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One argument could be the Yukawa coupling, which is responsible for the coupling to the fermions. In the Yukawa coupling term in the Lagrangian, $\mathcal{L}_{\text{Yukawa}}$ , there are no terms that contain a $\gamma^5$ matrix, defined as $$\gamma^5 := i\gamma^0 \gamma^1 \gamma^2 \gamma^3$$ This publication states how terms in the Lagrangian transform ...


It is not an assumption; both $0^+$ and $0^-$ were considered as possible Higgs states. The angular distribution of decay products (like in $h\to ZZ$, $h\to f\bar{f}$, $h\to \gamma\gamma$ or in Higgstrahlung) is dependent on the parity of the Higgs particle. Alternatively, you can measure the helicities of the outgoing photons (in the $h\to\gamma\gamma$ ...

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