1. Low-x and PDF studies at LHC Sept 2008 A M Cooper-Sarkar, Oxford At the LHC high precision (SM and BSM) cross section predictions require precision Parton Distribution Functions (PDFs) How do PDF Uncertainties affect SM physics W/Z production, Higgs profuction How do PDF uncertainties affect BSM physics? - sometimes it will only affect precision e.g. Z’ in high-mass Drell-Yan -sometimes it will compromise discovery e,g, contact interactions in highET jet production What measurements can we make at LHC to improve the PDF uncertainty? Do we even understand QCD a small-x?

2. First pp collisions in Sep 2008  s = 10 TeV Spring ’09  s = 14 TeV at Low luminosity L= 1 fb -1 /year (  10 32 cm -2 s -1 ) End ’09  s = 14 TeV at High luminosity L= 10 fb -1 /year (  10 33 cm -2 s -1 ) Process  (nb) Ev./10fb -1 W  e 15~10 8 Z  e + e  1.5~10 7 t tbar0.8~10 7 jets (p T >200 GeV) 100~10 9 LHC is W, Z, top … factory Large statistics for SM processes  SM precision physics (EW, top-,b-physics, multijets…) Big potential for new physics (Higgs, Extra Dimensions, SUSY…) So when is it all going to happen?

3. The Standard Model is not as well known as you might think pApA pBpB fafa fbfb x1x1 x2x2 X The central rapidity range for W/Z production AT LHC is at low-x (5 ×10 -4 to 5 ×10 -2 ) particularly in the QCD sector and particlarly in the non-perturbative part of the QCD sector At the LHC high precision (SM and BSM) cross section predictions require precision Parton Distribution Functions (PDFs

4. Pre HERAPost HERA ZEUS data Look at predictions for W/Z rapidity distributions Pre- and Post-HERA Why such an improvement ? It’s due to the improvement in the low-x gluon At the LHC the q- qbar which make the boson are mostly sea-sea partons at low-x And at Q2~MZ2 the sea is driven by the gluon

5. 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

6. Not just statistical improvement. Each experiment can be used to calibrate the other since they have rather different sources of experimental systematics Before combination the systematic errors are ~3 times the statistical for Q2< 100 After combination systematic errors are < statistical → very consistent data input HERAPDFs use Δχ2=1 Recent development: Combining ZEUS and H1 data sets

7. This is post HERA but just one experiment (ZEUS) This is post HERA using the new (2008) HERA combined PDF fit However there is still the possibility of trouble with the formalism at low-x

8. MRST PDF NNLO corrections small ~ few% NNLO residual scale dependence < 1% W/Z production have been considered as good standard candle processes with small theoretical uncertainty. PDF uncertainty is THE dominant contribution and most PDF groups quote uncertainties <~5% (but note HERAPDF ~1-2%) BUT the central values differ by more than some of the uncertainty estimates. Experimental errors are now very small- but how about model uncertainty? Some differences are not just choices, massless heavy quark treatments won’t do. PDF set σ W+ B W →lν (nb) σ W- B W →lν (nb) σ z B z →ll (nb) ZEUS-200511.87±0.458.74±0.311.97±0.06 MRST0111.61±0.238.62±0.161.95±0.04 HERAPDF12.13±0.139.13±0.152.01±0.025 CTEQ6512.47±0.479.14±0.362.03±0.07 MRST0411.748.711.97 CTEQ6111.61±0.568.54±0.431.89±0.09

9. Can we improve the situation 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 (actually use the decay lepton spectra) Central value of prediction shifts and uncertainty is reduced e+ rapidity spectrum and gluon PDF BEFORE these data are included in the PDF fit BEFORE including W dataAFTER including W data e+ rapidity spectrum and gluon PDF AFTER these pseudodata are included in the PDF fit Gluon PDF uncertainties are reduced

10. The uncertainty on the W + W - and Z rapidity distributions are all dominated by gluon PDF uncertainty BUT there is cancellation of this uncertainty in the ratio Z W = Z/(W + + W - ) the PDF uncertainty on this ratio is ~1% and there is agreement between PDFsets cteq66 HERAPDF0.1 Mrst04(1)

11. But the same is not true for the W asymmetry Aw = (W+ - W-)/(W+ + W-) the PDF uncertainty on this ratio is reduced compared to that on the W rapidity spectra within any one PDF set BUT there is not good agreement between PDF sets- a difference in valence PDFs is revealed Dominantly, at LO Aw= (u dbar – d ubar) (u dbar + d ubar) And ubar = dbar = qbar at small x So Aw~ (u – d) = (uv – dv) (u + d) (uv + dv + 2 qbar ) Actually this pretty good even quantitatively The difference in valence PDFs you see here explains the difference in AW x- range affecting W asymmetry in the measurable rapidity range uv – dv cteq65 mrst04 cteq65

12. Generate data with 4% error using MRST04 PDF and then include this pseudo-data in the global ZEUS PDF fit (actually use the lepton asymmetry data) The PDF uncertainty of the valence distributions is improved by the input of such data and the central value can be changed MRST04pseudodata ZEUS-S prediction BEFORE including A e pseudo-data AFTER including A e pseudo-data ATLAS/CMS LHC Aw data can measure valence distributions at x~0.005

13. CTEQ6.5MSTW08 But what about the formalism at LOW-X ?: LHC will be a low-x machine (at least for the early years of running) And note: even conventionally our knowledge of PDFs is decreases as x < 10 -4 Q 2 =10 Q 2 =10000 Note CTEQ in general bigger uncertainties…but NOT for low-x gluon where more flexible parametrization of MSTW08 gives larger errors

14. But what about the formalism at LOW-X ?: LHC will be a low-x machine (at least for the early years of running) Is NLO (or even NNLO) DGLAP good enough? The QCD formalism may need extending at small-x MRST03 is a toy PDF set produced without low-x data MRST02 MRST03 200k events of W+- -> e+- generated with MC@NLO using MRST03 and MRST02 Reconstructed Electron Pseudo-Rapidity Distributions (ATLAS fast simulation) 6 hours running Reconstructed e - Reconstructed e + If something is very different about low-x behaviour it will show up in the our measurable rapidity range

15. But the TOY PDF is unlikely to be realistic - a better way cold be to look at pt spectra for W and Z production Pt spectra show PDF differences, but also show differences in modelling – e.g. PYTHIA/HERWIG differences Probably needs more sophisticated treatment e.g. RESBOS. There has been an interesting recent calculation of how lack of pt ordering at low-x may affect the pt spectra for W and Z production at the LHC (See hep-ph/0508215)

16.  M W (fit) Same pattern Pt spectra are also used to measure MW Raw dM W from PDF uncertainties as of today, when using pt(e), is ~20 MeV So we’d better be sure we’ve got the calculations for Pt spectra right

17. x 1 =0.52 x 2 =0.000064 x 1 =0.006 x 2 =0.006 How to probe down to really low-x experimentally? Well the kinematics are such that it’s bound together with probing to higher-x. We had hoped to learn about valence PDFs (d/u )at high-x by looking at the W-/W+ ratio at large rapidity, but this is bound up with our knowldege of low-x LHCB kinematics

18. So it’s better to look at the PDF uncertainty on the total Drell-Yan cross-sections Improvement with LHCb measurements And this will feed into PDFs

20. Moving on to BSM physics Tevatron jet data were originally taken as evidence for new physics— i These figures show inclusive jet cross-sections compared to predictions in the form (data - theory)/ theory Theory CTEQ6M Today Tevatron jet data are considered to lie within PDF uncertainties And the largest uncertainty comes from the uncertainty on the high x gluon Theory MRST2002

21. SM + structure function uncertainty band M c = 2 TeV 2XD + structure function uncertainty band 4XD + structure function uncertainty band Up to ~50% at high mass :  Enough to lose sensitivity to higher compactification scales S.Ferrag M JJ (GeV) d/dM (a.u) Such PDF uncertainties in the jet cross sections compromise the LHC potential for discovery of any new physics which can written as a contact interaction E.G. Dijet cross section has potential sensitivity to compactification scale of extra dimensions (M c ) And what consequences might this have?

22. Can we know the high-x gluon better? mrst01 mstw08 There is newer Tevatron Run-II jet data in the latest PDF fits but no very striking improvement in the high-x gluon uncertainty- is there further hope from HERA jets? Note there is now new Tevatron Run-II jet data But it does not make MUCH difference to the level of PDF uncertainties

23. Can we know the high-x gluon better? And how might this impact on LHC high-ET jet cross-sections? HERA now completed second stage of operation (HERA-II) HERA-II projection shows significant improvement to high-x PDF uncertainties

24. And will we be able to use LHC data itself to improve the situation? Recently grid techniques have been developed to NLO cross-sections in PDF fits (e.g ZEUS-JETs fit) This technique can be used for LHC high-ET jet cross-sections Use data at lower PT and higher η-where new physics is not expected Pseudo-data has been generated up to PT= 3 TeV for pseudo rapidity ranges And then used in a global PDF fit to assess the impact of ATLAS data on PDFs

25. Impact of increasing statistics Impact of decreasing experimental systematic uncertainty Impact of decreasing experimental correlated systematic uncertainty Challenging! Can we decrease Jet Energy Scale systematic to 1%?

26. 1 year (10 fb -1 ) ATLAS TDR But not all BSM physics is strongly compromised: e.g PDF Uncertainty in High-mass Drell-Yan- won’t stop us seeing Z’s dominant Gluons dominant 7 – 9 % Uncertainty d-Valence dominant Sea dominant Different mass ranges have different contributions to the PDF uncertainty

27. And how do PDF uncertainties affect the Higgs discovery potential?- not too badly g g H t q q W/Z H S Ferrag

28. Summary PDF uncertainties impact significantly on Precise W/Z cross-sections, hence on use of these as luminosity monitor (however Z/W ratio is a golden calibration measurement) High Et jet cross-sections, hence on discovery of new physics which can be written in terms of contact interactions PDF uncertainties should not obscure discovery of Higgs in mass range 100-1000 GeV High mass Z’ in mass range 150-2500 GeV Measurements from LHC itself may improve knowledge of Gluon PDF at low-x (W prodn) and high-x (high ET jets/direct photon) Low-x / high-x valence PDFs ( W asymmetry) Low-x partons/ Low-x theory (low-mass Drell-Yan)

29. extras