Standard Model and Beyond · Problem 6.6

The Weak Interactions

Physics — Particle Physics · event-shape-thrust

Problem

Perhaps the best known event shape variable is thrust, τ≡max⁡n^τ∑i∣p⃗i⋅n^τ∣∑i∣p⃗i∣,\tau \equiv \max_{\hat{n}_\tau} \frac{\sum_i |\vec{p}_i \cdot \hat{n}_\tau|}{\sum_i |\vec{p}_i|}, where the sum is over all of the particles in the event, and the thrust axis n^τ\hat{n}_\tau is chosen to maximize the sum. (At hadron colliders one can replace p⃗i\vec{p}_i by p⃗iT\vec{p}_{iT}.) Calculate τ\tau for (a) two back-to-back particles (or highly-collimated jets); (b) many particles, distributed isotropically; (c) three particles in a plane with equal energies and separated by 120∘120^\circ.

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