Fine Structure

The Weak Interaction Scale

I came across the term "weak interaction scale" in a blog post recently and I found myself wondering what this term actually meant. I have a sense of what weak interactions are, if only from the other forces I know more about, but no clear recognition of what is meant by 'scale'. I figured I'd learn more about it by comparing it to the other forces so I took a shot at some logical comparison of the forces with respect to their scale. I'm trying to work through some new material here so I'd appreciate pointers to any factual errors or misconceptions in the comments.

For reference, we have four fundamental forces: gravitation, electromagnetic, strong and weak. Gravity may be the most obvious example and if we think about it's 'scale' we can recognize that it acts on very, very large things. Roughly planet-size things attract other things with mass (even smaller things, like yourself) but other things that we consider 'large' don't attract each other (think cruise ships, pyramids, etc). So we have a pretty decent idea of what the gravity scale is - really freakin' huge and no smaller.

The next most obvious force is the electromagnetic force which should be familiar with if you've ever played with a magnet. It seems more difficult to understand this scale since we're unfamiliar with it's borders. You can pick up a car with a big enough magnet and you can watch charged particles change path with a small magnet so we already cover a large portion of the scales we interact on. All the positively and negatively charged things on planets generally even out so that we consider large bodies electrically neutral but even if something that large was overwhelmingly charged, I doubt it would have much of an effect giving that gravitation is so strong at that scale. Conversely, if things on the scale of protons and electrons provide the basic unit for electric charge, what kind of electromagnetic forces can occur on scales smaller than the electron? I honestly don't know the answer to this question so I can't give a definite explanation. It's good fodder for a future post, however, and something interesting to think about.

Now we're getting into the more obscure forces but before we tackle our original question, we'll cover the strong force which binds quarks together, forming our more familiar particles like protons and neutrons. The strong nuclear force is named such because of it's strength in holding quarks together - it's so strong that you'll never see a quark on it's own. The 'nuclear' term is often thrown in because residual effects from the strong force are responsible for overcoming electromagnetic forces when binding protons together in atomic nuclei. This alone narrows down our idea of what scale the strong force acts on. Clearly, we don't feel the strong force acting on scales we're used to living in and it's not a significant player at planetary scales either. We've narrowed the strong force down to the quark scale and slightly larger. Additionally, this may be confusing if you hear that the strong force doesn't diminishing with distance. I haven't looked into the details of why this occurs and what it means so we're again reaching the limits of my knowledge.

Finally, the weak force! Let's get right to the general region where we know it acts - the very small. Wikipedia suggests that it has 1013 times less strength than the strong force - really, really tiny. We haven't talked about force carriers but at the scale we're looking at, it seems like it may be the only way we can describe this force. Weak interactions aren't usually defined as we're used to defining forces, repulsions or attractions, but emitting or absorbing W or Z bosons. These incredibly heavy particles have incredibly short lives. Their heavyness (weight is the wrong word) is defined in billions of electron volts (GeV) much like other very small particles. Within this definition is the key to talking about things that exist in the "weak interaction scale". Take neutron beta decay for example; a neutron emits a W boson and the neutron becomes a proton, the W boson then decays into an electron and electron antineutrino. This can only occur if the original neutron has enough energy to "create" a W boson. The heavyness we defined earlier for the W boson is around 80 GeV (and Z bosons just a little higher at around 90 GeV) so a neutron must be incredibly energetic to decay like this. This is when you see articles talking about particle accelerators on the "weak interaction scale" - they're talking about the energies needed to produce weak interactions, or W and Z bosons. The scale they're talking about is in energy rather than distance.

Our definition of scale for weak interactions is very different than our scale for other forces so it doesn't make sense when we first see the term 'scale' and compare it to other forces. Luckily, with some research we can determine what's actually going on! As I mentioned before, it's very strange to go from a notion of repulsion and attraction of two existing bodies to a force where you spontaneously decay with no previously existing second party. Perhaps I'm wrong (or I'm missing something) but it seems like there's some mystery still hidden in these very small places.