)

f

ξ16π

(t)βdtd

σd

totpIP

IP/p

IP

Total & EL Cross Sections

1-(0)

0

2tot

IP

ss

(0)β)(σ

s

176 (1996) 389 PLB in 0.104ε

α'tε1(t)αIP

1]-(t)2[α

0

4EL

IP

ss

16π(t)β

dt

(s)dσ


Unitarity ProblemSingle Diffractive Cross Section

ε12

2ε

2SD

2ε1SD

)(Ms

dM

dσ)(

ξ1

dξ

dσ s2Mξ

εξs

Total Cross Sectionε

tot sσ

ε

tot

SD sσ

σ

[ε=0.104 in PLB 389 (1996) 176]

The ratio σDPE/σSD reaches unity at √s~2 TeV.

In data, s2ε in dσSD/dM2 1


Soft Single Diffraction Results

KG&JM, PRD 59 (1999) 114017 KG, PLB 358 (1995)379

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

dσSD/dM2 σSDtot versus √s


RenormalizationSingle Diffractive Cross Section

ε12

2ε

2SD

2ε1SD

)(Ms

dM

dσ)(

ξ1

dξ

dσ s2Mξ

εξs

In data, s2ε 1

Renormalization

K. Goulianos, Phys. Lett. B 358 (1995) 379

2ε0.1

/sM 2ε1ren sdξξ

11/N

20

ε12ε12

2ε

ren2SD

)(M1

)(Ms

NdM

dσ


Soft Double Diffraction Results

CDF, Phys. Rev. Lett 87 (2001) 141802

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

dσDD/dΔη0 σDDtot versus √s

')'( )()( yyt

c

DD eeydydtd

d

0

4

0 2

23


Past Experimental Results : UA8 Collaboration

NLB 514 (1998) 3, PLB 481 (2000) 177, EPJC 25 (2002) 361.

Extracted σIPIPtot using FIP/p(ξ,t) from their

SD analysis.

The extracted σIPIPtot shows an

enhancement at low MX. They attributed it to the glueball

production......

Note : If the standard ε~0.1 is used, the enhancement is reduced significantly. But, the extracted σIPIP

tot is overall higher than the expectation.

GeV 630s at collider SpSpCERN the at events DPE and SD studied ionCollaborat UA8

)(s'σ)t,(ξF)t,(ξFdtdξdtdξ

σd totIPIPppIP/ppppIP/

pppp

DPE4

Consistent with our results


Beam-Beam Counters

In 35% of events(“A”),

Red : Dead ChannelsLight blue : Channels

used to reconstruct ξX

In 65% of events (“B”),

East BBC

East BBC

West BBC

West BBC


Reconstruction of ξpX : BBC

BBC (ξpBBC) : 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

η is chosen randomly within the η range of the BBC counter which has a hit.

.ξξs

)ηexp(Eξ CAL

pBBCp

i iiT,Xp

Use calorimeter towers and BBC hits to reconstruct ξX,

).0.065s(M ,/1.27)p(1pdpdσ 0.3)]35.8/ln(M/[4

TTT

OK. is 0.065sM setting soM, with slowly very changes spectrum p The T


Reconstruction of ξpX :Calorimeter

Calorimeter (ξpCAL) : use ET and η of towers above the noise level

ξpCAL has to be corrected for

Calorimeter non-linearity at low ET region

Particles below the applied ET threshold

The correction factor for ξCAL is obtained so that ξX(median):ξRPS=1:1.

.ξξs

)ηexp(Eξ CAL

pBBCp

i iiT,Xp

2.7f ,fed)(uncorrectξξξ corrcorrCALp

BBCp

Xp


ξX Calibration :ξpbar

X distributions in 9 ξpbarRPS intervals

ξX distribution inevery ξRPS bin isfitted to

.)exp(0.5P3exp)f(P2

P1ξ

P2

P1ξ

P1 : Peak, P2 : Width

•ξX(median) = 0.94 ξRPS

calibrated later to obtain ξX(median)=ξRPS

•P2/P1 = 0.57 (ξX resolution is ~60%.)


ξpbarX Distribution

We calibrated ξX so that ξX(median) : ξRPS becomes 1 : 1.

The choice of P1/median/mean does NOT make adifference in R[DPE/SD(incl)], since the choice is takeninto account by the ξX resolution correction, Fresol.


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”


BBC Contribution to ξX

(A) (B)


ξpX resolution correction

Generate ξ by using dσ/dξ from F. Abe et al., PRD 50 (1994)

5535. K. Goulianos & J. Montanha,

PRD 59 (1999) 114017.

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.

.)exp(0.5P3exp)f(P2

P1ξ

P2

P1ξ

Fresol=1.04±0.04

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Inclusive Double-Pomeron Exchange at the Fermilab Collider

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