Flavour physics from an approximate U(2)^3 symmetry

TL;DR

This work argues that an approximate $U(2)^3$ flavour symmetry acting on the first two quark generations, broken by spurions $\Delta Y_u$, $\Delta Y_d$, and $\boldsymbol{V}$, can reproduce the CKM pattern with a single physical phase while allowing TeV-scale flavour deviations. It develops a full EFT treatment of the resulting $\Delta F=2$ and $\Delta F=1$ operators, compares the predictions to $U(3)^3$ (MFV) expectations, and derives current bounds that permit a relatively low new-physics scale with potentially observable CP-violating effects. The paper then shows how to implement $U(2)^3$ in composite Higgs models, outlining Left- and Right-compositeness scenarios and detailing their distinct flavour- and CP-violating signatures, including correlations among meson mixing and rare decays. Finally, it extends the discussion to the lepton sector, analyzing Lepton Flavour Violation and its interplay with the muon $g-2$ anomaly, arguing that a coherent $U(2)^3$-based picture could yield testable flavour phenomena at present or near-future experiments.

Abstract

The quark sector of the Standard Model exhibits an approximate U(2)^3 flavour symmetry. This symmetry, broken in specific directions dictated by minimality, can explain the success of the Cabibbo-Kobayashi-Maskawa picture of flavour mixing and CP violation, confirmed by the data so far, while allowing for observable deviations from it, as expected in most models of ElectroWeak Symmetry Breaking. Building on previous work in the specific context of supersymmetry, we analyze the expected effects and we quantify the current bounds in a general Effective Field Theory framework. As a further relevant example we then show how the U(2)^3 symmetry and its breaking can be implemented in a generic composite Higgs model and we make a first analysis of its peculiar consequences. We also discuss how some partial extension of U(2)^3 to the lepton sector can arise, both in general and in composite Higgs models. An optimistic though conceivable interpretation of the considerations developed in this paper gives reasons to think that new physics searches in the flavour sector may be about to explore an interesting realm of phenomena.

Figures (5)

• Figure 1: Fit predictions (68 and 95% Bayesian credible regions) in $\Delta F=2$ fits with $c_{LL}^B=0$ (top left), $c_{LL}^K=0$ (top centre), $c_{LL}^B=c_{LL}^K$, $\phi_B=0$ (top right, relevant to $U(3)^3$) and with all 3 parameters independent (bottom). The gray region in the bottom left plot is disfavoured by direct searches only in the SUSY case with dominance of gluino contributions.
• Figure 2: 68 and 95% C.L. allowed regions for the $\Delta F=1$ coefficients in $U(2)^3$, using the results of a global analysis of inclusive and exclusive $b\to s$ decays Altmannshofer:2011gn.
• Figure 3: Four-fermion operator contributing to the $\Delta F = 2$ amplitudes in the $U(3)^3$ case with Right-compositeness.
• Figure 4: Leading contributions to chirality breaking bilinears (mass terms) from insertions of composite fermions, in the two cases of right- and left-handed compositeness. Crosses denote the mixings that break flavour symmetry, while dots denote the diagonal mixings. The strong dynamics in the first two diagrams in $(a)$ is the same, as it is in the last two diagrams in $(b)$.
• Figure 5: Leading contribution to flavour conserving bilinears, in the case of left-handed compositeness. Flavour violation arises after rotating to the physical quark basis.