1. Analysis Techniques in High Energy Physics Claude A Pruneau Wayne State Univeristy

2. Overview Some Observables of Interest Elementary Observables More Complex Observables Typical Analysis of (Star) data

3. Some Observables of Interest Total Interaction/Reaction Cross Section Differential Cross Section: I.e. cross section vs particle momentum, or production angle, etc. Particle life time or width Branching Ratio Particle Production Fluctuation (HI)

4. Cross Section Total Cross Section of an object determines how “big” it is and how likely it is to collide with projectile thrown towards it randomly. Small cross section Large cross section

5. Scattering Cross Section Differential Cross Section Flux Target Unit Area d  solid angle  – scattering angle Total Cross Section Average number of scattered into d 

6. Particle life time or width Most particles studied in particle physics or high energy nuclear physics are unstable and decay within a finite lifetime. –Some useful exceptions include the electron, and the proton. However these are typically studied for their own sake but to address some other observable… Particles decay randomly (stochastically) in time. The time of their decay cannot be predicted. Only the the probability of the decay can be determined. The probability of decay (in a certain time interval) depends on the life-time of the particle. In traditional nuclear physics, the concept of half-life is commonly used. In particle physics and high energy nuclear physics, the concept of mean life time or simple life time is usually used. The two are connected by a simple multiplicative constant.

7. Half-Life

8. Half-Life and Mean-Life The number of particle (nuclei) left after a certain time “t” can be expressed as follows: where “  ” is the mean life time of the particle “  ” can be related to the half-life “t 1/2 ” via the simple relation:

9. Examples - particles Mass (MeV/c 2 ) or c Type Proton (p)938.2723>1.6x10 25 yVery long…Baryon Neutron (n)939.5656887.0 s2.659x10 8 kmBaryon N(1440)1440350 MeVVery short!Baryon resonance  (1232) 1232120 MeVVery short!!Baryon resonance  1115.682.632x10 -10 s7.89 cmStrange Baryon resonance Pion (  +- ) 139.569952.603x10 -8 s7.804 mMeson Rho -  (770) 769.9151.2 MeVVery shortMeson Kaon (K +- )493.6771.2371 x 10 -8 s3.709 mStrange meson D +- 1869.41.057x10 -12 s 317  m Charmed meson

10. Examples - Nuclei Radioactive Decay Reactions Used to data rocks Parent NucleusDaughter Nucleus Half-Life (billion year) Samarium ( 147 Sa)Neodymium ( 143 Nd)106 Rubidium ( 87 Ru)Strontium ( 87 Sr)48.8 Thorium ( 232 Th)Lead ( 208 Pb)14.0 Uranium ( 238 U)Lead ( 206 Pb)4.47 Potassium ( 40 K)Argon ( 40 Ar)1.31

11. Particle Widths By virtue of the fact that a particle decays, its mass or energy (E=mc 2 ), cannot be determined with infinite precision, it has a certain width noted . The width of an unstable particle is related to its life time by the simple relation h is the Planck constant.

12. Decay Widths and Branching Fractions In general, particles can decay in many ways (modes). Each of the decay modes have a certain relative probability, called branching fraction or branching ratio. Example (  0 s ) Neutral Kaon (Short) –Mean life time = (0.8926  0.0012)x10 -10 s –c  = 2.676 cm –Decay modes and fractions mode  i   +  - (68.61  0.28) %  0 (31.39  0.28) %  +  -  (1.78  0.05) x10 -3

13. Elementary Observables Momentum Energy Time-of-Flight Energy Loss Particle Identification Invariant Mass Reconstruction

14. Momentum Measurements Definition –Newtonian Mechanics –Special Relativity But how does one measure “p”?

15. Momentum Measurements Technique Use a spectrometer with a constant magnetic field B. Charged particles passing through this field with a velocity “v” are deflected by the Lorentz force. Because the Lorentz force is perpendicular to both the B field and the velocity, it acts as centripetal force “F c ”. One finds

16. Momentum Measurements Technique Knowledge of B and R needed to get “p” B is determined by the construction/operation of the spectrometer. “R” must be measured for each particle. To measure “R”, STAR and CLEO both use a similar technique. –Find the trajectory of the charged particle through detectors sensitive to particle energy loss and capable of measuring the location of the energy deposition.

17. Star Time-Projection-Chamber (TPC) Large Cylindrical Vessel filled with “P10” gas (10% methane, 90% Ar) Imbedded in a large solenoidal magnet Longitudinal Electrical Field used to supply drive force needed to collect charge produced ionization of p10 gas by the passage of charged particles.

18. STAR TPC

19. Pad readout 2 × 12 super-sectors 60 cm 127 cm 190 cm Outer sector 6.2 × 19.5 mm 2 pad 3940 pads Inner sector 2.85 × 11.5 mm 2 pad 1750 pads

20. JT: 20 The Berkeley Lab O STAR Pixel Pad Readout Readout arranged like the face of a clock - 5,690 pixels per sector

21. Momentum Measurement ++ B=0.5 T Collision Vertex Trajectory is a helix in 3D; a circle in the transverse plane Radius: R

22. JT: 22 The Berkeley Lab O STAR Au on Au Event at CM Energy ~ 130 A GeV Real-time track reconstruction Pictures from Level 3 online display. ( < 70 ms ) Data taken June 25, 2000. The first 12 events were captured on tape!

23. Time-of-Flight (TOF) Measurements Typically use scintillation detectors to provide a “start” and “stop” time over a fixed distance. Electric Signal Produced by scintillation detector Use electronic Discriminator Use time-to-digital-converters (TDC) to measure the time difference = stop – start. Given the known distance, and the measured time, one gets the velocity of the particle Time S (volts)

24. Energy Measurement Definition –Newtonian –Special Relativity

25. Energy Measurement Determination of energy by calorimetry Particle energy measured via a sample of its energy loss as it passes through layers of radiator (e.g. lead) and sampling materials (scintillators)

26. More Complex Observables Particle Identification Invariant Mass Reconstruction Identification of decay vertices

27. Particle Identification Particle Identification or PID amounts to the determination of the mass of particles. –The purpose is not to measure unknown mass of particles but to measure the mass of unidentified particles to determine their species e.g. electron, pion, kaon, proton, etc. In general, this is accomplished by using to complementary measurements e.g. time-of-flight and momentum, energy-loss and momentum, etc

28. PID by TOF Since The mass can be determined In practice, this often amounts to a study of the TOF vs momentum.

29. PID with a TPC The energy loss of charged particles passing through a gas is a known function of their momentum. (Bethe-Bloch Formula)

30. O STAR Particle Identification by dE/dx dE/dx PID range: ~ 0.7 GeV/c for K /  ~ 1.0 GeV/c for K/p Anti - 3 He

31. Invariant Mass Reconstruction In special relativity, the energy and momenta of particles are related as follow This relation holds for one or many particles. In particular for 2 particles, it can be used to determine the mass of parent particle that decayed into two daughter particles.

32. Invariant Mass Reconstruction (cont’d) Invariant Mass Invariant Mass of two particles After simple algebra

33. But – remember the jungle of tracks… Large likelihood of coupling together tracks that do not actually belong together…

34. Example – Lambda Reconstruction Good pairs have the right invariant mass and accumulate in a peak at the Lambda mass. Bad pairs produce a more or less continuous background below and around the peak.

35. STAR STRANGENESS! K0sK0s  K+K+ (Preliminary)        _ _ _

36. Finding V0s proton pion Primary vertex

37. In case you thought it was easy… Before After

38. Strange Baryon Ratios Ratio = 0.73 ± 0.03 (stat) ~0.84  /ev, ~ 0.61  /ev _ Reconstruct: Ratio = 0.82 ± 0.08 (stat) Reconstruct: ~0.006   /ev, ~0.005   /ev _ STAR Preliminary

39. Resonances    