particleExperimental physics
units, quantities, 1. kinematics, measurements
Marco Delmastro Experimental Particle Physics 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
Marco Delmastro Experimental Particle Physics 2 HEP, SI and “natural” units
Quantity HEP units SI units length 1 fm 10-15 m charge e 1.602⋅10-19 C energy 1 GeV 1.602 x 10-10 J mass 1 GeV/c2 1.78 x 10-27 kg ħ = h/2 6.588 x 10-25 GeV s 1.055 x 10-34 Js c 2.988 x 1023 fm/s 2.988 x 108 m/s ħc 197 MeV fm …
“natural” units (ħ = c = 1) mass 1 GeV length 1 GeV-1 = 0.1973 fm time 1 GeV-1 = 6.59 x 10-25 s
Marco Delmastro Experimental Particle Physics 3 How much energy to probe these distances?
h 2⇡~c 2⇡ 197 MeV fm = = = ⇥ p pc pc
What? Dimension p [m] [GeV/c]
Atom 10-10 0.00001
Nucleus 10-14 0.
Nucleon 10-15 1
Quark 10-18 100
Marco Delmastro Experimental Particle Physics 4 What do we want to measure?
2012: CERN H!
Higgs boson!
Marco Delmastro Experimental Particle Physics 5 Baryons and Mesons
Marco Delmastro Experimental Particle Physics 6 Measuring particles • Particles are characterized by ! Mass [Unit: eV/c2 or eV] Particle identification via ! Charge [Unit: e] measurement of: ! Energy [Unit: eV] ! Momentum [Unit: eV/c or eV] e.g. (E, p, Q) or (p, β, Q) ! (+ spin, lifetime, …) (p, m, Q) ...
• … and move at relativistic speed 1 = 1 2 length contraptionp
time dilatation
Marco Delmastro Experimental Particle Physics 7 Relativistic kinematics in a nutshell
Marco Delmastro Experimental Particle Physics 8 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:
Marco Delmastro Experimental Particle Physics 9 2-bodies decay
Marco Delmastro Experimental Particle Physics 10 Invariant mass
Marco Delmastro Experimental Particle Physics 11 3-bodies decay
Marco Delmastro Experimental Particle Physics 12 3-bodies decay
Marco Delmastro Experimental Particle Physics 13 3-bodies decay: pion decays
in most cases muon decays at rest
Marco Delmastro Experimental Particle Physics 14 3-bodies decay: Dalitz plot
Marco Delmastro Experimental Particle Physics 15 Multi-bodies decay
Marco Delmastro Experimental Particle Physics 16 Reaction threshold
Marco Delmastro Experimental Particle Physics 17 Fixed target vs. collider
How much energy should a fixed target experiment have to equal the center of mass energy of two colliding beam?
Marco Delmastro Experimental Particle Physics 18 Collider experiment coordinates
y
Φ z r θ
x
Marco Delmastro Experimental Particle Physics 19 Rapidity
Lorentz factor Hyperbolic cosine of “rapidity”
• Particle physicists prefer to use modified rapidity along beam axis
Marco Delmastro Experimental Particle Physics 20 Pseudorapidity
if E >> m
Marco Delmastro Experimental Particle Physics 21 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!
pT (i)=0 X
Marco Delmastro Experimental Particle Physics 22 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
Marco Delmastro Experimental Particle Physics 23 W " e ν discovery
Marco Delmastro Experimental Particle Physics 24 Marco Delmastro Experimental Particle Physics 25 W " e ν CDF II preliminary L dt 2.2 fb-1 V e G
5 . 0
/
s 10000 t even
5000 MW = (80408 ± 19stat) MeV
2/dof = 52 / 48
0 60 70 80 90 100
mT(e ) (GeV)
Marco Delmastro Experimental Particle Physics 26 Interaction cross section
Flux [L-2 t-1]
area obscured by target particle Reactions per unit of [t-1] time [L-2 t-1] [?] [L-1] [L]
Reaction rate [t-1] per target particle
Cross section per target [L2] = reaction rate per unit of flux particle
1b = 10-28 m2 (roughly the area of a nucleus with A = 100) Marco Delmastro Experimental Particle Physics 27 Fermi Golden Rule
From non-relativistic perturbation theory…
transition probability matrix element energy density of final states
[t-1] [E] [E-1]
Marco Delmastro Experimental Particle Physics 28 Cross section: magnitude and units
Marco Delmastro Experimental Particle Physics 29 Proton-proton scattering cross-section
Marco Delmastro Experimental Particle Physics 30 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
Marco Delmastro Experimental Particle Physics 31