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## Quark Mixing Triangle from CP Invariant and CP Violating Quantities

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**Quark Mixing Triangle from CP Invariant and CP Violating**Quantities Workshop on Neutrino Oscillations Venice , April 15-18,2008 Konrad Kleinknecht Johannes-Gutenberg Universität Mainz**Direct CP violation: εʹ≠0discovered by NA31(1988)**,confirmed by NA48 and kTeV New measurement of kTeV Re(εʹ ∕ε)=(19.2±2.1) 10-4 confirms present (2003) value Re(εʹ ∕ε)=(16.7±1.6) 10-4 WA shifted to(16.8±1.4) 10-4 Conclude: Origin of CP violation comes from complex phase in quark mixing matrix a la Kobayashi- Maskawa (1973) NO-VE2008,Venice 15 04 08**Results for complex amplitudes ε (left side) and εʹ∕ε**(right hand side) NO-VE2008,Venice 15 04 08**Results**Average of all experiments Direct CP- Violation exists through a complex phase in K-M-Quark Mixing 2004: CP- Violation confirmed in decays of B mesons through the same mechanism. Not sufficient by far to explain baryon asymmetry of 10-9 in the universe. A much larger CP- Violation must exist somewhere else to satisfy Sacharovs criteria, maybe in the lepton sector. Through Leptogenesis an asymmetry in the lepton number could cause a quark asymmetry in a B-L conserving interaction NO-VE2008,Venice 15 04 08 K. Kleinknecht, Universität Mainz**Quark Mixing of 6 quarks by weak mixing K-M- matrix relates**quark mass eigenstates and weak eigenstates NO-VE2008,Venice 15 04 08**Standard parametrization**of KM-Matrix has 3 angles connecting generations θ12 , θ23 , θ13, and one phase δ13 NO-VE2008,Venice 15 04 08**Unitarity triangle**Unitarity applied to first and third column yields: NO-VE2008,Venice 15 04 08**New element:Observation of Bs and Bd mixing**• Measurement of BOTH mixing parameters enables a new constraint on one side of the K-M-unitarity triangle: • CDF and D0 obtain: Using the relation: And from lattice calculations : We obtain the constraint: NO-VE2008,Venice 15 04 08**Other CP conserving constraints**• K decays : Vus=0.2244 ± 0.0022 • B decays: Vcb=(41.4 ± 0.8) 10-3 Vub=(4.39 ± 0.46) 10-3 Vub and Vts/Vtd both yield circle-shaped range of allowed values for top of unitarity triangle NO-VE2008,Venice 15 04 08**CKM Unitarity triangle from CP conserving quantities**NO-VE2008,Venice 15 04 08**CP violating constraints**-- |ε| = (2.281±0.020) 10-3 from K decay -- sin2β = 0.687± 0.032 from Bd(Bd¯)→ψKS decay asymmetry (BaBar, Belle) -- α=(99 -9+12) degrees from Bd(Bd¯) →ρρ, ρπ, ππ asymmetries (BaBar, Belle) yield constraints coinciding in upper half of complex plane: NO-VE2008,Venice 15 04 08**Unitarity triangle from CP violating processes**NO-VE2008,Venice 15 04 08**All constraints together**Fit with sin sin sin and CP-phase Area of unitarity triangle NO-VE2008,Venice 15 04 08**Vertex of triangle from CP conservingand CP violating**processes NO-VE2008,Venice 15 04 08**Conclusion**• In the framework of the KM scheme, measurements of CP invariant quantities allow for the first time the prediction that CP violation exists with two solutions • CP violating observables determine both the same sign of the phase δ13 • CP conserving and violating constraints agree within 2σ • Phase δ13 = + 63 ± 4 degrees. NO-VE2008,Venice 15 04 08