# What is $\mathbb{Z}_2$ Parity?

While reading about exotic decays of Higgs boson one of the simplest interaction that we come up with which leads to BSM decays is:

$$\Delta L = \frac{\zeta}{2}s^{2}|H|^{2}.$$

This is the interaction of a singlet scalar field $$s$$ through the Higgs portal. It is mentioned in this document arXiv:1312.4992 on page 10 that for simplicity it is assumed that $$s$$ has a conserved $$\mathbb{Z}_2$$ parity.

I know about the intrinsic parity of fundamental particles, but I have never come across $$\mathbb{Z}_2$$ parity. What does it mean?

Generally, such a statement implies that there is a $$\mathbb{Z}_2$$ symmetry of the theory, i.e. a symmetry operation that yields the identity if applied twice. Then basically, fields can be "even" or "odd" under the $$\mathbb{Z}_2$$ action, menaing the flip sign or not, and the Lagrangean itself is even, i.e. invariant.
In the case you mention, it presumably means that under this $$\mathbb{Z}_2$$, the new field transforms as $$s\mapsto-s$$ and all the SM fields are even. Then the $$\mathbb{Z}_2$$ symmetry forbids any linear coupling $$\mathcal{L}\supset s\cdot (\text{SM fields only})$$.