The latest fits to the CKM matrix indicate that alpha=(90.7+4.5-2.9) degrees. The proximity of alpha to a right-angle raises the question: is it merely accidental or is it due to some physics beyond the Standard Model? In the framework of our recently-proposed flavour permutation symmetry, we consider the similarities between the quark and lepton mixing matrices, V and U, arguing that the relative smallness of one element in each suggests common constraints. These constraints link the smallness of V_ub and U_e3 with each other, and with the approximate mu-tau symmetry observed in leptonic mixing, together with a prediction of a large Dirac CP phase in both the quark and lepton sectors. In the quark case, we predict alpha=(89.0\pm 0.2) degrees, in agreement with data and suggesting that the unitarity triangle is in fact very nearly, but not exactly right.
The angles of all unitarity triangles of the Cabibbo-Kobayashi-Maskawa matrix are determined from the experimental data. Our analysis is independent of the parameterization of the CKM matrix and it is based on the predictions of the unitarity for the angles and the areas of the unitarity triangles. We note that the lengths of the sides of the four unitarity triangles determined from the experimental data do not form a triangle. We resolve this incompatibility by performing a constrained fit, assuming the equality of the area of the unitarity triangles. We demonstrate that the measured data are…
在类比夸克混合情形下的db三角形的基础上，我们利用Bjorken { \it et al.} through通过generalization推广of the tribimalimax最大scenario方案.特别地，对于U_{e3}范围0.05-0.15，轻子么正三角形的存在表明具有非零CP破坏的相当好的可能性。
Geometric representation of CP phases $δ_{\rm PDG}, δ_{\rm KM}$ in flavor mixing matrix and its sum rule by alternative unitarity triangle and quadrangle
The UTfit Collaboration Report on the Status of the Unitarity Triangle beyond the Standard Model I. Model-independent Analysis and Minimal Flavour Violation
We have investigated a possible connection between the Majorana phases and geometric parameters of leptonic unitarity triangle(LUT) in two-texture zero neutrino mass matrix. Such analytical relations can, also, be obtained for other theoretical models viz. hybrid textures, neutrino mass matrix with vanishing minors and have profound implications for geometric description of $CP$ violation. As an example, we have considered two-texture zero neutrino mass model to obtain relation between Majorana phases and LUT parameters. In particular, we find that Majorana phases depend on only one of the thr…
We investigate the sensitivity with which two angles of the "flat" unitarity triangle, defined by $V_{ub}^* V_{us} + V_{cb}^* V_{cs} + V_{tb}^* V_{ts} =0$, can possibly be measured directly at FCCee. We show that the measured errors on the angle $α_s = \arg(- V_{ub}^* V_{us} /V_{tb}^* V_{ts})$ and $β_s = \arg(-V_{tb}^* V_{ts} / V_{cb}^* V_{cs})$ should be better than $0.4^\circ$ and $0.035^\circ$, respectively. These measurements, combined with the measurement of the 3rd angle $γ_s = \arg(- V_{cb}^* V_{cs}/ V_{ub}^* V_{us})$, discussed in a different paper, will contribute to probe further the…
We formulate an alternative approach based on unitarity triangles to describe neutrino oscillations in presence of non-standard interactions (NSI). Using perturbation theory, we derive the expression for the oscillation probability in case of NSI and cast it in terms of the three independent parameters of the leptonic unitarity triangle (LUT). The form invariance of the probability expression (even in presence of new physics scenario as long as the mixing matrix is unitary) facilitates a neat geometric view of neutrino oscillations in terms of LUT. We examine the regime of validity of perturba…
We present a comprehensive analysis of leptonic unitarity triangles, using both current neutrino oscillation data and projections of next-generation oscillation measurements. Future experiments, sensitive to the degree of CP violation in the lepton sector, will enable the construction of precise triangles. We show how unitarity violation could manifest in the triangles and discuss how they serve as unitarity tests. We also propose the use of Jarlskog factors as a complementary means of probing unitarity. This analysis highlights the importance of testing the unitarity of the leptonic mixing ma…
