Precision Cross section measurements at LHC (CMS) Some remarks from the Binn workshop

1. Precision Cross section measurements atLHC (CMS) Some remarks from the Binn workshop André Holzner IPP ETH Zürich DIS 2004 Štrbské Pleso 14-18 April 2004

2. Outline • Cross section measurements in general • Luminosity: The status in 1993 • How to do better ? • PDF uncertainties • Constraining PDFs at LHC: Quarks, Gluons • Higher order calculations • Summary • Outlook Many numbers quoted here were originally presented at the Binn Workshop 2003 http://wwweth.cern.ch/WorkShopBinn

3. Cross section measurements • A basic method: • We want to compare to Model predictions: • where the pp luminosity can be measured as: • but this is difficult to calculate / predict

4. Luminosity: The status in 1993 • From the CMS technical proposal:"...will aim to measure the [proton-proton] luminosity at CMS with a precision of better than 5%. This precision is chosen to match approximately the precision which theorists expect to achieve in predictions for hard scattering cross- sections at LHC energies at the time CMS takes data." • This limits precision of cross section measurements to 5% ! • Are we really looking for the proton-protoncross section ?

5. How to do better ? • Need process which • has high statistics • is well understood theoretically • can be well measured pp  W  l and pp  Z  llare perfect candidates ! LHC event rates at 'nominal luminosity' CMS Trigger TDR

6. How to better measure the luminosity ? • Measure parton-parton luminosity, using e.g. single Z or W production: • Need however to propagate the PDFs to different • x1, x2 (rapidity distribution) • Q2 (mass2)

7. Example • Measure W pair production cross section: • taking the ratio: • The proton-proton-Luminosity cancels !

8. PDF uncertainties • Need to extrapolate the PDFs from HERA (and other) data to the LHC: • for similar masses, go to lower x • go to higher Q2 • Need smaller x at LHC, especially when moving to higher rapidity how good will the extrapolation be ?

9. PDF uncertainties • Today's PDF uncertainties: • inconsistencies of different data sets • large uncertainties for x<0.005 • negative gluon content at low Q2 • To solve this, one needs: • more measurements (e.g. from HERA) • higher order (full NNLO) calculations • theoretical corrections for extremely small and extremely large x • theoretical corrections at low Q2 • As an estimate of extrapolation uncertainties: Take differences of predictions of different pdfs • Note that this uncertainty is also present when using proton-proton luminosities

10. Constraining PDFs at LHC • However, can also restrict the PDFs from the data • Different detector regions are related to different x values • Different Q2 regions can e.g. be selected by constraints on the invariant mass rapidity distribution of single W production

11. Constraining PDFs at LHC: Quarks • Use the single W,Z rapidity distributions • Detector uncertainties largely cancel out due to ratio building ! ~1 day of low luminosity symmetric sea ratio ! non-symmetric sea example of PDFs which differ only slightly Dittmar, Pauss, Zürcher Phys.Rev.D56:7284-7290,1997

12. Constraining PDFs at LHC: Quarks • Further advantages: • well measured couplings of W,Z to fermions (1% or better) • muons/electrons easily identifiable over a large detector region • cross sections of the order of nanobarns, Event rates larger than 10 Hz • When normalizing to e.g. single W production: Cross section uncertainties from variation of single PDF (MRST): ~4% MRST hep-ph/0308087

13. Constraining the PDFs at LHC: gluons • about half of the momentum of the proton is carried by gluons • In DIS: Gluons from the proton usually involvedonly at higher order  it is important to determine / constrain the gluon pdfs at LHC

14. Constraining the PDFs at LHC: gluons • use to constrain gluon pdf • Signature: Jet + Photon • Photons can be identified and measured very well

15. Constraining the PDFs at LHC: gluons • Use e.g. the photon pseudorapidity distributionafter a cut on the photon energy and jet pseudorapidity • 10-20% background (mainly from leading 0) • 10% uncertainty from choice of QCD renormalization scale statistical errors of data of 10 days at L = 1032cm-2 s-1 Reid, Heath CMS NOTE 2000/063

16. Higher order calculations • Need to have a good calculation of the cross section used for measuring the luminosity • Want to have fully differential (e.g. in pT and rapidity) cross sections: • pT is important for trigger efficiencies • rapidity is important for the acceptance • Otherwise, we (experimentalists) do not know exactly, which fraction of the signal of interest is within our trigger / geometrical acceptance Davatz, Dissertori, Dittmar, Grazzini, Pauss hep-ph/0402218

17. Why do we want NNLO calculations ? • renormalisation scale dependence is smaller • better matching of parton-level 'jet' with experimental hadron-level jet • better description of transverse momentum These improvements will be necessary once we (experimentalists) can measure something (e.g. a cross section) to an accuracy better than 10% ! Binn Talk by W.J.Stirling

18. Example: Higgs cross section at LHC • E.g. for mH = 120 GeV, the uncertainty due to PDF uncertainties (using the NNLO cross section) is 3% • However, the uncertainty from scale variation at NNLO (NNLL) precision is larger: 10% (8%) higher order calculations would be helpful here, to compare the measured cross section to theory • But (as always for searches), it is more important to have a precise knowledge of the backgrounds on top of which the signals are looked for... Catani et. al. hep-ph/0306211 Binn Talk by W.J.Stirling

19. Summary • Best estimates on uncertainties of PDFs today: ~4% • uncertainties of W/Z production cross sections due to exp. uncertainties in PDFs: ~2% • Ratio measurements can be much better (e.g. ~0.5%) • Relative cross section measurements will be limited by precision of single W/Z cross section (perhaps 1%), but this is much better than the previous 5-10% proton-proton luminosity uncertainty • Gluon distributions can be constrained using Jet + Photon events • NNLO calculations most likely necessary wherever we (experimentalists) can measure a quantity to better than ~10%

20. Outlook • Need to study the selection efficiencies for leptonic W and Z decays in detail, using full detector simulation.Other processes can then follow later. • sometimes large differences between LO and NLO calculations  need to redo the physics potential studies using (N)NLO monte carlos (once the fully differential cross sections become available)