Q:

What is the decay rate of strong and weak forces? For example, gravity decays at the rate of 1 / r2. Is there such a ratio (in terms of r) for strong and weak forces?

- Mehran (age 64)

- Mehran (age 64)

A:

Hello Mehran,

The strength of a force between two bodies or particles as a function of the separation distance is called the *range*. As you point out the range of the electromagnetic and gravitational forces goes a 1/r^{2}. In the technical jargon it's called an infinite range. In the case of nuclear, or strong forces, the range is about the size of a medium sized nucleus, 10^{-15} meters In the case of the weak force it's much smaller, about 10^{-18} meters. These latter two forces fall off much more rapidly than 1/r^{2}, exponentially or worse.

Now comes the hard part, how to explain it. In quantum field theory the forces between particles are mediated by the exchange of bosons. In the electromagnetic case it is the photon, a massless spin one particle. In gravity the force is mediated by massless spin two particles called gravitons. The photon is well known and well studied. The graviton is only hypothetical since it hasn't been observed in the laboratory yet even though many experiments have been tried. More sensitive experiments will continue the search. The nuclear force is mediated mainly by exchange of spin zero mesons called pions, particles with mass of the order a tenth of the mass of a nucleon. The weak forces are mediated by vector bosons, the Z_{0}, W^{+} and W^{-}. These bosons have masses of the order of 80 to 100 times that of a proton and been observed at high energy accelerators.

The correlation is evident: the heavier the exchange particle, the shorter the range of the equivalent force. The mathematical details are formidable! Here is a web site you might want to look at:

LeeH

*(published on 04/25/2015)*