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...e r2 d − 2θd plane (bottom). The recent γ and α measurements determine ¯ρ, ¯η from (effectively) tree-level B decays for the first time, independent of mixing, and agree with the other SM constraints =-=[50, 9, 51]-=-. The disfavored "non-SM" region around 2θd ∼ 90◦ is due to the η < 0 region in the top right plot and discrete ambiguities. Thus, NP in B0 − B0 mixing is severely constrained for the first time. The ...

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... light quark loops [11, 12]. In this mode three events have been observed so far, yielding [13] PoS(LAT2005)012 B(K + → π + ν ¯ν) = ( 1.5 +1.3) −10 −0.9 × 10 . (1.4) 1We use the following definitions =-=[7, 8, 9]-=-, so that the apex of the unitarity triangle in Fig. 1 is exactly ¯ρ, ¯η: |Vus| λ = √ |Vud| 2 1 Vcb , A = + |Vus| 2 λ ∣Vus ∣ , V ∗ ub = Aλ 3 (ρ + iη) = Aλ 3 ( ¯ρ + i ¯η) √ 1 − A2λ 4 √ . (1.1) 1 − λ 2 ...

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... is not much below ∼ 0.2 then studying single Cabibbo-suppressed D → KK∗ decays may be advantageous [43], or in three-body B decays the color suppression can be avoided [44]. It was recently realized =-=[45, 46]-=- that both D0 and D0 have Cabibbo-allowed decays to certain three-body final states, such as KSπ + π− . This analysis can be optimized by studying the Dalitz plot dependence of the interference, and t...

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...n of ASL is possible from first principles only in the mb ≫ ΛQCD limit, using an operator product expansion to evaluate the relevant nonleptonic rates. Last year the NLO QCD calculation was completed =-=[22, 23]-=-, predicting ASL = −(5.5 ± 1.3) × 10 −4 , where I averaged the central values and quoted the larger of the two theory error estimates. (The similar asymmetry in the Bs sector is expected to be λ 2 sma...

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...lly accessible soon. Recently, the leading power corrections to the HQS relations between the B and D decay form factors were analyzed [72]. With data from LHCB and a super-B-factory the double ratio =-=[73]-=- B(B → ℓ ¯ν) B(Bs → ℓ + ℓ− ) × B(Ds → ℓ ¯ν) B(D → ℓ ¯ν) (6.3) could give a determination of |Vub| with theoretical errors at the few percent level. Interestingly, the most recent CLEO-c [74] and FOCUS...

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... data to constrain f+(m 2 π ) [94]. Using the lattice calculations of f+, the experimental measurements and dispersion relation to constrain f+(q 2 ) at all q 2 , yields |Vub| = (3.92 ± 0.52) × 10 −3 =-=[96]-=-. PoS(LAT2005)012 012 / 18The CKM matrix and CP violation Zoltan Ligeti γ g b c O2 s Figure 9: Dominant contribution to the "wrong-helicity" amplitude, A(B 0 → Xfs γR). 6.3.1 B → ργ vs. K ∗ γ The fac...

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...ape function can also be reduced by extending the measurements into the B → Xcℓ ¯ν region. Recent analyses could measure the B → Xue ¯ν rates for pe ≥ 1.9 GeV, which is well below the charm threshold =-=[63]-=-. Averaging the inclusive measurements, HFAG quotes |Vub| = (4.38±0.19±0.27)×10 −3 [19], which is in slight tension with the CKM fit for |Vub| dominated by the sin2β measurement; see Fig. 8. HFAG uses...

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...nsate. This sector of the SM contains 10 physical quark flavor parameters, the 6 quark masses and the 4 parameters in the CKM matrix: 3 mixing angles and 1 CP violating phase (for reviews, see, e.g., =-=[5, 6]-=-). Therefore, the SM predicts intricate correlations between dozens of different decays of s, c, b, and t quarks, and in particular between CP violating observables. Possible deviations from CKM parad...

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... has also been resolved by ingenious studies of the time dependent angular analysis of B → ψK ∗0 and the time dependent Dalitz plot analysis of B 0 → D 0 h 0 with D 0 → KSπ + π − , pioneered by BABAR =-=[25]-=- and BELLE [26], respectively. As a result, the negative cos2β solutions are excluded, eliminating two of the four discrete ambiguities. To summarize, SψK was the first observation of CP violation out...

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...he B → Xcℓ ¯ν background introduce O(1) dependence on a nonperturbative b quark light-cone distribution function (sometimes called the shape function). At leading order, one universal function occurs =-=[60]-=-, which can be extracted from B → Xsγ and applied to the analyses of the measured Eℓ, mX or P + X (= EX −|⃗pX|) spectra in B → Xuℓ ¯ν. At order ΛQCD/mb several new functions occur [61], and it is not ...

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...function occurs [60], which can be extracted from B → Xsγ and applied to the analyses of the measured Eℓ, mX or P + X (= EX −|⃗pX|) spectra in B → Xuℓ ¯ν. At order ΛQCD/mb several new functions occur =-=[61]-=-, and it is not known how to extract these from data. The hadronic physics being parameterized by functions is a significant complication compared to the determination of |Vcb|, where it is encoded by...

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...ble ratio [73] B(B → ℓ ¯ν) B(Bs → ℓ + ℓ− ) × B(Ds → ℓ ¯ν) B(D → ℓ ¯ν) (6.3) could give a determination of |Vub| with theoretical errors at the few percent level. Interestingly, the most recent CLEO-c =-=[74]-=- and FOCUS [75] data are still consistent with no SU(3) breaking in the D → ρℓ ¯ν vs. D → K ∗ ℓ ¯ν form factors. Averaging these measurements gives B(D + → ρ 0 ℓ + ν)/B(D + → K 0∗ ℓ + ν) = 0.041 ± 0.0...

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... form factors and |Vub| It has been proven using SCET that at leading order in ΛQCD/Q (Q = E,mb), to all orders in αs, the semileptonic form factors for q2 ≪ m2 B can be written as a sum of two terms =-=[84, 78, 85]-=-, F(Q) = Ci(Q)ζi(Q)+ mB ∫ fB fM dzdxdk+ T(z,Q)J(z,x,k+,Q)φM(x)φB(k+), (6.5) 4E 2 where we omitted the µ-dependences. The two terms arise from matrix elements of distinct time ordered products of the f...

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... → (ρ/ω)γ decay [97]. Assuming isospin symmetry, the average of the BELLE and BABAR data (without including the ω) is B(B → ργ)/B(B → K∗γ) = 0.017 ± 0.006 [19]. Using ξγ = 1.2 ± 0.15 for this average =-=[98]-=- implies |Vtd/Vts| = 0.16 ± 0.03. The smallness of B(B → ργ), due to its non-observation at BABAR, may be a fluctuation or indicate that ∆mBs could be not near the experimental lower bound. While the ...

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...0%) power corrections. The Bs → Dsπ decay only proceeds via a T contribution, so it can help to determine the relative size of E vs. C. CDF measured B(Bs → D − s π + )/B(B 0 → D − π + ) ≃ 1.35 ± 0.43 =-=[108]-=- (using the production ratio fs/ fd = 0.26 ± 0.03), the central value of which suggests that C and E may be comparable [109]. Since factorization relates the tree amplitudes to the semileptonic form f...

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... → Λ + c π − , as shown in Fig. 13, and SCET implies the power counting T = O(1), C,E = O(ΛQCD/Q), and B = O(Λ 2 QCD /Q2 ) [109]. The usual factorization relation connects B(Λb → Λcπ) measured by CDF =-=[112]-=- to dΓ(Λb → Λcℓ ¯ν)/dq 2 at q 2 = m 2 π (maximal recoil). Thus, either an 012 / 22The CKM matrix and CP violation Zoltan Ligeti A(D*M) A(D M) 2.0 1.5 color allowed color suppressed * ω + ω D 0 π 0 0 ...

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...e as the phase between the penguin and the color-suppressed tree (up to ΛQCD/Q corrections). A possible resolution is a large enhancement of electroweak penguins, or NP with the same flavor structure =-=[130]-=-. These are fascinating developments, however, more work and data are needed to understand why some predictions work better than 10%, while others receive O(30%) corrections. Hopefully, the role of ch...