Download 1. units, quantities, kinematics, measurements

Experimental
particle
physics
1.
Marco Delmastro
Experimental Particle Physics
units, quantities, kinematics, measurements
1
Order of magnitudes
Optical microscope resolution 1
r⇠
sin ✓
with θ = angular aperture of the light beam De Broglie wave length
h
r⇠
p
with p = transferred momentum
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Experimental Particle Physics
2
HEP, SI and “natural” units
Quantity
length
charge
energy
HEP units
1 fm
e
1 GeV
SI units
10-15 m
1.602⋅10-19 C 1.602 x 10-10 J
mass
ħ = h/2
c
ħc
1 GeV/c2
6.588 x 10-25 GeV s
2.988 x 1023 fm/s
197 MeV fm
1.78 x 10-27 kg
1.055 x 10-34 Js
2.988 x 108 m/s
… mass
length
time
“natural” units (ħ = c = 1)
1 GeV
1 GeV-1 = 0.1973 fm
1 GeV-1 = 6.59 x 10-25 s
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Experimental Particle Physics
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How much energy to probe these distances?
2⇡~c
2⇡ ⇥ 197 MeV fm
h
=
= =
p
pc
pc
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What?
Dimension
[m]
p [GeV/c]
Atom
10-10
0.00001
Nucleus
10-14
0.
Nucleon
10-15
1
Quark
10-18
100
Experimental Particle Physics
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What do we want to measure?
2012: CERN!
H!
Higgs boson!
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Experimental Particle Physics
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Baryons and Mesons
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Experimental Particle Physics
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Measuring particles
• 
Particles are characterized by
! Mass
[Unit: eV/c2 or eV]
! Charge [Unit: e]
! Energy [Unit: eV]
! Momentum
[Unit: eV/c or eV]
! (+ spin, lifetime, …)
• 
Particle identification via
measurement of:
e.g.
(E, p, Q) or (p, β, Q)
(p, m, Q) ...
… and move at relativistic speed
=p
1
1
2
length contraption
time dilatation
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Experimental Particle Physics
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Relativistic kinematics in a nutshell
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Experimental Particle Physics
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Center of mass energy
• 
• 
In the center of mass frame the total momentum is 0
In laboratory frame center of mass energy can be computed as:
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Experimental Particle Physics
9
2-bodies decay
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Experimental Particle Physics
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Invariant mass
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Experimental Particle Physics
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3-bodies decay
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Experimental Particle Physics
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3-bodies decay
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Experimental Particle Physics
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3-bodies decay: pion decays
in most cases
muon decays
at rest
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Experimental Particle Physics
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3-bodies decay: Dalitz plot
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Experimental Particle Physics
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Multi-bodies decay
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Experimental Particle Physics
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Reaction threshold
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Experimental Particle Physics
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Fixed target vs. collider
How much energy should a fixed
target experiment have to equal
the center of mass energy of
two colliding beam?
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Experimental Particle Physics
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Collider experiment coordinates
y
z
Φ
r
θ
x
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Experimental Particle Physics
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Rapidity
Lorentz factor
• 
Hyperbolic cosine of “rapidity”
Particle physicists prefer to use modified rapidity along beam axis
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Experimental Particle Physics
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Pseudorapidity
if E >> m
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Transverse variables
• 
• 
At hadron colliders, a significant and unknown fraction of the beam
energy in each event escapes down the beam pipe. Net momentum can only be constrained in the plane transverse to the
beam z-axis! Marco Delmastro
X
pT (i) = 0
Experimental Particle Physics
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Missing transverse energy and tranaverse mass
• 
If invisible particle are created, only their transverse momentum can be
constrained: missing transverse energy
• 
If a heavy particle is produced and decays in two particles one of which
is invisible, the mass of the parent particle can constrained with the
transverse mass quantity
if
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Experimental Particle Physics
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W " e ν discovery
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Experimental Particle Physics
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Experimental Particle Physics
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W " e ν
events / 0.5 GeV
CDF II preliminary
L dt
2.2 fb-1
10000
5000
MW = (80408 ± 19stat) MeV
2/dof
0
60
70
= 52 / 48
80
90
100
mT (e ) (GeV)
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Experimental Particle Physics
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Interaction cross section
Flux
[L-2 t-1]
area obscured by target particle
Reactions
per unit of
time
Reaction rate
per target particle
Cross section
per target
particle
[t-1]
[L-2 t-1]
[?]
[L-1]
[L]
[t-1]
[L2]
= reaction rate per unit of flux
1b = 10-28 m2 (roughly the area of a nucleus with A = 100)
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Experimental Particle Physics
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Fermi Golden Rule
From non-relativistic perturbation theory…
transition probability
[t-1]
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matrix element
[E]
Experimental Particle Physics
energy density of final states
[E-1]
28
Cross section: magnitude and units
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Experimental Particle Physics
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Proton-proton scattering cross-section
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Experimental Particle Physics
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Cross-sections at LHC
108 events/s
~1010
10-2 events/s ~ 10 events/min
[mH ~ 120 GeV]
0.2% H " γγ
1.5% H " ZZ
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Experimental Particle Physics
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