CKM Fits: What the Data Say (Focused on B Physics)

Abstract

An up-to-date profile of the Cabibbo-Kobayashi-Maskawa matrix is given with emphasis on the interpretation of recent results on CP violation from the B factories. We provide a review of the relevant experimental and theoretical inputs from the contributing domains of the electroweak interaction. We give numerical and graphical constraints on the CKM parameters and predictions of related physical observables. We discuss the impact of what the data actually say on model-independent studies of new physics. The Unitary-exact Wolfenstein Parametrization and Rephasing-invariant QuantitiesThe Standard Model (SM) of electroweak interactions describes CP violation in weak interactions as a consequence of a single non-vanishing complex phase in the three-generation Cabibbo-Kobayashi-Maskawa (CKM) quark-mixing matrix [1,2]. The CKM matrix V has four quantities which are fundamental constants. These may be parametrized in a variety of ways. The standard parametrization, proposed by Chau-Keung [3] and advocated by the Particle Data Group [4], uses three mixing angles θ 12 , θ 23 , θ 13 and one CP-odd phase δ 13 which generates CP violation. The fact that there is only one independent CP-violating parameter in the electroweak sector means that this is a very predictive and testable model. Following the observation of a hierarchy between different matrix elements, Wolfenstein [5] proposed an expansion of the CKM matrix in terms of four parameters, A, λ, ρ and η (λ being the expansion parameter). Defining [6] λ ≡ sin θ 12 , Aλ 2 ≡ sin θ 13 and Aλ 3 (ρ + iη) ≡ sin θ 13 e −iδ13 to all orders in λ (i.e., these expressions are exact by definition; they are not corrected by terms of higher order in λ) ensures a unitary-exact Wolfenstein parametrization. Moreover, physically meaningful quantities must be rephasing-invariant quantities. Such invariants are the moduli, |V ij |, and the quadri-products, V ij V kl V * il V * jk . The Wolfenstein parameters, being physical quantities, must be phase-convention invariant:. ρ and η with ρ + iη = V * ub /(Aλ 3 ) are not phaseconvention invariant, in contrast to ρ + iη [7]. The results given in this paper use the unitary-exact Wolfenstein parametrization and rephasing-invariant quantities. λ is determined from |V ud | (superallowed nuclear transitions) and |V us | (semileptonic kaon decays) to a combined precision of 0.5%. A is determined from |V cb | (inclusive and exclusive semileptonic B decays) to a combined precision of about 2%. While λ and A are well-known, the parameters ρ and η are much more uncertain (about 20% for ρ and 7% for η). The main goal of CP-violation experiments is to over-constrain these parameters by measuring both the three angles and the sides of the unitarity triangle (UT) and, possibly, to find inconsistencies suggesting the existence of physics beyond the SM. What is important is thus the capability of the CKM mechanism to describe flavor dynamics of many constraints from vastly different scales and not the measurement of the CKM phase's value per se. CKM Metrology:...