We use the SI System of measurement which is a human made system.

In order to accurately describe forces/fields in nature we need to use certain experimentally determined constants to "scale" our SI Units into a form that accurately describes nature.

An example is the factor $G$ in Newton's gravitational force law: $G \frac{m_1 m_2}{r^2 }$

In the electromagnetic world we have experimentally calculate $\epsilon_0, \mu_0$ which describe the electric permittivity and magnetic permeability of the vacuum in order to state maxwell's equations. [Although the following link suggests the electromagnetic lagrangian itself can be written with one magic constant, $c$. I believe this is probably hiding some experimental details and that $\epsilon_0$ and $\mu_0$ will eventually need to be experimentally determined to make use of the lagrangian]

So now my question then is the following: I haven't heard (in the laymans world at least) of any Strong Force or Weak Force, or Higgs Mechanism constants. Are there any? If so, what are they numerically? and what units do they usually take?

If there aren't any, why is that? It seems unnatural that our units require no rescaling and I would like to get some intuition as to how this happened.

  • 3
    $\begingroup$ I think you essentially want to look at the Gauge and Higgs boson properties starting on page 27 of the Particle Data Group review of particle physics (Phys. Rev. D 86, 010001): cds.cern.ch/record/1481544/files/PhysRevD.86.010001.pdf. You can see the coupling parameters are dimensionless. The masses and "widths" (inverse decay times) have units of mass, in units where $\hbar=c=1$. $\endgroup$
    – Andrew
    Aug 25 '21 at 17:08

Strong, Weak, and Higgs "forces" are a metaphor to mollify the public; these are short-range interactions, and lack long-range effects of the electromagnetism or gravity type. An implicit conceptual "bridge" through electromagnetism is implied, to help non-HEP physicists find their bearings. It routinely confuses laymen, and might as well be avoided.

In HEP, one focuses on the analog of the electron charge, e, and uses rationalized natural units, involving ℏ𝑐 and unit space permittivity, to quantify electromagnetism's "strength" as a dimensionless number! $$ \alpha_e=\frac{e^2}{4\pi \hbar c} \sim 1/137. $$

One then piggybacks the two electroweak couplings for the SU(2) and U(1) groups, respectively, $$ \alpha_g=\frac{g^2}{4\pi \hbar c} \sim 0.03 \\ \alpha_{g'}=\frac{g'^2}{4\pi \hbar c} \sim 0.01 \sim (M_Z/M_W)^2 \alpha_e~. $$

There is a practical dimensionfull constant depending on these, $G_F=\sqrt{2} g^2/8M_W^2$ used in β-decays, but don't worry about it here.

Now, the couplings of the strong interactions vary fast with energy, so they are not "constants" anymore, and one has to specify an energy scale for these numbers, which conventionally is taken to be the mass of the Z boson, $$ \alpha_s(M_Z)=\frac{g_{QCD}^2}{4\pi \hbar c}\sim 0.118. $$

Finally, the Higgs self coupling is $$ \lambda \sim 1/8, $$ nowhere near as important/crucial as the six Yukawa couplings of the quarks to the Higgs, proportionately related to their masses (in units of a quarter of a TeV), and the three (6?) for the leptons, likewise linear in their masses.

The PDG summarizes half a century's work by thousands of HEPhysicists pinning those down and mapping out their behavior and consequences.


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