I recently read an old physics news about the Higgs boson where it was observed to decay into 2 photons and I was wondering why it wouldn't have decayed into a single photon with the combined energy of 2 photons?
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$\begingroup$ Related: physics.stackexchange.com/q/427466/2451 and links therein. $\endgroup$– Qmechanic ♦Jan 13, 2019 at 0:05
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2 Answers
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No massive particle can decay into a single photon.
In its rest frame, a particle with mass $M$ has momentum $p=0$. If it decayed to a single photon, conservation of energy would require the photon energy to be $E=Mc^2$, while conservation of momentum would require the photon to maintain $p=0$. However, photons obey $E=pc$ (which is the special case of $E^2 = (pc)^2 + (mc^2)^2$ for massless particles). It's not possible to satisfy all these constraints at once. Composite particles may emit single photons, but no massive particle may decay to a photon.
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$\begingroup$ Massive particle as in fermion with half integer spin right, so it have to decay into some other particles on top of a photon to conserve energy and spin momentum is this what you are saying? $\endgroup$– user6760Jan 12, 2019 at 6:04
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3$\begingroup$ @user6760 This argument is about linear, not angular, momentum. And there are plenty of massive particles which obey Bose-Einstein statistics and have integer spins. $\endgroup$– rob ♦Jan 12, 2019 at 7:12
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The Higgs boson has spin $0$. A photon has spin $1$. The total angular momentum cannot change in the decay, so a Higgs boson cannot decay into a single photon, regardless of the energy. But the total angular momentum of two photons can be zero (because their spins can be oriented in opposite directions), so this decay mode can conserve angular momentum.
As emphasized in a comment, conservation of angular momentum is only a necessary condition, not a sufficient one. Please see rob's answer for clarification about this.
answered Jan 12, 2019 at 3:52
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1$\begingroup$ I just look up spin so spin can be negative $\endgroup$– user6760Jan 12, 2019 at 4:14
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$\begingroup$ @Chiral Anomaly When you write ".....(because their spins can be oriented in opposite directions), so this decay mode can conserve angular momentum". Are you talking about spin projection? $\endgroup$ May 5, 2022 at 3:31
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$\begingroup$ @N.Ginlabs My statement was loose. The two-photon state with total spin zero is an entangled state, in which the orientations of the individual photons' spins are not individually defined. The point of my statement was simply that a single photon can't have a total angular momentum of zero (zero projection along every direction), but a pair of photons can. $\endgroup$ May 6, 2022 at 15:13