1. PDFs from HERA to the LHC March 2005 A.M Cooper-Sarkar
At the LHC high precision (SM and BSM) cross section predictions require precision Parton Distribution Functions (PDFs)
What are the uncertainties on these determinations?
How do PDF uncertainties affect discovery physics?
Investigate ‘standard candle’ processes which are insensitive to PDF uncertainties to
calibrate experiment
measure machine luminosity?
Increase precision on PDFs using LHC SM measurements
W+/W– → gluon and sea quark
Learn more about QCD in extended kinematic regions
small –x
high density

2. Transporting PDFs to hadron-hadron cross-sections
QCD factorization theorem for short-distance inclusive processes
where X=W, Z, D-Y, H, high-ET jets, prompt-γ
and  is known
to some fixed order in pQCD and EW
in some leading logarithm approximation (LL, NLL, …) to all orders via resummation ^ pA pB fa fb x1 x2 X
Need PDFs to calculate any cross-section
Need estimates of the uncertainties on PDFs to estimate the uncertainty on any cross-section

3. LHC is a low-x machine (at least for the early years of running)
Low-x information comes from evolving the HERA data
W/Z production have been considered as good standard candle processes possibly even monitors of the luminosity
But how do the uncertainties on PDFs affect these cross-sections?

4. What has HERA data ever done for us?Z
Pre-HERA W+/W-/Z and
W→ lepton rapidity spectra
~ ± 15% uncertainties !
Why? Because the central rapidity range AT LHC is at low-x ( to )
NO WAY to use these cross-sections as a good luminosity monitor
Lepton+
Lepton-

5. W+ W- Z
Lepton+
Lepton-
Post-HERA W+/W-/Z and
W → lepton rapidity spectra
~ ± 5% uncertainties !
Why? Because there has been a tremendous improvement in our knowledge of the low-x glue and thus of the low-x sea

6. Pre-HERA sea and glue distributions
Post HERA sea and glue distributions

7. 9
The uncertainty on the W/ Z rapidity distributions is dominated by –- gluon PDF dominated eigenvectors
We can decompose the uncertainties on the PDF parameters into eigenvector combinations -the largest uncertainty is along eigenvector 9 –which is dominated by the low- x gluon uncertainty .
Differences are visible within the measurable range of rapidity
It may at first sight be surprising that W/Z distns are sensitive to gluon parameters BUT our experience is based on the Tevatron where Drell-Yan processes can involve valence-valence parton interactions.
At the LHC we will have dominantly sea-sea parton interactions at low-x
And at Q2~MZ2 the sea is driven by the gluon- which is far less precisely determined for all x values

8. How to constrain gluon-PDFs at LHC single Z and W± Production
MRST PDF
NNLO corrections small ~ few%
NNLO residual scale dependence < 1% W±
Symmetric
W+- diff. cross section
Theoretical uncertainties are dominated by PDFs. Note that central values differ by more than the MRST estimate of the error
To improve the situation we NEED to be more accurate than this:~3%
Statistics are no problem we are dominated by systematic uncertainty
PDF Set
ZEUS-S
CTEQ6.1
MRST01
(nb)

9. Look at the lepton rapidity spectra and asymmetry at generator level -TOP
and after passing through ATLFAST –BOTTOM
Generation with HERWIG+k-factors using CTEQ6.1M ZEUS_S MRST2001 PDFs with full uncertainties

10. Study of the effect of including the LHC W Rapidity distributions in global PDF Fits by how much can we reduce the PDF errors?
Generate data with CTEQ6.1 PDF, pass through ATLFAST detector simulation and then include this pseudo-data in the global ZEUS PDF fit.
Central value of prediction shifts and uncertainty is reduced
BEFORE including W data
AFTER including W data
W+ to lepton rapidity spectrum data generated with CTEQ6.1 PDF compared to predictions from ZEUS PDF AFTER these data are included in the fit
W+ to lepton rapidity spectrum data generated with CTEQ6.1 PDF compared to predictions from ZEUS PDF
Specifically the low-x gluon shape parameter λ, xg(x) = x –λ , was
λ = ± .046 for the ZEUS PDF before including this pseudo-data
It becomes λ = ± .030 after including the pseudodata

11. Now look at PDF uncertainties more generally
The general trend of PDF uncertainties is that
The u quark is much better known than the d quark
The valence quarks are much better known than the sea and the gluon at high-x
The valence quarks are poorly known at small-x - but they are not important for physics in this region since the sea quarks are dominant
The sea and the gluon are well known at low-x
The sea is poorly known at high-x, but the valence quarks are more important in this region
The gluon is poorly known at high-x
And it can still be very important for physics e.g.– high ET jet xsecn
need to tie down the high-x gluon

12. Example of how PDF uncertainties matter– Tevatron jet data were originally taken as evidence for new physics-- i
These figures show inclusive jet cross-sections compared to predictions based on theory in the form (data - theory)/ theory
Something seemed to be going on at the highest E_T
And special PDFs like CTEQ4/5HJ were tuned to describe it better- note the quality of the fits to the rest of the data deteriorated.
But this was before uncertainties on the PDFs were seriously considered

13. Today Tevatron jet data are considered to lie within PDF uncertainties
Today Tevatron jet data are considered to lie within PDF uncertainties. (Example from CTEQ hep-ph/ )
We can decompose the uncertainties into eigenvector combinations of the fit parameters-the largest uncertainty is along eigenvector 15 –which is dominated by the high x gluon uncertainty

14. And we can translate the current level of PDF uncertainty into the uncertainty on LHC jet cross-sections. This will impact on any BSM physics signal which can be expressed as a contact term

15. Mc = 2 TeV, no PDF error Mc = 6 TeV, no PDF error Mc = 2 TeV,
E.G. Dijet cross section potential sensitivity to compactification scale of extra dimensions (Mc) reduced from ~6 TeV to 2 TeV. (Ferrag et al)
Mc = 2 TeV,
no PDF error
Mc = 6 TeV,
no PDF error
Mc = 2 TeV,
with PDF error
2XD
4XD
6XD SM

16. And how do PDF uncertainties affect the Higgs discovery potential?
Higgs at LHC
Higgs at Tevatron

17. q
W/Z H
Higgs from qq at LHC

18. Gluon fractional error
HERA now in second stage of
operation (HERA-II)
substantial increase in luminosity
possibilities for new measurements
The good news: PDF uncertainties could get much better before LHC
turn on
Gluon fractional error x
HERA-II projection shows significant improvement to high-x PDF uncertainties
relevant for high-scale physics
at the LHC
 where we expect new physics !!

19. - Inclusive jet cross sections and PDF uncerts. -
HERA-II projection gives significant improvement in all  bins

20. LHC is a low-x machine (at least for the early years of running)
Low-x information comes from evolving the HERA data
Is NLO (or even NNLO) DGLAP good enough?
The QCD formalism may need extending at small-x
BFKL ln(1/x) resummation
High density non-linear effects etc.
(Devenish and Cooper-Sarkar, ‘Deep Inelastic Scattering’, OUP 2004, Section and Chapter 9 for details!)

21. MRST have produced a set of PDFs derived from a fit without low-x data –ie do not use the DGLAP formalism at low-x- called MRST03 ‘conservative partons’. These give VERY different predictions for W/Z production to those of the ‘standard’ PDFs. Z W+ W-
MRST02 W+ Z W-
MRST03

22. Differences persist in the decay lepton spectra and even in their ratio and asymmetry distributions
Reconstructed Electron Pseudo-Rapidity Distributions (ATLAS fast simulation)
200k events of W+- -> e+- generated with HERWIG NLO K factors
Reconstructed e-
Reconstructed e+
6 hours running
MRST02
MRST03
MRST02
MRST03 h h
Reconstructed e+- e- Asymmetry
Reconstructed e- / e+ Ratio
MRST02
MRST03 h
MRST02
MRST03

23. Note of caution. MRST03 conservative partons DO NOT describe the HERA data for x< which is not included in the fit which produces them. So there is no reason why they should correctly predict LHC data at non-central y, which probe such low x regions.
What is really required is an alternative theoretical treatment of low-x evolution which would describe HERA data at low-x, and could then predict LHC W/Z rapidity distributions reliably – also has consequences for pt distributions.
The point of the MRST03 partons is to illustrate that this prediction COULD be very different from the current ‘standard’ PDF predictions. When older standard predictions for HERA data were made in the early 90’s they did not predict the striking rise of HERA data at low-x. This is a warning against believing that a current theoretical paradigm for the behaviour of QCD at low-x can be extrapolated across decades in Q2 with full confidence.
→ The LHC measurements may also tell us something new about QCD

24. Summary
At the LHC high precision (SM and BSM) cross section predictions require precision Parton Distribution Functions
Measure ‘standard candle’ processes which are insensitive to PDF uncertainties
Increase precision on PDFs using LHC measurements
Improve limits for discovery physics
Learn more about QCD in extended kinematic regions
small –x
high density

25. EXTras after here

26. Thus PDF uncertainties will affect our ability to set limits on the presence of new physics in present and future data. Example using
(D0 jet data –SM theory)/SM theory
Introducing a contact interaction at a scale of Λ= 1.6, 2.0, 2.4 TeV
The limit one can derive is only Λ>1.6 TeV- it could be much stronger without PDF uncertainties

27. W -> e n rapidity distributions (I) (A. Cooper-Sarkar, A
W -> e n rapidity distributions (I) (A.Cooper-Sarkar, A.Tricoli, Oxford Univ.)
Experimentally we detect electrons from W decays: W+- -> e+-n
Generator Level
ATLAS
Detector Level
with sel. cuts
CTEQ61
MRST02
ZEUS02
MRST03
e- rapidity
e+ rapidity
e+ - e- asymmetry:
Error boxes
Are the
Full PDF Uncertainties
HERWIG MC Simulations with NLO Corrections
At y=0 the total uncertainty is
~ ±5% from ZEUS-S
~ ±3% from MRST01E
~ ±8% from CTEQ6.1M
ZEUS-S to MRST01E central value difference ~5%
ZEUS-S to CTEQ6.1 central value difference ~3.5%
Asymmetry has small sensitivity to
PDF parameters: PDF uncertainty ~4%
=> SM benchmark
GOAL: syst. exp. error ~3%

28. W -> e n rapidity distributions (II)
Signal vs Background
Effect of including the
W Rapidity distributions
in global PDF Fits:
how much can we reduce
the PDF errors?
W -> tn
Z -> e-e+
Z -> t+t-
e- No Cuts
e+ No Cuts
e- After Sel. Cuts
e+ After Sel. Cuts
Signal:W -> en
(CTEQ6.1)
Generate data with CTEQ6.1 PDF through ATLAS detector simulation and then include this pseudo-data in the global ZEUS PDF fit.
Central value of prediction shifts and uncertainty is reduced:
ZEUS BEFORE including W data
ZEUS AFTER including W data
e+ CTEQ6.1
pseudo-data
e+ CTEQ6.1
pseudo-data
Small Background contamination: ~1%
low-x gluon shape parameter λ, xg(x) = x –λ :
BEFORE λ = ± .046
AFTER λ = ± .030
35% error reduction

29. Can we use Herwig & K-Factors to simulate NLO
Can we use Herwig & K-Factors to simulate NLO ? – seems good enough for rapidity distributions when K-Factors applied on rapidity distributions
HERWIG with K-factors (NLO/LO):
hard emission properly treated at NLO
Analytically
calculated W+ W-
MRST02-PDF used
on both
HERWIG and
weighted mean
with uncertainty band
Fractional
HERWIG with K-Factors: Shape OK, Normalisation: 3.5% higher (HW not purely LO, but also PS)

30. Can we use Herwig & K-Factors to simulate NLO
Can we use Herwig & K-Factors to simulate NLO ? – is it still good for pT distributions when K-Factors applied on rapidity distributions?
HERWIG with K-factors (NLO/LO):
hard emission properly treated at NLO
Analytically
calculated W+ W-
weighted mean
with uncertainty band
Fractional
HERWIG with K-Factors: Overall is OK, but Shape not well enough modelled

31. PDF Weights for CTEQ61, ZEUS02 from MRST02 (calculated using LHAPDFv3)
CTEQ61/MRST02
ZEUS02/MRST02 W- W+ yW

32. Can we use PDF re-weighting to simulate other PDFs - seems OK for RAPIDITY distributions
Events generated with
HERWIG+MRST02
and re-weighted
with CTEQ61
are compared to
HERWIG+CTEQ61 W- W+
CTEQ61
Generated
Re-weighted
from MRST02
Relative difference
between Re-weighted
and Generated
distributions
Weighted mean
on all range
PDF Re-weighting: for rapidity Distributions good to ~0.5%
and no evidence of a y-dependent bias.

33. Can we use PDF re-weighting to simulate other PDFs - seems over all OK for Pt distributions
Events generated with
HERWIG+MRST02
and re-weighted
with CTEQ61
are compared to
HERWIG+CTEQ61
CTEQ61
Generated
Re-weighted
from MRST02
CTEQ61
Generated
Re-weighted
from MRST02 W- W+
Relative difference
between Re-weighted
and Generated
distributions W- W+
Weighted mean
on all range
PDF Re-weighting: for rapidity Distributions overall good to better than 1%
but evidence of a slight Pt-dependent bias.