Precision Cross section measurements atPrecision Cross section measurements atLHC (CMS) LHC (CMS)

Some remarks from the Binn workshopSome remarks from the Binn workshop

André Holzner André Holzner IPP ETH ZürichIPP ETH Zürich

DIS 2004DIS 2004 Štrbské PlesoŠtrbské Pleso

14-18 April 200414-18 April 2004

OutlineOutline• Cross section measurements in generalCross section measurements in general

• Luminosity: The status in 1993Luminosity: The status in 1993

• How to do better ? How to do better ?

• PDF uncertaintiesPDF uncertainties

• Constraining PDFs at LHC: Quarks, GluonsConstraining PDFs at LHC: Quarks, Gluons

• Higher order calculationsHigher order calculations

• SummarySummary

• OutlookOutlook

Many numbers quoted here were originally numbers quoted here were originally presented at the presented at the

Binn Workshop 2003 Binn Workshop 2003 http://wwweth.cern.ch/WorkShopBinnhttp://wwweth.cern.ch/WorkShopBinn

Cross section measurementsCross 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

Signal

expectedbackgroundobserved

signal

NNN

proton-proton2

21Xpartonsexpectedsignal ),,(PDF LQxxN

X)pp(ppX)pp(pp

X)pp(ppprotonproton

N

L

Luminosity: The status in 1993Luminosity: 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

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 ?How to do better ?

• Need process whichNeed process which– has high has high

statisticsstatistics– is well is well

understood understood theoreticallytheoretically

– can be well can be well measuredmeasured

LHC event rates at 'nominal luminosity'

pp W l and pp Z ll are perfect candidates !

CMS Trigger TDR

How to better measure the How to better measure the luminosity ?luminosity ?

• Measure Measure parton-parton luminosityparton-parton luminosity, using e.g. , using e.g. single Z or W production:single Z or W production:

• Need however to propagate the PDFs to different Need however to propagate the PDFs to different

– xx11, x, x22 (rapidity distribution) (rapidity distribution)

– QQ22 (mass (mass22) )

Zqq

Zppprotonproton

221partonparton ),,(

N

LQxxPDFL

ExampleExample

• 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 !

protonproton2

21ZqqZpp ),,()ho( LQxxPDFN

protonproton2

21WWqqWWpp ),,()ho( LQxxPDFN

),,(PDF

),,(PDF2

21

221

qq

WWqqZppWWpp Qxx

QxxNN

Z

PDF uncertaintiesPDF uncertainties

how good will the extrapolation be ?

• Need to extrapolate Need to extrapolate the PDFs from HERA the PDFs from HERA (and other) data to the (and other) data to the LHC:LHC:– for similar masses, for similar masses,

go to lower xgo to lower x– go to higher Qgo to higher Q22

• Need smaller x at LHC, Need smaller x at LHC, especially when especially when moving to higher moving to higher rapidityrapidity

PDF uncertaintiesPDF uncertainties• Today's PDF uncertainties:Today's PDF uncertainties:

– inconsistencies of different data setsinconsistencies of different data sets– large uncertainties for x<0.005large uncertainties for x<0.005– negative gluon content at low Qnegative gluon content at low Q22

• To solve this, one needs:To solve this, one needs:– more measurements (e.g. from HERA)more measurements (e.g. from HERA)– higher order (full NNLO) calculations higher order (full NNLO) calculations – theoretical corrections for extremely small and theoretical corrections for extremely small and

extremely large xextremely large x– theoretical corrections at low Qtheoretical corrections at low Q22

• As an estimate of extrapolation uncertainties: Take As an estimate of extrapolation uncertainties: Take differences of predictions of differences of predictions of different pdfsdifferent pdfs

• Note that this uncertainty is also present when using Note that this uncertainty is also present when using proton-proton luminositiesproton-proton luminosities

Constraining PDFs at LHCConstraining PDFs at LHC

• However, can also However, can also restrict the PDFs from restrict the PDFs from the datathe data

• Different detector Different detector regions are related to regions are related to different x valuesdifferent x values

• Different QDifferent Q22 regions regions can e.g. be selected can e.g. be selected by constraints on the by constraints on the invariant massinvariant mass

rapidity distribution of single W production

• Use the single W,Z rapidity distributionsUse the single W,Z rapidity distributions

• Detector uncertainties Detector uncertainties largely cancel out due to ratio building !

Constraining PDFs at LHC: QuarksConstraining 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

• 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: QuarksConstraining PDFs at LHC: Quarks

MRST hep-ph/0308087

Constraining the PDFs at LHC: Constraining the PDFs at LHC: gluonsgluons

• about half of the about half of the momentum of the momentum of the proton is carried by proton is carried by gluonsgluons

• In DIS: Gluons from the In DIS: Gluons from the proton usually involvedproton usually involvedonly at higher order only at higher order

it is important to it is important to determine / constrain determine / constrain the gluon pdfs at LHCthe gluon pdfs at LHC

Constraining the PDFs at LHC: Constraining the PDFs at LHC: gluonsgluons

• useuse to constrain gluon pdf to constrain gluon pdf

• Signature: Jet + PhotonSignature: Jet + Photon

• Photons can be identified and measured very wellPhotons can be identified and measured very well

Constraining the PDFs at LHC: Constraining the PDFs at LHC: gluonsgluons

• Use e.g. the photon Use e.g. the photon pseudorapidity distributionpseudorapidity distributionafter a cut on the photon after a cut on the photon energy and jet energy and jet pseudorapiditypseudorapidity

• 10-20% background 10-20% background (mainly from (mainly from leading leading 00) )

• 10% uncertainty from 10% uncertainty from choice of QCD choice of QCD renormalization scalerenormalization scale statistical errors of data of 10 days

at L = 1032cm-2 s-1

Reid, Heath CMS NOTE 2000/063

Higher order calculationsHigher order calculations• Need to have a good calculation of the cross section used Need to have a good calculation of the cross section used

for measuring the luminosityfor measuring the luminosity

• Want to have fully differential (e.g. in pWant to have fully differential (e.g. in pTT and rapidity) cross and rapidity) cross sections:sections:– ppTT is important for trigger efficiencies is important for trigger efficiencies– rapidity is important for the rapidity is important for the

acceptanceacceptance• Otherwise, we Otherwise, we

(experimentalists) do not know (experimentalists) do not know exactly, which exactly, which fraction fraction of the of the signal of interest is within our signal of interest is within our trigger / geometrical trigger / geometrical acceptanceacceptance

Davatz, Dissertori, Dittmar, Grazzini, Pauss hep-ph/0402218

Why do we want NNLO Why do we want NNLO calculations ?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 These improvements will be necessary once we (experimentalists) can measure something (e.g. a (experimentalists) can measure something (e.g. a cross section) to an accuracy better than 10% !cross section) to an accuracy better than 10% !

Binn Talk by W.J.Stirling

Example: Higgs cross section at Example: Higgs cross section at LHCLHC

• E.g. for mE.g. for mHH = 120 GeV, the uncertainty due to PDF = 120 GeV, the uncertainty due to PDF uncertainties (using the NNLO cross section) is uncertainties (using the NNLO cross section) is 3%3%

• However, the uncertainty from scale variation at However, the uncertainty from scale variation at NNLO (NNLL) precision is larger: NNLO (NNLL) precision is larger: 10% (8%)10% (8%)

higher order calculations would be helpful here, higher order calculations would be helpful here, toto

compare the measured cross section to theorycompare the measured cross section to theory

• But (as always for searches), it is But (as always for searches), it is more important more important to to have a precise knowledge of the have a precise knowledge of the backgroundsbackgrounds on top on top of which the signals are looked for...of which the signals are looked for...

Catani et. al. hep-ph/0306211

Binn Talk by W.J.Stirling

SummarySummary• Best estimates on uncertainties of PDFs today: Best estimates on uncertainties of PDFs today: ~4%~4%

– uncertainties of W/Z production cross sections due to uncertainties of W/Z production cross sections due to exp. uncertainties in PDFs: exp. uncertainties in PDFs: ~2%~2%

– Ratio measurements can be much better (e.g. Ratio measurements can be much better (e.g. ~0.5%~0.5%))

• Relative cross section measurements will be limited by Relative cross section measurements will be limited by precision of single W/Z cross section (perhaps precision of single W/Z cross section (perhaps 1%1%), but this ), but this is much better than the previous 5-10% proton-proton is much better than the previous 5-10% proton-proton luminosity uncertaintyluminosity uncertainty

• Gluon distributions can be constrained using Jet + Photon Gluon distributions can be constrained using Jet + Photon eventsevents

• NNLO calculations most likely necessary wherever we NNLO calculations most likely necessary wherever we (experimentalists) can measure a quantity to better than (experimentalists) can measure a quantity to better than ~10%~10%

OutlookOutlook

• Need to study the selection efficiencies for Need to study the selection efficiencies for leptonic W and Z decays in detail, using full leptonic W and Z decays in detail, using full detector simulation.detector simulation.Other processes can then follow later.Other processes can then follow later.

• sometimes large differences between LO and NLO sometimes large differences between LO and NLO calculations calculations

need to redo the physics potential studies need to redo the physics potential studies using using (N)NLO monte carlos (once the fully (N)NLO monte carlos (once the fully differentialdifferential

cross sections become available)cross sections become available)