• venomxx
In summary, according to the book, energy momentum conservation is what allows photons to have momentum. If photons are massless, this does not make sense, but if we assume that they have a relativistic rest mass, then it works.
venomxx
Reading on pions the book glanced over this idea:

Aloud:
Neutral pion --> photon and photon

Not aloud:
Neutral pion --> photon

the book says its due to energy momentum conservation? but if photons are massless how does this work?

Cheers

You can try this by just putting up the equations of momentum- and energy conservation.. it is really simple.

cheers for the reply, but if the photon is massless how does it have any momentum to carry away?

If you apply the relativistic rest mass, momentum, total energy equation to photons:

E2 = (βγ m0c2)2 + (m0c2)2 to photons, we get

E = pc, or p = E/c

So massless photons of energy E have momentum E/c.

Bob S

Still, to understand the complete problem we need other question: can a Z0 meson decay to two photons?

So, using p=E/c for the photon and using the energy and momentum of neutral pion, you can determine that it needs two photons to carry away the momentum as one would not be sufficient. Would i be correct in saying that?

arivero: i believe a Z0 is able decay into two photons with no problems...at least from what iv just looked up!

venomxx said:
So, using p=E/c for the photon and using the energy and momentum of neutral pion, you can determine that it needs two photons to carry away the momentum as one would not be sufficient. Would i be correct in saying that?
Consider a pi zero from the proton capture of a pi minus at rest going to a neutron plus pi zero. The pi zero momentum is miniscule. How could it decay to a single 135 MeV photon?

arivero: i believe a Z0 is able decay into two photons with no problems...at least from what iv just looked up!
The Z0 branching ratio to two photons is less than ~5 x 10-5.
Bob S

venomxx said:
So, using p=E/c for the photon and using the energy and momentum of neutral pion, you can determine that it needs two photons to carry away the momentum as one would not be sufficient. Would i be correct in saying that?

arivero: i believe a Z0 is able decay into two photons with no problems...at least from what iv just looked up!

no Z0 BOSON does not have couplings to the photon (at tree level), they are orthogonal states..

arivero said:
still, to understand the complete problem we need other question: Can a z0 meson decay to two photons?

z0 meson?

venomxx said:
So, using p=E/c for the photon and using the energy and momentum of neutral pion, you can determine that it needs two photons to carry away the momentum as one would not be sufficient. Would i be correct in saying that?

No, the correct answer is that energy and momentum conservation can not be simoultatneously fulfilled in the case of pi0 decaying into one photon.

ansgar said:
z0 meson?

Zee IV.7.2 said:
Following the reasoning in Chapter IV.2 and using the erroneus (10) show that the decay amplitude for the decay $\pi^0 \to \gamma + \gamma$ would vanish in the ideal world in which the $\pi^0$ is massless. ... since our world is close to the ideal world, this provided the first indication historically that (10) cannot posibly be valid

Some textbooks propose, to deep in the understanding of the "triangle", to compare the decay where the spin 0 pion goes to quark antiquark and then to two photons with other two triangles: the one with an spin 1 meson (pho, sigma, J/Psi, etc) decaying to the same mechanism, and the one with the Z0 decaying to any of their particle/antiparticle couplings and then to two photons.

The point I want to make is that, while the kinematic answer is enough for the Original Post goal, the OP has unfortunately chosen the most famously complicated example of electromagnetic decay.

Last edited:
Consider this senario. The pion is initially at rest in its frame. The pion has a certain amount of rest energy mc^2 and when it decays into photons all of this energy is converted into the momentum of the photon E=pc. In order to uphold conservation of momentum, if the pion with initial momentum of zero were to decay into one photon, then that photon would necessarily be at rest. Well we know that this can't be the case because the photon must have velocity c and some energy corresponding to its energy (from the pion rest mass).
From that simple argument its straight forward to see that the number of photons must be greater than one (and using the quantum charge operator, must be even number of photons).

Hope this helps.

That helps alot, cheers for the great replys! its so simple when you think about it...:)

## 1. What is a Pion decay?

A Pion decay is a process in which a pion, a subatomic particle made up of a quark and an antiquark, transforms into other particles.

## 2. How does a Pion decay occur?

A Pion decay occurs through the weak force, which is one of the four fundamental forces of nature. During the decay process, the pion transforms into a muon and a muon neutrino, or an electron and an electron antineutrino.

## 3. What is the significance of studying Pion decay?

Pion decay is important for understanding the weak force and its role in interactions between subatomic particles. It also helps us gain insights into the structure of matter and the origin of the universe.

## 4. How is Pion decay studied?

Pion decay is studied in particle accelerators, where high-energy collisions between particles can produce pions. Scientists can then observe the decay of these pions and gather data about the process.

## 5. Are there any practical applications of Pion decay?

While there are currently no practical applications of Pion decay, the knowledge gained from studying this process could potentially lead to advancements in technology and medicine in the future.

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