Powered by Indico
v3.2.7
The Standard Model (SM) flavor puzzle is obscured by the possibility of different choices of basis and parameterization. However, physical observables cannot depend on such arbitrary and unphysical choices. Hence, a new and un-obscured view of the flavor puzzle is offered by formulating it in a basis invariant language. In this talk I will present to you such a basis invariant formulation for the SM quark sector. To achieve this, we use the Hilbert series to construct the full ring of basis invariants. Furthermore, we construct a complete basis of orthogonal invariants for this ring using the simple and intuitive technique of birdtrack diagrams. This yields a set of ten independent CP-even invariants, corresponding to the ten independent physical parameters of the SM quark sector. An eleventh, CP-odd invariant - the well-known Jarlskog invariant - is related to the CP-even invariants by an algebraic relation of the invariant ring (a syzygy), which takes a particularly compact form for our orthogonal basis of invariants. Since all relevant data in the quark sector is available at precision, we can "measure" the invariants. I will show that hierarchical masses and hierarchical CKM elements correspond to strongly positively correlated invariants. Hence, the (quark sector) flavor puzzle can be rephrased as to why the, a priori independent, basis invariants are so strongly correlated. Likewise, any solution to the flavor puzzle will have to provide an explanation for the observed strong correlation among the invariants. I will pedagogically introduce all necessary techniques and comment on the CP transformation behavior of invariants.