The thumb rule is "Any particle will decay into lighter ones unless forbidden by some conservation rules." You cannot find any electrically charged particle lighter than electron, i guess, that explains the stability of electron.

A proton could decay into positron and two neutrinos (say). But we don't see proton to decay. To explain this, we had to 'invent new set of conservation rules'. In this case, it is BARYON no. conservation.

So, the game is simple. You start with some basic conservation principle and try to explain as many processes as you can. If anything escapes, try to figure out a new rule which doesn't affect the previous ones but can explain the odd processes and so on ... Some examples are BARYONIC q. no., LEPTONIC q. no., STRANGENESS q. no. (in strong processes) etc ...

Of course, one may ask why these things should be conserved. As we know, every conservation principle is the result of an underlying symmetry. One example is, translational symmetry dictates total linear momentum to be conserved. But as far as I know, till now there is no underlying symmetry discovered which dictates baryon or lepton no. conservation. It is an accidental symmetry of the standard model. It is still an open question.

Let me conclude by saying that there are GUT models which predicts that proton should decay!

Hope it helps.

Good luck

Dipankar

The thumb rule is "Any particle will decay into lighter ones unless forbidden by some conservation rules." You cannot find any electrically charged particle lighter than electron, i guess, that explains the stability of electron.

A proton could decay into positron and two neutrinos (say). But we don't see proton to decay. To explain this, we had to 'invent new set of conservation rules'. In this case, it is BARYON no. conservation.

So, the game is simple. You start with some basic conservation principle and try to explain as many processes as you can. If anything escapes, try to figure out a new rule which doesn't affect the previous ones but can explain the odd processes and so on ... Some examples are BARYONIC q. no., LEPTONIC q. no., STRANGENESS q. no. (in strong processes) etc ...

Of course, one may ask why these things should be conserved. As we know, every conservation principle is the result of an underlying symmetry. One example is, translational symmetry dictates total linear momentum to be conserved. But as far as I know, till now there is no underlying symmetry discovered which dictates baryon or lepton no. conservation. It is an accidental symmetry of the standard model. It is still an open question.

Let me conclude by saying that there are GUT models which predicts that proton should decay!

Hope it helps.

Good luck

Dipankar

Thanks for the answer Dipankar. I have one more question to ask you. In the answer you have written that, " the thumb rule is "Any particle will decay into lighter ones unless forbidden by some conservation rules." Is there any reason why elementary particles decay into lighter ones unless forbidden by some rule.

Particles decay because they interact. Symmetry dictates how they should interact. Now if you take any decay in your mind, the first thing to check is that if there is any interaction (weak, EM, strong) that could connect all the particles involved in the decay. More specifically, try to draw a "Feynman Diagram" involving all the particles.

The second point to be checked is whether it is allowed kinematically or not. For example neutron can decay into proton, electron, antineutrino but the reverse i.e. proton decaying into neutron, positron, neutrino is not possible kinematically because proton is lighter than neutron. In is way, you can check whether a decay is possible or not.

But I suspect, that is not the total answer. You asked a philosophically deeper question, why should particles decay at the first place. The answer is, we don't know !

That is our starting point. We see some particles decay ane some don't and we want to explain it and that's why we invent SYMMETRIES. You may as well ask, why are those symmetries and not some other. The answer others don't explain nature! It's something like we see that things fall to the ground ... we explain it by gravity ... we hypothesise that two massive bodies attract each other... one may wonder, why they attract.. why not repel ... The answer is the same.. repulsion doesn't explain things ..

Moral : We have to start from somewhere. Pushing the starting point farther enriches our understanding of nature. In my answer, the 'thumb rule' I quoted may be taken as the starting point.

Good luck

Hi,

Let me add to Dipankar excellent answers that for some reason Nature likes to reduce the energy of every given system, and a heavy particle has higher energy than that of its lighter components. (well, it is not exact. but Nature wants to maximize Entropy and the entropy is increased by the decay process). Why is that? At a certain point we need to accept that some things are just as they are. Probably the best situation you can think about is if we show that things are the way they are just because this is the only way (mathematical?) they can be. Still you may ask why is this mathematically so?

But I like yoour questions :-)

Ehud

One should also use U(1), SU(2) and SU(3) and may be other symmetries to understand conservation of some quantum nos.