Analysis Techniques in High Energy Physics

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Analysis Techniquesin High Energy Physics

• Claude A Pruneau
• Wayne State Univeristy

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Overview

• Some Observables of Interest
• Elementary Observables
• More Complex Observables
• Typical Analysis of (Star) data

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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)

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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
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Scattering Cross Section

• Differential Cross Section

dW - solid angle
Flux
q scattering angle
Target
Unit Area

• Average number of scattered into dW

• Total Cross Section

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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.

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Half-Life
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Half-Life and Mean-Life

• The number of particle (nuclei) left after a
  certain time t can be expressed as follows
• where t is the mean life time of the particle
• t can be related to the half-life t1/2 via
  the simple relation

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Examples - particles
Mass (MeV/c2) t or G c t Type
Proton (p) 938.2723 gt1.6x1025 y Very long Baryon
Neutron (n) 939.5656 887.0 s 2.659x108 km Baryon
N(1440) 1440 350 MeV Very short! Baryon resonance
D(1232) 1232 120 MeV Very short!! Baryon resonance
L 1115.68 2.632x10-10 s 7.89 cm Strange Baryon resonance
Pion (p-) 139.56995 2.603x10-8 s 7.804 m Meson
Rho - r(770) 769.9 151.2 MeV Very short Meson
Kaon (K-) 493.677 1.2371 x 10-8 s 3.709 m Strange meson
D- 1869.4 1.057x10-12 s 317 mm Charmed meson
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Examples - Nuclei
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Particle Widths

• By virtue of the fact that a particle decays, its
  mass or energy (Emc2), cannot be determined with
  infinite precision, it has a certain width noted
  G.
• The width of an unstable particle is related to
  its life time by the simple relation
• h is the Planck constant.

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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 (K0s) Neutral Kaon (Short)
• Mean life time (0.89260.0012)x10-10 s
• ct 2.676 cm
• Decay modes and fractions

mode Gi/ G
p p- (68.61 0.28)
p0 p0 (31.39 0.28)
p p- g (1.78 0.05) x10-3
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Elementary Observables

• Momentum
• Energy
• Time-of-Flight
• Energy Loss
• Particle Identification
• Invariant Mass Reconstruction

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Momentum Measurements

• Definition
• Newtonian Mechanics
• Special Relativity
• But how does one measure p?

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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 Fc.
• One finds

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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.

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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.

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STAR TPC
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Pad readout

• 212 super-sectors

190 cm
Outer sector 6.2 19.5 mm2 pad 3940 pads
Inner sector 2.85 11.5 mm2 pad 1750 pads
127 cm
60 cm
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Pixel Pad Readout
Readout arranged like the face of a clock - 5,690
pixels per sector
JT 20 The Berkeley Lab
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Momentum Measurement
B0.5 T
p
Radius R
Trajectory is a helix in 3D a circle in the
transverse plane
Collision Vertex
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Au on Au Event at CM Energy 130 A GeV
Data taken June 25, 2000. The first 12 events
were captured on tape!
Real-time track reconstruction Pictures from
Level 3 online display. ( lt 70 ms )
JT 22 The Berkeley Lab
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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)
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Energy Measurement

• Definition
• Newtonian
• Special Relativity

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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)

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More Complex Observables

• Particle Identification
• Invariant Mass Reconstruction
• Identification of decay vertices

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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

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PID by TOF

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

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PID with a TPC

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

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Particle Identification by dE/dx
Anti - 3He
dE/dx PID range 0.7 GeV/c for K/?
1.0 GeV/c for K/p
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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.

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Invariant Mass Reconstruction (contd)

• Invariant Mass
• Invariant Mass of two particles
• After simple algebra

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But remember the jungle of tracks
Large likelihood of coupling together tracks that
do not actually belong together
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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.
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STAR STRANGENESS!
(Preliminary)
_
K
_
W-
L
W
f
K0s
L
X-
_
X
K
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Finding V0s
proton
Primary vertex
pion
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In case you thought it was easy
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Strange Baryon Ratios
STAR Preliminary
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Resonances
f K K-