Universal Unitarity Triangle and Physics Beyond the Standard Model

TL;DR

The paper addresses extracting CKM parameters in a framework where new physics does not introduce new operators or CKM phases, by defining a universal unitarity triangle (UUT) valid for the SM and MFV-like extensions. It proposes determining the UUT from CKM-sensitive, hadronic-uncertainty-free observables such as the ratio $\Delta M_d/\Delta M_s$ to fix $R_t$ and $\sin 2\beta$ from CP asymmetries or rare decays to fix the apex via $\bar{\varrho}$ and $\bar{\eta}$, with gamma accessible through tree-level B decays. The key contributions are the explicit construction of the UUT, the identification of clean observables to determine its sides and angles, and a framework to contrast universal and model-specific triangles to reveal or constrain new physics. This has practical impact by providing a transparent, hadronic-uncertainty-resistant benchmark for testing MFV-like theories and for signaling deviations that point to physics beyond the considered class.

Abstract

We make the simple observation that there exists a universal unitarity triangle for all models, like the SM, the Two Higgs Doublet Models I and II and the MSSM with minimal flavour violation, that do not have any new operators beyond those present in the SM and in which all flavour changing transitions are governed by the CKM matrix with no new phases beyond the CKM phase. This universal triangle can be determined in the near future from the ratio (Delta M)_d/(Delta M)_s and sin(2 beta) measured first through the CP asymmetry in B_d^0 to psi K_S and later in K to pi nu nubar decays. Also suitable ratios of the branching ratios for B to X_{d,s} nu nubar and B_{d,s} to mu^+ mu^- and the angle gamma measured by means of CP asymmetries in B decays can be used for this determination. Comparison of this universal triangle with the non-universal triangles extracted in each model using epsilon, (Delta M)_d and various branching ratios for rare decays will allow to find out in a transparent manner which of these models, if any, is singled out by experiment. A virtue of the universal triangle is that it allows to separate the determination of the CKM parameters from the determination of new parameters present in the extensions of the SM considered here.

Figures (1)

• Figure 1: Unitarity Triangle.