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PARTICLE PHYSICS 2022

QUIZ 2 (WEEK 2)

Reinforcing understanding of angular momentum/spin and special relativity.

Consider some neutral meson Ⅹ〇 that decays to a pair of photons, Ⅹ〇 → 礻礻 .

(a) What value(s) of the orbital angular momentum quantum number L can, in prin- ciple, the quark-antiquark system comprising the Ⅹ〇 possess? Briefly explain your logic.

(b) What value(s) of the orbital angular momentum quantum number L can, in princi- ple, the photon pair that the Ⅹ〇 decays into possess? Briefly explain your logic.

An example of such a neutral meson is the π〇. When it decays, the π〇 decays almost all of the time to a pair of photons, π〇 → 礻礻 .

(c) If a π〇 decays in its rest frame, what is the magnitude of the momentum of each of the two daughter photons?

(d) If the π〇 instead has an energy of 1.0 GeV, what fraction of the speed of light is it traveling at?

(e) If the π〇 in (d) is traveling along the positive 之-axis and, in its rest frame it decayed

such that the two daughter photons were traveling perpendicular to the 之-axis, what would be the magnitude of the momentum of each photon in the frame in which the π〇 is moving?