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The Cabibbo-Kobayashi-Maskawa matrix is a key element to describe flavour dynamics in the Standard Model. With only four parameters, this matrix is able to describe a large range of phenomena in the quark sector, such as CP violation and rare decays. It can thus be constrained by many different processes, which have to be measured experimentally with a high accuracy and computed with a good theoretical control. With the advent of the B factories and the LHCb experiment taking data, the precision has significantly improved recently. The most relevant experimental constraints and theoretical inputs are reviewed and fits to the CKM matrix are presented for the Standard Model and for some topical model-independent studies of New Physics.
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The CKM matrix, V, relates the quark mass and flavor bases. In the standard model, V is unitary 3X3, and specified by four arbitrary parameters, including a phase allowing for $CP$ violation. We review the experimental determination of V, including the four parameters in the standard model context. This is an active field; the precision of experimental measurements and theoretical inputs continues to improve. The consistency of the determination with the standard model unitarity is investigated. While there remain some issues the overall agreement with standard model unitarity is good.
An overview of the most important progresses in charm physics since the last CKM Workshop (2014) is presented. Due emphasis is given to the experimental measurements directly related to the CKM matrix.
The LHC is the new b-hadron factory and will be dominating flavour physics until the start of Belle II, and beyond in many decay modes. While the $B$ factories and Tevatron experiments are still analysing their data, ATLAS, CMS and LHCb are producing interesting new results in CP violation and rare decays, that set strong constraints on models beyond that SM and exhibit some discrepancies with the SM predictions. The LHCb collaboration used the LHC 50 ns ramp-up period of July 2015 to measure the double-differential $J/psi$, $J/psi$-from-$b$-hadron and charm cross-sections at $sqrt{s} = 13$ TeV. Both measurements were performed directly on triggered candidates using a reduced data format that does not require offline processing.
The vector charmoniumlike state $Y(4220)$ was reported recently in the cross sections of $e^+e^-to omega chi_{c0}$, $pi^+pi^-h_c$, $pi^+pi^- J/psi$, and $D^0 D^{*-}pi^+ + c.c.$ measured by the BESIII experiment. A combined fit is performed to the cross sections of these four final states to extract the resonant parameters of the $Y(4220)$. We determine a mass $M=(4219.6pm 3.3pm 5.1)$~MeV/$c^2$ and a total width $Gamma=(56.0pm 3.6pm 6.9)$~MeV for the $Y(4220)$, where the first uncertainties are statistical and the second ones systematic. Assuming the $Y(4220)$ decays dominantly to the above four modes and their isospin symmetric modes, we also estimate its leptonic decay width and decay branching fractions. These information is essential for the understanding of the nature of this state.
Nuclear beta decays between (J^pi,T) = (0^+,1) analog states yield the best value for the Vud element of the Cabibbo-Kobayashi-Maskawa matrix. Current world data establish the corrected Ft values of 14 separate superallowed transitions to a precision of order 0.1% or better. The validity of the small theoretical correction terms is confirmed by excellent consistency among the 14 Ft values and by recent measurements that compare pairs of mirror superallowed transitions. With consistency established, the results now yield |Vud| = 0.97420(21). This value is consistent with the considerably less precise results obtained from beta decays of the neutron, the pion and T=1/2 mirror nuclei, which are hampered by experimental challenges.
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