How is weak force explained?

The weak force is mediated by (happens because of) the “intermediate vector bosons” which are just incredibly massive - roughly 90 times the mass of a nucleon. As a result it (a) takes a huge amount of energy to produce one and (b) the force is extremely short range (#c. 10^-18m#)

The bosons that transfer the force are also electrically charged (in 2 of the 3 bosons) which is otherwise unknown. This means the bosons can change the charge of the interacting particles, effectively carrying charge between them as well as mass/energy etc.

The other forces all tend to make matter (or nuclei) stick together, but the weak force tends to make matter fall apart into its constituent parts. Thus it is involved in #beta# decay in its various forms.

To understand a little more it would be helpful to be able to appreciate Feynman diagrams before anything else, try here: https://simple.m.wikipedia.org/wiki/Feynman_diagram

And then for a general overview of fundamental forces try this:
http://hyperphysics.phy-astr.gsu.edu/hbase/Forces/funfor.html

Then a primer on the weak force here:
http://home.fnal.gov/~cheung/rtes/RTESWeb/LQCD_site/pages/weakforce.htm

Before you plunge into the deep end with:
https://en.m.wikipedia.org/wiki/Weak_interaction

Enjoy!

The weak force isn't really a force at all because, unlike the other forces, it is neither attractive or repulsive between particles. When an atomic nucleus has either too many protons or two many neutrons it is unstable. The strong force, which has a very short range, is unable to hold the nucleus together.

An unstable nucleus has to disintegrate in some way. There are several options. It have split into two lighter nuclei which is nuclear fission. It can emit an alpha particle - alpha radiation. It can emit a photon to reduce energy - gamma radiation.

The final alternative is that it can convert a proton into a neutron or a neutron into a proton. This is beta radiation which requires the weak force.

Let's consider the most common form of #beta# radiation. A neutron gets converted into a proton. It is not that simple. Charge is conserved so as the neutron has neutral charge the positive charge of the proton needs to be balanced. So the neutron becomes a proton plus an electron. There is another problem. The electron is a lepton and lepton numbers must be conserved. There is also some missing energy. This is explained by the emission of an electron antineutrino.

#n->p + e^(-) + nu_e#

The story is not complete as there is more to it. Protons and neutrons are both composite. A proton consists on two up quarks with a charge of +2/3 and a down quark with charge -1/3. A neutron consists of one up quark and two down quarks. The #beta# decay requires the creation of a massive particle called a #W^-# boson which mediates the weak force.

So, what actually happens is that a down quark gets converted into an up quark and a W boson. The W then rapidly decays into the electron and the antineutrino and everything is conserved.

#u->d+W^-#

#W^(-)->e^(-) + nu_e#

There is also a #W^+# boson which does the reverse reaction. As the W bosons are very massive, Their creation is a relatively rare event. This is why weak reactions are so very slow.