The Basis Invariant Flavor Puzzle

by Andreas Trautner (MPIK)

Thursday 18 Apr 2024, 14:00 → 15:00 Europe/Berlin

HS2 (Physikdepartment)

The Standard Model (SM) flavor puzzle is obscured by different possible choices of basis and parametrization. However, physical observables cannot depend on such unphysical choices. Hence, a new and un-obscured view of the flavor puzzle is offered by formulating it in a basis invariant language. To achieve this for the SM quark sector, 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 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 amongst the invariants. I will pedagogically introduce all necessary techniques and comment on the CP transformation behavior of invariants, which is also useful knowledge for theories and model building beyond the Standard Model.