Preliminary results as of ICHEP 2010

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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 in the large (ρs-bar,ηs-bar) plane
Constraint from BR(B+→τ+ ν)
Constraint from decays B→ V γ
Constraints on the angle α/ϕ2 from charmless B decays
Constraints on the angle γ/ϕ3 from B decays to charm
Constraints on |sin(2β+γ)|
New Physics in Mixing

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

Zoomed constraints in the (ρ-bar,η-bar) plane. The |Vub| 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

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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 not including the angle measurements in the global fit.
α, β, γ
convention
ϕ1, ϕ2, ϕ3
convention

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Zoomed constraints in the (ρ-bar,η-bar) plane including only the angle measurements in the global fit.
α, β, γ
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ϕ1, ϕ2, ϕ3
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Zoomed constraints in the (ρ-bar,η-bar) plane including the CP conserving quantities in the global fit, i.e., |Vub| (semileptonic and B+→τ+ ν), Δmd, Δmd & Δms.
α, β, γ
convention
ϕ1, ϕ2, ϕ3
convention

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Zoomed constraints in the (ρ-bar,η-bar) plane including the CP violating quantities in the global fit, i.e., sin(2β), α, γ and εK.
α, β, γ
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ϕ1, ϕ2, ϕ3
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Zoomed constraints from "Tree" quantities in the (ρ-bar,η-bar) plane (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
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ϕ1, ϕ2, ϕ3
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Zoomed constraints from "Loop" quantities in the (ρ-bar,η-bar) plane.
α, β, γ
convention
ϕ1, ϕ2, ϕ3
convention

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Zoomed 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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Zoomed 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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The global CKM fit in the large ρs-bar,ηs-bar) plane:

Constraints in the (ρs-bar,ηs-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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Constraint from the B+→τ+ ν branching ratio:

There is a discrepancy in the CKM global fit, because of the world average for sin2β and the world average for BR(B→τν).
There is a specific correlation between the two quantities in the global fit that is a bit at odds with the direct experimental determination. This is best viewed in the (sin2β,BR(B→τν)) plane, regarding the prediction from the global fit without using these measurements. The cross corresponds to the experimental values with 1 sigma uncertainties.
α, β, γ
convention
ϕ1, ϕ2, ϕ3
convention

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The shape of the correlation can be understood by considering the ratio BR(B→τν)/Δmd, where the decay constant fBd cancels, leaving limited theoretical uncertainties (the ratio depends only on the bag parameter BBd). Thus from the observables BR(B→τν) and Δmd one gets an interesting constraint in the (ρbar,ηbar) plane, which does not match perfectly with the global fit output.
α, β, γ
convention
ϕ1, ϕ2, ϕ3
convention

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To have a closer look, one can write the full formula for the ratio

where one explicitly sees that the correlation between BR(B→τν) and the angle β is controlled by the values of BBd, and the angles α and γ. This can be checked explicitly by comparing the above analytical formula with the colored region in the (sin2β,BR(B→τν)) plane. In other words the discrepancy is not driven by the value of semileptonic |Vub|, nor by the decay constant fBd.

To quantify the discrepancy one can compare the indirect fit prediction for BR(B→τν) with the measurement. The deviation here is 2.8 sigmas.

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A simpler test is the comparison of the prediction of BBd from the above analytical formula (having only BR(B→τν), Δmd, α, β, γ and |Vud| as inputs, that is an almost completely theory-free determination of BBd) with the current lattice determination BBd = 1.221 +0.087-0.085. For this test the deviation is 2.8 sigmas, dominated by the error on BR(B→τν), α, γ and BBd.

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From the above branching ratio one can derive a value for fBd (281+26-29 MeV) as well and compare it with respect to our Lattice QCD average (191± 21 MeV).

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Finally one can compare the contributions to the global fit and our Lattice averages on the quantities fBd vs.fBd Sqrt(BBd).

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Constraint from decays B →V γ:

No update See Summer 08 results (here).

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

No update See Moriond 09 results (here).

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) compared to the prediction from the global CKM fit (not including these measurements): γ[combined] = (71+21-25
α, β, γ
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ϕ1, ϕ2, ϕ3
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Constraint on the ratio of interfering amplitudes rB of the decay B → DK from world average D(*)K(*) decays (GLW+ADS) and Dalitz analyses (GGSZ): rB(DK) = 0.103+0.015-0.024.

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Constraint on the ratio of amplitudes rB of the decay B → D*K: rB(D*K)= 0.116+0.025-0.025.

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Constraint on the ratio of amplitudes rB of the decay B → DK*: rB(DK*)= 0.111+0.061-0.047.

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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): δB(DK) = (115+17-26)°.

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Constraint on the strong phase between the interfering amplitudes of the decay B → D*K: δB(D*K) = (-49+17-26)°.

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Constraint on the strong phase between the interfering amplitudes of the decay B → DK*: δB(DK*) = (93+62-39)°.

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Constraints on |sin(2β+γ)|:

No update See Beauty 09 results (here).

Constraints on New physics in Bd,s-Meson Mixing:

individual constraints correspond to 68% CL (see: arXiv:1008.1593 [hep-ph][FPCP10 inputs]).
Constraints on New Physics in the (ReΔd,ImΔd) plane. A 2.5 σ deviation is obtained for the 2-dimensional SM hypothesis Δd = 1 (Re(Δd)=1, Im(Δd)=0). Include the new ASL(D0) but not the new D0(6.1 fb-1)/CDF(5.2 fb-1) φs.

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Constraints on New Physics in the (ReΔs,ImΔs) plane. A 2.7 σ deviation is obtained for the 2-dimensional SM hypothesis Δs = 1 (Re(Δs)=1, Im(Δs)=0). Include the new ASL(D0) but not the new D0(6.1 fb-1)/CDF(5.2 fb-1) φs.

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Constraints on New Physics in the (ReΔd,ImΔd) plane removing BR(B+ → τ+ ν ) observable from the fit. A 1.1 σ deviation is obtained for the 2-dimensional SM hypothesis Δd = 1 (Re(Δd)=1, Im(Δd)=0). Include the new ASL(D0) but not the new D0(6.1 fb-1)/CDF(5.2 fb-1) φs.

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Constraints on New Physics in the (ReΔs,ImΔs) plane removing BR(B+ → τ+ ν ) observable from the fit. A 2.7 σ deviation is obtained for the 2-dimensional SM hypothesis Δs = 1 (Re(Δs)=1, Im(Δs)=0). Include the new ASL(D0) but not the new D0(6.1 fb-1)/CDF(5.2 fb-1) φs.

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Constraints on New Physics in the (ReΔd,ImΔd) plane without including the new ASL(D0). A 2.2 σ deviation is obtained for the 2-dimensional SM hypothesis Δd = 1 (Re(Δd)=1, Im(Δd)=0). Does not include the new D0(6.1 fb-1)/CDF(5.2 fb-1) φs.

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Constraints on New Physics in the (ReΔs,ImΔs) plane without including the new ASL(D0). A 1.9 σ deviation is obtained for the 2-dimensional SM hypothesis Δs = 1 (Re(Δs)=1, Im(Δs)=0). Does not include the new D0(6.1 fb-1)/CDF(5.2 fb-1) φs.

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