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

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

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

4. Luminosity: The status in 1993 From the CMS technical proposal: 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-proton cross section ?

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

6. How to better measure the luminosity ? Measure parton-parton luminosity, using e.g. single Z or W production: Measure parton-parton luminosity, using e.g. single Z or W production: Need however to propagate the PDFs to different Need however to propagate the PDFs to different –x 1, x 2 (rapidity distribution) –Q 2 (mass 2 )

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

8. PDF uncertainties how good will the extrapolation be ? Need to extrapolate the PDFs from HERA (and other) data to the LHC: Need to extrapolate the PDFs from HERA (and other) data to the LHC: –for similar masses, go to lower x –go to higher Q 2 Need smaller x at LHC, especially when moving to higher rapidity Need smaller x at LHC, especially when moving to higher rapidity

9. PDF uncertainties Today's PDF uncertainties: Today's PDF uncertainties: –inconsistencies of different data sets –large uncertainties for x<0.005 –negative gluon content at low Q 2 To solve this, one needs: 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 Q 2 As an estimate of extrapolation uncertainties: Take differences of predictions of different pdfs 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 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 However, can also restrict the PDFs from the data Different detector regions are related to different x values Different detector regions are related to different x values Different Q 2 regions can e.g. be selected by constraints on the invariant mass Different Q 2 regions can e.g. be selected by constraints on the invariant mass rapidity distribution of single W production

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

12. 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% Constraining PDFs at LHC: Quarks MRST hep-ph/0308087

13. Constraining the PDFs at LHC: gluons about half of the momentum of the proton is carried by gluons about half of the momentum of the proton is carried by gluons In DIS: Gluons from the proton usually involved only at higher order  it is important to determine / constrain the gluon pdfs at LHC In DIS: Gluons from the proton usually involved only 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 use to constrain gluon pdf Signature: Jet + Photon Signature: Jet + Photon Photons can be identified and measured very well Photons can be identified and measured very well

15. Constraining the PDFs at LHC: gluons Use e.g. the photon pseudorapidity distribution after a cut on the photon energy and jet pseudorapidity Use e.g. the photon pseudorapidity distribution after a cut on the photon energy and jet pseudorapidity 10-20% background (mainly from leading  0 ) 10-20% background (mainly from leading  0 ) 10% uncertainty from choice of QCD renormalization scale 10% uncertainty from choice of QCD renormalization scale statistical errors of data of 10 days at L = 10 32 cm -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 Need to have a good calculation of the cross section used for measuring the luminosity Want to have fully differential (e.g. in p T and rapidity) cross sections: Want to have fully differential (e.g. in p T and rapidity) cross sections: –p T 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 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 m H = 120 GeV, the uncertainty due to PDF uncertainties (using the NNLO cross section) is 3% E.g. for m H = 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 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... 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% 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 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 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% 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. 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 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)