(π0,η,η’) mass splittings and mixings

A particularly challenging topic in the phenomenological study of QCD is the 0,η,η’) particle mass splittings and mixings. With exact SU(3) flavour symmetry of the u, d and s quarks, the decomposition of the familiar eigenstates of the π0,η,η’ is known. However, when SU(3) and isospin are broken due to differing quark masses and electromagnetic charges, these states mix to form the experimentally observed mass spectrum. Previous works have employed isospin-symmetric simulations and hence have focussed on the η,η’ mixing. In [1], we make use of the natural breaking of isospin that occurs when electromagnetic effects are incorporated into a lattice simulation and have performed full Nf = 1 + 1 + 1 simulations to investigate the mass splittings and mixings of these states.

Figure 1: Left panel: Masses for the π0,η,η’ mesons along a trajectory holding the down quark mass fixed. The avoided level crossing shows the dynamical interaction between the two light pseudoscalars, π0 and η. Right panel: Plot of the evolution of the decay amplitudes of the flavour composition for the π0,η,η’ states along this trajectory.

In the study, [1], we have chosen quark masses to be as close to the QCD flavour symmetric point as possible in order to maximise our ability to amplify the QED part of the splitting. While our starting point has only approximate SU(3) symmetry, it does have exact U-spin symmetry (down and strange quarks are exactly the same). Hence in this study, it is natural to consider mass splittings and mixings between U-spin-zero states, see Fig. 1. In this study we were able to reproduce phenomenological results, for example the η – η’ mixing angle.

[1] Z. R. Kordov et al., [CSSM/QCDSF/UKQCD], Phys. Rev. D 104 (2021) 114514.