# Half life of elementary particles

Do elementary particles have half life? Can we theoretically calculate half of a particle which is in complete isolation?

• Unstable particles will decay. For some particles it is not known if they are stable or not - for example electron,proton have just a lower bound of lifetime calculated. Proton lifetime must be greater than 10^29 years. For others situation is clear - for example free neutron is very unstable and will decay in a 15 minutes. – Agnius Vasiliauskas Aug 26 '19 at 10:03

Some elementary particles, such as the electron, are stable; others, like its more massive sibling the muon, are unstable and decay into other particles. A muon decays through the weak interaction into an electron, a muon neutrino, and a electron antineutrino, all of which are elementary. The muon’s half life is 1.56 microseconds, and this can be calculated from Fermi’s Golden Rule.

The free neutron decays, but physicists do not consider it an elementary particle because it is a composite bound state of other particles.

According to the Standard Model, the only elementary particles are the three charged leptons $$(e, \mu, \tau)$$; their corresponding neutrinos $$(\nu_e, \nu_\mu, \nu_\tau)$$; six kinds of quarks $$(u, d, s, c, t, b)$$; the gluon $$(g)$$; the photon $$(\gamma)$$; the two weak bosons $$(W, Z)$$; the Higgs boson $$(H)$$; and their antiparticles. (Some particles are their own antiparticle.)

• In your list you group the quarks, gluons, and neutrinos, but list the charged leptons and weak bosons separately. Perhaps a more consistent approach would be better? – dmckee --- ex-moderator kitten Aug 26 '19 at 18:22
• @dmckee I’ve made an edit. – G. Smith Aug 26 '19 at 18:35

Can we theoretically calculate half of a particle which is in complete isolation?

Yes, and in fact that's generally the easier case. Neutrons, for instance, decay over about 880 seconds - but only in isolation, not within a nucleus (although the reason gets complex).

In a general fashion, you can see a correspondence between the mass of the particle and its lifetime. So, for instance, a W masses 80400 MeV and lasts a very short time around 10^-25 seconds, while a neutral pion masses 135 and lasts 10^-17. However this is not a solid rule; the proton masses 938 and lasts, from what we can tell, forever.

• You say "Neutrons [...] only in isolation, not within a nucleus (although the reason gets complex)". I thought it was simply because the mass of the neutron is higher than the proton (I am currently in a introductory nuclear physics course). Are the complexities that arise related to the underlying QCD? Does it have anything to do with the different decay times measured for the neutron with spectroscopy and dispersion? Is there a book or other resource where I could read about that?... Thanks in advance. – S V Aug 26 '19 at 15:11
• @SV - this is the best explanation I've found: sjsu.edu/faculty/watkins/neutronnucleus.htm – Maury Markowitz Aug 26 '19 at 17:34
• Isolated Neutron is composed of three quarks and dont know how many number of gluons. Since length scale is small so we need QFT to explain things here. At most it can give is probability of decay. So how do we get some number from this probability calculation which we call half life? – Neeraj kumar Sep 30 '19 at 4:30