Precision cross section measurements at lhc cms some remarks from the binn workshop
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Precision Cross section measurements at LHC (CMS) Some remarks from the Binn workshop. André Holzner IPP ETH Zürich DIS 2004 Štrbské Pleso 14-18 April 2004. Outline. Cross section measurements in general Luminosity: The status in 1993 How to do better ? PDF uncertainties

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

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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


  • 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

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

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 expectto 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 ?

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

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)


  • Measure W pair production cross section:

  • taking the ratio:

  • The proton-proton-Luminosity cancels !

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 ?

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

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

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

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

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

Constraining the PDFs at LHC: gluons

  • use to constrain gluon pdf

  • Signature: Jet + Photon

  • Photons can be identified and measured very well

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

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

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

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, tocompare 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


  • 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%


  • 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 differentialcross sections become available)

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