Basic Measurements:
What do we want to measure?
Fundamental Measurements:
From Quarks to Lifetimes
Prof. Robin D. Erbacher
University of California, Davis
References: R. Fernow, Introduction to Experimental Particle Physics, Ch. 15
D. Green, The Physics of Particle Detectors, Ch. 13
http://pdg.lbl.gov/2004/reviews/pardetrpp.pdf
Fundamental Particle Properties
Charge: Charge of a particle can be determined two
ways
1) Sign of charge: Direction of deflection in a magnetic field
2) Magnitude of charge:
 Infer from knowledge of momentum and B-field
strength
 Charge-dependent quantity, such as ionization
energy loss, or Rutherford scattering cross section
Direction: tracking detectors, B-field
Momentum: tracking detectors, B-field
Ionization energy loss: sampling w/ scintillation, TOF (for )
(Example: combine  from time of flight (TOF) with dE/dx
and use Bethe Bloch equation to get charge)
Fundamental Particle Properties
Mass: Complicated: mainly specialized techniques
One Example:
1) Measure two independent mass-dependent quantities:
Momentum often one; ionization, range, or velocity
Momentum/range: tracking detectors, B-field
v
Ionization/velocity: scintillation, TOF/ dE/dx, C, TOF
Example: (Fernow) Use conservation of energy and momentum to
measure mass of muon neutrino 
m  p2  m2  p 2  m2
m2  m2  m2  2m ( p 2  m2 )
1
2
Use knowledge of mass of pion and muon, and measure
momentum and B-field strength accurately
 p ~ 0.001 MeV  m  0.25 MeV (90% CL)
Scintillator stops s, magnets guide s, silicon gives momentum
Fundamental Particle Properties
Mass: Complicated: mainly specialized techniques
Second Example:
2) Measure most quantities in an event, reconstruct mass:
Jet energies, lepton momenta, missing ET for examples
Jet energies: em and hadron calorimeters (fragmentation, etc)
Momenta: tracking detectors, B-field
Missing ET: all of the above, plus missing
info & corrections
Example: Measure top quark mass from tt pair production events
Use best combination (2) of partons
to reconstruct top mass to best
resolution possible.
Fundamental Particle Properties
Spin: Spins complicated for decaying particles
1) Ground state particles, electrons and nucleons:
Hyperfine structure in optical spectroscopy, atomic/molecular beam
experiments, bulk matter measurements using NMR.
2) Other low energy particles:
Various techniques… eg: charged pions determined by relating the
cross section for reaction to the cross section for the inverse reaction.
3) High energy interactions:
Spins can be found from the decay angular distributions, and from the
production angular distributions for particle interactions.
Example: Measure top quark pair spin correlations using angles of
decay products.
Fundamental Particle Properties
Magnetic Moment: Closely related to spin   gB S
1) Ground state particles, electrons and nucleons:
Again use optical spectroscopy, atomic/molecular beam
experiments, bulk matter measurements using NMR.

2) Muons:
Original measurement of g-factor done at CERN storage rings including
a precise demonstration of relativistic time dilation. Details of these,
and current g-2 experiments (BNL) leave for homework.
3) Measuring the hyperon:
Fermilab protons on beryllium target, s 8% polarized, sent through
1
magnet and spin precession measured, giving G  2 (g  2), and hence .
Keys to measurement: s produced inclusively w/ large cross section,
large detector acceptance, high energy long decay length
Fundamental Particle Properties
Lifetime: Time dilation, lab distance: Decay  ( p mc)c
Distribution of decays at distance x is exponential:
dN(x)  N(x)dx D
so that
N(x)  N0 exp(x D )

Slope depends on D, hence on c , measure slope/D to get lifetime .
Example: Lifetime fraction of the new particle X(3872)
Not quite a lifetime measurement, since
need to know branching ratios and
production. Measure fraction of X that
are long-lived (from B meson decays)
versus prompt.
3) Measuring muon lifetime:
Senior lab course: measure the muon
lifetime in the lab. Leave setup
and procedures for homework exercise.
Fundamental Particle Properties
Total Cross Section (prod rate): Two main methods
1) Measure every event (4 colliders & bubble chambers):
Often called a “counting experiment” :
T  R/L  N /L
Example: Top Pair Production
Rate of production of tt pairs one of
first things to measure upon discovery
2) Transmission Experiment:
Measure particle intensity before and
After target and extract cross section.
I  I0 exp(NT ) where N  # target nuclei
Used at fixed target experiments, most often.
Fundamental Measurements
New Particle Searches: Many categories/methods
-Counting excess events over Standard Model background
-Fits kinematic distributions to expected shapes
1) Expected Particles:
Searching for particles that are predicted
by theory, or expected by data. May or
may not know mass or other properties.
(W, Z, J/psi, top, Higgs…)
Example: Single Top Production
Never yet observed, but expected by
electroweak production, |Vtb|
Fundamental Measurements
New Particle Searches: Many categories/methods
(Counting excess events, or fits to distributions)
2) Completely New Phenomena:
Beyond Standard Model, unexpected. Sometimes theories exist, sometimes not. Difficult:
little information to optimize the search.
Carefully control background… don’t want
false positive!
Example: Search for Z’: “bump hunts”
Look for excess, usually in tails of
distributions. Statistics of small
numbers.
Problem: optimize
differently for discovery than for
searches (setting limits).
What Makes Particle
Detection Possible?
Next time-Passage of particles through matter:
How we “see” particles