In a fixed-target experiment

PHYSICS · Multi-part · Fermi University Physics · Relativity & Gravitation · Special relativity: spacetime and kinematics · Special relativity: spacetime and kinematics

Symmetry and Flavour, Ch Four-vectors at work: boosts, invariants and the shape of a final state

Problem

In a fixed-target experiment, secondary pions have a lab-frame rapidity distribution

\mathrm{d}N/\mathrm{d}y_{\rm lab}

that has a single peak at

y_{\rm lab} = 2.20

, is symmetric about it, and is non-zero only for

1.40 \le y_{\rm lab} \le 3.00

. The centre-of-mass frame of the beam-target collision moves with rapidity

y_b = 1.80

relative to the laboratory frame. ((a)) Predict the peak position and the full range of

\mathrm{d}N/\mathrm{d}y^*

in the centre-of-mass frame. ((b)) State which quantity, the peak position or the width of the range, is unchanged by the boost, and explain why in terms of how rapidity transforms under a longitudinal boost.

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