| MadSci Network: Physics |
An isolated particle can only decay into particles which are less
massive than the original particle. The rest mass energy of the
original particle E=mc^2 is converted into the masses of the decay
products and also into their kinetic energies. The decay must also
conserve energy, linear momentum, angular momentum, and electric
charge.
Let's start with the easy one. The electron is stable because there
are no lighter particles into which it can decay while still
conserving electric charge. As far as we know, electric charge is
strictly conserved in every circumstance. There are particles lighter
than the electron, such as the photon and the neutrino, but neither
carries electric charge, so a decay like the following is forbidden
electron --> photon + neutrino
because the left hand side has charge (-1) and the right hand side has
charge (0), in particle physics units.
The question of proton stability is more subtle. We know from
experiments such as Super-Kamiokande at Kamioka, Japan,
(http://www-sk.icrr.u-tokyo.ac.jp/doc/sk/index.html) that protons have
a lifetime in excess of 5*10^32 years. [Perkins "Introduction to High
Energy Physics" ISBN 0521621968] Do protons last forever? No one
knows. One of the decay modes looked for is
proton --> positron + neutral pion
This decay preserves all the quantities listed in the first paragraph,
but it violates two other laws: Conservation of Baryon Number and
Conservation of Lepton Number. Protons have a baryon number of 1 and
a lepton number of 0, while positrons have a baryon number of 0 and a
lepton number of -1 (negative because a positron is an anti-electron
and an electron has a lepton number of +1). Pions have baryon number
0 and lepton number 0. These two new conservation laws are ad hoc,
invented to explain the lack of experimental observation of certain
decays; they are not as "sacred" as conservation of energy and
momentum (which are rooted in time and space invariance) or
conservation of electric charge (which is a result of the gauge
invariance of Maxwell's theory of electromagnetism).
In fact, grand unified theories (GUTs) predict that baryon number and
lepton number are violated at some high energy E_gut, and hence also
that protons decay. The calculated proton lifetime in these theories
is proportional to [Perkins equation 9.7]
(E_gut)^4 / [(a_gut)^2 (M_proton)^5]
where E_gut is about 10^15 GeV, the proton mass M_proton is 1 GeV/c^2,
and a_gut=0.23 is the "coupling" or strength with which the particles
interact. The long proton lifetime can be attributed to the large
ratio of the grand unification energy scale E_gut compared to the
proton mass.
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The muon is a heavier version of the electron. It has a lifetime
of about 2 microseconds, which sounds very brief in human terms,
but compared to other particles mentioned below the muon decays
very slowly! The muon lifetime is (by analogy with the formula
above) proportional to
(M_w)^4 / [(a_weak)^2 (M_muon)^5]
where M_w is the mass of the W boson 80.2 GeV/c^2, M_muon is the mass
of the muon 0.105 GeV/c^2, and a_weak is the strength of the weak
nuclear force 1.17*10^-5.
The muon lifetime is small compared to the proton lifetime because the
ratio M_w / M_muon is about 10^3, while the ratio E_gut / M_proton is
approximately 10^15. That is, the muon mass is much closer to the
energy scale of the weak interaction; the proton mass is nowhere near
the GUT energy scale.
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Positively and negatively charged pions decay via the weak nuclear
force:
charged pion --> muon + neutrino
Replace the muon mass in the equation above with the larger charged
pion mass 0.140 GeV/c^2, and you will understand why the charged
pion lifetime 2.6*10^-8 seconds is about 80 times shorter than that
of the muon.
Neutral pions, however, decay via the electromagnetic force:
neutral pion --> 2 photons
The neutral pion lifetime is only 0.8*10^-16 seconds, reflecting the
larger electromagnetic coupling a_em=0.0073 compared to the feeble
weak coupling a_weak=1.17*10^-5.
Particles that decay via the strong nuclear force have typical
lifetimes of 10^-23 seconds. Their extremely brief existence is
due to the large (around 1) coupling of the strong force. This
is, after all, why it's called the "strong force" -- it's strong!
In general, the lifetime of a particle depends on the mass of the
original particle, the energy scale of the interaction and the
strength of the interaction through which the particle decays.
--Randall J. Scalise http://www.phys.psu.edu/~scalise/
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