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I have been searching around and cannot get an expression for the Higg's coupling constant.

By 'coupling constant', I mean for the strong force $$\alpha_S=\frac{{g_S}^2}{4 \pi \hbar c}\approx 0.1\tag{1}$$ and for the weak force $$\alpha_W=\frac{{g_W}^2}{4 \pi \hbar c}\approx 0.034\tag{2}$$ and for the EM force $$\alpha_{EM}=\frac{{e}^2}{4 \pi \epsilon_0\hbar c}\approx 0.0073$$

Where in $(1)$ and $(2)$, $g_S$ and $g_W$ is the vertex strength in the Feynman $\mathrm{diagram^{\chi}}$:

Coupling constants

Does a similar expression exist for the Higgs boson?

$\chi$ - Image from ICL dept. of physics.

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    $\begingroup$ But... but.. there are 18 couplings, not 1: 12 Yukawas, 1 self-coupling, and 1 gauge coupling (the three you wrote above are proportional to each other), since the Higgs couples (differently) to all particles of the SM, except for the gluons. So a neat high-school class chart you are seeking is never written down, because it would defocus you away from the structure of the SM. Read up on the SM! $\endgroup$
    – Cosmas Zachos
    Commented May 8, 2022 at 13:18
  • $\begingroup$ ... I meant "the two of the three you wrote above".... GUTs outrange your scope... $\endgroup$
    – Cosmas Zachos
    Commented May 8, 2022 at 13:40

2 Answers 2

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This article notes that particles can exert a force on one another via the Higgs field and assigns a dimensionless coupling constant (of the same form as the examples given): \begin{equation} \alpha_{Higgs} = \left ( \frac{mc^2}{4 \pi v} \right )^2 \end{equation} where $v$ is the vacuum expectation value of the Higgs field. Note that this force extremely short range due to the mass of the Higgs boson.

In the standard model, the Yukawa couplings of each of the fermions to the Higgs field are independent inputs. Therefore, the value of the expression above will depend on the particle you consider.

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  • $\begingroup$ Except this only holds for the 12 Yukawas, but fails for the trilinear and gauge couplings involved in the other answer. The question itself is moot: The Higgs is the linchpin of the SM and couples to different particles with just the right couplings to make the construction work... It actually does 3 jobs: breaks the symmetry, gives masses to gauge bosons, and gives masses to fermions, in very different ways. Unless the OP understands that, any answer is bound to be confusing... $\endgroup$
    – Cosmas Zachos
    Commented May 8, 2022 at 15:31
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The Higgs boson does not have a separate coupling to the rest of the particles in the table of elementary particles. The magnitude of the coupling is a combination of the weak and the electromagnetic coupling constant, depending on the reaction measured . There are efforts to quantify this from experimental data.

We estimate the expected precision at a multi-TeV muon collider for measuring the Higgs boson couplings with electroweak gauge bosons, HVV and HHVV (V=W±,Z), as well as the trilinear Higgs self-coupling HHH.

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