# Presentation: 499470

## QCD

**Jet Measurements**
**Inclusive Jets**
**Rapidity Dependence**
**CMS Energy Dependence**
**Dijet Spectra**
**QCD with Gauge Bosons**
**Production Cross Sections**
**Differential Cross Sections**
**W/Z and Jets**
**Diffractive Physics**
**Rapidity Gaps**
**Roman Pots**

## Jet Variables

- Jet 2: ET2, 2, 2

- Jet 1: ET1, 1, 1

-  = 0

## Jet Production

- 2R

- 1.3R

**Notes:**
Factorization Scale: Arbitrary parameter that separates the long and short distance physics. A parton with PT < mu will be absorbed into the hadron structure.

Renormalization Scale: scale introduced to remove divergences, as perturbation series reaches infinity dependence drops to zero. 

## Inclusive Jets- D0

## Inclusive Jets- CDF

## Inclusive Jet Cross Section

-        || < 0.5   PRL82, 2451 (1999)

-         0.1 < || < 0.7 Preliminary

**Data and theory agreement prob 47-90%**** ****	**

- NLO QCD describes the data well

**Notes:**
This is the result for the inclusive jet cross section in the central region. D0 and CDF use ~ 80pb-1 of data taken during 1992-1996. D0 uses jets produced with a pseudorapidity less than 0.5, CDF uses jets produced with an eta between 0.1 and 0.7. Shown here are the ratio plots data-theory/theory as a function of Jet Et for different choices of PDFs. The theory is NLO QCD. The data points are shown with statistical uncertainties only. The systematic uncertainty is shown as a band. A quantitative test shows that the probability that the D0 data and the theory describe the same distribution is between 50 and 90%.  CDF data is shown with stat uncertainties only. Overall we see a nice agreement between NLOQCD and data.

## Inclusive Jet Cross Section at 1.8TeV 

- PRL82, 2451 (1999)

_**Inclusive Jet Cross Section at 1.8TeV**_** **

- D0 and CDF data in good agreement.     NLO QCD describes the data well.

- Preliminary

**Notes:**
This plot shows the Data-Theory/Theory plot for CDF and D0 results together. The D0 x-sec has been remeasured  to match CDFs pseudorapidity range of 0.1 to 0.7. CDF is now presenting their systematic uncertainties for the final Run I measurement for the first time. They are plotted down here together with the uncertainties from D0. Roughly 10% for D0, 15% for CDF in the lowest Et bins; 22% for D0 and 27% for CDF at 400GeV. Overall nice agreement between the two experiments and with NLOQCD.

##  0.0 <   0.5

** ****0.0 < ******** ******** 0.5**
**  ****0.5 ******** ******** ******** 1.0**
**  ****1.0 ******** ******** ******** 1.5**

- DØ Preliminary

******d****2****** dE**T**** ****d******** (fb/GeV)**

- ( Data - Theory ) / Theory

- Data and NLO QCD in good agreement

- Extend measurement to ||  = 3
- Refine error analysis

- New

- DØ Preliminary

- ET (GeV)

**Notes:**
Shown here is a new result from D0. D0 has measured the Inclusive Jet Cross section in the forward rapidity regions, between 0.5 and 1.0, and between 1.0 and 1.5 in Jet eta. You can see the ratio plots in the three rapidity regions. Data and theory agree well in the forward regions. D0 plans to extend the measurement up to rapidities of 3 and to refine the error analysis.

##  Ratio of Scale Invariant Cross Sections d(630)/d(1800) vs xT 

******d ****= (E****T****3****/2********) (d****2********/dE****T****d********   **
**           **** ****X****T ********E****T ****/ (********s**** ****/ 2 )**

**Preliminary**

- Taking different renormalizations scales in theory for 630 vs 1800 GeV produces good quantitative agreement between D0 data and NLO QCD

**Notes:**
Although the Tevatron nominaly runs at a center of mass energy of 1.8TeV, CDF and D0 took some data during 1996 at a lower center of mass energy of 630GeV. Using that data, CDF and D0 measure the ratio of the scale invariant cross sections and plot it as a function of Jet xT. The D0 result is shown here, compared to NLOQCD predictions for various choices of PDFs. We see that QCD overestimated the ratio by almost 3 sigmas in the medium range of xT. CDF data is shown here. The discrepancy between data and theory is even worse at low xT. However, NLOQCD produces a good quantitative agreement with D0 data if different renormalization scales are used in the theory for 630 and 1800GeV. For instance, the full line uses a scale of 2times ET for the 630 x-sec and half an ET for the 1800 x-sec and agrees nicely with data as shown in this plot.

## Measurement of S from Inclusive Jet Production 

- NLO x-section can be parametrized as

- Measured
- by CDF

- Obtained from JETRAD

-  Fitting the NLO prediction to the data determines S(ET)
-  S(ET) is evolved to S(MZ) using  2-loop renormalization group equation
-  Systematic uncertainties (~8%) from understanding of calorimeter response
-  Measured value consistent with world average of S(MZ)=0.119

- New measurement of S by a single experiment & from a single observable over a wide range of Q2.

**Notes:**
CDF measures the value of the strong coupling constant from the inclusive jet cross section over a large range of transverse energies. The NLO x-sec can be parametrized as a function of the strong coupling constant and two parameters, A and B, that depend on the Jet transverse energy. CDF measures the x-section, the parameters A and B can be obtained from JETRAD. For simplicity the renormalization and factorization scale are set to Et/2. Fitting the NLO prediction to the measured x-sec determines alpha_s as a function of transverse energy. The result is shown in this plot in blue compared to the expected running of alpha_s with Et.
The measured alpha_s can then be evolved to the value of alpha_s at the Z mass using a 2 loop renormalization group equation. The result is shown in this plot in red. The measured value for alpha_s at the Z mass obtained when using the CTEQ4M parton distribution is 0.1129+-0.0001 (stat). The systematic uncertainty comes mostly from the understanding of the calorimeter response and is below 10%. This result extended the measurement of alpha_s to a very high Q2 range and clearly shows the running of alpha_s. The result is consistent with the world average for alpha_s at the Z mass of 0.119.

** **

_**Dijet Mass Cross Section**_** **

- NLO QCD in good agreement with data

**Notes:**
CDF and D0 measure the cross section as a function of dijet mass. Shown here is the data-theory/theory plot for both CDF and D0. CDF syst uncertainly is shown as the yellow band, D0's is shown as the full line. There is good agreement between the measurements by CDF and D0. Both results show the same feature of rising cross section with increasing dijet invariant mass when compared to NLOQCD.
 D0 has calculated the ratio of the dijet mass cross section for jets produced in the central and forward rapidity regions and used it to set a limit on the quark compositeness scale of 2.4TeV. This is the best limit on quark compositeness up to date.

## Inclusive Dijet Differential Cross Section 

- Beam line

- Trigger Jet
- 0.1<||<0.7

- Probe Jet ET>10 GeV
- 0.1<||<0.7,  0.7<||<1.4,  1.4<||<2.1,  2.1<||<3.0

- 1

- 2

-  Distributions are sensitive to PDFs - CTEQ4HJ shows better agreement with data at high ET

**Notes:**
CDF measures the inclusive dijet cross section for events with a central and a forward jet. The forward jet can be found in four different rapidity regions, which gives rise to four different cross sections shown here as a function  of the central jet  transverse energy. The ratio plots data-theory/theory are shown here for different PDFs. You can see that the measurement is sensitive to the choice of PDFs and that the data tends to be higher than QCD at large ET. CDF data agrees better with CTEQ4HJ at high jet ET.

## Inclusive Dijet Differential Cross Section 

_**Inclusive Dijet Differential Cross Section**_** **

- 

- Beam line

-   Consider 4 ranges:     0.0<||<0.5, 0.5<||<1.0, 1.0<||<1.5, 1.5<||<2.0
-  Divide data into two samples
-  Measure ET of both jets
- Total of 8 x-sections

- ||

- ||

- ||

- ||
- 

- D0 data agree with NLO QCD with CTEQ family PDFs within the systematic uncertainty.

- 

**Notes:**
D0 does a different measurement of the dijet differential cross section. Jets are divided into four eta bins. Events with two jets are divided into two samples: those events in which the two jets are opposite in eta, and those events in which the two jets are in the same eta bin. D0 then measures the transverse energy of both jets and plots the cross section as a function of jet ET once for each jet. This gives a total of 8 cross sections shown here for opposite side jets on the left and same side jets in the right, in the four eta bins. The theory is shown here with CTEQ3M as an example. The measurement is sensitive to PDFs, but in general there is good agreement between D0 data and NLO QCD even at high ET.

## Subjet Multiplicity in Quark & Gluon Jets

- Jet ET

- Jet ET

- Motivation:
-  Separate q jets from g jets (top, Higgs, W+Jets events)
-  Test SU(3) dynamics             (QCD color factors)
-  Measure the subjet multiplicity in quark and gluon jets

-  Contributions of different initial states to the cross section for fixed Jet ET vary with s
- compare jets at same (ET,)produced at different s & assume relative q/g content is known.

- 

- 630GeV

- gg

- qg

- qq

-      100     200    300

- Method:
- Select quark enriched & gluon enriched jet sample and compare jet properties
-  challenge is not to bias the samples.

- New

**Notes:**
D0 measures the subjet multiplicity in quark and gluon jets.
The goal of the analysis to separate jets produced from a quark parton from jets produced by a gluon parton. If we were able to separate  quark jets from gluon jets, this knowledge could then be used in various analyses (like top, higgs and W+Jet production). In itself the measurement can be used to test the dynamics of SU(3), for instance QCD color factors.
The first thing that needs to be done, is to select a quark enriched and a gluon enriched jet sample. We can then compare jet properties in the two samples. The real challenge is not to bias the jet properties by the sample selection.
This plot shows the contributions of the different initial states to the cross section as a function of jet Et for two different cme: 1800 and 630GeV. D0 compares jets with the same Et and eta produced at different cmes and assumes that the relative quark/gluon content is known.

## Mq =  

_**Subjet Multiplicity in Quark & Gluon Jets**_

- Method:
-  Subjet Multiplicity  ***M****** = ******f******g******M******g****** + (1-******f******g ******)M******q        ***(g jet fractions *** ******f******g ***obtained from theory)
***      ******f ******630 ******= 33%   ****** ******f ******1800****** = 59%***
-  Assuming that the subjet multiplicity is independent of s (verified with MC)

***M******q****** =**** ** *

***f ******1800******- ******f ******630***

***(1-******f ******630******)******M******1800****** - (1- ******f ******1800******)******M******630***

***M******g****** =**** ** *

-  Use kT algorithm; unravel jets until all subjets are separated by *y*cut =.001
-  Measure number of subjets for events with jets with 55<ET<100 GeV

- Dominant uncertainties come from g jet fraction and choice of jetET

- MC Prediction =1.860.08(stat)

-         1          2          3         4

- 0.5
- 0.4
- 0.3
- 0.2
- 0.1

- Quark Jets

- Gluon Jets

**Preliminary**

- New

**Notes:**
The method is as follows:
D0 will measure the subjet multiplicity that can be written as a linear combination of the gluon and quark multiplicity multiplied by the fraction of gluon and quark jets. The gluon jet fractions are obtained from theoretical predictions and are 33% at 630GeV and 59% for 1800GeV for a 50GeV Jet. Assuming that the subjet multiplicity is independent of cme (which is verified with MC), one can work out expressions for the quark and gluon observable that can be measured.
D0 uses the kT algorithm to do this analysis. Jets are unraveled until all subjets are separated by a relative kT greater than .1% of the total jet energy.
The result for the data before any corrections for detector effects is shown in this plot. The subjets multiplicity for gluon jets is shown in red, the one for quark jets is shown in blue. The average subjet multiplicity for quark jets is 2.28, and for gluon jets it is 3.08. 
After correcting for detector effects the ratio of multiplicities becomes 1.91+-0.04+0.23-0.19. The systematic uncertainty is dominated by the knowledge of the gluon jet fraction and the choice of minimum jet Et. 
The MC prediction for this ratio is 1.86+-0.08, in good agreement with our measurement.
This result shows that we are able to distinguish quarks from gluon jets on a statistical bases and we may be able to do it on a jet by jet basis in the future. 

## QCD with Vector Bosons

## W&Z Production at the Tevatron

- O(s0)

-  Production dominated by qq annihilation (~60% valence-sea, ~20% sea-sea)
-  Due to very large pp jj production, need to use leptonic decays (BR ~ 11% (W), ~3% (Z) per mode)

- O(s)

**Modifications**** ****due to QCD corrections:**

-  Boson produced with transverse momentum  ( < PT > ~ 10 GeV )
-  Boson + jet events possible  ( W + 1 jet ~ 7%, ETjet > 25 GeV )
-  Inclusive cross sections larger (K factor ~ 18%)
-  Boson decay angular distribution modified

-  Distinctive event signatures
-  Low backgrounds
-  Large Q2  (Q2 ~ Mass2 ~ 6500 GeV2)
-  Well understood Electroweak Vertex

**Benefits of studying QCD with W&Z Bosons:**

## DØ:   W e = 658  67 pb

******Cross section measurements**
**test O(********2****) QCD predictions for W/Z production**
-                 ******(*****pp***** ******** W + X) B(W ******** ************)**
**                  ********(*****pp***** ******** Z + X) B(Z ******** ********)**

******S=1.8 TeV**

******W****B(W ******** e********)**

******Z ****B(Z ******** ee)**

**R=**

**R=10.54 ******** 0.24**

******S=630 GeV**
**DØ:  **** ********W******** ****e******** = 658 ******** 67 pb**

**(DØ)**

**(CDF)**

**R=10.36 ******** 0.18**

- Preliminary

## Introduction to W, Z PT Theory

## Boson+ Jet Theory

- _Boson+ Jet Theory_

## D0 W PT measurement

**Preliminary**

- dof=7/19 (pT(W)<120 GeV/c)
-  dof=10/21 (pT(W)<200GeV/c)

- Resolution effects dominate at low PT
- High PT dominated by statistics & backgrounds

_**D0 W P**__**T**__** measurement**_

**Preliminary**

## D0 Z PT measurement

_**D0 Z P**__**T**__** measurement**_

- 2/dof = 17/16

- 2/dof = 83/16

- Ladinsky, Yuan, PRD 50, 4239 (94), O(s2), b-space.

- Arnold, Kauffman, NP B349, 381 (91), O(s2), b-space.

**Preliminary**

- Arnold, Reno, Nucl. Phys. B319, 37. O(s2), MRSA’, pQCD calculation

-  Data resolution allows to discriminate between  different models for VB production.

## CDF PT measurements

_**CDF P**__**T**__** measurements**_

- Ellis, Ross, Veseli, NP B503, 309 (97). O(s), qt space, after detector simulation.

- ResBos: Balas, Yuan,* *PRD 56, 5558 (1997), O(s2), b-space
- VBP: Ellis, Veseli,* *NP B511,649 (1998), O(s), qt-space

**Preliminary**

## W+ Jet Production

- _W+ Jet Production_

**LO**

******s**

**********s**

**A test of NLO**

## W+ Jet Production

- Depends on R, ETmin due to jet definition
- Calculations of A, B from NLO DYRAD (Giele, Glover**, **Kosower)

- _W+ Jet Production_

## W + Jets: CDF

## W/Z + Jets: CDF

## W+ Jet Ratio

- _W+ Jet Ratio_

## W + Jets: CDF

## Rapidity Gaps

- D0 and CDF study hadronic events with peculiar structure - a rapidity gap due to color-singlet exchange (pomeron). What is the Pomeron?

- pomeron

## Rapidity Gaps

**Typical event**

**Hard single diffraction**

**Hard double pomeron**

**Hard color singlet**

## Hard Color-singlet Exchange Dijet Production 

-  Count tracks and EM  Calorimeter Towers in   || < 1.0 for events with two jets.

- 

- Fraction rises with parton x
***Consistent****** ***with soft color rearrangement model preferring initial quark states
***Inconsistent*** with BFKL two-gluon or massive photon/U(1) gauge boson models

** ****Phys. Lett. B 440 189 (1998),  hep-ex / 9809016**

-  (ET > 30 GeV, s = 1800 GeV)

- Measured fraction of dijet events arising from color-singlet exchange is .94.04(stat).12(syst)%
- Too large to be explained by EW boson exchange indication of strong-interaction process.

**Notes:**
D0 measures the dijet production via hard color singlet exchange. D0 looks for events with two jets in the forward rapidity region and a central region free of particles which we call a rapidity gap. We then count the number of tracks and EM calorimeter towers in the gap region of eta<1 for the dijet events. This plot shows the number of events with a certain number of tracks and EM calorimeter towers for a jet Et threshold of 30GeV. You can clearlt see an excess of events with no tracks and no EM energy. The measures fraction of dijet events arising from color-single exchange for a jet Et threshold of 30GeV is 0.94+-0.04+-0.12%. This is too large to be explained by EW boson exchange and reprsents a clear indication of a strong-interacting process. D0 has measured the fraction of dijet events produced in hard color single exchange as a function of the second leading jet Et threshold. The result is shown in this plot. You can see that it rises as a function of Jet Et, implying that the fraction increases with parton x. The measurement is compared to various models as shown in the plot. The soft color rearrangement model, which has been used to explain rapidity gaps in positron-proton collisions gives consistent results with the D0 data. The fit prefers a model in which the color singlet is preferentially exchanged in processes with inital quarks. Other models shown in the plot are the BFKL two gluon exchange (dashed line) and the massive photon, massive U(1) gauge boson echange (dotted line) give results that are inconsistent with the data. This result has been recently published in Phys Lett B.

## Double Gaps at 1800 GeV |Jet | < 1.0, ET>15 GeV

**D0 Preliminary**

- Demand gap on one side,  measure multiplicity on opposite side

**Gap Region 2.5<|********|<5.2**

## Double Gaps at 630 GeV   |Jet | < 1.0, ET>12 GeV

**D0 Preliminary**

- Demand gap on one side,  measure multiplicity on opposite side

**Gap Region 2.5<|********|<5.2**

## DØ Preliminary

-  Demand gap on one side,  measure multiplicity on opposite side
-  Observe an excess of double gap events
-  Plot ET distribution of the leading two jets for three data samples: Inclusive Two Jet sample with |Jet|<1.0,  One forward gap & Double Gap events
-  ET spectra of double-gap events is harder than expected if Pomeron      carries 5% of the proton’s momentum

- s = 630GeV

- s = 1800GeV

_**Double Gaps at 1800 & 630 GeV**_** **

**Notes:**
D0 also studies events with two rapidity gaps. They select events with two jets in the central rapidity region and demand the presence of a gap in one side. They then measure the multiplicity of hits and calorimeter towers on the opposite side. The result is shown here for a cme of 1800GeV and 630GeV. You can see a clear excess of double gap events at both cme.
Do then plots the transverse energy of the two leading jets for three different data samples:
1) Inclusive dijet sample shown as solid line,
2)  Inclusive dijet sample with the additional requirement of a single forward rapidity gap (dashed), and the double gap sample (open circles). All three spectra are in good agreement with each other. This is interesting because it violates the rule of thumb that the pomeron carries less than 5% of the momentum of the proton. The results is valid at the two different cme.

## Kinematic Characteristics of Diffractive Dijets 

_**Kinematic Characteristics of Diffractive Dijets**_** **

- Absolute normalization
-     Stat errors only

-  Diffractive Dijet spectrum is steeper
-  Diffractive  Dijet system recoils against pot track
-  Diffractive events are cleaner (fewer 3rd jets)

**Notes:**
Shown here are the comparison of the leading and second leading jet transverse energy distribution for diffractive dijet events, shown as data points with stat error only, compared to the ones for non-diffractive dijet events shown as a solid line. The two distributions are of course absolutely normalized (the rate for diffractive dijet production is 100 times smaller than the non-diffractive production.)
You can see that the diffractive dijet spectrum falls steeper than the non-diffractive spectrum. Shown here are the mean dijet rapidity distribution and the difference in the azimuthal angle between the two jets for the two samples. You can see that the diffractive dijet mean rapidity peaks forward, showing that the dijet system recoils against the pot track as expected. The deltaphi distribution peaks of course at pi, but you can see that the diffractive events look cleaner, meaning that they are produced with fewer 3rd jets, again as expected.

## Diffractive Dijet Production 

_**Diffractive Dijet Production**_** **

-  Use roman-pot triggered data from Run 1C at 1800&630GeV
-  Select events with two jets and roman pot hits
-  Measure production rates and kinematic characteristics of difractive dijet events

**Notes:**
CDF took data during run 1C with a roman pot trigger at 1800 and 630 GeV. The Roman Pot is a scintillator fiber tracker located at ~50m from the CDF detector along the beam pipe that records the momentum of the tracks. CDF then selects events with two jets and hits in the roman pot and uses them to merasure production rates and kinematic characteristics of diffactive dijet events at the Tevatron

## Diffractive to Non-Diffractive Ratio vs  

- Rate of diffractive to non-diffractive events
- decreases with increasing

**Notes:**
These plots show the ratio of the production rate of diffractive to non-diffractive dijet events at two CME as a function of the momentum fraction of the parton from the antiproton participating in the dijet production. The two vertical dashed lines show the region in which the detector acceptance is well understood. You can see that the cross section ratio of diffractive to non-diffractive events decreases as a function of xp. You can get a detailed description of this analysis in the parallel session.