1. Why are PDF’s important for ATLAS Durham, Sep 18 th 2006 A M Cooper-Sarkar, Oxford SM CSC notes UK effort Min bias Glasgow, Sheffield W/Z cross-section RAL, Oxford, Liverpool(?) W mass Asymmetry in Z W/Z +jets RAL Dibosons Birmingham, Oxford Gamma + jet Birmingham(?) PDFs Oxford, Glasgow, UCL, RAL

2. Couple of examples of physics processes which could feed into the CSC note.. Think of more during this meeting? How do PDF uncertainties affect BSM physics? high ET jets..contact interactions/extra dimensions Dan Clements How do PDF uncertainties affect SM physics ? Investigate ‘standard candle’ processes- W/Z production which are insensitive to PDF uncertainties to calibrate experiment measure machine luminosity? Alessandro Tricoli What measurements can we make at ATLAS to improve the PDF uncertainty? Think of more during this meeting? PDF CSC note depends on all the rest (plus the jet notes)

3. HERA and the LHC- transporting PDFs to hadron-hadron cross-sections QCD factorization theorem for short- distance inclusive processes where X=W, Z, D-Y, H, high-E T 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 ^ pApA pBpB fafa fbfb x1x1 x2x2 X Knowledge of the PDFs is vital

4. 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 gluon and sea at high-x The valence quarks are poorly known at small-x but it is the sea which matters in this region 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

5. Example of how PDF uncertainties matter for BSM physics – Tevatron jet data were originally taken as evidence for new physics-- iThese figures show inclusive jet cross-sections compared to predictions 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

6. 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 We can translate the current level of PDF uncertainty into the uncertainty on LHC jet cross-sections.

7. 2XD 4XD 6XD SM Such PDF uncertainties on the jet cross sections compromise the potential for discovery. E.G. Dijet cross section potential sensitivity to compactification scale of extra dimensions (M c ) reduced from ~6 TeV to 2 TeV. (Ferrag et al) M c = 2 TeV, no PDF error M c = 2 TeV, with PDF error M c = 6 TeV, no PDF error

8. Can we improve our knowledge of PDFs using ATLAS data itself? Use data at lower E T ( ~ 1) -where new physics is not expected ………..talk of Dan Clements Note that inputting data to a PDF fit needs a prediction for the cross-section which can be easily obtained analytically –true for DIS inclusive cross- section. But NLO jet cross-sections can only be computed by MC and can take 1-2 CPU days to compute. This cannot be done for every iteration of a PDF fit. Recently grid techniques have been developed to include DIS jet cross- sections in PDF fits (ZEUS-JETs fit). This has been extended to p-p jet cross- sections within ATLAS ( Carli et al). This technique has been extended to LHC high-ET jet cross-sections

9. Example of how PDF uncertainties matter for SM physics W/Z production have been considered as good standard candle processes insensitive to PDF uncertainties……? This is true WITHIN a PDFset But how about comparing PDFsets? We actually measure the decay lepton spectra in limited rapidity range. SO.. Generate with HERWIG+k-factors (checked against MC@NLO) using CTEQ6.1M ZEUS_S MRST2001 PDFs with full uncertainties from LHAPDF eigenvectors At y=0 the total uncertainty is ~ ±6% from ZEUS ~ ±4% from MRST01E ~ ±8% from CTEQ6.1 ZEUS to MRST01 central value difference ~5% generator level electronpositron ATLFAST electronpositron Can we improve our knowledge of PDFs using ATLAS data? To improve the situation we NEED to be more accurate than ~4%

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 with early LHC data? Generate data with 4% error using 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 Lepton+ rapidity spectrum data generated with CTEQ6.1 PDF compared to predictions from ZEUS PDF BEFORE including W dataAFTER including W data Lepton+ rapidity spectrum data generated with CTEQ6.1 PDF compared to predictions from ZEUS PDF AFTER these data are included in the fit → the low-x gluon PDF is improved AMCS, A. Tricoli (Hep-ex/0509002) Ongoing work on W/Z for CSC note – see talk of Alessandro Tricoli

11. The uncertainty on the W/Z rapidity distributions is dominated by –- gluon PDF dominated eigenvectors and there could be cancellation in the ratios. Within the SM Z W = Z/(W + + W - ) IS very well known ~1% within a PDF set AND comparing PDF sets BUT A W = (W + - W - )/(W + + W - ) has uncertainty ~13% from valence PDF related eigenvectors generator level ATLFAST Within each PDF set uncertainty in A W, the lepton asymmetry, IS LESS than in the lepton rapidity spectra, e.g about 2% for the asymmetry at y=0, as opposed to about 4% for the lepton rapidity spectra themselves (using MRST2001 PDFerrors) However the PDF sets differ from each other more strikingly- MRST04 and CTEQ6.1 differ by about 13% at y=0! But this is an opportunity to use ATLAS measurements to increase knowledge of the valence PDFs at x~0.005 - see AMCS February06 SM session

12. Prompt photon cross-sections may also be useful to improve the gluon PDF –compare photon pt and η distributions for Cteq61 up and down eigenvector 15 - emphasizing the uncertainties in the high-x gluon (PT > 330 GeV) Ivan Hollins, Birmingham (no talk)

13. New ideas.. Strange quark PDFs and strange/antistrange asymmetry.. See talk of Laura Gilbert SUMMARY Work hard for the CSC notes Think of more new ideas

14. extras

15. And how do PDF uncertainties affect the Higgs discovery potential? g g H t q q W/Z H S Ferrag

16. The uncertainty on the W/Z rapidity distributions is dominated by –- gluon PDF dominated eigenvectors 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~M Z 2 the sea is driven by the gluon- which is far less precisely determined for all x values

17. Because the uncertainties in W+,W- and Z spectra are all coming from the gluon PDF there is cancellation in the ratios A W = (W + - W - )/(W + + W - ) Z W = Z/(W + + W - ) Remaining uncertainty comes from valence PDF related eigenvectors Well Known? Gold plated? Uncertainty in the lepton asymmetry IS LESS than in the lepton rapidity spectra, e.g about 4% for the asymmetry at y=0, as opposed to about 8% for the lepton rapidity spectra themselves (using CTEQ6.1M PDFS) We will actually measure the lepton asymmetry