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

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

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?

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 (5 10-4 to 5 10-2) NO WAY to use these cross-sections as a good luminosity monitor Lepton+ Lepton-

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

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

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

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)

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

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 = -.199 ± .046 for the ZEUS PDF before including this pseudo-data It becomes λ = -.181 ± .030 after including the pseudodata

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

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

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/0303013) 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

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

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

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

q W/Z H Higgs from qq at LHC

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 !!

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

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 6.6.6 and Chapter 9 for details!)

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

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 6.505 + 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

Note of caution. MRST03 conservative partons DO NOT describe the HERA data for x< 5 10-3 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

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

EXTras after here

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

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%

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 = -.187 ± .046 AFTER λ = -.155 ± .030 35% error reduction

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): MC@NLO: hard emission properly treated at NLO Analytically calculated W+ W- MRST02-PDF used on both HERWIG and MC@NLO weighted mean with uncertainty band Fractional difference:(HERWIG-MC@NLO)/MC@NLO HERWIG with K-Factors: Shape OK, Normalisation: 3.5% higher (HW not purely LO, but also PS)

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): MC@NLO: hard emission properly treated at NLO Analytically calculated W+ W- weighted mean with uncertainty band Fractional difference:(HERWIG-MC@NLO)/MC@NLO HERWIG with K-Factors: Overall is OK, but Shape not well enough modelled

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

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.

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.