Measurement of angular correlations of jets at √s = 1.96 TeV

and determination of the strong coupling at high momentum transfers

Markus WobischLouisiana Tech Universityfor the D0 Collaboration

FermilabJoint Experimental-Theoretical

SeminarMay 18, 2012

Outline• Introduction

- Physics of hadron collisions s and PDFs- What we have learned from jets in Run II so far

• A new multi-jet observable- Angular correlations of jets- Definition & examples- Measurement procedure & experimental results

• Determination of s- Study the running of s at high momentum transfers

Introduction

jet

jet

Jet productionin hadroncollisions

Introduction

jet

jet

Parton distribution

functions (PDFs)

of the hadrons

Jet productionin hadroncollisions

Introduction

jet

jet

Parton distribution

functions (PDFs)

of the hadrons

pQCD matrix elements

Jet productionin hadroncollisions

Introduction

jet

jet

Strong coupling constant s

Parton distribution

functions (PDFs)

of the hadrons

pQCD matrix elements

Jet productionin hadroncollisions

.

jet

jet

Strong coupling constant s

Experimental evidence: s depends on momentum transfer Q s(Q)

Not yet at scales > 208 GeV

8

Strong Coupling s

tested up to 208 GeV (LEP e+e- data)

S. Bethke, arXiv:0908.1135

Running ofs:s(Q) decreases with Q

9

s and the Renormalization Group Equation

s(R): depends on Rthe renormalization scale

RGE relates s(Q0) at one scale Q0 to s(Q) at any other scale Q

RGE predicts all s(Q) curves which are possible

Observables must be independent of R RGE

Renormalization Group Equation

10

s and the Renormalization Group Equation

s(R): depends on Rthe renormalization scale

RGE relates s(Q0) at one scale Q0 to s(Q) at any other scale Q

Agreement: label curves by s(R=MZ)

RGE predicts all s(Q) curves which are possible

Observables must be independent of R RGE

Renormalization Group Equation

11

Testing pQCD

Which is the right s(Q) curve?• Determine s(MZ) • Comparison of s(MZ) results for different

processes check universality(this usually assumes the RGE)

experimental tests two aspects:

Is the running of s(Q) correctly predicted?

• Test RGE prediction of the running of s(Q)

This analysis

1.

2.

12

s(Q) beyond 208 GeV ?

so far tested up to Q = 208 GeV

Running of s(Q) could be modified for scales Q > e.g. by extra dimensions

here:= 200 GeV and n=1,2,3 extra dim.(n=0 Standard Model)

This analysis: study s(Q) for Q 400 GeV

.

jet

jet

pQCD matrix elements

pQCD matrix elements

LO pQCD matrix elements

for 22 processes

Computed in a perturbative

expansion in s using the Feynman rules

Known to NLO in s for 2-jet and 3-jet production

.

jet

jet

Parton distribution

functions (PDFs)

of the hadrons

16

PDF knowledge PDFs are determined in globalanalyses: CTEQ, MSTW, NNPDF

17

PDF knowledge PDFs are determined in globalanalyses: CTEQ, MSTW, NNPDFMost experimental constraints on PDFs are from data at lower scales

18

PDF knowledge

PDF knowledge at high scalesfrom “DGLAP” evolution uses RGE fors(Q)

PDFs are determined in globalanalyses: CTEQ, MSTW, NNPDFMost experimental constraints on PDFs are from data at lower scalesDGLAP

DGLAP: Dokshitzer–Gribov–Lipatov–Altarelli–Parisi

19

s(Q) for Q >208 GeV (?)

Two results from inclusive jet cross section data

20

s results from inclusive jet cross section data

CDF Collaboration, T. Affolder et al.,

Phys. Rev. Lett. 88, 042001 (2002)

B. Malaescu, P. Starovoitov, arXiv:1203.5416

“Test running over 40 < ET < 440 GeV”

“Test running up to pT 600 GeV”

From ATLAS inclusive

jet cross section data

Statements:

21

s results from inclusive jet cross section data

Not really!because analyses use PDFsfor which DGLAP evolutionis already done under assumption of running s(Q) according to the RGE

“Test running over 40 < ET < 440 GeV”

“Test running up to pT 600 GeV”

RGE was already assumed

Not an independent test

Statements:

22

Run II jet results – so far

23

What we have learned fromjets in Run II so far

New result:• Measurement of a new multi-jet

observable• More reliable determination of s at high

pT

• Test: Standard Model vs. New Physics• Constraining PDFs and s

22

23 • Testing pQCD at higher orders• Further PDF constraints• Study multi-jet ratios

24

Do we see QCD dynamics – or …?

small y large y

New particle resonances in dijet mass

spectrum

Tails of new high-energy

phenomena in dijet angular distribution

25

Do we see QCD dynamics – or …?

Limits on new resonances

dijet angular distributions

dijet mass spectrum

Limits on quark compositeness

and extra spatial dimensions

No indications for New Physics

26

.

ConstrainingPDFs and s

Inclusive jet cross section Dijet mass cross section

27

PDF sensitivityTheory: pQCD @NLO is reliable (±10%) sensitivity to PDFs unique: high-x gluon

xT

28

Inclusive jet pT / dijet mass

Both data sets are sensitive to s and the PDFs

pT (GeV)

29

Three-jet mass spectrum: O(s

3) Phys. Lett. B (2011)

2-jet cross section: O(s

2) x PDF2

(correlation of andgluon density)

3-jet cross section: O(s

3) x PDF2

analyze 2-jet and 3-jet cross sections: decorrelatesand gluon density in PDF fits

additional PDF constraints from 3-jet mass data

30

Run II jets in MSTW2008 PDF fit

MSTW2008 paper (Fig 52. / see also Figs. 51, 53)

Tevatron jet data affect gluon for x > 0.2 – 0.3(so far only inclusive jet data have been used in PDF fits)

31

D0 s(pT) from Run II inclusive jet cross section data

jet

jet

pT (GeV)

Avoid potential inconsistencies

32

PDFs and input data MSTW2008 paper (Fig 52. / see also Figs. 51,

53)

Tevatron jet data don’t affect gluon for x < 0.2 – 0.3

Currently: Main constraints on high-x gluon density come from Tevatron jet data

Goal: Minimize correlations between data and PDF uncertainties

Restrict s analysis to kinematic regions where impact of Tevatron data for PDFs is small.

33

Data Sample for s analysis

22 (out of 110) inclusive jet cross section data points have small contributions from x > 0.2 – 0.3

Data points at 50 < pT < 145 GeV

Input in s analysisRestriction to 50 < pT < 145 GeV avoids pT regions in which RGE has not yet been tested!(no circular argument here)

pT (GeV)

34

Strong Coupling Constant Use best theory prediction:

NLO + 2-loop threshold corrections(Kidonakis/Owens) with MSTW2008NNLO PDFs

Most precise result from a hadron collider

Consistent with HERA results and world average

35

Going further …

… towards testing in the RGE

at higher momentum transfers

Should not use cross section data(Don’t want to rely on PDF

information)

Better use cross section ratios…

36

Cancelling PDFs in RatiosGoal: test pQCD (and s) independent of

PDFs Ratios of cross sections for 3-jet and 2-jet

observables

• Sensitive to s (3-jets: s3

/ 2-jets: s

2)• Significantly reduced PDF sensitivity

sR =

37

Cancelling PDFs in Ratios

sR =

However: no complete PDF cancellations • Slightly different x-coverage in numerator/denominator• Slightly different contributions from different partonic

subprocesses

Therefore: residal PDF uncertainties Residual dependence of the

RGE

But significant improvement w.r.t. cross sections

38

R3/2 = 3-jet / 2-jet

R3/2 = 3-jet / 2-jet

s

39

Dijet Azimuthal Decorrelations

s1/dijet * ddijet / ddijet

dijet angle between the two leading pT

jets

more inclusive than R3/2

don’t need to tag 3rd jet

PRL 94, 221801 (2005)

40

.

A new observable RR: Angular correlations of jets

DefinitionMeasurement

41

New Observable: RR

RR

average number of neighboring jets for jets from an inclusive jets sample s“Angular Correlations of

Jets”

Depends on 3 variables:• inclusive jet pT

• distanceR to neighbor jet in (y)

• neighbor jet pT-nbr requirement

42

New Observable: RR

RR looks at any jet and any neighboring jet… more inclusive than R3/2 (require to tag three leading

jets)… more inclusive than R (require to tag two leading

jets)

1. Start with central inclusive jet sample (|y|<1)

2. Loop over all inclusive jetsFor each inclusive jet: count No. of neighboring jets- in distance R in (y) - with pTnbr > pT

minnbr

3. Ratio: sum of all neighboring jets / total number of inclusive jets average number of neighboring jets RR(pT, R, pT

minnbr)Note: for R only contributions from (at least) 3-jet

events

43

RR : examples

If all events were like this RR = 0

• Two inclusive jets add “2” to denominator

• None has a neighbor “0” to numerator

• Three inclusive jets add “3” to denominator

• Two have one neighbor add “2” to numerator If all events were like this RR = 2/3

For simplicity: All jets have the same pT and we study R < 2/3

• Four inclusive jets add “4” to denominator

• Each has one neighbor add “4” to numerator If all events were like this RR = 1

44

RR : analysis phase space

Phase space for RR(pT, R, pT-nbr) measurement: • Central inclusive jets: |y|

< 1• Inclusive jets in pT range: 50 < pT < 450

GeV• 4 different pT requirements for neighbor jet: pT-nbr > 30, 50, 70,

90 GeV• Jet-jet distances in 3 ranges of R: 1.4 – 1.8 – 2.2 – 2.6

(

Criteria:• inclusive jet pT requirements ( high trigger

efficiencies)• y,R requirements such that (ymax + Rmax) < 3.6 ( in

acceptance)• R such that always R > 2 * Rcone ( no overlapping jet

cones)• pT-nbr requirements from soft to hard

Measure triple differentially: RR(pT, R, pT-nbr)

45

Presentation of RR

Measure dependence of RRon (pT, R, pT-nbr-min)

Average number of neighbor jets within R to an inclusive jet

46

RR in theory

Theory properties

Next slides show that RRis theoretically well-behaved:

• Small PDF uncertainties / small PDF set dependence

• Small k-factor (k = NLO/LO)• Small renormalization/factorization scale

dependencies• Small non-perturbative corrections

47

RR PDF sensitivity

• MSTW 68% C.L. PDF uncertainty: 2-3% • MSTW2008, CT10, NNPDFv2.1 agree better than 3%

PDF sensitivity is weak

48

RR scale dep. / k-factor

• inverse of k-Factor: LO/NLO (dotted line) close to unity

• Scale dependence (solid lines) small (5-10%)

49

RR non-pert corrections

• Small (<10%, typically 3-5%)• “old” and “new” PYTHIA tunes agree well at high pT

Product of correction

factors for:• Hadronization• Underlying

event

50

Measurement

Experimental procedure

following closely the D0 inclusive jet cross section measurement:

• Run / Event / Jet selection - good vertex in central tracking acceptance pT reconstruction- cut on missing pT to avoid cosmics- jet ID requirements to avoid noise jets and electron/photon

• Choices of inclusive jet triggers & trigger turn-ons

51

Jet TriggersUse inclusive jet triggers: fire on single jet above pT

threshold

Trigger efficiencies (plateau regions) are determined from ratios of the inclusive jet cross sections for subsequent triggers

52

Measurement

Experimental procedure

following closely the D0 inclusive jet cross section measurement:

• Jet ID efficiencies• Jet energy calibration   Phys. Rev. D 85, 052006 (2012)• Jet pT resolutionsIn addition:• Jet resolutions in y and

53

Measurement

Use fast parametrized simulation of the detector responseSimulate all relevant effects• Jet ID efficiencies• Jet pT resolutions• Jet resolutions in y and Use also to simulate all corresponding uncertainties, plus:• Jet energy calibration uncertainty

54

Measurement

Determine detector response from the simulation Corrections for experimental effects (bin-by-bin) All experimental uncertainties

(dominated by jet energy calibration uncertainty)

Generate two sets of MC events (SHERPA, PYTHIA)subjected to detector simulation

Reweighted to describe jet pT, y, R distributions in data

55

RR experimental corrections

Use smoothed average to correct the data Treat spread between SHERPA, PYTHIA as

uncertainty

Total correction factors for experimental effects

Determined usingthe simulation with SHERPA, PYTHIA

• Small corrections (typically < 2-3%)

• Small model dependence (typically below 1-2%)

56

RR experimental uncertainties

• Small (typically 2-5%)• Dominated by jet energy calibration uncertainty

Total relativeexperimental uncertainties

57

RR results

Dependence of RRon (pT , pT-nbr , R) described by pQCD

58

RR data/theory

• Good agreement for pT-nbr-min = 50 GeV and higher• Not so good for requirement pT-nbr-min = 30 GeV (low pT

physics?)

59

.

The strong couplingfrom RR

60

s from RR

Groups of data points:Determine s by minimizing 2 function

Single data point: Determine s from projection

Both procedures require to parameterize theory result vs. s use PDF set for different s values: interpolate /

extrapolate

61

s from RR - theoryPerturbative:• NLOJET++/fastNLO for 2-jet and 3-jet NLO

calculation• PDFs: MSTW2008NLO• PDF uncertainty: MSTW 68% C.L. PDFs / CT10,

NNPDFv2.1 • Central scale R = F = 0 = pT • Scale uncertainty by independent variation

R, F in (0.5, 2) 0 with 0.5 < (R/F) < 2 Non-Perturbative Corrections:PYTHIA with different tunes

- tune “DW” (old parton shower, old underlying event)- tune “AMBT1” (new parton shower, new underlying event)

cross checked with tunes “A”, “S Global”

62

s from RR

no R dependence!

138 data points: up to 12 pT bins in 12 (pTnbr , R) regions (4 R * 3 pTnbr) Initial check: Is there any (pTnbr , R) dependence

In each (pTnbr , R) region: determine combined s(MZ) and 2

Consistency for pTnbr >=50 GeV

Always good 2

Confirm RGE

63

s(pT) resultsUse pTnbr > 50, 70, 90 GeV

At each pT, combine all data points with different pTnbr and R requirments

Determine results for s(pT)at 12 pT values

s(pT) results up to 400 GeV

s(pT) decreases with pTas predicted by the RGE

Main result!

64

s(pT) resultsUse pTnbr > 50, 70, 90 GeV

At each pT, combine all data points with different pTnbr and R requirments

Determine results for s(pT)at 12 pT values

s(pT) results up to 400 GeV

s(pT) decreases with pTas predicted by the RGE Results agree with results from

ALEPH event shape data Previous D0 results from

inclusive jets

Main result!

65

Combined s(MZ) resultCombining all data points with pTnbr > 50, 70, 90 GeV (all R,

all pT):

This results (obtained at NLO-only) has slightly larger uncertainty as compared to result from inclusive jets (obtained at NLO+2-loop)

Due to scale dependencePrevious result from inclusive jets:

Summary

66

Introduced a new observable: multi-jet cross section ratio

probing angular correlations of jets: RR

Average number of neighboring jets for inclusive jet sample

Determination of s from RR

Largely independent of PDFs New test of RGE & running of s

Measured triple differentially: RR(pT, R, pT-nbr-min)Precise measurement w/ systematic uncertainties

<5%Well described by pQCD for pTnbr > 50 GeV

First time:Demonstrate that s continues to decrease

above 208 GeV up to 400 GeV

67

Backup

68

PDF sensitivity

Inclusive jet cross section:

3-jet / 2-jet cross section ratio:

69

Theoretical Precision for s(MZ)

Main result: use best theory predictions NLO + 2-loop threshold corrections (Kidonakis/Owens) with MSTW2008NNLO PDFs

Use only NLO with MSTW2008NLO PDFs

• Larger value of “NLO-only” result: due to missing O(s

4) contributions• Larger uncertainty of “NLO-only” result:

due to increased scale dependence (main effect)

and increased PDF uncertainty (minor effect)s extraction at large pT requires high (experimental & theory)

precision

s from D0 inclusive jet cross section data

70

Inclusive Jets: x-sensitivity

What is the x-value for a given incl. jet data point @(pT , |y|) ?

Not completely constrained – unknown kinematics since we integrate over other jet(s)

Construct a “test-variable” (treat as if other jet was at y=0):

Jet cross section has access to x-values of: (in LO kinematics)

Apply cut on this test-variable to restrict accessible x-range

Find: requirement xtest < 0.15 removes most of the contributions with x > 0.2 – 0.3

71

xmin / xmax distributions

Every analysis bin one plotEach plot: xmin/xmax distributions Cut on test-variable xtest < 0.15

keep 22 (of 110) data points

These have small contributions fromx > 0.2 – 0.3

Only data points above green line are used

72

M3-jet data / theoryAccepted by Phys. Lett. B (2011)

similar to dijet mass result:• MSTW2008: slightly higher than data at all M3-jet (but

consistent)• CT10 agrees at low M3-jet - different shape: too high at high

M3-jet • CT10, MSTW2008 68% CL uncertainty bands: no overlap at

high M3-jet

73

M3-jet Constraining PDFs

ratios data/theory show different shapes / magnitudes for recent PDFs

consistency with D0 dijet mass results

74

detailed analysis test PDFs

Phys. Lett. B (2011)

Agreement between theory and data depends on• value of s(MZ) • choice of PDFs• choice of renormalization/factorization scales Quantify agreement: Study chi2 for all variations best agreement for MSTW2008, NNPDFv2.1 not so good for CTEQ10, HERAv1.0

75

Overview .

Theory-data comparison

for jet cross section data

in processes with initial-state hadrons • RHIC• HERA 1, 2

(high Q2 only)• Tevatron Run I, II

(central rapidities only)

• First LHC results(central rapidities only)

fastNLO Collab., arXiv: 1109.1310

Highest pT reach by LHC data

76

Overview: xT dependencefastNLO Collab., arXiv: 1109.1310

hadron-hadron collisions only

plot vs. xT = 2pT /sqrt(s)

Interpretation:for y1=y2 =0 xT =

xdemonstrate PDF sensitivityhighest xT-reach

by Tevatron data