Preliminary results as of Summer 2019
(EPS 2019 conference)

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The global CKM fit: Inputs and Numerical results
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: Pulls
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


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).

Numerical Results

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

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Constraints in the (ρ̅, η̅) plane using the expressions used in the previous updates for K-K mixing in the ct convention. This update uses the ut convention as described in Brod, Gorbahn, Stamou arXiv:1911.06822.
α, β, γ
convention
ϕ1, ϕ2, ϕ3
convention

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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

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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

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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

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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

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

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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

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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

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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

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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

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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

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

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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

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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

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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

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

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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

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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

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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)].


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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

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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

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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

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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

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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

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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 yellow region of the global combination corresponds to 68% CL. We use the value quoted by J.C. Hardy at the Amherst workshop: |Vud| = 0.97418 ± 0.00021. This leads to a minimum χ2=23.7 and a deviation from unitarity (based only on direct determinations) of |Vud|2+|Vus|2 +|Vub|2-1 =-0.00082+0.00084-0.00013


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Constraints in the (|Vud|,|Vus|) plane. The indirect constraints (coming from b transitions) are related to |Vud| and |Vus| through unitarity. The yellow region of the global combination corresponds to 68% CL. A recent reestimation of radiative corrections was proposed by Gorchtein and Ramsey-Musolf [arXiv:1807.10197, arXiv:1812.03352, arXiv:1812.04229], leading to an updated estimate |Vud| = 0.97371 ±  0.00033. This leads to a minimum χ2=27.9 and a deviation from unitarity (based only on direct determinations) of |Vud|2+|Vus|2 +|Vub|2-1 =-0.00198+0.00141-0.00012


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Constraints in the (|Vud|,|Vus|) plane. The indirect constraints (coming from b transitions) are related to |Vud| and |Vus| through unitarity. The yellow region of the global combination corresponds to 68% CL. Another recent reestimation of radiative corrections was proposed by Czarnecki et al [arXiv:1907.06737], leading to an updated estimate |Vud| = 0.97390 ± 0.00035. This leads to a minimum χ2=25.7 and a deviation from unitarity (based only on direct determinations) of |Vud|2+|Vus|2 +|Vub|2-1 =-0.00162+0.00146-0.00015


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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 yellow region of the global combination corresponds to 68% CL.


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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.


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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).


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


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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.


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


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


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