Is It Interesting? Mike Strauss

Outline Statistics and probability Statistics and probability Experimental uncertainties Experimental uncertainties Particle decays and invariant mass distributions Particle decays and invariant mass distributions Quarks to jets Quarks to jets CDF W + 2 Jet signal CDF W + 2 Jet signal

Enough Data? If you flip a coin ten times and there are 4 heads and 6 tails, is the coin properly weighted? If you flip a coin ten times and there are 4 heads and 6 tails, is the coin properly weighted? 21% probability 21% probability (or 38% probability of ≥ 6) If you flip a coin 1000 times and there are 400 heads and 600 tails, is the coin properly weighted? If you flip a coin 1000 times and there are 400 heads and 600 tails, is the coin properly weighted? 4.6 × % probability 4.6 × % probability (or 1.4 × % probability of ≥ 600) The conclusion depends on the amount of data available The conclusion depends on the amount of data available

Statistics For a Gaussian (normal) distribution For a Gaussian (normal) distribution 1σ deviation: 32% probability 1σ deviation: 32% probability 2σ deviation: 5% probability 2σ deviation: 5% probability 3σ deviation: 0.3% probability 3σ deviation: 0.3% probability 4σ deviation: 0.006% probability 4σ deviation: 0.006% probability 5σ deviation: % probability 5σ deviation: % probability

Experimental Uncertainties Uncertainties (not errors) come in two varieties Uncertainties (not errors) come in two varieties Statistical Statistical Well defined based on the amount of data you have Well defined based on the amount of data you have Some interesting experimental signals occur because of “statistical fluctuations.” These will disappear with more data Some interesting experimental signals occur because of “statistical fluctuations.” These will disappear with more data Systematic Systematic Not as well defined but with general learned guidelines Not as well defined but with general learned guidelines Some “discoveries” have occurred because systematic uncertainties were not fully accounted for. These tend to go away with a better understanding of apparatus, or because another experiment doesn’t see the same effect. Some “discoveries” have occurred because systematic uncertainties were not fully accounted for. These tend to go away with a better understanding of apparatus, or because another experiment doesn’t see the same effect.

Particle Decay E P = E 1 + E 2 p = p 1 + p 2 E 2 = p 2 c 2 + m 2 c 4 E 2 = p 2 + m 2 m 2 = E 2 – p 2 Parent Daughters m P 2 = E P 2 – p P 2 m P 2 = (E 1 + E 2 ) 2 – (p 1 + p 2 ) 2

Discovering new particles: Synopsis A new particle can be discovered by observing peaks in an energy distribution when plotting the invariant mass of chosen decay products. A new particle can be discovered by observing peaks in an energy distribution when plotting the invariant mass of chosen decay products. The peak must have enough statistical significance. The peak must have enough statistical significance. We must understand our background shape to know the statistical significance of the peak. We must understand our background shape to know the statistical significance of the peak. Other experiments should be able to verify new discoveries. Other experiments should be able to verify new discoveries.

Seeing quarks in the detector Hadronization q 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 event

CDF W + 2 jet ?

Latest CDF W + 2 jet data Options?

Discussion?