Preliminary results as of Summer 2018
(ICHEP 2018 conference)

 The global CKM fit: Inputs and Numerical results The global CKM fit: Pulls The global CKM fit in the large (ρ-bar,η-bar) plane The global CKM fit in the small (ρ-bar,η-bar) plane (zoom) The global CKM fit in the large (ρ̅M, η̅M) plane with M = sb, ds, ct, ut, uc The global CKM fit in the (|Vud|,|Vus|) plane The global CKM fit in the (|Vcd|,|Vcs|) plane The global CKM fit in the (|Vub|,|Vcb|) plane The global CKM fit for |Vtd| and |Vts| Branching ratio of Bs→μ+ μ- Constraints on the angle α/ϕ2 from charmless B decays

Numerical results:

 The results of the global CKM analysis include: Wolfenstein parameters, UT angles and sides, UTsangle and apex, CKM elements, theory parameters, rare branching fractions (B->lν, B->ll). Information on other fits (in particular the fit including only tree observables) is also provided. Numerical Results

 Pulls for various inputs or parameters involved in the Standard Model global fit. Each pull (in units of σ) is computed by taking the square root of the difference between χ2min obtained including or not including direct information on the quantity. This corresponds to consider Δχ2X;min=χ2with data on X;min- χ2without data X;min as a random variable distributed with 1 degree of freedom, and reinterpret the probability of reaching the observed value in units of σ. The presence of a plateau in the Rfit model for systematic uncertainties may lead to a vanishing pull for some quantities even in cases where the predicted and observed values are not identical. Some of the pulls presented in this plot are correlated [this is for instance the case for sin 2β and Br(B→τν)].

Constraints in the (ρ-bar,η-bar) plane. The red hashed region of the global combination corresponds to 68% CL.
 α, β, γconvention ϕ1, ϕ2, ϕ3convention eps png eps png
Constraints in the (ρ-bar,η-bar) plane. The |Vub| constraint has been split in three contributions: |Vub| from inclusive and exclusive semileptonic B decays (plain dark green), |Vub| from B+→τ+ ν (hashed darker green), and |Vub|/|Vcb| from Λb decays (hashed ligher green). The red hashed region of the global combination corresponds to 68% CL.
 α, β, γconvention ϕ1, ϕ2, ϕ3convention eps png eps png
Constraints in the (ρ̅, η̅) plane using only exclusive determinations of |Vub| and |Vcb| from semileptonic B decays as inputs.
 α, β, γconvention ϕ1, ϕ2, ϕ3convention eps png eps png
Constraints in the (ρ̅, η̅) plane using only inclusive determinations of |Vub| and |Vcb| from semileptonic B decays as inputs.
 α, β, γconvention ϕ1, ϕ2, ϕ3convention eps png eps png

The global CKM fit in the small (ρ-bar,η-bar) plane (zoom):

Zoomed constraints in the (ρ-bar,η-bar) plane.The red hashed region of the global combination corresponds to 68% CL.
 α, β, γconvention ϕ1, ϕ2, ϕ3convention eps png eps png
Zoomed constraints in the (ρ-bar,η-bar) plane. The |Vub| constraint has been split in three contributions: |Vub| from inclusive and exclusive semileptonic B decays (plain dark green), |Vub| from B+→τ+ ν (hashed darker green), and |Vub|/|Vcb| from Λb decays (hashed ligher green). The red hashed region of the global combination corresponds to 68% CL.
 α, β, γconvention ϕ1, ϕ2, ϕ3convention eps png eps png
Zoomed constraints in the (ρ-bar,η-bar) plane not including the angle measurements in the global fit.
 α, β, γconvention ϕ1, ϕ2, ϕ3convention eps png eps png
Constraints in the (ρ-bar,η-bar) plane including only the angle measurements.
 α, β, γconvention ϕ1, ϕ2, ϕ3convention eps png eps png
Constraints from CP conserving quantities (|Vub / Vcb|, Δmd, (Δmd and Δms) and B+ →τ+ ν) in the (ρ-bar,η-bar) plane.
 α, β, γconvention ϕ1, ϕ2, ϕ3convention eps png eps png
Constraints from CP violating quantities (sin(2β), α, γ and εk) in the (ρ-bar,η-bar) plane.
 α, β, γconvention ϕ1, ϕ2, ϕ3convention eps png eps png
Constraints from "Tree" quantities in the (ρ-bar,η-bar) plane (involving γ(DK) and α from the isospin analysis with the help of sin2β (charmonium), which gives another tree only γ measurement (the only assumption is that the ΔI=3/2 b-->d EW penguin amplitude is negligible)).
 α, β, γconvention ϕ1, ϕ2, ϕ3convention eps png eps png
Constraints from "Tree" quantities in the (ρ-bar,η-bar) plane (involving γ(DK) and α from the isospin analysis with the help of sin2β (charmonium), which gives another tree only γ measurement (the only assumption is that the ΔI=3/2 b-->d EW penguin amplitude is negligible)). The constraints from γ(DK) and γ(α)=π-α-β are shown.
 α, β, γconvention ϕ1, ϕ2, ϕ3convention eps png eps png
Constraints from "Tree" quantities in the (ρ-bar,η-bar) plane, with only input on |Vub| from semileptonic decays (involving γ(DK) and α from the isospin analysis with the help of sin2β (charmonium), which gives another tree only γ measurement (the only assumption is that the ΔI=3/2 b-->d EW penguin amplitude is negligible)).
 α, β, γconvention ϕ1, ϕ2, ϕ3convention eps png eps png
Constraints from "Tree" quantities in the (ρ-bar,η-bar) plane (only γ(DK) is used).
 α, β, γconvention ϕ1, ϕ2, ϕ3convention eps png eps png
Constraints from "Tree" quantities in the (ρ-bar,η-bar) plane with only input on |Vub| from semileptonic decays (ony γ(DK) is used).
 α, β, γconvention ϕ1, ϕ2, ϕ3convention eps png eps png
Constraints from "Tree" quantities in the (ρ-bar,η-bar) plane with only input on |Vub| from exclusive semileptonic B decays (only γ(DK) is used).
 α, β, γconvention ϕ1, ϕ2, ϕ3convention eps png eps png
Constraints from "Tree" quantities in the (ρ-bar,η-bar) plane with only input on |Vub| from inclusive semileptonic B decays (only γ(DK) is used).
 α, β, γconvention ϕ1, ϕ2, ϕ3convention eps png eps png
Constraints from "Loop" quantities in the (ρ-bar,η-bar) plane.
 α, β, γconvention ϕ1, ϕ2, ϕ3convention eps png eps png
Constraints in the (ρ-bar,η-bar) plane, not including the braching ratio of B+ → τ+ν in the global fit.
 α, β, γconvention ϕ1, ϕ2, ϕ3convention eps png eps png
Constraints in the (ρ-bar,η-bar) plane not including the measurement of sin2β in the global fit.
 α, β, γconvention ϕ1, ϕ2, ϕ3convention eps png eps png

The global CKM fit in the large (ρ̅M, η̅M) plane
with M = sb, ds, ct, ut, uc:

 The constraints can be expressed in the unitarity triangles associated with the different mesons of interest, with the relative coordinates of the upper appex of each triangle defined as ρ̅d1d2+iη̅d1d2 =-(Vud1Vud2*)/(Vcd1Vcd2*),     ρ̅u1u2+iη̅u1u2 =-(Vu1dVu2d*)/(Vu1sVu2s*).
Constraints in the (ρ̅sb, η̅sb) plane. The red hashed region of the global combination corresponds to 68% CL.
 α, β, γconvention ϕ1, ϕ2, ϕ3convention eps png eps png
Constraints in the (ρ̅ds, η̅ds) plane. The red hashed region of the global combination corresponds to 68% CL.
 α, β, γconvention ϕ1, ϕ2, ϕ3convention eps png eps png
Constraints in the (ρ̅tc, η̅tc) plane. The red hashed region of the global combination corresponds to 68% CL.
 α, β, γconvention ϕ1, ϕ2, ϕ3convention eps png eps png
Constraints in the (ρ̅tu, η̅tu) plane. The red hashed region of the global combination corresponds to 68% CL.
 α, β, γconvention ϕ1, ϕ2, ϕ3convention eps png eps png
Constraints in the (ρ̅cu, η̅cu) plane. The red hashed region of the global combination corresponds to 68% CL.
 α, β, γconvention ϕ1, ϕ2, ϕ3convention eps png eps png

 Constraints in the (|Vud|,|Vus|) plane. The indirect constraints (coming from b transitions) are related to |Vud| and |Vus| through unitarity. The red hashed region of the global combination corresponds to 68% CL. Prediction for the normalisation of the vector form factor FK→π+(0), compared to our current average of lattice resuls.

 Constraints in the (|Vcd|,|Vcs|) plane. The indirect constraints (combing from b and s transitions) are related to |Vcd| and |Vcs| through unitarity. The direct constraints combine leptonic and semileptonic D and Ds decays as well as information from neutrino-nucleaon scattering and W → cs decays. The red hashed region of the global combination corresponds to 68% CL. Constraints in the (|Vcd|,|Vcs|) plane where direct constraints involve only leptonic D and Ds decays with our inputs for lattice averages for fD and fDs. Constraints in the (|Vcd|,|Vcs|) plane where direct constraints involve only semileptonic D and Ds decays with our inputs for lattice averages FD → π(0) and FD → K (0). Constraints in the (|Vcd|,|Vcs|) plane where direct constraints involve only information from neutrino-nucleaon scattering and W→ cs decays (no lattice input).

 Constraints in the (|Vub|,|Vcb|) plane. The horizontal and vertical coloured bands represent our average of the determinations from semileptonic B decays. The white bands with solid (dashed) borders correspond to the determination from exclusive (inclusive) semileptonic B decays. The diagonal coloured band corresponds to the determination of |Vub|/|Vcb| from Λb decays. The rainbow oval region indicates the indirect determination of |Vub| and |Vcb| from the global fit, without any information from semileptonic or leptonic decays of b-hadrons. Constraints on |Vub| from inclusive and exclusive B decays, as well as our average, compared to the indirect determination from the global fit. Constraints on |Vcb| from inclusive and exclusive B decays, as well as our average, compared to the indirect determination from the global fit.

 Constraint on |Vtd/Vts| from the global fit, using only information on Bd and Bs mixings, and using only tree-level quantities. In all three cases, we use our average of lattice inputs. Constraint on |Vtd/Vts| from the global fit, using only information on Bd and Bs mixings, and using only tree-level quantities. We use our average of lattice inputs apart from the bag parameters for Bd and Bs mixings which are taken from FNAL-MILC 2016 with a linear combination of uncertainties (linked to the Rfit approach). For the fit using neutral-meson mixing only, we also provide the results using a quadratic combination (Gaussian approach). A discrepancy occurs only in the latter case. Constraint on |Vtd| from the global fit, using only information on Bd and Bs mixings, and using only tree-level quantities. In all three cases, we use our average of lattice inputs. Constraint on |Vtd| from the global fit, using only information on Bd and Bs mixings, and using only tree-level quantities. We use our average of lattice inputs apart from the bag parameters for Bd and Bs mixings which are taken from FNAL-MILC 2016 with a linear combination of uncertainties (linked to the Rfit approach). For the fit using neutral-meson mixing only, we also provide the results using a quadratic combination (Gaussian approach). A discrepancy occurs only in the latter case. Constraint on |Vts| from the global fit, using only information on Bd and Bs mixings, and using only tree-level quantities. In all three cases, we use our average of lattice inputs. Constraint on |Vts| from the global fit, using only information on Bd and Bs mixings, and using only tree-level quantities. We use our average of lattice inputs apart from the bag parameters for Bd and Bs mixings which are taken from FNAL-MILC 2016 with a linear combination of uncertainties (linked to the Rfit approach). For the fit using neutral-meson mixing only, we also provide the results using a quadratic combination (Gaussian approach). A discrepancy occurs only in the latter case.

 Prediction for Br(Bs→μ+ μ-) to be compared with the current measurement (we consider here the branching ratio at t=0, not including effects due to Bs mixing). Prediction for Br(Bd→μ+ μ-) to be compared with the current measurement. Prediction on the two dileptonic branching ratios Br(Bs→μ+ μ-) and Br(Bd→μ+ μ-) coming from the global fit (without input on dileptonic branching ratios) compared to current experimental information.

Constraints on the angle α/ϕ2 from charmless B decays:

Constraints on α/ϕ2 from B→ππ (BABAR, Belle and WA) compared to the prediction from the global CKM fit (not including the α-related measurements).
 α, β, γconvention ϕ1, ϕ2, ϕ3convention eps png eps png
Constraints on α/ϕ2 from B→ππ, ρπ and ρρ (WA) compared to the prediction from the global CKM fit (not including the α-related measurements).
 α, β, γconvention ϕ1, ϕ2, ϕ3convention eps png eps png
Constraint on the reduced isospin amplitude a+− = A+−/A+0 in the complex plane for the B→ππsystem. The individual constraint from the B0→π+π- system and from the B0→π0π0 observables are indicated by the yellow and green circular areas, respectively. The corresponding isospin triangular relation is represented by the black triangle.
Constraint on the reduced isospin amplitude a+− = A+−/A+0 in the complex plane for the B→ππsystem. The individual constraint from the B0→π+π- system and from the B0→π0π0 observables are indicated by the yellow and green circular areas, respectively. The corresponding isospin triangular relation is represented by the black triangle.