CKMfitter

Preliminary results as of SUMMER 2008 (ICHEP08/CKM08)

Menu:

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 (ρ_s-bar,η_s-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,
UT_sangle 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 convention
eps png	eps png

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

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 not including the angle measurements in the global fit.

α, β, γ convention	ϕ₁, ϕ₂, ϕ₃ convention
eps png	eps png

Zoomed constraints in the (ρ-bar,η-bar) plane including only the angle measurements in the global fit.

α, β, γ convention	ϕ₁, ϕ₂, ϕ₃ convention
eps png	eps png

Zoomed constraints in the (ρ-bar,η-bar) plane including the CP conserving quantities in the global fit, i.e., |V_ub| (semileptonic and B⁺→τ⁺ ν), Δm_d, Δm_d & Δm_s.

α, β, γ convention	ϕ₁, ϕ₂, ϕ₃ convention
eps png	eps png

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 ε_K.

α, β, γ convention	ϕ₁, ϕ₂, ϕ₃ convention
eps png	eps png

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 convention	ϕ₁, ϕ₂, ϕ₃ convention
eps png	eps png

Zoomed constraints from "Loop" quantities in the (ρ-bar,η-bar) plane.

α, β, γ convention	ϕ₁, ϕ₂, ϕ₃ convention
eps png	eps png

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
eps png	eps png

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
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

Constraints on the angle β_s =arg(-V_tsV_tb*/V_csV_cb*) from the global CKM fit (no input from the time-dependent CP asymmetry in B⁰→J/ψφ decays is used.)

eps png

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

A new discrepancy in the CKM global fit has appeared, because of the new world average for sin2β, which is smaller than before, and the new world average for BR(B→τν). From the experimental point of view both new averages are in good agreement with previous determinations.

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
eps png	eps png

The shape of the correlation can be understood by considering the ratio BR(B→τν)/Δm_d, where the decay constant f_{B_d} cancels, leaving limited theoretical uncertainties (the ratio depends only on the bag parameter B_{B_d}). Thus from the observables BR(B→τν) and Δm_d 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
eps png	eps png

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 B_{B_d}, 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 |V_ub|, nor by the decay constant f_{B_d}.

To quantify the discrepancy one can compare the indirect fit prediction for BR(B→τν) with the measurement. The deviation here is 2.4 sigmas.

eps png

A simpler test is the comparison of the prediction of B_{B_d} from the above analytical formula (having only BR(B→τν), Δm_d, α, β, γ and |V_ud| as inputs, that is an almost completely theory-free determination of B_{B_d}) with the current lattice determination B_{B_d} = 1.17 ^+0.15_-0.13. For this test the deviation is 2.5 sigmas, dominated by the error on BR(B→τν), α, γ and B_{B_d}.

eps png

Constraint from decays B →V γ:

Constraints on |V_td/V_ts| from exclusive b → d γ and b → s γ transitions, following the theoretical analysis of Ball et al. [hep-ph/0612081] and using the branching ratios of B → K^* γ (charged and neutral), ρ γ (charged and neutral), ω γ [our ICHEP08 average for the five channels], together with B_s → φ γ [0712.2659] and the asymmetry in B⁺ → ρ⁺ γ [0804.4770].

eps png

In the (ρbar, ηbar) plane, there is a large overlap with the constraints from B_d and B_s mixing, indicated with yellow and orange borders.

α, β, γ convention	ϕ₁, ϕ₂, ϕ₃ convention
eps png	eps png

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

Constraint on α/ϕ₂ from B→ππ 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 α/ϕ₂ from B→ρρ 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 α/ϕ₂ from B→ρπ (U and I only) compared to the prediction from the global CKM fit (not including the α-related measurements). The global constraint on α from B→ρπ is a combination of the most recent BABAR and Belle data. This combination is not just a naive average in α but a combination in the 26 experimentally measured U and I coefficients which are correlated among each others. The correlation matrices are provided by both experiments (BABAR and Belle). The combined constraint has a preferred region around 120 degrees, and two suppressed regions around 30 and 85 degrees.

α, β, γ convention	ϕ₁, ϕ₂, ϕ₃ convention
eps png	eps png

Constraints on α/ϕ₂ from B→ππ, ρπ, and ρρ (BABAR, Belle, 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 from α in the (ρ-bar,η-bar) plane compared to the prediction from the global CKM fit (not including these α-related measurements).

α, β, γ convention	ϕ₁, ϕ₂, ϕ₃ convention
eps png	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) compared to the prediction from the global CKM fit (not including these measurements): γ[combined] = (70⁺²⁷_-29)°

α, β, γ convention	ϕ₁, ϕ₂, ϕ₃ convention
eps png	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) = 0.087^+0.022_-0.018.

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) = 0.101 ^+0.034_-0.040.

eps png

Constraint on the ratio of amplitudes r_B of the decay B → DK^*: r_B(DK^*)= 0.161^+0.079_-0.084.

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) = (110⁺²²_-27)°.

eps png

Constraint on the strong phase between the interfering amplitudes of the decay B → D^*K: δ_B(D^*K) = (-42⁺²⁶_-32)°.

eps png

Constraint on the strong phase between the interfering amplitudes of the decay B → DK^*: δ_B(DK^*) = (47⁺¹⁰³_-28)°.

eps png

Constraints from γ in the (ρ-bar,η-bar) plane compared to the prediction from the global CKM fit (not including these γ-related measurements).

α, β, γ convention	ϕ₁, ϕ₂, ϕ₃ convention
eps png	eps png

Constraints on |sin(2β+γ)|:

Constraints on |sin(2β+γ)| from the measurement of time-dependent CP asymmetries in D(*)π (ρ); Summer 08 HFAG average including a preliminary Belle ICHEP08 update for D*π is used as input. The extraction of the UT-angle combination relies on SU(3) symmetry for the estimates of the suppressed-to-leading amplitude ratios. We use for r^(*) the values of BABAR Collaboration, arXiv:0803.4296 [hep-ex] (aka Phys.Rev.D78:032005,2008) with an updated average for the ratio fDs/fD equal to 1.163 ± 0.007 (using recent inputs from ETMC08, FNAL-MILC07, and HPQCD07 Lattice groups) and treat the SU(3) uncertainty by using the method described in Max Baak's talk presented at CKM06 workshop (here)

α, β, γ convention	ϕ₁, ϕ₂, ϕ₃ convention
eps png	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)|] = (76 ⁺¹⁶_-23)°.

α, β, γ convention	ϕ₁, ϕ₂, ϕ₃ convention
eps png	eps png

Constraints from |sin(2β+γ)| in the (ρ-bar,η-bar) plane.

α, β, γ convention	ϕ₁, ϕ₂, ϕ₃ convention
eps png	eps png

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

individual constraints correspond to 68% CL (see: arXiv:1008.1593 [hep-ph]).

Constraints on New Physics in the (ReΔ_d,ImΔ_d) plane from B_d-meson mixing.

eps png

Constraints on New Physics in the (ReΔ_s,ImΔ_s) plane from B_s-meson mixing.

eps png