# Pair production and electron

When an gamma foton interacts with matter it can produce an Electron-pisitron pair. Why dont lower enery fotons sometime's produce an neutrino-antineutrino pair.

Lepton number and charche wil be concerved

So wath is the problem then?
A foton is also an neutral particle.
Al electron and positron pair is also neutral.
why must the particles be charged ?

Staff Emeritus
Gold Member
Dearly Missed
I think it has to do with handedness. The neutrino and antineutrino are both left handed, according to the standard model, that breaks a symmetry.

Physics Monkey was right to notice the importance of charge here : neutrinos are not sensitive to electric charge, they only interact through the weak interaction. But pair creation in matter occurs in the electromagnetic field of the nucleus, and this is very important.

Then selfAdjoint is almost right : neutrinos are always left-handed, whereas antineutrinos are always right-handed.
http://hyperphysics.phy-astr.gsu.edu/hbase/particles/neutrino3.html#c1
They both have spin 1/2. So in the process of creating a pair $$\nu\bar{\nu}$$ you see that you end up with zero angular momentum. The photon cannot have zero angular momentum because it is spin 1 and massless.

vanesch
Staff Emeritus
Gold Member
humanino said:
Then selfAdjoint is almost right : neutrinos are always left-handed, whereas antineutrinos are always right-handed.
http://hyperphysics.phy-astr.gsu.edu/hbase/particles/neutrino3.html#c1
They both have spin 1/2. So in the process of creating a pair $$\nu\bar{\nu}$$ you see that you end up with zero angular momentum. The photon cannot have zero angular momentum because it is spin 1 and massless.

I don't get this: the momenta are also opposite, so I'd say that the state of a neutrino going left, and an anti-neutrino going right, you'd have a spin-1 state, no ? Or have I been drinking ?

I gues it has to do with the fact that its an anti neutrino/

thank you al for you answers , i thank you all very much.

vanesch said:
I don't get this: the momenta are also opposite, so I'd say that the state of a neutrino going left, and an anti-neutrino going right, you'd have a spin-1 state, no ? Or have I been drinking ?
No no no you right : I probably had been drinking when I wrote this !

antoon said:
I gues it has to do with the fact that its an anti neutrino
you have teased my interest now I want to understand : I am not satisfied yet

So, I realize that Physics Monkey is right from the beginning : I never saw any Feynman diagram coupling a photon to a neutrino, and indeed neutrino do not carry electric charge. In the standard model this is forbiden. Correct ?

Now beyond the SM, I still am not totally sure that, even with a corresponding Feynman diagram for a possible photon-neutrino coupling, one cannot find a further reason for the process not to occur. So let's admit for all purpose that all those particles are massless (this known to be a very good approximation). Let's assume the photon incident along the z-axis. As vanesh pointed out, the neutrino and it's anti-buddy have to fly away back-to-back for angular momentum conservation. If the direction were not z-direction, then both transverse impulsion should compensate each other. However, since neutrinos are massless, this implies exact same total impulsion (since we already know they are flying back-to-back, at the same angle). Now we come to a contradiction : the photon was not at rest initially. I want to point out that this is very much due to the fact that photon and neutrinos are both chargeless : they cannot interact with the nuclei around to compensate for impulsion (this is known to be an ingredient in $$e^+e^-$$ creation). Then both neutrinos have to fly away back to back in the z-direction. However, there is no phase space avalaible ! For energy conservation to be respected, the forward going (anti-)neutrino must carry all the impulsion (whether this is the neutrino or the anti-neutrino forward going depends only on the inital polarization of the photon). The backward going buddy must be "at rest" which is impossible for a massless particle.

is a neutrino treuly massless?
i though it had a mass

antoon said:
is a neutrino treuly massless?
i though it had a mass
Well, for the purpose of understanding why photons cannot produce neutrino-antineutrino pairs at low energy, it is a vey sufficient approximation to assume they have no mass. Currently :
• $$m_{\nu_e}<3$$ eV
• $$m_{\nu_{\mu}}<190$$ keV
• $$m_{\nu_{\tau}}<18.5$$ MeV
with 90% confidence level.

What is also known today, is that they cannot have the same mass. So for sure they can't (at least not all) be massless. The available bounds on $$\Delta m^2$$ are still under discussions. Using cosmic microwave background anisotropy, they found $$\sum_{i=\nu_e,\nu_{\mu},\nu_{\tau}} m_{i}<0.7$$ eV (possible model dependence however). If one accepts this bound, then only the other bound on $$m_{\nu_e}$$ is relevant.

See PDG : Electron, muon, and tau neutrino Listings (Rev.) for further details.

reilly
Photoproduction of neutrino pairs does indeed occur.
See, for example
www.yars.free.net/English/Science/YSU/Dept/Phys/DivTheorPhys/[/URL]
papers/jetpl75.pdf
To be sure, the reaction gamma + N(ucleon) -> N + gamma + neutrino pair has an extra gamma in the final state, but that's hardly a big deal, not a claim buster. What is interesting is that the experiment discussed takes place in a strong magnetic field, which is an odd-parity field.

Rrgards,
Reilly Atkinson

(Google will give you riches beyond belief in the photoproduction of neutrino world.)

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Physics Monkey
Hey guys, I see the discussion continues, so I thought I would stop back by and comment. Reilly is quite correct to point out that neutrino pair production is not actually forbidden. My original response was oversimplified. What is forbidden within the Standard Model is the "direct" production of a neutrino-antineutrino pair by a photon. There is no vertex for this interaction because neutrinos are electrically neutral. The typical process for producing a neutrino-antineutrino pair would involve the decay of a $$Z_0$$ boson. This neutral boson can interact with other leptons that directly couple to photons. In this way, the process of neutrino pair production by light is allowed, but it must proceed through intermediaries. Of course, the usual concerns about various conservation laws must also be remembered.