# In particle physics, what does 'coupling' mean?

1. Jan 12, 2010

### ryanwilk

Hi,

In particle physics, what does 'coupling' mean? I can't find a definition anywhere and books just assume you know what it is. For example, "the Higgs couples to light particles".

Also, what does it mean to say that something strongly or weakly couples to something else?

Any help would be appreciated.
Thanks.

2. Jan 13, 2010

### blechman

Re: Coupling

"coupling" is really just fancy-talk for "interaction". For example when you say "the photon couples to charge", you mean "the photon interacts with particles that have charge." A "coupling constant" is a parameter of the theory (usually dimensionless but not always) that determines the strength of the interaction. Often in practice, we drop the word "constant" since by the context it is always clear what you mean.

If the coupling constant is dimensionless, you can talk about "strong" or "weak" by whether or not the coupling is greater than or less than 1 (sometimes you also have factors of $\pi$ in the formulas, but let's not worry too much about that!). If the coupling is "weak" (< 1) then you can apply the technique of "perturbation theory". Therefore we often use the word "perturbative" to mean "weak".

At "strong coupling" (> 1) you cannot use perturbation theory and you must try to solve the problem some other way. This is the challenge! This is what happens in the strong nuclear force at low energies, for example.

For dimensionful couplings, you can only talk about "strong" or "weak" WITH RESPECT TO SOME SCALE, where "scale" means some fixed energy. So for example, the Newton constant has dimensions of 1/energy^2 (when $\hbar=c=1$). So that means that the gravity is "weak" when the energy of the particles is smaller than $G_N^{-1/2}$, and "strong" when it is greater. This energy scale is the "Planck scale" at roughly $10^{18}$ GeV, far higher energies than anything we can produce in accelerators. So this is why particle physicists say that "gravity is weakly coupled."