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Experimental uncertainties in the parton distributions on Higgs production

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Experimental uncertainties in the parton distributions on Higgs production

Stan Bentvelsen

Michiel Botje

Job Thijssen

This is somewhat ‘older’ work of last year

Have not been able to update since…

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 obtained from QCD DGLAP evolution fits to data.

DIS data from fixed target and HERA

Jet cross sections pp colliders

Drell-Yan processes

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)

Q02 = 1.3 GeV2

20 (effectively independent) free parameters

Q2> 4 GeV2

Total 1757 data points, 2min =1980

MRST (Nov 2002)

Q02 = 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)

Botje

Needs update with latest data

‘CTEQ6’ series

Gluon distribution somewhat harder wrt CTEQ5

‘MRST02’ series

Gluon distribution slightly harder wrt MRST2001

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

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

Covariance of any F and G:

Botje:

Store covariance matrix Vijp, parton densities, and all derivatives q/piin tables

Error propagation done by EPDFLIB library

User supplies FORTRAN function with definition F and G in terms of pdf’sas well as derivatives F/q and G/q.

EPDFLIB calculates <FG>

CTEQ, MRS:

Diagonalize the covariance matrix Vijp 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 parameters

CTEQ: sum over 40 sets

MRST: sum over 30 sets

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

Up-valence distribution

As 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

Botje

CTEQ

MRST

Distributions normalized to MRST

MRST

Relative

uncertainty

CTEQ

Botje

At larger Q2 values the uncertainties tend to get smaller

Up-valence distribution at Q2=106 GeV2

Distributions normalized to MRST

MRST

Relative

uncertainty

CTEQ

Botje

Gluon distribution at two scales

Botje

Cteq

MRS

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 x

MRST smallest uncertainties

Distributions normalized to MRST

MRST

Relative

uncertainty

CTEQ

Botje

Gluon distribution at Q2=106 GeV2

Uncertainties at small values of xare getting very small

Distributions normalized to MRST

MRST

Relative

uncertainty

CTEQ

Botje

- ‘gluon-gluon’ luminosity
- Uncertainties remarkable small
- At Mh=100:
- Botje: 5.6%, CTEQ: 4.6%, MRST: 2.2%

- At Mh=1000:
- Botje: ~10%, CTEQ: ~10%, MRST: 5%

Distributions normalized to MRST

MRST

CTEQ

Relative

uncertainty

Botje

Log10(Mh)

- 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

Born

At TevaTron the uncertainties forthis process are larger

NLO

Cm energy=2 TeV

Log10(Mh)

Log10(Mh)

- 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

- Propagation of experimental uncertainties to pdf 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

- Cleary theoretical uncertainties –not treated here, are important
- And probably more important

- Most interesting distributions not looked at so far.
- I’m afraid I don’t have the ‘manpower’ to pursue very far…