The Higgs boson has 2 by-products which can be detected, 2 photons or charged leptons, we will study the 4 charged leptons

This can be done directly from the quark quark interaction or from gluon gluon interaction

🗒️ Note: here you shouldn’t think of a proton proton interaction but rather a bag of gluons and quarks interacting with a bag of gluons and quarks

When we get data from a particle collider we only detect the products so we don't know what created them

Cross sections

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Partons: particles composing a proton ie gluons, quarks and quark antiquark pairs

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The cross section will be the probability that a parton interacts with another particle called parton distribution functions (PDF’s)

To get the PDF we need to know the collider properties:

• The LHC: bunches of $10^{10}$ protons, of combined energy $6.5\,\rm TeV$
• The spread (tightness) depends on bunch size
• We need to know the collision frequencies, for LHC $25\,\rm ms$

All this information gets compiled into the Luminosity

💎 Conclusion: combining luminosity, beam energy and the theoretical cross section you can predict the production rate of Higgs bosons

Now we need to know the probability of the rest of the reaction ie $H\to ZZ\to \ell^+\ell^-\ell^+\ell^-$

• We calculate the probability of $H\to ZZ$ and $Z\to \ell^+\ell^-$ theoretically and then we multiply

💎 Conclusion: multiplying the number we got here plus the PDF we get the number we expect to see in the detector output

Simulations

Now that we know the count we need to know the expected energy and momentum of the $\ell$ which complicated everything, thus we use simulations to do the calculations. Particularly Monte Carlo generations, these use theoretical probabilities (Feynman diagrams) combined with the probabilities of other parts, like PDFs and hadronization to create random events accordingly.

We have the theoretical truth, ie what we expect the distribution to look like, but the problem is that ATLAS detectors are not perfect and the output of the detectors are electrical signals not actual particle physics data. Thus we need 2 processes 1 data reconstruction which takes the electric signal and remaps it to event space, then we need unfolding which corrects this “phase space” for detector effects such as limits in resolution and inefficiencies.