 Solution

Parity is full spatial reflection, $\mathbf{x}\mapsto -\mathbf{x}$, represented by a parity operator $\mathcal{P}$. A polar vector, such as momentum, reverses, whereas an axial vector, such as spin, does not. A state of definite parity has $\mathcal{P}|\psi ⟩={\eta }_P|\psi ⟩$, with ${\eta }_P=\pm 1$ in the usual convention. A multiparticle state's parity includes both the product of its intrinsic parities and its orbital spatial factor, for example $(-1{)}^L$ for relative orbital angular momentum $L$.

An interaction conserves parity when its dynamics are invariant under this transformation, equivalently $[H,\mathcal{P}]=0$ for a time-independent Hamiltonian. Parity violation means that a process and its fully reflected counterpart need not have the same probability. It is more than a left-right asymmetry in an unreflected laboratory apparatus.

The electromagnetic and strong sectors of the Standard Model conserve parity to the accuracy relevant here, taking the strong-sector Yang-Mills theta term to vanish. The weak charged current selects left-chiral fermions and right-chiral antifermions, as defined by fermion chirality; the reflected right-chiral charged current is not equally present. The neutral weak current also generally has different left- and right-chiral couplings. Consequently the weak sector violates parity; this does not mean that every individual weak decay must have opposite initial and final parity. For a massive particle, helicity and fermion chirality should be distinguished.