(see the corresponding Feynman diagram of (14.9) in the draft)
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so the final states in the first order calculation are the physical states? meaning, these states are the ones that register in the detector and via the summation of the four-momenta that come out we can know there was an initial state that carried in the needed four-momentum so as to fill in the summation of all four-momenta to zero. it would really be that complicated to detect that the fermion and anti-fermion in the lepton family of first generation that come out indeed coming directly from the decay of Higgs boson since fermion and anti-fermion pairs can be produced by other interactions and hard to know which that came directly from the HIggs boson decay
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https://foxtrotpaparomeo.wordpress.com/2023/05/06/06052023first-order-calculations-of-the-probability-amplitude-for-higgs-boson-to-electron-positron-decay/