referring to equations (10.5), (10.6) in the resource notes for Higgs decay into a fermion anti-fermion pair
https://lectures.lapth.cnrs.fr/standard_model/cours/cours10/

now, compare the results from my own workouts (14.7) in my own draft that ultimately leads to (17.3)
https://foxtrotpaparomeo.wordpress.com/2023/01/11/12012023first-order-calculations-of-the-probability-amplitude-for-higgs-boson-to-electron-positron-decay/

take note that (17.3), which is the absolute square of my probability amplitude, doesn't have a factor 2 because i haven't taken into account yet the other spin states of the fermion and anti-fermion in the decay process and you may refer to (10.5) in the resource material i have shared in the earlier toot and you may also notice that in the cited resource material, the reduced matrix (10.4) and the reduced matrix contained in (14.7) in my draft are the same although i have used different notations/symbols
https://foxtrotpaparomeo.wordpress.com/2023/01/11/12012023first-order-calculations-of-the-probability-amplitude-for-higgs-boson-to-electron-positron-decay/

updated draft here... concerning on what are the physical states
https://foxtrotpaparomeo.wordpress.com/2023/05/06/06052023first-order-calculations-of-the-probability-amplitude-for-higgs-boson-to-electron-positron-decay/

updated it to include (19.9.1), which is more general in looks, while giving the initial higgs boson state full four-momentum with more than one spatial components, the final answer retains its basic form
https://foxtrotpaparomeo.wordpress.com/2023/05/26/26052023first-order-calculations-of-the-probability-amplitude-for-higgs-boson-to-electron-positron-decay/

there were errors in the discussions that have been rectified in making this update and i should emphasize that
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The final states coming out with opposite spatial momenta, can happen only in the rest frame (center- of-mass frame) of the Higgs boson
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https://foxtrotpaparomeo.wordpress.com/2023/05/26/26052023first-order-calculations-of-the-probability-amplitude-for-higgs-boson-to-electron-positron-decay/

i wanted to re-emphasize this in the latest updated version of my draft
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The final states coming out with opposite spatial momenta, can happen only in the rest frame (center- of-mass frame) of the Higgs boson, where the Higgs boson doesn’t have spatial components of the four-momentum, as it decays, while the final states come out with equal energies in opposite directions, leading to (19.9.3).
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https://foxtrotpaparomeo.wordpress.com/2023/05/26/26052023first-order-calculations-of-the-probability-amplitude-for-higgs-boson-to-electron-positron-decay/

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Such measurements of Yukawa couplings to light fermions are experimentally challenging at the LHC, given that the SM predicts the coupling strengths to be proportional to the fermion mass [11–13]. Consequently, couplings of the Higgs boson to the first-generation fermions have yet to be confirmed experimentally.
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https://arxiv.org/abs/2208.00265

now, i have come to a more inclusive construction of the SU(2)XU(1) Lagrangian of the Standard Model Electro-weak theory. the other generations of the lepton family are included and as well as the three generations of the quark family.
https://foxtrotpaparomeo.wordpress.com/2023/10/15/15102023first-order-calculations-of-the-probability-amplitude-for-higgs-boson-to-electron-positron-decay/

terms that contain interactions of w^+- vector gauge bosons with members of lepton family. fermions involved expanded into + and - energy modes from such we get, for example, the term for the decay of w^+ vector bosons into an outgoing neutrino and outgoing positron, the anti-particle of electron