Because it is the lightest charged particle in electricity and magnetism, the electron should be stable.
Both energy-momentum and charge conservation immediately state that the most lightest charged particle must remain stable. One of these principles must be broken if the electron is to die.
This is more technical but it explains what would happen if an electron were unstable.
What are the Necessary Requirements to a Stable Electron?
It is unlikely that energy-momentum conservation will be broken due to technical reasons relating to quantum mechanical consistency of theories.
It is possible to violate charge conservations without making major changes to the theory. This happens in reality for electroweak interactions. The photon then becomes massive. The mass of the photon must be lower than 10-18 c2–10-24
The electron’s mass is ten times smaller than its weight. [1] This limit could be as low as 10-26 eV/c2
.[2]
It also requires a charged field, similar to the Higgs boson. This charged field must be very light in mass (similar to that of the photon). We would not have discovered a light-charged particle. This could only happen if the new particle was charged with a very small amount. Although I don’t recall the limits for these particles, the charges must be very small.
Estimated life expectancy of an unstable electron
The lifetime of an electron when the new light scalar particle is 1/q
The electron’s charge is multiplied by this number.
te~(MZmg)2qmec2
so if q
This lifetime enhancement factor is 10 10580 This is an enormous number, and we are in the range of more than 10500 The age of the Universe multiplied by 2. There are 1080 There are less than 1 part of the Universe that is made up of particles. 10400
Chances are that at least one electron will have died during the entire lifetime of the Universe.
Caveat Emptor
Although there are assumptions in these estimates, they are solid but not necessarily correct. We should assume that there may be things we don’t know. We should look for electron decaying but not assume that this will be a likely discovery channel.
Footnotes
[1] http://pdg.lbl.gov/2015/listings/rpp2015-list-photon.pdf [2] http://arxiv.org/pdf/hep-ph/0306245v2.pdf