# Charge Conservation in Neutron Decay

1. Mar 12, 2006

### Kestrel

A neutron can decay into a proton, a positron, and a neutrino.
A proton is made up of two up quarks and a down quark.
A neutron is made up of one up quark and two down quarks.
An up quark has a charge of +2/3, and a down quark has a charge of -1/3.

Given the statements above, can someone please explain how the charge is conserved and/or divided in the decay of a neutron? You start with three particles, two of which have a charge of -1/3 (down) and one of which has a charge of +2/3 (up). Then it decays, and you end up with 5 particles, one which has charge of -1/3 (down), two with charge of +2/3 (up), one with charge of +1 (the positron), and a neutral neutrino.

Charge is conserved, but where exactly does it get broken up? If you write it in equation form, you can cancel one up and one down quark from each side and end up with an up quark decaying to a down quark, a positron, and a neutrino. Is this indeed what happens? An up quark, with charge +2/3, loses 1 unit of charge (dropping to a -1/3), and in the process produces some extra particles? This would imply each up quark containing a positron, which, while I could be wrong, doesn't sound right.

Any and all clarification would be appreciated, thank you!

Scott

2. Mar 12, 2006

### Physics Monkey

Charge is explicitly not conserved in your hypothetical decay! You have a neutron with charge 0 going to a proton and a positron with total charge of +2. Conservation of charge is violated and the decay cannot occur. The correct decay channel is neutron to proton plus electron plus anti-neutrino. See here for more: http://hyperphysics.phy-astr.gsu.edu/HBASE/particles/proton.html

Hope this helps.

Last edited: Mar 12, 2006
3. Mar 12, 2006

### Kestrel

Wow! My mistake, that was a big error. Sorry about that! What I meant to ask was, in the decay of a neutron (as you point out to be correctly "neutron to proton plus electron plus anti-neutrino"), how does the charge get broken up?

u + d + d ---> u + u + d + e + antineutrino

Basically what I'm asking is, how is it that you end up with an integral charge when all you start with is fractional charges? We're dealing with leptons here. I understand that charge is conserved, but it is rearranged. Do we understand the process by which this happens? Going from the equation above, you could "cancel" the "spectators" (forgive the chemistry terminology) and end up with

d ---> u + e + antineutrino

(-1/3) ---> (+2/3) + (-1) + (0)

It appears that a down quark contains an up quark, an electron, and an antineutrino, but the extra particles could be a result of something else.

Thanks again!

Scott

4. Mar 12, 2006

### mathman

Down quark does not "contain" an up quark plus electron, anymore than an up quark "contains" a down quark plus positron (nucleus with excess protons leads to psitron emission). These changes are transformations, not decompositions.

5. Mar 12, 2006

### Kestrel

So what is the mechanism of the transformation? Or is it one of those things we just say "happens?"

Scott

6. Mar 12, 2006

### Physics Monkey

The decay changes the flavor of the quarks so it must be a weak decay. The lowest order Feynman diagram corresponds to a down quark decaying into a $$W^-$$ and an up quark. The $$W^-$$ then decays into an electron and an anti-neutrino.

Last edited: Mar 12, 2006
7. Mar 12, 2006

### Kestrel

Excellent! Thank you mathman and Physics Monkey, that was exactly what I was looking for!

I just found it odd that you could get integral charges from fractional charges, but the W boson (after some research) has cleared this up. I still find it a little odd (just as I find .999... = 1 odd), but this certainly clears a lot up.

Thanks again!

Scott

8. Mar 13, 2006

### dextercioby

An explicit discussion on this specific matter, including calculations is found in Griffiths' introductory text on particle physics...

Daniel.