Physics / advanced
Invariant kinematics and scattering observables
Master invariant variables, phase-space measures, helicity descriptions, and collider coordinate systems before interpreting particle interaction measurements.
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Module 01 advanced
Invariant kinematics and scattering observables
Master invariant variables, phase-space measures, helicity descriptions, and collider coordinate systems before interpreting particle interaction measurements.
- 01
Locate a collision with invariant variables
Use a stated metric and on-shell constraints to connect Mandelstam variables, scattering angles, and the difference between laboratory and center-of-momentum energy.
35 min - 02
Count final states with an invariant measure
Derive the positive-energy on-shell measure and reduce two-body phase space while keeping all factors of two pi and identical-particle conventions explicit.
37 min - 03
Separate decay directions from laboratory collimation
Compute two-body rest-frame kinematics, identify when isotropy follows from rotational symmetry, and transform energies and angles into a boosted laboratory frame.
36 min - 04
Map a three-body decay onto invariant masses
Use pair-invariant constraints and pair-rest-frame angles to construct the physical Dalitz region and distinguish a constant-amplitude baseline from resonance dynamics.
38 min - 05
Expand near a physical threshold
Derive the square-root opening of a massive two-body channel, compare fixed-target and center-of-momentum thresholds, and state the dynamical assumptions behind threshold powers.
37 min - 06
Choose collider coordinates without losing the mass
Derive rapidity addition and transverse invariance, distinguish pseudorapidity from true rapidity for massive particles, and connect coordinate densities to detector geometry.
36 min - 07
Follow spin when the momentum frame changes
Distinguish helicity from a fixed-axis spin label, explain Wigner rotations through standard boosts, and test why massive helicity can change between inertial frames.
40 min - 08
Turn an invariant amplitude into an event yield
Normalize scattering with invariant incoming flux, phase space, spin sums, and identical-particle counting before relating a cross section to integrated luminosity and efficiency.
38 min - 09
Factor a resonance only when the integral permits it
Derive the narrow-width delta-function approximation, retain spin correlations when needed, and connect an energy width to proper lifetime and laboratory decay length.
39 min - 10
Constrain an invisible decay without inventing its momentum
Define missing transverse momentum from a stated detector model, derive the transverse-mass bound, and demonstrate the residual longitudinal ambiguity even with a parent-mass constraint.
39 min