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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

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

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 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 ?

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)

Example

- 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, 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

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%

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)

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