In this example we determine the flavor invariants for a four-fermion operator such as [Q_ℓℓ]_prst=( γ_μℓ_r)( γ^μℓ_t) under the assumption of as U(2)⁵ flavor symmetry considering the insertion of a single spurion V_ℓ transforming as a doublet.

First, we define the symmetry as a global symmetry group, by specifying the simple Lie Groups, i.e., we have to identify U(2) ~ SU(2)U(1) since Matchete does not allow to directly define a U(2) group.

The flavor invariants considering either one insertion of the spurion or its conjugate can be determined using:

Parametrizing the spurion as V_ℓ=(0,1) we find

We can then associate these flavor structures to the coupling C_ℓℓ of the operator using:

where we first loaded the definition of the operator and coupling in the Warsaw basis.

Note that the symmetry (pr↔st) for the flavor indices of [Q_ℓℓ]_prst (which is of course shared by [C_ℓℓ]_prst) was used to symmetrize the flavor invariants. Furthermore, the invariants are grouped into conjugate pairs, which can be seen using: