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

coscosh2

2/tanln ,, :Jet

21212,1,2

TT

T

EEM

E

Jet 2: ET2, 2, 2

Jet 1: ET1, 1, 1

= 0

2,1,2

2

1

,21

exp

TT

ii

iT

EEQ

s

Ex

Jet Production

1P

2P

1xfi11Px

22Px

1jet

2jet

sij ̂

2xf j

,,,ˆ

,,

2

2

2

22

2211

22

2121

RFRsij

ijFjFi

QQPxPx

xfxfdxdx

2R

1.3R

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

TLdtE

NE

T

jet .vs

DD

PRL82, 2451 (1999)

Inclusive Jet Cross Section at 1.8TeV DD

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

Preliminary

Rapidity Dependence of the Inclusive Jet Cross Section

s = 1.8 TeV, || < 1.5

DD

0.0 < 0.5 0.5 1.0 1.0 1.5

DØ Preliminary

d2 d

ET

d

(fb

/GeV

)

0.5 1.0

0.0 0.5

1.0 1.5

ET (GeV)

( D

ata

- T

heor

y )

/ Th e

ory

Data and NLO QCD in good agreement Extend measurement to || = 3

Refine error analysis

New

DØ Preliminary

ET (GeV)

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

DD d = (ET3/2) (d2/dETd

XT ET / (s / 2 )

DDPreliminary

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

Measurement of S from Inclusive Jet Production

)(),()()( 3,

22

TFRSTFRST

EBEAddE

d

NLO x-section can be parametrized as

Measuredby CDF

Obtained from JETRAD

2TE

FR

• 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

0089.0

0078.00001.01129.0)( ZS M

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

1

dMddd3

dM dd Nevents

L M =

Dijet Mass Cross Section DD

NLO QCD in good agreement with data

Inclusive Dijet Differential Cross Section 211

3

dddE

dT

Beam line

Trigger Jet0.1<||<0.7

Probe Jet ET>10 GeV0.1<||<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

Inclusive Dijet Differential Cross Section DD 212,1

3

dddE

dT

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.

Subjet Multiplicity in Quark & Gluon JetsDD

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.

1800GeV

100 200 300

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.

s

New

Subjet Multiplicity in Quark & Gluon JetsDD

Method:

• Subjet Multiplicity M = fgMg + (1-fg )Mq

(g jet fractions fg obtained from theory)

f 630 = 33% f 1800 = 59%

• Assuming that the subjet multiplicity is independent of s (verified with MC)

Mq =

f 1800M630 - f 630M1800

f 1800- f 630

f 1800- f 630

(1-f 630)M1800 - (1- f 1800)M630

Mg =

• Use kT algorithm; unravel jets until

all subjets are separated by ycut

=.001

• Measure number of subjets for events with jets with 55<ET<100 GeV

1

1

q

g

M

MR

(sys) 0.19

0.23(stat) 04.091.1 R

Dominant uncertainties come from g jet fraction and choice of jetET

MC Prediction =1.860.08(stat)

jetsjets dN

dM

N

1

M 1 2 3 4

0.5

0.4

0.3

0.2

0.1

GeVs 1800

Quark Jets Gluon Jets

Preliminary

New

QCD with Vector BosonsTitle:PRJ$ROOT207:[WZ.NOTES.KUMAC]W_HIST.EPS;1Creator:HIGZ Version 1.22/09Preview:This EPS picture was not savedwith a preview included in it.Comment:This EPS picture will print to aPostScript printer, but not toother types of printers.

W&Z Production at the Tevatron

pq q

pW(Z)

l

(l )

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)

W

g

q

q’

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:q

q’

W

g

Production of W/Z BosonsCross section measurementstest O(2) QCD predictions for W/Z production

(pp W + X) B(W ) (pp Z + X) B(Z )

S=1.8 TeV

WB(W e)

Z B(Z ee)R=

R=10.54 0.24

S=630 GeVDØ: W e = 658 67 pb

(DØ)

(CDF)R=10.36 0.18

Preliminary

Introduction to W, Z PT Theory

• Small PT region (QCD < PT < 10 GeV): Resum large logs

Ellis, Martinelli, Petronzio (83); Arnold & Reno (89);Arnold, Ellis, Reno (89); Gonsalves, Pawlowski, Wai (89)

Altarelli, Ellis, Greco, Martinelli (84); Collins, Soper, Sterman (85)

b-space:Parisi-Petronzio (79); Davies-Stirling (84); Collins-Soper-Sterman (85); Davies, Webber, Stirling (85); Arnold- Reno-Ellis (89); AK: Arnold-Kaufann (91); LY: Ladinsky-Yuan (94)

qt-space:Dokshitser-Diaknov-Troian (80); Ellis-Stirling (81); Altarelli-Ellis-Greco-Martinelli (84); Gonsalves-Pawlowksl-Wai (89); ERV: Ellis-Ross-Veseli (97); Ellis-Veseli (98)

• Large PT region (PT 30 GeV): Use pQCD, O(s2) calculations exist

• Very low PT region (PT ~ QCD): Non-perturbative parameters extracted from data

)(ln)ln(~

2

22

212

2

22T

Ws

T

W

T

s

T p

Mvv

p

M

pdp

d

Boson+ Jet Theory

Arnold-Kauffman Nucl. Phys. B349, 381 (91). O(s

2), b-

space, MRSA’ (after detector simulation)

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

DD D0 W PT measurement

Preliminary

D0 Z PT measurementDD2/dof = 17/16

2/dof = 83/16

Ladinsky, Yuan, PRD 50, 4239 (94), O(s

2), b-space.

Arnold, Kauffman, NP B349, 381 (91), O(s

2), b-space.

Preliminary

Arnold, Reno, Nucl. Phys. B319, 37. O(s

2), MRSA’, pQCD calculation

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

CDF PT measurementsEllis, 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

RW JetW Jets

10 10

( )( )

R R

W

q

q

E ET T min

W

g

q

E ET T min

g

W

q

q

W+ Jet Production

LO

s

s

A test of NLO

W

q

q

• Sensitive to PDF’s, higher orders

• Depends on R, ETmin due to jet definition

• Calculations of A, B from NLO DYRAD (Giele, Glover, Kosower)

R E RW JetW JetsT

10 10

( , )( )( )

min

( ) ( )minW Jets A B Es T 0 0 0

( ) ( ) ( , )min minW Jet A E B E Rs T s T 1 12

1

W+ Jet Production

W + Jets: CDF

Title:DISK$F0:[CDF.TEMP.HENNESSY.3077]XSYS_4JET.PS;2 (Portrait A 4)Creator:HIGZ Version 1.22/09Preview:This EPS picture was not savedwith a preview included in it.Comment:This EPS picture will print to aPostScript printer, but not toother types of printers.

W/Z + Jets: CDFTitle:DISK$F0:[CDF.TEMP.HENNESSY.3077]RFACTOR_BLESS_NEW_2 (Portrait A 4)Creator:HIGZ Version 1.22/09Preview:This EPS picture was not savedwith a preview included in it.Comment:This EPS picture will print to aPostScript printer, but not toother types of printers.

Jets) 0N(W

Jets) 1N(W10

R

W+ Jet Ratio

W + Jets: CDF

Title:DISK$23:[DITTMANN.PS]PS_OUT.PS;1Creator:HIGZ Version 1.22/09Preview:This EPS picture was not savedwith a preview included in it.Comment:This EPS picture will print to aPostScript printer, but not toother types of printers.

Rapidity Gaps• D0 and CDF study hadronic events with peculiar structure - a rapidity gap

due to color-singlet exchange (pomeron). What is the Pomeron?

(gap)

p

hard single diffraction

(gap)

p

hard double pomeron

(gap)

p

hard color singlet

(gap)

p

p

p

p

p

p

} Probe thepomeronstructure

CDF and D0 made the first studies of thesetopologies.}

pomeron

Rapidity Gaps

Typical event

Hard single diffraction

Hard double pomeron

Hard color singlet

Hard Color-singlet Exchange Dijet Production

DD

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

jet

jet

Fraction rises with parton x

Consistent with soft color rearrangement model preferring initial quark statesInconsistent 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.

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

D0 PreliminaryD0 Preliminary

Demand gap on one side, measure multiplicity on opposite sideDemand 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 PreliminaryD0 Preliminary

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

Gap Region 2.5<||<5.2

Gap Region 2.5<||<5.2

• Demand gap on one side, measure Demand gap on one side, measure multiplicity on opposite sidemultiplicity on opposite side Observe an excess of double gap events

• Plot EPlot ET T distribution of the leading two jets distribution of the leading two jets for three data samples: Inclusive Two Jet for three data samples: Inclusive Two Jet sample with |sample with |JetJet|<1.0, One forward gap & |<1.0, One forward gap & Double Gap eventsDouble 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

DØ PreliminaryDD Double Gaps at 1800 & 630 GeV

Kinematic Characteristics of Diffractive Dijets

GeVE

GeVt

T 7

2.0||

10.004.02

GeVs 630

Absolute normalization

Stat errors only

• Diffractive Dijet spectrum is steeper

• Diffractive Dijet system recoils against pot track

• Diffractive events are cleaner (fewer 3rd jets)

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

Diffractive to Non-Diffractive Ratio vs px

p

JetT

JetT

p p

eEeEx

02

2211

TeVs 8.1 GeVs 630

Rate of diffractive to non-diffractive events

decreases with increasing p

x