Theory behind the experimental signatures of Higgs-Boson As I understand it, the Higgs-Boson itself is unstable and has a transient existence. So, the particle detectors cannot detect it directly. Instead, the detectors register all the decay products and from the data, this decay process is reconstructed. If the observed decay products match a possible decay channel of the Higgs-Boson it indicates the existence of the Higgs-Boson.
From what I have read, the two important decay channels used to prove the existence of the Higgs-Boson are the 'two-photon event' and the 'four-lepton event'. My questions are the following:


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*What is the exact decay process of the above two events and what exactly do the particles detectors detect? (or references for the same)

*Why did we look for these particular events as there apparently are other decay channels as well which we could look for? (I understand that these events have a higher probability of occurrence, I want to know why exactly.) 
 A: Within the standard model of physics , before its discovery the higgs could have any mass starting with ~100 GeV( a limit given by LEP), the upper limit depending on the theory used* .
Its decay channels are known and characterize it. This is a good representation.

What is the exact decay process of the above two events and what exactly do the particles detectors detect? (or references for the same)

The two photon events and the four lepton events have the distinction of decaying through only  the weak interaction ( to first order) and do not involve the strong interaction which introduces a lot of indeterminacy.  They are the "cleanest"decays.

Why did we look for these particular events as there apparently are other decay channels as well which we could look for? (I understand that these events have a higher probability of occurrence, I want to know why exactly.)

Establishing a resonance at these two channels gives enough confidence that what is found is the Higgs. They have looked and found a  number of the expected channels,with the correct rate. Please note that these are not the most probable channels, rather the opposite. They are the "cleaner " channels.
Please read the links to get a better understanding.


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*https://www.ugr.es/~adjouadi/Course2.pdf
