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Measurement of angular correlations of jets at vs = 1.96 TeV and determination of the strong coupling at high momentum transfers

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Title: Photon Cross Sections at Ecm=2TeV Author: wobisch Last modified by: Markus Wobisch Created Date: 3/12/2006 5:59:57 AM Document presentation format – PowerPoint PPT presentation

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Title: Measurement of angular correlations of jets at vs = 1.96 TeV and determination of the strong coupling at high momentum transfers


1
Measurement of angular correlations of jets at
vs 1.96 TeV and determination of the strong
coupling at high momentum transfers
  • Markus Wobisch
  • Louisiana Tech University
  • for the D0 Collaboration

Fermilab Joint Experimental-Theoretical
Seminar May 18, 2012
2
Outline
  • Introduction- Physics of hadron collisions
    as 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 as- Study the running of as at
    high momentum transfers

3
Introduction
Jet production in hadron collisions
4
Introduction
Jet production in hadron collisions
Parton distribution functions (PDFs) of the
hadrons
5
Introduction
pQCD matrix elements
Jet production in hadron collisions
Parton distribution functions (PDFs) of the
hadrons
6
Introduction
pQCD matrix elements
Jet production in hadron collisions
Parton distribution functions (PDFs) of the
hadrons
Strong coupling constant as
7
.
Strong coupling constant as
8
Strong Coupling as
S. Bethke, arXiv0908.1135
Experimental evidence as depends on momentum
transfer Q ? as(Q)
Running of asas(Q) decreases with Q
? tested up to 208 GeV (LEP ee- data)
Not yet at scales gt 208 GeV
9
as and the Renormalization Group Equation
as(mR) depends on mRthe renormalization scale
Observables must be independent of mR ?
RGE Renormalization Group Equation
RGE relates as(Q0) at one scale Q0 to as(Q) at
any other scale Q
RGE predicts all as(Q) curves which are possible
10
as and the Renormalization Group Equation
as(mR) depends on mRthe renormalization scale
Observables must be independent of mR ?
RGE Renormalization Group Equation
RGE relates as(Q0) at one scale Q0 to as(Q) at
any other scale Q
RGE predicts all as(Q) curves which are possible
Agreement label curves by as(mRMZ)
11
Testing pQCD
experimental tests ? two aspects
1.
  • Which is the right as(Q) curve?
  • Determine as(MZ)
  • Comparison of as(MZ) results for different
    processes ? check universality
  • (this usually assumes the RGE)

? This analysis
2.
  • Is the running of as(Q) correctly predicted?
  • Test RGE prediction of the running of as(Q)

12
as(Q) beyond 208 GeV ?
? so far tested up to Q 208 GeV Running of
as(Q) could be modified for scales Q gt m0 e.g.
by extra dimensions here m0 200 GeV and
n1,2,3 extra dim.(n0 ? Standard Model)
This analysis study as(Q) for Q ? 400 GeV
13
.
pQCD matrix elements
14
pQCD matrix elements
Computed in a perturbative expansion in as using
the Feynman rules
Known to NLO in as for 2-jet and 3-jet
production
LO pQCD matrix elements for 2?2 processes
15
.
Parton distribution functions (PDFs) of the
hadrons
16
PDF knowledge
PDFs are determined in global analyses CTEQ,
MSTW, NNPDF
17
PDF knowledge
PDFs are determined in global analyses CTEQ,
MSTW, NNPDF
Most experimental constraints on PDFs are from
data at lower scales
18
PDF knowledge
PDFs are determined in global analyses CTEQ,
MSTW, NNPDF
Most experimental constraints on PDFs are from
data at lower scales
DGLAP
PDF knowledge at high scales from DGLAP
evolution ? uses RGE for as(Q)
DGLAP DokshitzerGribovLipatovAltarelliParisi
19
as(Q) for Q gt208 GeV (?)
? Two results from inclusive jet cross section
data
20
as results from inclusive jet cross section data
CDF Collaboration, T. Affolder et al., Phys.
Rev. Lett. 88, 042001 (2002)
B. Malaescu, P. Starovoitov, arXiv1203.5416
From ATLAS inclusive jet cross section data
Statements
Test running over 40 lt ET lt 440 GeV
Test running up to pT ? 600 GeV
21
as results from inclusive jet cross section data
Statements
Test running over 40 lt ET lt 440 GeV
Test running up to pT ? 600 GeV
? Not really!because analyses use PDFsfor which
DGLAP evolutionis already done under assumption
of running as(Q) according to the RGE
  • RGE was already assumed
  • Not an independent test

22
Run II jet results so far
23
What we have learned fromjets in Run II so far
  • Test Standard Model vs. New Physics
  • Constraining PDFs and as

2?2
  • Testing pQCD at higher orders
  • Further PDF constraints
  • Study multi-jet ratios

2?3
  • New result
  • Measurement of a new multi-jet observable
  • More reliable determination of as at high pT

24
Do we see QCD dynamics or ?
New particle resonances in dijet mass spectrum
Tails of new high-energy phenomena in dijet
angular distribution
small ?y
large ?y
25
Do we see QCD dynamics or ?
dijet angular distributions
dijet mass spectrum
Limits on new resonances
Limits on quark compositeness and extra spatial
dimensions
? No indications for New Physics
26
.
ConstrainingPDFs and as
? Inclusive jet cross section ? Dijet mass cross
section
27
PDF sensitivity
  • Theory pQCD _at_NLO is reliable (10)
  • ? sensitivity to PDFs
  • ? unique high-x gluon

xT
28
Inclusive jet pT / dijet mass
pT (GeV)
? Both data sets are sensitive to as and the
PDFs
29
Three-jet mass spectrum O(as3)
Phys. Lett. B (2011)
  • 2-jet cross section
  • O(as2) x PDF2
  • (correlation of a and
  • gluon density)
  • 3-jet cross section
  • O(as3) x PDF2
  • analyze 2-jet and 3-jet cross sections
  • ? decorrelate as and 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 gt 0.2 0.3
  • (so far only inclusive jet data have been used in
    PDF fits)

31
D0 as(pT) from Run II inclusive jet cross
section data
pT (GeV)
? Avoid potential inconsistencies
32
PDFs and input data
MSTW2008 paper (Fig 52. / see also Figs. 51,
53)
Currently Main constraints on high-x gluon
density come from Tevatron jet data Goal
Minimize correlations between data and PDF
uncertainties ? Restrict as analysis to
kinematic regions where impact of Tevatron data
for PDFs is small.
? Tevatron jet data dont affect gluon for x lt
0.2 0.3
33
Data Sample for as analysis
22 (out of 110) inclusive jet cross section data
points have small contributions from x gt 0.2
0.3 ? Data points at 50 lt pT lt 145 GeV ?
Input in as analysis
Restriction to 50 lt pT lt 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 (Dont want to
rely on PDF information)
  • Better use cross section ratios

36
Cancelling PDFs in Ratios
Goal test pQCD (and as) independent of PDFs
? Ratios of cross sections for 3-jet and 2-jet
observables
as
R
  • Sensitive to as (3-jets as3 / 2-jets
    as2)
  • Significantly reduced PDF sensitivity

37
Cancelling PDFs in Ratios
  • However no complete PDF cancellations
  • Slightly different x-coverage in
    numerator/denominator
  • Slightly different contributions from different
    partonic subprocesses

as
R
  • Therefore
  • residal PDF uncertainties
  • Residual dependence of the RGE

? But significant improvement w.r.t. cross
sections
38
R3/2 s3-jet / s2-jet
R3/2 s3-jet / s2-jet
as
39
Dijet Azimuthal Decorrelations
1/sdijet dsdijet / dDfdijet
as
PRL 94, 221801 (2005)
Dfdijet angle between the two leading pT jets
more inclusive than R3/2 ? dont need to tag 3rd
jet
40
.
A new observable
  • RDR Angular correlations of jets
  • Definition
  • Measurement

41
New Observable RDR
RDR average number of neighboring jets for
jets from an inclusive jets sample
as
Angular Correlations of Jets
  • Depends on 3 variables
  • inclusive jet pT
  • distance DR to neighbor jet in (Df,Dy)
  • neighbor jet pT-nbr requirement

42
New Observable RDR
1. Start with central inclusive jet sample
(ylt1)
  1. Loop over all inclusive jetsFor each inclusive
    jet count No. of neighboring jets- in distance
    DR in (Df,Dy) - with pTnbr gt
    pTminnbr
  1. Ratio sum of all neighboring jets / total
    number of inclusive jets? average number of
    neighboring jets RDR(pT, DR, pTminnbr)

Note for DR lt p ? only contributions from (at
least) 3-jet events
? RDR looks at any jet and any neighboring jet
more inclusive than R3/2 (require to tag three
leading jets) more inclusive than RDf (require
to tag two leading jets)
43
RDR examples
For simplicity All jets have the same pT and we
study DR lt 2p/3
  • Two inclusive jets ? add 2 to
    denominator
  • None has a neighbor ? 0 to numerator

If all events were like this ? RDR 0
  • Three inclusive jets ? add 3 to
    denominator
  • Two have one neighbor ? add 2 to numerator

If all events were like this ? RDR 2/3
  • Four inclusive jets ? add 4 to
    denominator
  • Each has one neighbor ? add 4 to numerator

If all events were like this ? RDR 1
44
RDR analysis phase space
Measure triple differentially RDR (pT, DR,
pT-nbr)
  • Phase space for RDR (pT, DR, pT-nbr) measurement
  • Central inclusive jets
    y lt 1
  • Inclusive jets in pT range
    50 lt pT lt 450 GeV
  • 4 different pT requirements for neighbor jet
    pT-nbr gt 30, 50, 70, 90 GeV
  • Jet-jet distances in 3 ranges of DR
    1.4 1.8 2.2 2.6 (ltlt p)
  • Criteria
  • inclusive jet pT requirements
    (? high trigger efficiencies)
  • y, DR requirements such that (ymax DRmax) lt
    3.6 (? in acceptance)
  • DR such that always DR gt 2 Rcone (?
    no overlapping jet cones)
  • pT-nbr requirements from soft to hard

45
Presentation of RDR
Average number of neighbor jets within DR to an
inclusive jet
? Measure dependence of RDR on (pT, DR,
pT-nbr-min)
46
RDR in theory
Theory properties
  • Next slides show that RDR is 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
RDR PDF sensitivity
  • MSTW 68 C.L. PDF uncertainty 2-3
  • MSTW2008, CT10, NNPDFv2.1 agree better than 3

? PDF sensitivity is weak
48
RDR scale dep. / k-factor
  • inverse of k-Factor LO/NLO (dotted line) ?
    close to unity
  • Scale dependence (solid lines) ? small
    (5-10)

49
RDR non-pert corrections
  • Product of correction
  • factors for
  • Hadronization
  • Underlying event
  • Small (lt10, typically 3-5)
  • old and new PYTHIA tunes agree well at high pT

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 Triggers
Use 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 resolutions
  • In addition
  • Jet resolutions in y and f

53
Measurement
Use fast parametrized simulation of the detector
response
  • Simulate all relevant effects
  • Jet ID efficiencies
  • Jet pT resolutions
  • Jet resolutions in y and f
  • Use also to simulate all corresponding
    uncertainties, plus
  • Jet energy calibration uncertainty

54
Measurement
Generate two sets of MC events (SHERPA,
PYTHIA) subjected to detector simulation ?
Reweighted to describe jet pT, y, DR
distributions in data
  • Determine detector response from the simulation
  • Corrections for experimental effects
    (bin-by-bin)
  • All experimental uncertainties (dominated by
    jet energy calibration uncertainty)

55
RDR experimental corrections
  • Total correction factors
  • for experimental effects
  • Determined using
  • the simulation with
  • SHERPA, PYTHIA
  • Small corrections (typically lt 2-3)
  • Small model dependence (typically below 1-2)
  • Use smoothed average to correct the data
  • Treat spread between SHERPA, PYTHIA as uncertainty

56
RDR experimental uncertainties
Total relative experimental uncertainties
  • Small (typically 2-5)
  • Dominated by jet energy calibration uncertainty

57
RDR results
Dependence of RDR on (pT , pT-nbr , DR) described
by pQCD
58
RDR 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 coupling from RDR
60
as from RDR
Single data point Determine as from projection
Groups of data pointsDetermine as by
minimizing c2 function
Both procedures require to parameterize theory
result vs. as ? use PDF set for different as
values interpolate / extrapolate
61
as from RDR - theory
  • Perturbative
  • NLOJET/fastNLO for 2-jet and 3-jet NLO
    calculation
  • PDFs MSTW2008NLO
  • PDF uncertainty MSTW 68 C.L. PDFs / CT10,
    NNPDFv2.1
  • Central scale mR mF m0 pT
  • Scale uncertainty by independent variation mR,
    mF in (0.5, 2) m0 with 0.5 lt (mR/mF) lt
    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
as from RDR
138 data points up to 12 pT bins in 12 (pTnbr ,
DR) regions (4 DR 3 pTnbr)
Initial check Is there any (pTnbr , DR)
dependence ? In each (pTnbr , DR) region
determine combined as(MZ) and c2
Always good c2 ? Confirm RGE
no DR dependence!
Consistency for pTnbr gt50 GeV
63
as(pT) results
Use pTnbr gt 50, 70, 90 GeV At each pT, combine
all data points with different pTnbr and DR
requirments
Determine results for as(pT) at 12 pT values
  • as(pT) results up to 400 GeV
  • as(pT) decreases with pTas predicted by the RGE

Main result!
64
as(pT) results
Use pTnbr gt 50, 70, 90 GeV At each pT, combine
all data points with different pTnbr and DR
requirments
Determine results for as(pT) at 12 pT values
  • as(pT) results up to 400 GeV
  • as(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 as(MZ) result
Combining all data points with pTnbr gt 50, 70, 90
GeV (all DR, all pT)
This results (obtained at NLO-only) has slightly
larger uncertainty as compared to result from
inclusive jets (obtained at NLO2-loop) ? Due to
scale dependence
Previous result from inclusive jets
66
Summary
Introduced a new observable multi-jet cross
section ratio ? probing angular correlations of
jets RDR Average number of neighboring jets for
inclusive jet sample
Measured triple differentially RDR (pT, DR,
pT-nbr-min) Precise measurement w/ systematic
uncertainties lt5 Well described by pQCD for
pTnbr gt 50 GeV
Determination of as from RDR Largely independent
of PDFs ?New test of RGE running of as
First timeDemonstrate that as 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 as(MZ)
as from D0 inclusive jet cross section data
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(as4) contributions
  • Larger uncertainty of NLO-only result
  • ? due to increased scale dependence (main
    effect)
  • ? and increased PDF uncertainty (minor effect)

as extraction at large pT requires high
(experimental theory) precision
70
Inclusive Jets x-sensitivity
Jet cross section has access to x-values of
(in LO kinematics)
  • What is the x-value for a given incl. jet data
    point _at_(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 y0)
  • Apply cut on this test-variable to restrict
    accessible x-range
  • Find requirement xtest lt 0.15 removes most
    of the contributions with x gt 0.2 0.3

71
xmin / xmax distributions
Every analysis bin ? one plot Each plot
xmin/xmax distributions Cut on test-variable
xtest lt 0.15? keep 22 (of 110) data
points These have small contributions fromx gt
0.2 0.3
  • Only data points above green line are used

72
M3-jet data / theory
Accepted 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 c2 analysis ? test PDFs
Phys. Lett. B (2011)
  • Agreement between theory and data depends on
  • value of as(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 .
fastNLO Collab., arXiv 1109.1310
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)

Highest pT reach by LHC data
76
Overview xT dependence
fastNLO Collab., arXiv 1109.1310
hadron-hadron collisions only
plot vs. xT 2pT /sqrt(s) Interpretation for
y1y2 0 ? xT x
demonstrate PDF sensitivity
highest xT-reach by Tevatron data
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