[PPT] - Combination and PDF Fit tools Used in ATLAS. A. Cooper-Sarkar, S. PowerPoint Presentation

SLIDE 1

Combination and PDF Fit tools Used in ATLAS.

A. Cooper-Sarkar, S. Glazov, V. Radescu, A. Sapronov,
S. Whitehead.
Data Combination.
QCD Fit Programs.
Including LHC data in QCD Fits.

CERN, April 2011 1

SLIDE 2

Combination of Data

H1 and ZEUS

Q2 / GeV2 σr,NC(x,Q2)

x=0.0002 x=0.002 x=0.008 x=0.032 x=0.08 x=0.25

HERA I NC e+p ZEUS H1

+

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1 10 10

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Several combination tools on the market: BLUE, HERA combination package. HERA package is being used in ATLAS for e and µ channel data combination. HERA package takes into account correlated systematic errors, corrects for biases due to multiplicative nature of errors.

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QCD Fit Packages and Settings

Evolution code: publicly available QCDNUM package, version

17.00 (http://www.nikef.nl/h24/qcdnum/index.html). Active exchange with M. Botje.

Two independent fitting packages, originated and actively

developed within H1 and ZEUS collaborations.

Different approaches to experimental uncertainties: Hessian,
ffset, adding in quadrature.
Error propagation for PDFs: Hessian and MC method.
NLO and NNLO evolution.
FastNLO and APPLGRID interfaces.
Different codes for heavy flavor treatment: RT from R. Thorne,

flavours of ACOT from F. Olness.

Fits to DIS, jet and DY data.

HERA tools are more used in ATLAS, but some developers, e.g. orig- inal developer of the H1 fitter E. Perez, are in CMS. 3

SLIDE 4

Refernce: HERAPDF1.5 fit

H1 and ZEUS

HERA Inclusive Working Group August 2010

x = 0.00005, i=21 x = 0.00008, i=20 x = 0.00013, i=19 x = 0.00020, i=18 x = 0.00032, i=17 x = 0.0005, i=16 x = 0.0008, i=15 x = 0.0013, i=14 x = 0.0020, i=13 x = 0.0032, i=12 x = 0.005, i=11 x = 0.008, i=10 x = 0.013, i=9 x = 0.02, i=8 x = 0.032, i=7 x = 0.05, i=6 x = 0.08, i=5 x = 0.13, i=4 x = 0.18, i=3 x = 0.25, i=2 x = 0.40, i=1 x = 0.65, i=0

Q2/ GeV2 σr,NC(x,Q2) x 2i

+

HERA I+II NC e+p (prel.) Fixed Target HERAPDF1.5

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3

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1

1 10 10 2 10 3 10 4 10 5 10 6 10 7 1 10 10

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Fit to the combined preliminary inclusive HERA data, complete dataset.
Good agreement between data and NLO QCD.

How HERA PDFs compare to pp observables and how they can be improved by them ?

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SLIDE 5

HERAPDF1.5f fit

0.2 0.4 0.6 0.8 1

4

10

3

10

2

10

1

10 1 0.2 0.4 0.6 0.8 1 HERAPDF1.5 (prel.)

exp. uncert.

model uncert. parametrization uncert.

x xf

2

= 10 GeV

2

Q

v

xu

v

xd 0.05) × xS ( 0.05) × xg (

HERAPDF Structure Function Working Group March 2011

H1 and ZEUS HERA I+II 10 parameter PDF Fit

0.2 0.4 0.6 0.8 1 0.2 0.4 0.6 0.8 1

4

10

3

10

2

10

1

10 1 0.2 0.4 0.6 0.8 1 HERAPDF1.5f (prel.)

exp. uncert.

model uncert. parametrization uncert. HERAPDF1.5 (prel.)

x xf

2

= 10 GeV

2

Q

v

xu

v

xd 0.05) × xS ( 0.05) × xg (

HERAPDF Structure Function Working Group March 2011

H1 and ZEUS HERA I+II 14 parameter PDF Fit

0.2 0.4 0.6 0.8 1

Fits parameterise x ¯

U, x ¯ D, xuv, xdv and xg using x f(x) = AxB(1 − x)C(1 + Dx + Ex2) form.

Recently fits were extended from 10 to 14 parameters, by relaxing

assumptions that Buv = Bdv, using extra term for uv and flexible parameterisation for the gluon: xg(x) = AxB(1 − x)C − A′xB′(1 − x)25. → similar overall errors, more flexible shapes (important for NNLO).

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SLIDE 6

Tevatron yZ data

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Fit including tevatron yZ data

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Tevatron yZ data impact on PDF errors

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Fit Including Tevatron W data

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Tevatron W data impact on PDF errors

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SLIDE 11

LHCb W data in the fit

Fit including LHCb lepton asymmetry data gives χ2/dof = 7.9/5. Fit stays within HERAPDF error bands. HERAPDF1.5 (exp) HERAPDF1.5+LHCb (exp) → some improvement for dv at low x. 11

SLIDE 12

CMS yZ data

CMS data does not shift fit outside HERAPDF1.5 error band, but does behave as Tevatron data. The reduction of PDF uncertainties is marginal. 12

SLIDE 13

ATLAS and CMS W Lepton Asymmetry

0.5 1 1.5 2 2.5 0.05 0.1 0.15 0.2 0.25 0.3 0.5 1 1.5 2 2.5 0.05 0.1 0.15 0.2 0.25 0.3

ATLAS muon asymmetry HERAPDF1.5(prel.) total uncert.

0.5 1 1.5 2 2.5 0.05 0.1 0.15 0.2 0.25 0.3 0.5 1 1.5 2 2.5 0.05 0.1 0.15 0.2 0.25 0.3 0.5 1 1.5 2 2.5 0.05 0.1 0.15 0.2 0.25 0.3 0.5 1 1.5 2 2.5 0.05 0.1 0.15 0.2 0.25 0.3

Pt,e > 20 GeV, Pt,miss > 25 GeV

0.5 1 1.5 2 2.5 0.05 0.1 0.15 0.2 0.25 0.3 0.5 1 1.5 2 2.5 0.05 0.1 0.15 0.2 0.25 0.3

CMS lepton asymmetry HERAPDF1.5(prel.) total uncert.

0.5 1 1.5 2 2.5 0.05 0.1 0.15 0.2 0.25 0.3 0.5 1 1.5 2 2.5 0.05 0.1 0.15 0.2 0.25 0.3 0.5 1 1.5 2 2.5 0.05 0.1 0.15 0.2 0.25 0.3 0.5 1 1.5 2 2.5 0.05 0.1 0.15 0.2 0.25 0.3

Pt,e > 25 GeV

LO fits with k-factors calculated using MCFM, taking into

account different cuts.

HERAPDF1.5 provides good description of the CMS data with

χ2/dof = 6.5/12 and not so good of ATLAS with χ2/dof = 30/11. 13

SLIDE 14

Fit to ATLAS W asymmetry data

14 parameters fit, 6 free parameters for valence quarks,

reasonable description of ATLAS asymmetry shape, partial χ2/dof = 16/11.

Uncertainty estimated using MC method.

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SLIDE 15

Fits with LHC W asymmetry data

CMS data keep the central line within HERAPDF1.5 error band, χ2/dof = 3.7/12 is extremely good. For ATLAS data fit is pulled somewhat outside the bands, the χ2/dof = 16/11 is Ok. ATLAS and CMS pull uv in opposite direction. 15

SLIDE 16

Fit to HERA+Tevatron+LHC data

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SLIDE 17

Impact of LHC data on PDF errors

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Including HERA Jets

0.2 0.4 0.6 0.8 1

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1

10 1 0.2 0.4 0.6 0.8 1 HERAPDF1.5f (prel.) )

Z

(M

s

α free

exp. uncert.

model uncert. parametrization uncert.

x xf

2

= 10 GeV

2

Q

v

xu

v

xd 0.05) × xS ( 0.05) × xg (

HERAPDF Structure Function Working Group March 2011

H1 and ZEUS HERA I+II PDF Fit

0.2 0.4 0.6 0.8 1 0.2 0.4 0.6 0.8 1

4

10

3

10

2

10

1

10 1 0.2 0.4 0.6 0.8 1 HERAPDF1.6 (prel.) )

Z

(M

s

α free

exp. uncert.

model uncert. parametrization uncert.

x xf

2

= 10 GeV

2

Q

v

xu

v

xd 0.05) × xS ( 0.05) × xg (

v

xu

v

xd 0.05) × xS ( 0.05) × xg (

HERAPDF Structure Function Working Group March 2011

H1 and ZEUS HERA I+II PDF Fit with Jets

0.2 0.4 0.6 0.8 1

Free αS , inclusive Free αS , + jets

Freeing αS in fits increases xg(x) uncertainty at

low x.

Inclusing jets allows to reduce uncertainty back.
αS (MZ) = 0.1202±0.0013(exp)±0.0007(mod)±

0.0012(had)+0.0045

−0.0036(th).

)

Z

(M

S

α 0.114 0.116 0.118 0.12 0.122 0.124 0.126

min 2

χ

2

χ

5 10 15 20

H1 and ZEUS (prel.) HERAPDF1.5f HERAPDF1.6

HERAPDF Structure Function Working Group March 2011

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SLIDE 19

Tevatron jets

Tevatron jet data provides

additional constraints on gluon at high x.

HERAPDF1.5

provides “reasonable” description

f the data.
Putting the data in the fit

gives χ2/dof = 113/76.

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SLIDE 20

ATLAS jet data

| < 0.3 y |

1.5 1 0.5 [GeV]

T

p

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| < 2.1 y 1.2 < |

1.5 1 0.5 [GeV]

T

p

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| < 1.2 y 0.8 < |

1.5 1 0.5

| < 0.8 y 0.3 < |

1.5 1 0.5

Ratio wrt CTEQ 6.6

Preliminary ATLAS

statistical error Data with uncertainties Systematic

=7 TeV s

1

dt=37 pb L

∫

jets, R=0.4

t

anti-k

Non-pert. corr. × NLO pQCD CTEQ 6.6 MSTW 2008 NNPDF 2.1 HERAPDF 1.5

| < 2.8 y 2.1 < |

1.5 1 0.5

| < 3.6 y 2.8 < |

1.5 1 0.5 [GeV]

T

p

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| < 4.4 y 3.6 < |

1.5 1 0.5 [GeV]

T

p

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Ratio wrt CTEQ 6.6

Preliminary ATLAS

statistical error Data with uncertainties Systematic

=7 TeV s

1

dt=37 pb L

∫

jets, R=0.4

t

anti-k

Non-pert. corr. × NLO pQCD CTEQ 6.6 MSTW 2008 NNPDF 2.1 HERAPDF 1.5

New ATLAS measurement based on complete 2010 data set,

extending to forward and lower pt regions, with improved JES uncertainty.

Data tend to be below CTEQ6.6 prediction, best agreement with

HERAPDF1.5, however theory/experimental errors are sizable. 20

SLIDE 21

Summary

HERAPDF fits provide basis for QCD analysis with consistent,

high accuracy input data having well understood systematic uncertainties and minimal theoretical assumptions.

The set of tools within the framework, from various methods of

PDF error estimates to production of LHAPDF grid files are available for fast feedback to data analysers.

Extending dataset to p ¯

p data from Tevatron is important to improve accuracy for d-type quarks. W asymmetry data provide stronger constraints, however Z data are needed to separate light sea/valence quark effects.

Early LHC data already have some impact on PDF uncertainties

at small x. However, inclusion of ATLAS compared to CMS W lepton asymmetry data pulls PDFs in opposite direction.

ATLAS and CMS jet data should provide additional constraints

for the gluon density at high x. 21

SLIDE 22

Extras

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χ2 definition

Combination and QCD analysis are based on ∆χ2 minimization, taking into account stat. and systematic biases. Definition of χ2:

χ2

exp (m, b) = i

mi −

j γi jmib j − µi2

δ2

i,stat µi

mi −

j γi jmib j

+
δi,uncor mi2 +

j b2 j.

Correlated error can be treated using Hessian, offset methods and

be added in quadrature.

For Hessian fits, correlated errors nuisance parameters bj modify

predicted values mi.

Statistical error is re-calculated using expected number of events,

uncorrelated systematic errors re-calculated using expected cross sections. 23

SLIDE 24

HERAPDF Fit Settings

Input: combined HERA-I data for e±p NC and CC scattering.
∆χ2 = 1, treat experimental errors as uncorrelated, 3 procedural

uncertainties with offset method.

NLO evolution, RT-VFNS for charm and bottom, αS = 0.1176.
Evolution starting scale Q2 = 1.9 GeV2, below mmodel

c

= 1.4 GeV. Start fitting data at Q2

min = 3.5 GeV2.

Fitted PDFs are xg, xuv, xdv(x), x ¯

U, x ¯ D where x ¯ U = x¯ u and x ¯ D = x ¯ d + x¯ s at the starting scale. For the strange, x¯ s = fsx ¯ D with fs = 0.31 is assumed.

Standard parameterisation form

x f(x) = AxB(1 − x)C(1 + ǫ √x + Dx + Ex2) with only significant ǫ, D and E terms kept.

Ag, Auv, Adv fixed by sum rules. Extra constraints for small x

behaviour of d and u-type quarks: Buv = Bdv, B ¯

U = B ¯ D,

A ¯

U = A ¯ D(1 − fs)

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PDF uncertainties

0.2 0.4 0.6 0.8 1

2

=10 GeV

2

Q

v

xu

0.2 0.4 0.6 0.8 1

0.2

0.2

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1

10 1

x

0.2

0.2

0.2

0.2

0.2 0.4 0.6 0.8 1 0.2 0.4 0.6 0.8 1

2

=10 GeV

2

Q

v

xd

HERAPDF1.0

exp. uncert.

model uncert. param uncert.

0.2 0.4 0.6 0.8 1

0.2

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x

0.2

0.2

0.2

0.2

0.2 0.4 0.6 0.8 1 1 2 3 4 5 6 7 8

sea

xu

sea

xd

sea

xs

sea

xc 2

=10 GeV

2

Q xS

1 2 3 4 5 6 7 8

0.2

0.2

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1

10 1

x

0.2

0.2

0.2

0.2

1 2 3 4 5 6 7 8 2 4 6 8 10 12 14 16

2

=10 GeV

2

Q xg

2 4 6 8 10 12 14 16

0.2

0.2

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10 1

x

0.2

0.2

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H1 and ZEUS

HERAPDF1.0 — NLO QCD analysis

f

the combined HERA data. Separation of experimental, model and parameterisation uncertainties. Accurate xS and xg at low x due to precise measurement

f F2.

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SLIDE 26

Model and Parameterisation variations

Model variations are:

Change in strangeness fraction from fs = 0.31 to 0.23 and 0.38.
Change of Q2

min cut from Q2 min = 3.5 GeV2 to 2.5 GeV2 and

5.0 GeV2.

Change of mmodel

c

from 1.4 GeV to 1.35 and 1.6 GeV.

Change of mmodel

b

from 4.75 GeV to 4.3 and 5.0 GeV. they are evaluated as by adding in quadrature + and − deviations from the central fit. Parameterisation variations are:

Change of the evolution starting scale to Q2

0 = 1.5 GeV2 using

flexible gluon parameterisation term, xg(x) = AgxBg(1 − x)Cg − A′

gxB′

g(1 − x)25.

Change of Q2

0 to 2.5 GeV2 with increase of mmodel c

= 1.6 GeV.

Extra parameters Duv, D ¯

U and D ¯ D.

they are evaluated by building envelope of maximal deviations. 26