CKMfitter

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

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The global CKM fit in the large (ρ̅, η̅) plane:

Constraints in the (ρ̅, η̅) plane. The red hashed region of the global combination corresponds to 68% CL.

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Constraints in the (ρ̅, η̅) 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.

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Constraints in the (ρ̅, η̅) plane using only exclusive determinations of |Vub| and |Vcb| from semileptonic decays as inputs.

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Constraints in the (ρ̅, η̅) plane using only inclusive determinations of |Vub| and |Vcb| from semileptonic decays as inputs.

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The global CKM fit in the small (ρ̅, η̅) plane (zoom):

Zoomed constraints in the (ρ̅, η̅) plane.The red hashed region of the global combination corresponds to 68% CL.

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Zoomed constraints in the (ρ̅, η̅) 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.

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Zoomed constraints in the (ρ̅, η̅) plane not including the angle measurements in the global fit.

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Constraints in the (ρ̅, η̅) plane including only the angle measurements.

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Constraints from CP conserving quantities (|V_ub / V_cb|, Δm_d, (Δm_d and Δm_s) and B⁺ →τ⁺ ν) in the (ρ̅, η̅) plane.

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Constraints from CP violating quantities (sin(2β), α, γ and ε_k) in the (ρ̅, η̅) plane.

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Constraints from "Tree" quantities in the (ρ̅, η̅) 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)).

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Constraints from "Tree" quantities in the (ρ̅, η̅) plane (only γ(DK) is used).

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Constraints from "Tree" quantities in the (ρ̅, η̅) plane with only input on |V_ub| from semileptonic decays (ony γ(DK) is used).

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Constraints from "Tree" quantities in the (ρ̅, η̅) plane with only input on |V_ub| from exclusive semileptonic decays (only γ(DK) is used).

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Constraints from "Tree" quantities in the (ρ̅, η̅) plane with only input on |V_ub| from inclusive semileptonic decays (only γ(DK) is used).

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Constraints from "Loop" quantities in the (ρ̅, η̅) plane.

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Constraints in the (ρ̅, η̅) plane, not including the braching ratio of B⁺ → τ⁺ν in the global fit.

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Constraints in the (ρ̅, η̅) plane not including the measurement of sin2β in the global fit.

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The global CKM fit in the large (ρ̅_M, η̅_M) 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
ρ̅_d₁d₂+iη̅_d₁d₂ =-(V_ud₁V_ud₂^*)/(V_cd₁V_cd₂^*), ρ̅_u₁u₂+iη̅_u₁u₂ =-(V_u₁dV_u₂d^*)/(V_u₁sV_u₂s^*).

Constraints in the (ρ̅_sb, η̅_sb) plane. The red hashed region of the global combination corresponds to 68% CL. The constraint from the angle φ_s related to B_s meson mixing is indicated with light blue lines.

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Constraints in the (ρ̅_ds, η̅_ds) plane. The red hashed region of the global combination corresponds to 68% CL.

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Constraints in the (ρ̅_tc, η̅_tc) plane. The red hashed region of the global combination corresponds to 68% CL.

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Constraints in the (ρ̅_tu, η̅_tu) plane. The red hashed region of the global combination corresponds to 68% CL.

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Constraints in the (ρ̅_cu, η̅_cu) plane. The red hashed region of the global combination corresponds to 68% CL.

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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. The discrepancy between prediction and measurement is 1.6 σ.	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

New physics in neutral-meson mixing:

Individual constraints correspond to 68% CL (see: arXiv:1008.1593 [hep-ph] and arXiv:1203.0238. [hep-ph] for a detailed explanation of the hypotheses).

The DO result for the dimuon asymmetry A_SL has been recently corrected to take into SM contributions neglected beforehand (standard model CP violation in interference of decays with and without mixing of B<0$ to flavour non-specific states), based on arXiv:1303.0175 [hep-ex].

This estimate was later criticised in Uli Nierste's talk at CKM14 as being too large a correction. In order to take into account an underestimation of the systematics attached to this estimate, we consider the results both with and without including A_SL in the fit.

In scenario I, we have introduced NP in M₁₂^q = M₁₂^SM,qΔ_q independently for B_d, B_s and K, corresponding to NP with arbitrary flavour structure. In the absence of A_SL, constraints on New Physics in the (ReΔ_d,ImΔ_d) plane. A 0.9 σ deviation is obtained for the 2-dimensional SM hypothesis Δ_d = 1 (Re(Δ_d)=1, Im(Δ_d)=0).	eps png
In the absence of A_SL, constraints on New Physics in the (ReΔ_s,ImΔ_s) plane. A 0.3 σ deviation is obtained for the 2-dimensional SM hypothesis Δ_s = 1 (Re(Δ_s)=1, Im(Δ_s)=0). The pulls for the relevant observables are 1.1 σ for B->τν and 1.1 σ for φ_s^{J/Ψ Φ}.	eps png

In the presence of A_SL, constraints on New Physics in the (ReΔ_d,ImΔ_d) plane. A 1.2 σ deviation is obtained for the 2-dimensional SM hypothesis Δ_d = 1 (Re(Δ_d)=1, Im(Δ_d)=0).	eps png
In the presence of A_SL, constraints on New Physics in the (ReΔ_s,ImΔ_s) plane. A 0.3 σ deviation is obtained for the 2-dimensional SM hypothesis Δ_s = 1 (Re(Δ_s)=1, Im(Δ_s)=0). The pulls for the relevant observables are 0.2 σ for B->τν, 2.6 σ for φ_s^{J/Ψ Φ} and 2.4 σ for A_SL.	eps png

Branching ratio of B_s→μ⁺ μ^-

Prediction for Br(B_s→μ⁺ μ^-)=(3.34^+0.13_-0.25)x10^-9, to be compared with the current measurement (2.8^+0.7_-0.6)x10^-9.	eps png
Prediction on the two dileptonic branching ratios Br(B_s→μ⁺ μ^-) and Br(B_d→μ⁺ μ^-) coming from the global fit (without input on dileptonic branching ratios) compared to current experimental information. In both plots, we consider the value of the branching ratios without time integration, which would induce a further increase of O(ΔΓ_s/Γ_s), more precisely (1+y_s)=1.07.	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.

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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_Ds=245.3 ± 0.5 ± 4.5 MeV and f_Ds/f_D=1.201 ± 0.004 ± 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 ± 0.020 ± 0.048 and F_{D → K}(0)=0.747 ± 0.011 ± 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 α/ϕ₂ from charmless B decays:

Constraints on α/ϕ₂ from B→ππ, ρπ and ρρ (WA)

α[WA,ππ]∈=(95.0^+8.8_-7.9)°
α[WA,ρρ]=(89.9^+5.4_-5.3)°
α[WA,all]=(87.7^+3.5_-3.3)°

compared to the prediction from the global CKM fit (not including the α-related measurements).

α[fit]= (91.5^+4.2_-1.3)°

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Constraints on α/ϕ₂ from the combination of B→ππ, ρπ, and ρρ for BaBar, Belle and WA, compared to the prediction from the global CKM fit (not including the α-related measurements).

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Isospin triangles in B→ππ and B→ππ. One notices that the first triangle is flat, contrary to the second.

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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] = (73.2^+6.3_-7.0)°, compared to the prediction from the global CKM fit (not including these measurements):
γ[fit] = (66.9^+1.0_-3.7)°

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Constraints on γ/ϕ₃ from different set of measurements on D^(*)K^(*) decays (GLW+ADS) and Dalitz analyses (GGSZ) (methods shown separately):

γ[BaBar] = (70 ± 18) °
γ[Belle] = (73⁺¹³_-15)°
γ[LHCb] = (74.6^+8.4_-9.2)°
γ[combined] = (73.2^+6.3_-7.0)°

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Constraints on (r_B(DK) vs γ) and (δ_B(DK) vs γ):

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Constraint on the ratios of interfering amplitudes r_B and the strong phases between the interfering amplitudes of the different decays B → D^(*)K^(*) using GLW, ADS and GGSZ results from these decays:

r_B(DK) = 0.0970^+0.0062_-0.0063,
δ_B(DK) = (125.4^+7.0_-7.8)°

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r_B(D^*K) =0.119^+0.018_-0.019,
δ_B(D^*K) = (-49⁺¹²_-15)°

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r_B(DK^*) = 0.137^+0.051_-0.047,
δ_B(DK^*) = (112⁺³²_-44)°

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r_B(DK^*0) = 0.236^+0.043_-0.052,
δ_B(DK^*0) = (336⁺¹⁹_-23)° and (200⁺¹⁰_-9)°

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Constraints on |sin(2β+γ)|:

Constraints on \|sin(2β+γ)\| from the measurement of time-dependent CP asymmetries in D^(*) π (ρ).	eps png
Translation of this result into γ (using sin(2β) as additional input and choosing among the four solutions to the SM one). γ[GLW+ADS+GGSZ+\|sin(2β+γ)\|] = (73.3^+6.1_-6.5)°.	eps png
Constraints from \|sin(2β+γ)\| in the (ρ̅, η̅) plane.	eps png