# How much energy is carried away by neutrinos in matter-antimatter annihilation?

Some people say that neutrinos carry away most of the energy, some others say just a fraction. So what is the truth ? what is the percentage of energy lost due to neutrinos ?

-
That question sounded so poetic to me that I converted it into a poem: "How much energy is carried away", "by a neutrino in an annihilation", "Of matter and antimatter", "Some say the most", "Some say the the fraction", "So what's the truth", "So what's the percentage", "of energy lost due to", "Neutrinos...." – Sedat Kapanoglu Jan 20 '13 at 13:42

Annihilation of baryon antibaryon proceeds mainly by a multiplicity of pions . In this study , table 1, experimental.

Charged pions have a lifetime of of about $10^{-8}$ seconds and will decay into muons and neutrinos (anti too conserving quantum numbers), muons will decay with similar lifetime to electrons (positrons) and corresponding neurinos. The end stable particles will be neutrinos and electrons to share the charged pions energy.

Neutral pions decay within $10^{-16}$ seconds to two gammas.

Statistically, 2/3 of the energy goes to charged pions, and this is shared between neutrinos 3/4 and electrons 1/4 (2 $\nu_{\mu}$ and 1 $\nu_e$ and an electron).

Roughly neutrinos will get 1/2 of the available energy.

Gammas take 1/3 of the total energy.

So

-
So would it be correct if we said about 50% of the energy is carried away by neutrinos ? – Hurricane Jan 20 '13 at 18:25
yes, but as @JimGraber says if one waits for the end of the universe it will all be cold photons. – anna v Jan 20 '13 at 18:38
It is interesting of course to ask "over what distance scales are you measuring". At ranges of centimeters to decimeters the uncharged pions have decayed, but the many of the charged ones remain; out to meters some muons (first generation products of the pion decays) remain. – dmckee Jan 20 '13 at 19:05
@dmckee true, average energy,lifetime, and at what time after the annihilation. I asumed something on cosmic scales. – anna v Jan 20 '13 at 19:15

Anna's answer is good, but it doesn't go far enough. If you start with equal amounts of matter and antimatter, you end up with equal amounts of electrons and positrons, which eventually annihilate to photons. You also end up with equal amounts of neutrinos and antineutrinos, which also eventually annihilate to photons. So those (anti-)neutrinos only keep that energy temporarily. The only other permanent outlet is gravitons, which are entirely negligible. So eventually, all the energy ends essentially up as photons.

-
I was going to add the electron positron annihilation, but neutrino on antineutrino has a very low cross section and needs also an extra loop to interact electromagnetically. will the lifetime of the present universe be enough ? – anna v Jan 20 '13 at 10:44
Yes, especially in an expanding universe they may not all collide. But then there is the cosmic neutrino background to consider. I think this very substantially increases the likelihood that all the neutrinos would eventually annihilate. So it is complicated – Jim Graber Jan 21 '13 at 14:11