Illustrated Physics
physics, drawn
Concept

Transverse momentum — where it appears

The part of a particle's momentum perpendicular to a collider's beams. The colliding partons carry an unknown share of the beam momentum along the axis but almost none across it, so the transverse components of everything produced must balance, and an imbalance reveals an unseen particle.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

One spray of particles, seen from two frames. Massless particles sprayed evenly in every direction from a source, as distributions in two variables. Left: against the cosine of the angle from the beam axis, for the source at rest (flat) and the same source moving along the axis at 0.8c (peaked forward), which crowds the particles forward until 81 times as many go straight ahead as straight back. Right: the same two sprays against pseudorapidity, η = −ln tan(θ/2). In η the moving spray is the resting one moved over by 1.099, the rapidity of 0.8c, with its shape — ½ sech² η, a peak of 0.5 and a width of 1.76 at half height — unchanged. A boost along the beam that distorts every distribution in angle or velocity only translates a distribution in rapidity.

The angle a collider counts in logarithms

The two proton beams of the Large Hadron Collider meet head on with equal energies, so the collisions ought to happen at rest in the laboratory. They do not. Each collision is really between two fragments of protons carrying unknown, unequal shares of the momentum, and every one is moving along the beam at a different speed. Particle physicists therefore describe what comes out in a variable that a boost along the beam simply shifts: rapidity, the quantity in which speeds add. A detector cannot measure rapidity directly. It measures an angle, and converts it to a logarithm.

relativity · Velocity-addition A peak at half the mass, made by a sine. The momentum across the beam of the electron from 200,000 simulated W decays, as a probability density per GeV, for a W of mass 80.37 GeV. For a W exactly at rest across the beam, of exactly its mass (dashed), the electron carries M/2 = 40.19 GeV in the W's frame and shows a fraction sin θ of it across the beam, so the distribution climbs to a sharp peak at M/2 and stops: the Jacobian peak, piled up because sin θ hardly changes near θ = 90°. The W's natural width of 2.1 GeV rounds the peak (solid, peak at 39.9 GeV); its motion across the beam, a few GeV on average, smears it further and pushes a tail past M/2 (lighter). The position of the peak measures the mass, and is shifted by anything that moves the W.

The mass weighed without one of its pieces

A W boson decays into an electron and a neutrino, and the neutrino leaves every detector without a trace. Its mass cannot be found the usual way, by adding up the energy and momentum of what it decayed into, because half of what it decayed into is missing. What survives is the part of the motion across the beam, where the neutrino's momentum can be inferred from the imbalance it leaves. There the electron's momentum piles up at half the W's mass, and a quantity built from both particles ends at a sharp edge at the full mass. The world's best measurements of that edge disagree by seventy-five parts in eighty thousand.

relativity · Mass-energy

Named alongside it

The objects these essays reach for when they reach for this one.

RapidityCentre of mass frameInvariant massJacobianJacobian peakLorentz boostLorentz invarianceNeutrinoParticle colliderPseudorapidityTransverse massTwo-body decay

All concepts