# Presentation: 636741

## Hard Diffraction at DØ During Run I

- Michael Strang
- DØ Collaboration / Fermilab
- University of Texas, Arlington

- Central Rapidity Gaps (Hard Color Singlet         	Exchange)
-  Forward Rapidity Gaps (Hard Single
- Diffraction)

- Lishep02, Feb 5, 2002, Rio de Janeiro, Brazil

- Michael Strang

## DØ Detector

- EM Calorimeter

- L0 Detector

**beam**

*(**n*l0 = # tiles in L0 detector with signal
- 	2.3 < || < 4.3)

**Central Gaps**
-      EM Calorimeter	ET > 200 MeV	|| < 1.0
**Forward Gaps**
-      EM Calorimeter 	E > 150 MeV	2.0 < || < 4.1
-      Had. Calorimeter	E > 500 MeV	3.2 < || < 5.2)

- Central Drift Chamber

*(**n*trk = # charged tracks with  	|| < 1.0)

- End Calorimeter

- Central Calorimeter

*(**n*cal = # cal towers with energy above threshold)

- Hadronic Calorimeter

- Lishep02, Feb 5, 2002, Rio de Janeiro, Brazil

- Michael Strang

**Notes:**
Eta is pseudo-rapidity = -ln(tan(theta/2)) where cos(theta) = pz/p. For p>>m it is a good approximation of y (rapidity) and can be measured when the mass and momentum of the particle are unknown.
ET is transverse energy = E . sin(theta) or the total energy in a cell and theta is the angle from the beam to the vector from the vertex to the cell
Switch to Energy from ET for threshold between studies since noise is in units of Energy and it allows us to set the threshold lower for better gap tagging.

## Particle Multiplicity Distributions

- Lishep02, Feb 5, 2002, Rio de Janeiro, Brazil

- Michael Strang

## Measuring CSE

- Lishep02, Feb 5, 2002, Rio de Janeiro, Brazil

- Michael Strang

## Hard Color Singlet Studies

- jet

- jet

- 

- 

- 

- QCD color-singlet signal observed in ~ 1 % opposite-side events (p   )

_**Publications**_
-     DØ: PRL 72, 2332(1994)
-     CDF: PRL 74, 885 (1995)
-     DØ: PRL 76, 734 (1996)
-     Zeus: Phys Lett B369, 55 (1996) (7%)
-     CDF: PRL 80, 1156 (1998)
-     **DØ: PLB 440, 189 (1998)**
-     CDF: PRL 81, 5278 (1998)

**                    **_**Newest Results**__** **_
- Color-Singlet fractions at
-     s = 630 & 1800 GeV
-  Color-Singlet Dependence on:
-     ,   ET, s (parton-x)

- Lishep02, Feb 5, 2002, Rio de Janeiro, Brazil

- Michael Strang

## Data Selection

- Four data samples collected during 1994 - 1996:

- s = 1800 GeV
-    high, medium, & low
-    jet ET triggers
- s =  630 GeV
-     low ET trigger

-   Require centered event vertex
-   Cut events with spurious jets
-   Require single interaction
-   Leading jets with || > 1.9
-    > 4.0   (Opposite-side events)
-   ET cut:
-     ET > 12 GeV  (low-ET 630,    7k events)
- 		    (low-ET 1800, 48k events)
-     ET > 25 GeV  (med-ET 1800, 21k events)
-     ET > 30 GeV  (high-ET 1800, 72k events)

- (Also same-side control samples at both CM energies using L0 trigger to suppress SD signal for background studies)

- Lishep02, Feb 5, 2002, Rio de Janeiro, Brazil

- Michael Strang

**Notes:**
Vertex within 50cm of nominal center
SI: Timing of LM, single vertex and calorimeter energy
ET dependence study comes from all three triggers
Eta dependence study comes from low and high triggers

## Measurement of fs

- Count tracks and EM  Calorimeter Towers in || < 1.0

*E**T* >30 GeV

*f**S **1800* = 0.94  0.04*stat*  0.12*sys* %

- jet

- jet

- 

- 

- 

*f**S** =  ***color-singlet fraction*** =(N**data**- N**fit**)/N**total*

- (Includes correction for multiple interaction contamination.
- Sys error dominated by background fitting.)

- High-ET  sample (ET > 30 GeV, s = 1800 GeV)

- Lishep02, Feb 5, 2002, Rio de Janeiro, Brazil

- Michael Strang

**Notes:**
Figure (b) is a Negative Binomial fit extrapolated to 0 to remove background
Various starting bins are used to determine systematics
High ET sample has highest statistics and hence most accurate measure of gap fraction
Corrections: Residual Multiple Interaction contamination, Single Interaction tagged as Multiple Interaction (30% correction)
Gap fraction doesn’t depend on method used to measure multiplicity

## 630 vs. 1800 Multiplicities

- Jet ET > 12 GeV,   Jet || > 1.9,   > 4.0

*R**1800* = 3.4  1.2

- _Opposite-Side Data_

- _Same-Side Data_

- 1800 GeV:

- 630 Gev:

- ncal

- ncal

- ncal

- ncal

- ntrk

- ntrk

- ntrk

- ntrk

-  *f**S **1800* *(E**T** =19.2 GeV)* = 0.54  0.06*stat*  0.16*sys* %
*f**S **630*  *(E**T** = 16.4 GeV)*  = 1.85  0.09*stat*  0.37*sys* %

*630*

- Lishep02, Feb 5, 2002, Rio de Janeiro, Brazil

- Michael Strang

**Notes:**
Gap fraction for low trigger is 2sigma lower indicating some dependence on ET
Significance of difference is 3.1sigma in limiting case that uncertainties are uncorrelated

## Color Singlet Models

- 	If color-singlet couples preferentially to quarks or gluons, fraction depends on initial quark/gluon densities (parton *x*)
-      **larger x ********  more quarks**
- Gluon preference:  perturbative two-gluon models have 9/4 color factor for gluons
***Naive Two-Gluon model*** (Bj)
***BFKL model***:  LLA BFKL dynamics
- _Predictions_:
-           *f**S *(ET) falls,   *f**S *() falls (2 gluon) / rises (BFKL)
- Quark preference:
***Soft Color model***: non-perturbative “rearrangement” prefers quark initiated processes (easier to neutralize color)
***Photon ***and*** U(1)***: couple only to quarks
- _Predictions_:
-                *f**S *(ET)  &  *f**S *() rise

- Lishep02, Feb 5, 2002, Rio de Janeiro, Brazil

- Michael Strang

**Notes:**
Couples to gluons would fall with x
Couple to quarks would rise with x (gluon fraction suppressed as x increases)
Implies
Gluon is a decrease with ET or eta or decreasing root-s
Quark is an increase with the same

## Model Fits to Data

- Using* Herwig 5.9*

-  Soft Color  model describes data

- s = 1800 GeV

- Lishep02, Feb 5, 2002, Rio de Janeiro, Brazil

- Michael Strang

**Notes:**
F2D is a 2D fitting method using (0,0) (0,1) (1,0) bins
1D background is NBD method converted to 2D by using normalizations from Same Side sample
Background is roughly 25%
2D method has 80% acceptance needed as correction

## Fit Results

- Data favor “free-factor” and “soft-color” models
- “single-gluon” not excluded, but all other models
- excluded (assuming S not dependent on ET and )

- Apply Bayesian fitting method, calculate  	likelihood relative to “free-factor model” 	(parametrization as weighted sums of relative 	fractions of quarks and gluons in pdf)

- Color factors for free-factor model:
*C**qq **: C**qg  **: C**gg*= 1.0 : 0.04 : 0  **(coupling to quarks dominates)**

- Lishep02, Feb 5, 2002, Rio de Janeiro, Brazil

- Michael Strang

**Notes:**
Bayesian since chisquare introduces normalization bian in correlated uncertainties (subsequent studies found that with sufficient manipulation of errors, this is not necessarily the case)
Free Factor is just a parametrization of gap as weighted sums of relative fractions of quarks and gluons in pdf
Color Factors are:
Soft:	Cqq = 1/9, Cqg = 1/24, Cgg = 1/64
Two Gluon:	Cqq = 1, Cqg = 9/4, Cgg = (9.4)^2
Single Gluon: all 1 (same as QCD)
BFKL with S~10% normalization is 6-9 lower than data

## Survival Probability

-  Assumed to be independent of parton *x *(ET , )
-  Originally weak *s *dependence
-       Gotsman,  Levin, Maor  Phys. Lett B 309 (1993)
-  Subsequently recalculated
-    GLM hep-ph/9804404
-  Using free-factor and soft-color model
-                                         (uncertainty from MC stats and  model difference)
-     with

- Lishep02, Feb 5, 2002, Rio de Janeiro, Brazil

- Michael Strang

**Notes:**
Use free factor and soft color to predict ratio
Difference between prediction and measured is due to root-s dependence of S

## Hard Color Singlet Conclusions

- DØ has measured color-singlet fraction for:
- 630 GeV and 1800 GeV same ET, 
- as a function of ET and  at 1800 GeV
-                      *f**S  *shows  rising trend with ET, 
**Measured fraction rises with initial quark content **(Assuming the Survival Probability is constant with ET and ):
***Consistent ***with a soft color rearrangement model preferring initial quark states
-  ***Inconsistent*** with two-gluon, photon,
-      or U(1) models
-   Cannot exclude single-gluon model

- Lishep02, Feb 5, 2002, Rio de Janeiro, Brazil

- Michael Strang

## Modifications to Theory

- BFKL: Cox, Forshaw (manhep99-7) use a non-running s to flatten the falling ET prediction of BFKL (due to higher order corrections at non-zero t)

- Soft Color: Gregores subsequently performed a more careful counting of states that produce color singlets to improve prediction.

- Lishep02, Feb 5, 2002, Rio de Janeiro, Brazil

- Michael Strang

## Hard Single Diffraction Studies

-    -4.0        -1.6               3.0           5.2

- Measure min multiplicity  here

- -5.2           -3.0  -1.        1.    3.0       5.2

- OR

- Gap fractions (central and forward) 	at s = 630 & 1800 GeV
-  Single diffractive distribution

- hep-ex/9912061, submitted to PLB

- Measure multiplicity  here

- Lishep02, Feb 5, 2002, Rio de Janeiro, Brazil

- Michael Strang

## Data Selection

** ****Require single interaction**
** ****Require central vertex**
** ****Gap Fraction :**
-      (diffractive dijet events / all dijet events)
-           *Forward Jet Trigger
- 	       two 12GeV Jets ||>1.6
- 		(@ 630, 28k events)
- 		(@ 1800, 50k events)
-           * Central Jet Trigger
- 	       two 15(12) GeV Jets ||<1.0
- 		(@ 630(12), 48k events)
- 		(@ 1800(15), 16k events)
** ****SD Event Characteristics:**
-           *Single Veto Trigger
-  	       two 15(12) GeV Jets and no hits in 			L0 North of South array
- 		(@ 630(12), 64k events)
- 		(@ 1800(15), 170k events)

- Lishep02, Feb 5, 2002, Rio de Janeiro, Brazil

- Michael Strang

**Notes:**
Single Veto trigger used since inclusive jet that is used otherwise in heavily prescaled

## Event Characteristics

- 1800 Forward Jets

- Solid lines show show HSD candidate events
- Dashed lines show non-diffractive events

-  Less jets in diffractive events
-  Jets are narrower and more back-to-back
-  Diffractive events have less overall radiation
-  Gap fraction has little dependence on average jet ET

- Lishep02, Feb 5, 2002, Rio de Janeiro, Brazil

- Michael Strang

## 630 vs. 1800 Multiplicities

-  s = 1800 GeV:

- s = 630 GeV:

- Lishep02, Feb 5, 2002, Rio de Janeiro, Brazil

- Michael Strang

## Fitting Method

- Example of fit for 1800 forward sample
- Signal is fit with a 2D falling exponential while background is
- 	fit with a 4 parameter polynomial surface
- Shapes are in agreement with Monte Carlo, the residual
- 	distributions are well behaved
- Distributions have 2/dof < 1.2

- Lishep02, Feb 5, 2002, Rio de Janeiro, Brazil

- Michael Strang

**Notes:**
Background shape comes from correlations between ncal and nl0 which get smeared as multiplicity rises
Pull is residual distributions

## Single Diffractive Results

**Data Sample****	****     ****	****     Measured Gap Fraction**
-   1800 Forward Jets	     0.65% + 0.04% - 0.04%
-   1800 Central Jets	     0.22% + 0.05% - 0.04%
-   630 Forward Jets	     1.19% + 0.08% - 0.08%
-   630 Central Jets	     0.90% + 0.06% - 0.06%

- * Forward Jets Gap Fraction > Central Jets Gap Fraction
- * 630 GeV Gap Fraction > 1800 GeV Gap Fraction

**Data Sample****	****     ****	****	****Ratio**
-    630/1800 Forward Jets	1.8 + 0.2 - 0.2
-    630/1800 Central Jets		4.1 + 0.8 - 1.0
-    1800 Fwd/Cent Jets		3.0 + 0.7 - 0.7
-    630 Fwd/Cent Jets		1.3 + 0.1 - 0.1

-   -4.0          -1.6   -1.0          1.0       3.0              5.2

- or

- Measure Multiplicity here

- (Gap Fraction = # diffractive Dijet Events / # All Dijets)

- Lishep02, Feb 5, 2002, Rio de Janeiro, Brazil

- Michael Strang

**Notes:**
Uncertainties dominated by fits

## Comparison to MC

-  **f****visible**** = ********gap**** · f****predicted**

-  gap
- *Add diffractive multiplicity from MC to background data distribution
- *Fit to find percent of signal events extracted

-  Find predicted rate  POMPYT x 2 / PYTHIA
- *Apply same jet  cuts as data, jet ET>12GeV
- *Full detector simulation

- * Model pomeron exchange in POMPYT26 		          (Bruni & Ingelman)
-  	* based on PYTHIA 				* define pomeron as beam particle   	* Use different structure functions

- Lishep02, Feb 5, 2002, Rio de Janeiro, Brazil

- Michael Strang

**Notes:**
Pompyt x 2 to account for diffractive event being either proton or anti-proton breaking up

## Slide 22

- Lishep02, Feb 5, 2002, Rio de Janeiro, Brazil

- Michael Strang

**Notes:**
Quark gives best fit but predicts too much diffractive W production
Predicted gluon fractions are all about 2 times bigger
Double ratios (which are flux factor independent) are off as well so the difference between data and prediction is not a normalization problem
Leads us to need to look at some sort of Pomeron Fit (which shows a need for significant soft gluon contribution)

## Pomeron Structure Fits

- Demand data fractions composed of linear combination of hard and soft gluons, let overall  s normalization and fraction of hard and soft at each energy be free parameters
- If we have a  s independent normalization then the data prefer :
- 1800: hard gluon  0.18±0.05(stat)+0.04-0.03(syst)
- 630: hard gluon 0.39±0.04(stat)+0.02-0.01(syst)
- Normalization: 0.43±0.03(stat)+0.08-0.06(syst)
- 	with a confidence level of 56%.
- If the hard to soft ratio is constrained the data prefer:
- Hard gluon: 0.30±0.04(stat)+0.01-0.01(syst)
- Norm. 1800: 0.38±0.03(stat)+0.03-0.02(syst)
- Norm. 630: 0.50±0.04(stat)+0.02-0.02(syst)
- 	with a confidence level of 1.9%.
- To significantly constrain quark fraction requires additional experimental measurements.
- CDF determined 56% hard gluon, 44% quark but this does not describe our data without significant soft gluon or 100% quark at 630

- Lishep02, Feb 5, 2002, Rio de Janeiro, Brazil

- Michael Strang

**Notes:**
Hard gluon of 0.18 means 0.82 of soft gluon
Pompyt did not allow for Hera structure functions or detailed fits to data
Future Plans : Combine Diffractive W, jet and double pomeron results using Pomwig

##  Calculation

- 	*Can use calorimeter *only* to measure
- 	*Weights particles in well-measured region
- 	*Can define for all events

- *  calculation works well
- * not dependent on structure function or center-of-mass energy

- *Collins
-   (hep-ph/9705393)

- true = calc · 2.2± 0.3

-  Calculation

- Lishep02, Feb 5, 2002, Rio de Janeiro, Brazil

- Michael Strang

**Notes:**
Left: Measure all particles and compare to xi from proton
Right: After full detector simulation using only EM towers (giving us 2.2 correction factor)
MC only used to verify method and obtain the correction factor

## Single Diffractive  Distributions

- p
-   p

- =

-   0.2 for s = 630 GeV

- Single Diffractive  Distributions

- Lishep02, Feb 5, 2002, Rio de Janeiro, Brazil

- Michael Strang

**Notes:**
Shadow is the variance due to energy scale uncertainties
Notice change of scale between 1800 and 630. 630 values are not in region where we normally think of diffraction

## Summary

- Measurements at both CM energies with same detector adds critical new information for examining pomeron puzzle
- The higher rates at 630 were not widely predicted before the measurements
- Pioneering work in Central Rapidity Gaps
- Assuming x-independent survival probability, data support soft color rearrangement models (single gluon not excluded)
- Modifications to theory based on data have occured
- Forward gaps data
- In a partonic pomeron framework require reduced flux factor combined with gluonic pomeron containing significant hard and soft components
- Found larger fractional momentum lost by scattered proton than expected by traditional pomeron exchange
- Results imply a non-pomeron based model should be considered.

- Lishep02, Feb 5, 2002, Rio de Janeiro, Brazil

- Michael Strang

## Gap Efficiencies

-  Efficiency tag events with gap = gap
- 	*Add diffractive multiplicity from MC to 				background data distribution
- 	*Fit to find percent of signal events extracted
- 	*Statistical error + MC energy scale error

**MC Sample****	****1800 FWD JET****	****	****1800 CENT JET **
- Hard Gluon	74%  10%		34%  5%
- Flat Gluon	66%  9%		55%  7%
- Quark		61%  8%		18%  2%
- Soft Gluon	22%  3%		2.2%  0.8%

**MC Sample****	****630 FWD JET****	****	****630 CENT JET **
- Hard Gluon	92%  16%		48%  6%
- Flat Gluon	71%  14%		60%  8%
- Quark		55%  11%		26%  3%
- Soft Gluon	23%   4% 		6.0%  4.8%

- Lishep02, Feb 5, 2002, Rio de Janeiro, Brazil

- Michael Strang

**Notes:**
BACKUP SLIDE