Preliminary results as of Summer 2018
(ICHEP 2018 conference)

Menu:

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

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;min2with 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)].


eps png

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

Constraints in the (ρ-bar,η-bar) plane. The red hashed region of the global combination corresponds to 68% CL.
α, β, γ
convention
ϕ1, ϕ2, ϕ3
convention

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, γ
convention
ϕ1, ϕ2, ϕ3
convention

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, γ
convention
ϕ1, ϕ2, ϕ3
convention

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, γ
convention
ϕ1, ϕ2, ϕ3
convention

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, γ
convention
ϕ1, ϕ2, ϕ3
convention

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, γ
convention
ϕ1, ϕ2, ϕ3
convention

eps png


eps png

Zoomed constraints in the (ρ-bar,η-bar) plane not including the angle measurements in the global fit.
α, β, γ
convention
ϕ1, ϕ2, ϕ3
convention

eps png


eps png

Constraints in the (ρ-bar,η-bar) plane including only the angle measurements.
α, β, γ
convention
ϕ1, ϕ2, ϕ3
convention

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, γ
convention
ϕ1, ϕ2, ϕ3
convention

eps png


eps png

Constraints from CP violating quantities (sin(2β), α, γ and εk) in the (ρ-bar,η-bar) plane.
α, β, γ
convention
ϕ1, ϕ2, ϕ3
convention

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, γ
convention
ϕ1, ϕ2, ϕ3
convention

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, γ
convention
ϕ1, ϕ2, ϕ3
convention

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, γ
convention
ϕ1, ϕ2, ϕ3
convention

eps png


eps png

Constraints from "Tree" quantities in the (ρ-bar,η-bar) plane (only γ(DK) is used).
α, β, γ
convention
ϕ1, ϕ2, ϕ3
convention

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, γ
convention
ϕ1, ϕ2, ϕ3
convention

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, γ
convention
ϕ1, ϕ2, ϕ3
convention

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, γ
convention
ϕ1, ϕ2, ϕ3
convention

eps png


eps png

Constraints from "Loop" quantities in the (ρ-bar,η-bar) plane.
α, β, γ
convention
ϕ1, ϕ2, ϕ3
convention

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, γ
convention
ϕ1, ϕ2, ϕ3
convention

eps png


eps png

Constraints in the (ρ-bar,η-bar) plane not including the measurement of sin2β in the global fit.
α, β, γ
convention
ϕ1, ϕ2, ϕ3
convention

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, γ
convention
ϕ1, ϕ2, ϕ3
convention

eps png


eps png

Constraints in the (ρ̅ds, η̅ds) plane. The red hashed region of the global combination corresponds to 68% CL.
α, β, γ
convention
ϕ1, ϕ2, ϕ3
convention

eps png


eps png

Constraints in the (ρ̅tc, η̅tc) plane. The red hashed region of the global combination corresponds to 68% CL.
α, β, γ
convention
ϕ1, ϕ2, ϕ3
convention

eps png


eps png

Constraints in the (ρ̅tu, η̅tu) plane. The red hashed region of the global combination corresponds to 68% CL.
α, β, γ
convention
ϕ1, ϕ2, ϕ3
convention

eps png


eps png

Constraints in the (ρ̅cu, η̅cu) plane. The red hashed region of the global combination corresponds to 68% CL.
α, β, γ
convention
ϕ1, ϕ2, ϕ3
convention

eps png


eps png

The global CKM fit in the (|Vud|,|Vus|) plane:

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.


eps png

Prediction for the normalisation of the vector form factor FK→π+(0), compared to our current average of lattice resuls.


eps png

The global CKM fit in the (|Vcd|,|Vcs|) plane:

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.


eps png

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.


eps png

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).


eps png

Constraints in the (|Vcd|,|Vcs|) plane where direct constraints involve only information from neutrino-nucleaon scattering and W→ cs decays (no lattice input).


eps png

The global CKM fit in the (|Vub|,|Vcb|) plane:

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.


eps png

Constraints on |Vub| from inclusive and exclusive B decays, as well as our average, compared to the indirect determination from the global fit.


eps png

Constraints on |Vcb| from inclusive and exclusive B decays, as well as our average, compared to the indirect determination from the global fit.


eps png

The global CKM fit for |Vtd| and |Vts|:

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.


eps png

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.


eps png

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.


eps png

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.


eps png

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.


eps png

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.


eps png

Branching ratio of Bs→μ+ μ-

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).


eps png

Prediction for Br(Bd→μ+ μ-) to be compared with the current measurement.


eps png

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.


eps png

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, γ
convention
ϕ1, ϕ2, ϕ3
convention

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, γ
convention
ϕ1, ϕ2, ϕ3
convention

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.


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.


eps png