# How are computed Branching decay modes (for Higgs boson and from a general point of view)

I would like to know how are computed the branching decay diagram, like for example with Higgs boson represented below (source):

It seems there are 5 ways of decays for Higgs boson.

I suppose there are theorical calculus behind this diagram but concretely, what are the origins and the hypothesis to get these curves ?

Are cross sections implied into these calculus ?

• In general, the answer to your question is quantum field theory (the theoretical framework for modern particle physics) and Feynman diagrams. If you want more detail, definitely consult a textbook on the topic. Jul 12, 2018 at 23:54

For instance, for the decay of K-short meson into charged pions, $$\mathrm{BR}(K \rightarrow \pi^+ \pi^-) = \frac{\Gamma (K_S \rightarrow \pi^+ \pi^-)}{\Gamma (K_S)}$$ where the total decay width is $\Gamma (K_S)=\Gamma (K_S \rightarrow \pi^+ \pi^-)+\Gamma (K_S \rightarrow \pi^0 \pi^0)$. (Here, I have given K-short as an example because it has only two decay modes which makes it easy to talk about. I could write the complete list of the Higgs decays but it would just make the answer more crowded. See for example the Particle Data Group's booklet for all decay modes of all particles)
In order to calculate the decay width, you need to calculate the matrix element, $\mathcal{M}$, for the process in question, which is done by applying Feynman rules of the model on that process. For more details, you need to refer to a quantum field theory textbook, e.g., Griffiths or Peskin/Schröder.