experimental uncertainties in the parton distributions on higgs production
DESCRIPTION
Experimental uncertainties in the parton distributions on Higgs production. Stan Bentvelsen Michiel Botje Job Tijssen. For proper error estimation on hadronic cross sections we need the uncertainty on the PDF’s: Propagation of uncertainties on experimental data to the fitted PDF’s - PowerPoint PPT PresentationTRANSCRIPT
Experimental uncertainties in the parton distributions on Higgs production
Stan BentvelsenMichiel BotjeJob Tijssen
Parton parameterizations For proper error estimation on
hadronic cross sections we need the uncertainty on the PDF’s: Propagation of uncertainties on
experimental data to the fitted PDF’s Statistical uncertainties and
(correlated) systematic effects Uncertainties in the theoretical
description of the fit procedure Flavour thresholds, s Scales uncertainties Nuclear effects Higher twist, …
A number of groups have published the PDF fits with propagated experimental uncertainties: Botje (Eur Phys J C14 (dec 1999)) CTEQ (J. Pumplin et al, hep-ph/0201195) MRST (A. Martin et al, hep-ph/0211080)
Alekhin (S. Alekhin, hep-ph/0011002) Fermi2001 (Giele et al, hep-ph/0104052)
Theoretical uncertainties not treated here
PDF’s cannot be calculated from theory and are obtained from QCD DGLAP evolution fits to data.
DIS data from fixed target and HERA
Jet cross sections pp colliders Drell-Yan processes
The hadronic cross section
The uncertainty due to the gluon distribution (error propagation)
Have to take all correlations of the gluon distribution into account
Higgs production SM Higgs production
dominated by gluon fusion:
Zeroth width approximation
PDF uncertainties In the past:
Errors associated with parton densities were often determined from the spread of different parton distribution sets.
By no means representation of experimental and theoretical uncertainties
Relatively recently: Error propagation in global
QCD fits (increasing accuracy HERA/Tevatron data)
Based on: Least squares minimization
and linear error propagation (Monte Carlo integration
techniques)
Available pdf data sets Botje (Dec 1999)
Q02 = 4 GeV2, 28 free parameters
X>10-3
Q2> 3 GeV2
W2>7 GeV2
Total 1578 data points, 2min=1537
Structure function data only (no pp jet data, no W± asymmetry) Not including ‘latest’ HERA structure functions
CTEQ (Dec 2002) Q0
2 = 1.3 GeV2
20 (effectively independent) free parameters Q2> 4 GeV2
Total 1757 data points, 2min =1980
MRST (Nov 2002) Q0
2 = 1 GeV2
15 (effectively independent) free parameters, Q2> 2 GeV2
Total 2097 data points, 2min ~2267
All parameterizations use NLO DGLAP evolution inMS-scheme.CTEQ and MRST also providepdf’s in DIS scheme, as well asleading order (event generators)
‘CTEQ6’ seriesGluon distribution
somewhat harder wrt CTEQ5
‘MRST02’ seriesGluon distribution slightly
harder wrt MRST2001
BotjeNeeds update with latest data
Correlations between the mutual pdf’s important. The largest origin of the correlations are the momentum sum rules
Uncertainty on gluon- and quark integrals separately much larger than on the sum of the two (Q2=4 GeV2):
Also large correlation of gluon distribution and value of s. The value of s is kept fixed in the QCD evolution, at values obtained
from precision e+e- collisions. As consistency checks the fits are repeated for varying s Quoted obtained errors on s from these checks range between 1 – 6 %
In this study uncertainties on s are ignored
Correlations
Error estimates on PDF’s Input parameters pi from least squares 2 minimalization
Covariance matrix of input parameters pi obtained from expansion around minimim 2
Two methods to propagate the experimental systematic uncertainties:(Botje: hep-ph/0110123) Covariance matrix method (Hessian method)
CTEQ, MRS, H1, … Rigorous statistical technique
Assume errors are gaussian distributed, use linear approximation Exact in 1st order approximation
Offset method Botje, ZEUS. Offset data by systematic error, redo fit, add deviations in quadrature
Gives a conservative error of uncertainties
Using uncertainties Covariance of any F and G:
Botje: Store covariance matrix Vij
p, parton densities, and all derivatives q/pi in tables
Error propagation done by EPDFLIB library User supplies FORTRAN function with definition F and G in terms of pdf’s
as well as derivatives F/q and G/q. EPDFLIB calculates <FG>
CTEQ, MRS: Diagonalize the covariance matrix Vij
p using ‘rotated’ parameters zi Uncertainty on F and G simplifies to
In order to sample quadratic behavior 2 accurately, pdf sets are determined for both zi+z, zi-z : (F+
I,F-I)
Store set of 2Np pdf’s for systematic uncertainties. Uncertainty on F corresponds to:
pi: free fit paramete
rs
CTEQ: sum over 40 setsMRST: sum over 30 sets
Error definition with tolerance Uncertainty on quantity F given by
Deviation from 2=1 by CTEQ and MRS groups, by the factor:
CTEQ: produce pdf sets with tolerance T2=100 MRST: produce pdf sets with tolerance T2=50
Rather arbitrary definition to get the standard deviations of a quantity Motivated by investigation probabilities of individual data sets
Botje: produce sets for statistical and systematic errors separately Tolerance T2=1 for statistical uncertainty Added in quadrature to systematic uncertainty
Tolerance T2= 2
Example: valence distributions
BotjeCTEQMRST
Up-valence distributionAs function of log10(x) at Q2=10
GeV2
Relative uncertainties large at very small and very large values of x
Region around x=10-2 where the three sets are not compatible at 1
Relativeuncertainty
Distributions normalized to
MRST
MRSTCTEQBotje
Up-valence at high Q2 value At larger Q2 values the
uncertainties tend to get smaller
Up-valence distribution at Q2=106 GeV2
Relativeuncertainty
Distributions normalized to
MRST
MRSTCTEQBotje
Uncertainty on gluon distribution
Gluon distribution at two scales
Relativeuncertainty
Distributions normalized to
MRST
MRSTCTEQBotje
BotjeCteqMRS
Gluon distribution at Q2=10 GeV2
Larger uncertainties (note the scale)Botje deviates from MRST/CTEQ at low x(cf data cut at x>10-3)Very typical small uncertainty around x~0.2, rapid increase for larger xMRST smallest uncertainties
Gluon at large Q
Relativeuncertainty
Distributions normalized to
MRST
MRSTCTEQBotje
Gluon distribution at Q2=106 GeV2
Uncertainties at small values of xare getting very small
Higgs production cross section
Relativeuncertainty
Distributions normalized to
MRST
MRSTCTEQBotje
Higgs production cross sectionas function of log10(MH)Or rather the ‘gluon-gluon’ luminosityUncertainties remarkable smallAt Mh=100:
Botje: 5.6%, CTEQ: 4.6%, MRST: 2.2%At Mh=1000:
Botje: ~10%, CTEQ: ~10%, MRST: 5%
Log10(Mh)
Higgs production uncertainty Full check by interfacing to HiGlu package with pdf sets
NLO ggHiggs production in MS-scheme Matches the PDF sets scheme evolution
Cross section ratio NLO to LO given by K-factor (1.5-1.7) Pdf uncertainty very similar for LO and NLO
At TevaTron the uncertainties forthis process are larger
Log10(Mh)
BornNLO
Log10(Mh)
Cm energy=2 TeV
Rapidity distribution At large rapidity the
uncertainty is largest, and is somewhat larger at central rapidity
Select range in rapidity -1 < y < 1
Redo the error analysis on gg:
Uncertainty increases From 4-6% To 6-9%Mh=115 GeV
y
All y-1<y<1
Rapidity y
WW production Other luminosity functions readily be
obtained Example of W+ and W- production at
LHC Uncertainty fairly constant over range
s MRS smallest uncertainty, -1-2% Botje and CTEQ in range 4-5%
qqW+
qqW-
Correlation between Higgs
and W production,
~0.6
Conclusions Propagation of experimental uncertainties to pdf are
getting available Correlations and systematic experimental uncertainties are
important and are taken into account
Definition of the uncertainty on pdf’s not straightforward cf ‘tolerances’ MRST/CTEQ
Uncertainty on ggH process remarkably small All are below 6% for mH=115 GeV, upto 2%.
Cleary theoretical uncertainties –not treated here, are important
And probably more important