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/
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
W^+ boson decays into an outgoing lefthanded top quark and outgoing lefthanded anti-bottom quark, seeing such interaction in the split up of involved fermions into + & - energy modes
updated from pages 53 to 58 it's clear in the construction that for the case of leptons, for example, righthanded leptons don't interact with the W^+- vector gauge bosons only their lefthanded counterparts and this is so since righthanded leptons have zero isospin however, seeing this would wait for the next updates in which we construct the covariant derivative terms for righthanded fermion singlets
https://foxtrotpaparomeo.wordpress.com/2024/01/29/29012024first-order-calculations-of-the-probability-amplitude-for-higgs-boson-to-electron-positron-decay/
now we have come to a basic l^(2)_(alpha)-lepton theory in the SU(2)XU(1) construction as we are still following the notations used in [5]. in the next update a basic higgs boson theory will be presented.
https://foxtrotpaparomeo.wordpress.com/2024/03/01/01032024first-order-calculations-of-the-probability-amplitude-for-higgs-boson-to-electron-positron-decay/
updated (10052024) from pp.58 to 60: one thing we can highlight in those update pages is eq'n(29.1), where the vector gauge bosons W and Z acquire their masses and this involves the vacuum expectation value of the Higgs field as well as the coupling constant g_2
https://foxtrotpaparomeo.wordpress.com/2024/05/10/10052024first-order-calculations-of-the-probability-amplitude-for-higgs-boson-to-electron-positron-decay/
typo in (30.2) prev post 09052024 has been corrected now
https://foxtrotpaparomeo.wordpress.com/2024/05/10/10052024first-order-calculations-of-the-probability-amplitude-for-higgs-boson-to-electron-positron-decay/
For the Higgs sector we have, in addition to the Lagrangian for the Higgs field, those terms coming from the Yukawa interaction Lagrangian that contain the interactions of the Higgs boson with the leptons (with the exception of the neutrinos) and quarks.
https://foxtrotpaparomeo.wordpress.com/2024/07/02/03072024first-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