Why can a particle decay into two photons but not one?












10















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?






particle-physics photons momentum conservation-laws higgs







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  • Related: physics.stackexchange.com/q/427466/2451 and links therein.

    – Qmechanic♦
    2 hours ago


















10















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?






particle-physics photons momentum conservation-laws higgs







share|cite|improve this question

























  • Related: physics.stackexchange.com/q/427466/2451 and links therein.

    – Qmechanic♦
    2 hours ago
















10












10








10


1






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?






particle-physics photons momentum conservation-laws higgs







share|cite|improve this question
















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?






particle-physics photons momentum conservation-laws higgs




particle-physics photons momentum conservation-laws higgs






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share|cite|improve this question













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edited 1 hour ago









Ben Crowell

49k4151294




49k4151294










asked 22 hours ago









user6760user6760

2,50111737




2,50111737













  • Related: physics.stackexchange.com/q/427466/2451 and links therein.

    – Qmechanic♦
    2 hours ago





















  • Related: physics.stackexchange.com/q/427466/2451 and links therein.

    – Qmechanic♦
    2 hours ago



















Related: physics.stackexchange.com/q/427466/2451 and links therein.

– Qmechanic♦
2 hours ago







Related: physics.stackexchange.com/q/427466/2451 and links therein.

– Qmechanic♦
2 hours ago












2 Answers
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28














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.






share|cite|improve this answer
























  • 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?

    – user6760
    20 hours ago








  • 2





    @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.

    – rob♦
    19 hours ago





















16














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.






share|cite|improve this answer





















  • 1





    I just look up spin so spin can be negative

    – user6760
    22 hours ago






  • 5





    I think this answer is misleading because it discusses only angular momentum. The hypothetical decays $Ztogamma$ or $text{ortho-}(e^+e^-) to gamma$ can conserve angular momentum, but don't occur for the more basic reason given in my answer.

    – rob♦
    19 hours ago













  • @rob You are absolutely right. Angular momentum conservation is only necessary, not sufficient, and the way my answer is worded is misleading in that respect. I edited my answer to include a link to your answer. Thanks for clarifying this.

    – Dan Yand
    11 hours ago











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2 Answers
2






active

oldest

votes








2 Answers
2






active

oldest

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active

oldest

votes






active

oldest

votes









28














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.






share|cite|improve this answer
























  • 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?

    – user6760
    20 hours ago








  • 2





    @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.

    – rob♦
    19 hours ago


















28














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.






share|cite|improve this answer
























  • 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?

    – user6760
    20 hours ago








  • 2





    @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.

    – rob♦
    19 hours ago
















28












28








28







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.






share|cite|improve this answer













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.







share|cite|improve this answer












share|cite|improve this answer



share|cite|improve this answer










answered 20 hours ago









rob♦rob

40k972165




40k972165













  • 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?

    – user6760
    20 hours ago








  • 2





    @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.

    – rob♦
    19 hours ago





















  • 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?

    – user6760
    20 hours ago








  • 2





    @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.

    – rob♦
    19 hours ago



















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?

– user6760
20 hours ago







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?

– user6760
20 hours ago






2




2





@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.

– rob♦
19 hours ago







@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.

– rob♦
19 hours ago













16














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.






share|cite|improve this answer





















  • 1





    I just look up spin so spin can be negative

    – user6760
    22 hours ago






  • 5





    I think this answer is misleading because it discusses only angular momentum. The hypothetical decays $Ztogamma$ or $text{ortho-}(e^+e^-) to gamma$ can conserve angular momentum, but don't occur for the more basic reason given in my answer.

    – rob♦
    19 hours ago













  • @rob You are absolutely right. Angular momentum conservation is only necessary, not sufficient, and the way my answer is worded is misleading in that respect. I edited my answer to include a link to your answer. Thanks for clarifying this.

    – Dan Yand
    11 hours ago
















16














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.






share|cite|improve this answer





















  • 1





    I just look up spin so spin can be negative

    – user6760
    22 hours ago






  • 5





    I think this answer is misleading because it discusses only angular momentum. The hypothetical decays $Ztogamma$ or $text{ortho-}(e^+e^-) to gamma$ can conserve angular momentum, but don't occur for the more basic reason given in my answer.

    – rob♦
    19 hours ago













  • @rob You are absolutely right. Angular momentum conservation is only necessary, not sufficient, and the way my answer is worded is misleading in that respect. I edited my answer to include a link to your answer. Thanks for clarifying this.

    – Dan Yand
    11 hours ago














16












16








16







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.






share|cite|improve this answer















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.







share|cite|improve this answer














share|cite|improve this answer



share|cite|improve this answer








edited 11 hours ago

























answered 22 hours ago









Dan YandDan Yand

8,16211134




8,16211134








  • 1





    I just look up spin so spin can be negative

    – user6760
    22 hours ago






  • 5





    I think this answer is misleading because it discusses only angular momentum. The hypothetical decays $Ztogamma$ or $text{ortho-}(e^+e^-) to gamma$ can conserve angular momentum, but don't occur for the more basic reason given in my answer.

    – rob♦
    19 hours ago













  • @rob You are absolutely right. Angular momentum conservation is only necessary, not sufficient, and the way my answer is worded is misleading in that respect. I edited my answer to include a link to your answer. Thanks for clarifying this.

    – Dan Yand
    11 hours ago














  • 1





    I just look up spin so spin can be negative

    – user6760
    22 hours ago






  • 5





    I think this answer is misleading because it discusses only angular momentum. The hypothetical decays $Ztogamma$ or $text{ortho-}(e^+e^-) to gamma$ can conserve angular momentum, but don't occur for the more basic reason given in my answer.

    – rob♦
    19 hours ago













  • @rob You are absolutely right. Angular momentum conservation is only necessary, not sufficient, and the way my answer is worded is misleading in that respect. I edited my answer to include a link to your answer. Thanks for clarifying this.

    – Dan Yand
    11 hours ago








1




1





I just look up spin so spin can be negative

– user6760
22 hours ago





I just look up spin so spin can be negative

– user6760
22 hours ago




5




5





I think this answer is misleading because it discusses only angular momentum. The hypothetical decays $Ztogamma$ or $text{ortho-}(e^+e^-) to gamma$ can conserve angular momentum, but don't occur for the more basic reason given in my answer.

– rob♦
19 hours ago







I think this answer is misleading because it discusses only angular momentum. The hypothetical decays $Ztogamma$ or $text{ortho-}(e^+e^-) to gamma$ can conserve angular momentum, but don't occur for the more basic reason given in my answer.

– rob♦
19 hours ago















@rob You are absolutely right. Angular momentum conservation is only necessary, not sufficient, and the way my answer is worded is misleading in that respect. I edited my answer to include a link to your answer. Thanks for clarifying this.

– Dan Yand
11 hours ago





@rob You are absolutely right. Angular momentum conservation is only necessary, not sufficient, and the way my answer is worded is misleading in that respect. I edited my answer to include a link to your answer. Thanks for clarifying this.

– Dan Yand
11 hours ago


















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