Reconstruction of Monte Carlo replicas from Hessian parton distributions

Hou, Tie-Jiun; Gao, Jun; Huston, Joey; Nadolsky, Pavel; Schmidt, Carl; Stump, Daniel; Wang, Bo-Ting; Xie, Ke-Ping; Dulat, Sayipjamal; Pumplin, Jon

doi:10.1007/JHEP03(2017)099

Reconstruction of Monte Carlo replicas from Hessian parton distributions

Tie-Jiun Hou
(
- Southern Methodist U.
)
,
Jun Gao
(
- Argonne
)
,
Joey Huston
(
- Michigan State U.
)
,
Pavel Nadolsky
(
- Southern Methodist U.
)
,
Carl Schmidt
(
- Michigan State U.
)

Jul 20, 2016

17 pages

Published in:

JHEP 03 (2017) 099

Published: Mar 20, 2017

e-Print:

1607.06066 [hep-ph]

DOI:

10.1007/JHEP03(2017)099

Report number:

SMU-HEP-16-06

View in:

ADS Abstract Service

reference search57 citations

Citations per year

Abstract: (arXiv)

We explore connections between two common methods for quantifying the uncertainty in parton distribution functions (PDFs), based on the Hessian error matrix and Monte-Carlo sampling. CT14 parton distributions in the Hessian representation are converted into Monte-Carlo replicas by a numerical method that reproduces important properties of CT14 Hessian PDFs: the asymmetry of CT14 uncertainties and positivity of individual parton distributions. The ensembles of CT14 Monte-Carlo replicas constructed this way at NNLO and NLO are suitable for various collider applications, such as cross section reweighting. Master formulas for computation of asymmetric standard deviations in the Monte-Carlo representation are derived. A correction is proposed to address a bias in asymmetric uncertainties introduced by the Taylor series approximation. A numerical program is made available for conversion of Hessian PDFs into Monte-Carlo replicas according to normal, log-normal, and Watt-Thorne sampling procedures.

Note:

21 pages, 10 figures; final JHEP version, extended Sec. 2 to discuss sampling of asymmetric PDF replica distributions with imposed positivity constraints

QCD Phenomenology
Deep Inelastic Scattering (Phenomenology)
quantum chromodynamics
parton: distribution function
numerical methods
numerical calculations: Monte Carlo

References(47)

Figures(21)

[1]

New parton distribution functions from a global analysis of quantum chromodynamics

Sayipjamal Dulat
(
- Xinjiang U. and
- Michigan State U.
)
,
Tie-Jiun Hou
(
- Southern Methodist U.
)
,
Jun Gao
(
- Argonne
)
,
Marco Guzzi
(
- Manchester U.
)
,
Joey Huston
(
- Michigan State U.
)

et al.

- Phys.Rev.D 93 (2016) 3, 033006
•
e-Print:
- 1506.07443
•
DOI:
- 10.1103/PhysRevD.93.033006

[2]

Parton distributions in the LHC era: MMHT 2014 PDFs

L.A. Harland-Lang
(
- University Coll. London and
- Durham U., IPPP
)
,
A.D. Martin
(
- Durham U., IPPP
)
,
P. Motylinski
(
- University Coll. London
)
,
R.S. Thorne
(
- University Coll. London
)

- Eur.Phys.J.C 75 (2015) 5, 204
•
e-Print:
- 1412.3989
•
DOI:
- 10.1140/epjc/s10052-015-3397-6

[3]

Parton distributions for the LHC Run II

NNPDF

Collaboration

•

Richard D. Ball
(
- U. Edinburgh, Higgs Ctr. Theor. Phys. and
- CERN
)

et al.

- JHEP 04 (2015) 040
•
e-Print:
- 1410.8849
•
DOI:
- 10.1007/JHEP04(2015)040

[4]

Combination of measurements of inclusive deep inelastic ${e^{\pm }p}$ scattering cross sections and QCD analysis of HERA data

H1 and
ZEUS

Collaborations

•

H. Abramowicz
(
- Tel Aviv U.
)

et al.

- Eur.Phys.J.C 75 (2015) 12, 580
•
e-Print:
- 1506.06042
•
DOI:
- 10.1140/epjc/s10052-015-3710-4

[5]

The ABM parton distributions tuned to LHC data

S. Alekhin
(
- DESY, Zeuthen and
- Serpukhov, IHEP
)
,
J. Blumlein
(
- DESY, Zeuthen
)
,
S. Moch
(
- DESY, Zeuthen and
- Hamburg U., Inst. Theor. Phys. II
)

- Phys.Rev.D 89 (2014) 5, 054028
•
e-Print:
- 1310.3059
•
DOI:
- 10.1103/PhysRevD.89.054028

[6]

Constraints on large- $x$ parton distributions from new weak boson production and deep-inelastic scattering data

A. Accardi
(
- Hampton U. and
- Jefferson Lab
)
,
L.T. Brady
(
- Jefferson Lab and
- UC, Santa Barbara
)
,
W. Melnitchouk
(
- Jefferson Lab
)
,
J.F. Owens
(
- Florida State U.
)
,
N. Sato
(
- Jefferson Lab
)

- Phys.Rev.D 93 (2016) 11, 114017
•
e-Print:
- 1602.03154
•
DOI:
- 10.1103/PhysRevD.93.114017

[7]

Uncertainties of predictions from parton distribution functions. 2. The Hessian method

et al.

- Phys.Rev.D 65 (2001) 014013
•
e-Print:
- hep-ph/0101032
•
DOI:
- 10.1103/PhysRevD.65.014013

[8]

Implications of hadron collider observables on parton distribution function uncertainties

Walter T. Giele
(
- Fermilab
)
,
Stephane Keller
(
- Fermilab
)

- Phys.Rev.D 58 (1998) 094023
•
e-Print:
- hep-ph/9803393
•
DOI:
- 10.1103/PhysRevD.58.094023

[9]

Parton Distribution Function Uncertainties

e-Print:
- hep-ph/0104052

[10]

Uncertainties of predictions from parton distribution functions. 1. The Lagrange multiplier method

et al.

- Phys.Rev.D 65 (2001) 014012
•
e-Print:
- hep-ph/0101051
•
DOI:
- 10.1103/PhysRevD.65.014012

[11]

Uncertainties on parton distribution functions from the ZEUS NLO QCD fit to data on deep inelastic scattering

Amanda M. Cooper-Sarkar
(
- Oxford U.
)

- J.Phys.G 28 (2002) 2669-2678,
•
e-Print:
- hep-ph/0205153
•
DOI:
- 10.1088/0954-3899/28/10/311

[12]

New generation of parton distributions with uncertainties from global QCD analysis

J. Pumplin
(
- Michigan State U.
)
,
D.R. Stump
(
- Michigan State U.
)
,
J. Huston
(
- Michigan State U.
)
,
H.L. Lai
(
- Michigan State U.
)
,
Pavel M. Nadolsky
(
- Michigan State U.
)

et al.

- JHEP 07 (2002) 012
•
e-Print:
- hep-ph/0201195
•
DOI:
- 10.1088/1126-6708/2002/07/012

[13]

PDF Uncertainties in WH Production at Tevatron

Pavel M. Nadolsky
(
- Michigan State U. and
- Southern Methodist U.
)
,
Z. Sullivan
(
- Argonne and
- Fermilab
)

- eConf C010630 (2001) P510
•
e-Print:
- hep-ph/0110378

[14]

Neural network parametrization of deep inelastic structure functions

Stefano Forte
(
- INFN, Rome3
)
,
Lluis Garrido
(
- Barcelona U., ECM
)
,
Jose I. Latorre
(
- Barcelona U., ECM
)
,
Andrea Piccione
(
- INFN, Genoa and
- Genoa U.
)

- JHEP 05 (2002) 062
•
e-Print:
- hep-ph/0204232
•
DOI:
- 10.1088/1126-6708/2002/05/062

[15]

Neural network determination of parton distributions: The Nonsinglet case

NNPDF

Collaboration

•

Luigi Del Debbio
(
- Edinburgh U.
)

et al.

- JHEP 03 (2007) 039
•
e-Print:
- hep-ph/0701127
•
DOI:
- 10.1088/1126-6708/2007/03/039

[16]

A Determination of parton distributions with faithful uncertainty estimation

NNPDF

Collaboration

•

Richard D. Ball
(
- Edinburgh U. and
- Bohr Inst.
)

et al.

- Nucl.Phys.B 809 (2009) 1-63,
- Nucl.Phys.B 816 (2009) 293 (erratum)
•
e-Print:
- 0808.1231
•
DOI:
- 10.1016/j.nuclphysb.2008.09.037

[17]

Parton distributions with LHC data

Richard D. Ball
(
- Edinburgh U.
)
,
Valerio Bertone
(
- Freiburg U. and
- CERN
)
,
Stefano Carrazza
(
- INFN, Milan and
- Milan U.
)
,
Christopher S. Deans
(
- Edinburgh U.
)
,
Luigi Del Debbio
(
- Edinburgh U.
)

et al.

- Nucl.Phys.B 867 (2013) 244-289
•
e-Print:
- 1207.1303
•
DOI:
- 10.1016/j.nuclphysb.2012.10.003

[18]

Study of Monte Carlo approach to experimental uncertainty propagation with MSTW 2008 PDFs

G. Watt
(
- CERN
)
,
R.S. Thorne
(
- University Coll. London
)

- JHEP 08 (2012) 052
•
e-Print:
- 1205.4024
•
DOI:
- 10.1007/JHEP08(2012)052

[19]

A meta-analysis of parton distribution functions

- JHEP 07 (2014) 035
•
e-Print:
- 1401.0013
•
DOI:
- 10.1007/JHEP07(2014)035

[20]

An Unbiased Hessian Representation for Monte Carlo PDFs

Stefano Carrazza
(
- Milan U. and
- INFN, Milan
)
,
Stefano Forte
(
- Milan U. and
- INFN, Milan
)
,
Zahari Kassabov
(
- Turin U. and
- INFN, Turin and
- Milan U. and
- INFN, Milan
)
,
Jose Ignacio Latorre
(
- Barcelona U., ECM
)
,
Juan Rojo
(
- Oxford U.
)

- Eur.Phys.J.C 75 (2015) 8, 369
•
e-Print:
- 1505.06736
•
DOI:
- 10.1140/epjc/s10052-015-3590-7

[21]

Specialized minimal PDFs for optimized LHC calculations

Stefano Carrazza
(
- Milan U. and
- INFN, Milan and
- CERN
)
,
Stefano Forte
(
- Milan U. and
- INFN, Milan
)
,
Zahari Kassabov
(
- Milan U. and
- INFN, Milan and
- Turin U. and
- INFN, Turin
)
,
Juan Rojo
(
- Oxford U., Theor. Phys.
)

- Eur.Phys.J.C 76 (2016) 4, 205
•
e-Print:
- 1602.00005
•
DOI:
- 10.1140/epjc/s10052-016-4042-8

[22]

Reweighting NNPDFs: the W lepton asymmetry

NNPDF

Collaboration

•

Richard D. Ball
(
- Edinburgh U.
)

et al.

- Nucl.Phys.B 849 (2011) 112-143,
- Nucl.Phys.B 854 (2012) 926-927 (erratum),
- Nucl.Phys.B 855 (2012) 927-928 (erratum)
•
e-Print:
- 1012.0836
•
DOI:
- 10.1016/j.nuclphysb.2011.03.017

[23]

Reweighting and Unweighting of Parton Distributions and the LHC W lepton asymmetry data

Richard D. Ball
(
- Edinburgh U.
)
,
Valerio Bertone
(
- Freiburg U.
)
,
Francesco Cerutti
(
- Barcelona U., ECM
)
,
Luigi Del Debbio
(
- Edinburgh U.
)
,
Stefano Forte
(
- Milan U. and
- INFN, Milan
)

et al.

- Nucl.Phys.B 855 (2012) 608-638
•
e-Print:
- 1108.1758
•
DOI:
- 10.1016/j.nuclphysb.2011.10.018

[24]

A compression algorithm for the combination of PDF sets

Stefano Carrazza
(
- Milan U. and
- INFN, Milan
)
,
José I. Latorre
(
- Barcelona U., ECM
)
,
Juan Rojo
(
- Oxford U., Theor. Phys.
)
,
Graeme Watt
(
- Durham U., IPPP
)

- Eur.Phys.J.C 75 (2015) 474
•
e-Print:
- 1504.06469
•
DOI:
- 10.1140/epjc/s10052-015-3703-3

[25]

PDF4LHC recommendations for LHC Run II

Jon Butterworth
(
- University Coll. London
)
,
Stefano Carrazza
(
- INFN, Milan and
- Milan U.
)
,
Amanda Cooper-Sarkar
(
- Oxford U.
)
,
Albert De Roeck
(
- CERN and
- U. Antwerp (main)
)
,
Joel Feltesse
(
- CEA, DSM, Saclay
)

et al.

- J.Phys.G 43 (2016) 023001
•
e-Print:
- 1510.03865
•
DOI:
- 10.1088/0954-3899/43/2/023001

1-25 of 47
1
2
25 / page