CKMfitter

Preliminary results as of Winter 2014
(Moriond 2014 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 (ρ_s-bar,η_s-bar) plane

Constraint from BR(B⁺→τ⁺ ν)

The global CKM fit in the (|V_ud|,|V_us) plane

The global CKM fit in the (|V_cd|,|V_cs) plane

Constraints on the angle γ/ϕ₃ from B decays to charm

Numerical results:

The results of the global CKM analysis include:

Wolfenstein parameters,
UT angles and sides,
UT_sangle and apex,
CKM elements,
theory parameters,
rare branching fractions (B->lν, B->ll).

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 χ²_min obtained including or not including direct information on the quantity. This corresponds to consider Δχ²_X;min=χ²_{with data on X;min}- χ²_{without 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 theoretical uncertainties may lead to a vanishing pull for some quantities even in cases where the predicted and observed values are not identical.

Many of the pulls presented in this plot are correlated [this is for instance the case for sin 2β and Br(B→τν)], so that the distribution of the corresponding p-values should not be expected to be flat

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 |V_ub| constraint has been splitted in the two contributions: |Vub| from inclusive and exclusive semileptonic decays (plain dark green) and |Vub| from B⁺→τ⁺ ν (hashed 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

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 |V_ub| constraint has been splitted in the two contributions: |V_ub| from inclusive and exclusive semileptonic decays (plain dark green) and |V_ub| from B⁺→τ⁺ ν (hashed 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 (|V_ub / V_cb|, Δm_d, (Δm_d and Δm_s) 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 ε_k) 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 (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 |V_ub| 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 |V_ub| from exclusive semileptonic 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 |V_ub| from inclusive semileptonic 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 (ρ_s-bar,η_s-bar) plane:

Constraints in the (ρ_s-bar,η_s-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

Constraint from the B⁺→τ⁺ ν branching ratio:

There is a specific correlation between sin2β and BR(B→τν), regarding the prediction from the global fit without using these measurements. The cross corresponds to the experimental value with 1 sigma errors.	eps png
The constraint can also be seen from the point of view of lattice inputs, with the predictions on the decay constant f_{B_d} and f_{B_d} Sqrt[B_{B_d}]	eps png

The global CKM fit in the (|V_ud|,|V_us|) plane:

Constraints in the (|V_ud|,|V_us|) plane. The indirect constraints (coming from b transitions) are related to |V_ud| and |V_us| through unitarity. The red hashed region of the global combination corresponds to 68% CL.

eps png

The global CKM fit in the (|V_cd|,|V_cs|) plane:

Constraints in the (\|V_cd\|,\|V_cs\|) plane. The indirect constraints (combing from b and s transitions) are related to \|V_cd\| and \|V_cs\| through unitarity. The direct constraints combine leptonic and semileptonic D and D_s 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 (\|V_cd\|,\|V_cs\|) plane where direct constraints involve only leptonic D and D_s decays with our inputs for lattice averages f_D=249.2 ± 1.2 ± 4.5 MeV and f_Ds/f_D=1.185 ± 0.005 ± 0.010.	eps png
Constraints in the (\|V_cd\|,\|V_cs\|) plane where direct constraints involve only semileptonic D and D_s decays with our inputs for lattice averages F_{D → π}(0)=0.666 ± 0.017 ± 0.048 and F_{D → K}(0)=0.747 ± 0.010 ± 0.034.	eps png
Constraints in the (\|V_cd\|,\|V_cs\|) plane where direct constraints involve only information from neutrino-nucleaon scattering and W→ cs decays (no lattice input).	eps png

Constraints on the angle γ/ϕ₃ from B decays to charm :

Constraints on γ/ϕ₃ from world average D()K() decays (GLW+ADS) and Dalitz analyses (GGSZ): γ[combined] = 70.0^+7.7_-9.0°, compared to the prediction from the global CKM fit (not including these measurements): γ[fit] = 66.4^+1.2_-3.3°	eps png
Constraints on γ/ϕ₃ from all measurements on D()K() decays (GLW+ADS) and Dalitz analyses (GGSZ) (methods shown separately): γ[combined] = 70.0^+7.7_-9.0°	eps png
Constraints on γ/ϕ₃ from BaBar measurements on D()K() decays (GLW+ADS) and Dalitz analyses (GGSZ) (methods shown separately): γ[BaBar] = 72⁺¹⁷_-19°	eps png
Constraints on γ/ϕ₃ from Belle measurements on D()K() decays (GLW+ADS) and Dalitz analyses (GGSZ) (methods shown separately): γBelle] = 73⁺¹³_-15°	eps png
Constraints on γ/ϕ₃ from LHCb measurements on D()K() decays (GLW+ADS) and Dalitz analyses (GGSZ) (methods shown separately):: γ[LHCb] = 68⁺¹²_-15°	eps png

Constraint on the ratio of interfering amplitudes r_B of the decay B → DK from world average D()K() decays (GLW+ADS) and Dalitz analyses (GGSZ): r_B(DK) = 0.0972^+0.0063_-0.0064.	eps png
Constraint on the ratio of amplitudes r_B of the decay B → D^K: r_B(D^K) =0.120^+0.018_-0.020.	eps png
Constraint on the ratio of amplitudes r_B of the decay B → DK^: r_B(DK^) = 0.137^+0.045_-0.047.	eps png
Constraint on the strong phase between the interfering amplitudes of the decay B → DK from world average D()K() decays (GLW+ADS) and Dalitz analyses (GGSZ): δ_B(DK) = 121.1^+8.2_-9.3°.	eps png
Constraint on the strong phase between the interfering amplitudes of the decay B → D^K: δ_B(D^K) = -50⁺¹³_-15°.	eps png
Constraint on the strong phase between the interfering amplitudes of the decay B → DK^: δ_B(DK^) = 107⁺³⁵_-42°.	eps png