Is It Interesting?Is It Interesting?

Mike StraussMike Strauss

OutlineOutline Statistics and probabilityStatistics and probability Experimental uncertaintiesExperimental uncertainties Particle decays and invariant mass distributionsParticle decays and invariant mass distributions Quarks to jetsQuarks to jets CDF W + 2 Jet signalCDF W + 2 Jet signal

Enough Data?Enough Data? If you flip a coin ten times and there If you flip a coin ten times and there

are 4 heads and 6 tails, is the coin are 4 heads and 6 tails, is the coin properly weighted?properly weighted?21% probability 21% probability

(or 38% probability of ≥ 6)(or 38% probability of ≥ 6) If you flip a coin 1000 times and there If you flip a coin 1000 times and there

are 400 heads and 600 tails, is the are 400 heads and 600 tails, is the coin properly weighted?coin properly weighted?4.6 × 104.6 × 10-9-9 % probability % probability

(or 1.4 × 10(or 1.4 × 10-8-8 % probability of ≥ 600) % probability of ≥ 600) The conclusion depends on the The conclusion depends on the

amount of data availableamount of data available

StatisticsStatistics For a Gaussian (normal) distributionFor a Gaussian (normal) distribution

11σσ deviation: 32% probability deviation: 32% probability22σσ deviation: 5% probability deviation: 5% probability33σσ deviation: 0.3% probability deviation: 0.3% probability44σσ deviation: 0.006% probability deviation: 0.006% probability55σσ deviation: 0.00006% probability deviation: 0.00006% probability

Experimental UncertaintiesExperimental Uncertainties Uncertainties (not errors) come in two varietiesUncertainties (not errors) come in two varieties

StatisticalStatisticalWell defined based on the amount of data you haveWell defined based on the amount of data you haveSome interesting experimental signals occur because Some interesting experimental signals occur because

of “statistical fluctuations.” These will disappear with of “statistical fluctuations.” These will disappear with more datamore data

SystematicSystematicNot as well defined but with general learned guidelinesNot as well defined but with general learned guidelinesSome “discoveries” have occurred because systematic Some “discoveries” have occurred because systematic

uncertainties were not fully accounted for. These tend uncertainties were not fully accounted for. These tend to go away with a better understanding of apparatus, or to go away with a better understanding of apparatus, or because another experiment doesn’t see the same because another experiment doesn’t see the same effect.effect.

Particle DecayParticle Decay

EEPP = E = E11 + E + E22

pp = = pp11 + + pp22

EE22 = p = p22cc22 + m + m22cc44

EE22 = p = p22 + m + m22

mm22 = E = E22 – p – p22

Parent

Daughters

mmPP22 = E = EPP

22 – p – pPP22

mmPP22 = (E = (E11 + E + E22))22 – ( – (pp11 + + pp22))22

Discovering new particles: SynopsisDiscovering new particles: Synopsis A new particle can be discovered by observing A new particle can be discovered by observing

peaks in an energy distribution when plotting the peaks in an energy distribution when plotting the invariant mass of chosen decay products.invariant mass of chosen decay products.

The peak must have enough statistical The peak must have enough statistical significance.significance.

We must understand our background shape to We must understand our background shape to know the statistical significance of the peak.know the statistical significance of the peak.

Other experiments should be able to verify new Other experiments should be able to verify new discoveries.discoveries.

Seeing quarks in the detectorSeeing quarks in the detector

Hadronizationq

As quarks leave a collision, they change into a ‘shotgun blast’ of particles called a ‘jet’

q

Remember that quarks are always confined!

A 2 jet eventA 2 jet event

CDF W + 2 jetCDF W + 2 jet

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Latest CDF W + 2 jet dataLatest CDF W + 2 jet data

Options?

Discussion?Discussion?