Data Analysis in High Energy Physics

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Data Analysisin High Energy Physics
Wen-Chen Chang Institute of Physics, Academia
Sinica ??? ????? ?????
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Outline

• Some Observables of Interest
• Elementary Observables
• More Complex Observables
• Analysis tools.

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Some Observables of Interest

• Total Interaction/Reaction Cross Section
• Differential Cross Section
• Particle mass or width
• Branching Ratio

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Cross Section

• Cross Section defines the strength of a
  particular interaction between two particles.

Small cross section
Large cross section
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Cross SectionInteraction Matrix Element
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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.
• 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.

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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
• 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 (magnetic field) and R (bending
  radius) needed to get p
• B is determined by the construction/operation of
  the spectrometer.
• R must be measured for each particle.

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Bending Magnet in Spectrometer
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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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TPC Inside the Solenoid Magnet at SPring-8
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Pad Plane of TPC

• Inner radius lt 1.25 cm.
• Outer radius lt 30 cm.
• Maximum drift distance about 70 cm.
• 1000 pads and 100 wires for readout,
• ?xy 350mm and ?z 500mm,
• B 1.5 2.5T.

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32-channel SPring-8 FADC cards

• Use TEXONO FADC and IHEP BES version as the
  starting point.
• 40 MHz clock, maximum 1024 sampling bins for one
  strobe.
• 10-bit FADC ADC input 0-2 V range.
• Shift register inside FPGA max length 100 time
  bin.
• On-board threshold suppression performed by FPGA.
• Buffer FIFO 16 bits x 4096 depth dual port
  memory, large enough to hold 5 events before
  issuing IRQ.
• CPLD controlling VME actions.
• Adjustable zero-suppression level channel by
  channel and number of events per IRQ.
• VME 9U 32 channels/module 8 detachable
  cards/module 4 channel/card.

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Determination of Particle Trajectory
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Operation of Time-Projection Chamber
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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

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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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LEPS Detector System
Dipole Magnet (0.7 T)
TOF wall
Start counter
Aerogel Cherenkov (n1.03)
MWDC 3
Silicon Vertex Detector
MWDC 2
MWDC 1
1m
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Target, Upstream Spectrometer, Dipole Magnet
LH2 Target (50 mm long)
Drift Chamber
g
SSD
Start Counter
Cherenkov Detector
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Dipole Magnet and Drift Chambers
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Time-of-Flight Wall
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Particle Identification by TOF
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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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How Do We Identifiy Resonances?
J/?
Resonance Broad states with finite widths and
lifetimes, which can be formed by collision
between the particles into which they decay.
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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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Example ?(1115)Reconstruction
?(1115)?p?-
Decay vertex (p?-) outside target
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Finding V0s
proton
Primary vertex
pion
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Dalitz Plot

• The Dalitz plot is a way to represent the entire
  phase space, viz. all essential kinematical
  variables, of any three-body final state in a
  scattered plot or two-dimensional histogram.
  Dalitz introduced it in 1953.
• Let a reaction be 12?345. For fixed p1 and
  p2, i.e. fixed total energy, the physical region
  of a Dalitz plot is inside a well-defined area,
  and in the absence of resonances or interferences
  can be shown to be uniformly populated. Resonant
  behaviour of two of the final state particles
  gives rise to a band of higher density, parallel
  to one of the coordinate axes or along a 45
  degree line.

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n-Particle Phase space, n3

• 2 Observables
• From four vectors 12
• Conservation laws -4
• Meson masses -3
• Free rotation -3
• S 2
• Usual choice
• Invariant mass m12
• Invariant mass m13

Dalitz plot
p1
pp
p2
p3
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ppbar??0?0?0 Its All a Question of Statistics
...

• pp 3p0
• with
• 100 events

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ppbar??0?0?0 Its All a Question of Statistics
... ...

• pp 3p0
• with
• 100 events
• 1000 events

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ppbar??0?0?0 Its All a Question of Statistics
... ... ...

• pp 3p0
• with
• 100 events
• 1000 events
• 10000 events

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ppbar??0?0?0 Its All a Question of Statistics
... ... ... ...

• pp 3p0
• with
• 100 events
• 1000 events
• 10000 events
• 100000 events

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ppbar??0?0?0
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Offline Analysis
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Introduction of PAW
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Introduction of PAW
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Introduction of PAW
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PAWhttp//wwwasd.web.cern.ch/wwwasd/paw/
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ROOThttp//root.cern.ch
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References

• Analysis Techniques in High Energy Physics,
  Claude A Pruneau, Wayne State University.
  (http//rhic.physics.wayne.edu/REU/talks/Analysis
  20Techniques.ppt)
• Introduction to High Energy Physics, R.H.
  Perkins, Cambridge University Press 2000.
• Data Analysis Techniques for High-Energy
  Physics, R. Fruhwirth, M. Regler, R.K. Bock, H.
  Grote, D. Notz, Cambridge University Press 2000.