Quark Mixing Triangle from CP Invariant and CP Violating QuantitiesWorkshop on Neutrino Oscillations Venice , April 15-18,2008Konrad KleinknechtJohannes-Gutenberg Universitt Mainz

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Direct CP violation: 0discovered by NA31(1988) ,confirmed by NA48 and kTeVNew measurement of kTeV Re( )=(19.22.1) 10-4 confirms present (2003) value Re( )=(16.71.6) 10-4 WA shifted to (16.81.4) 10-4Conclude: Origin of CP violation comes from complex phase in quark mixing matrix a la Kobayashi- Maskawa (1973)

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Results for complex amplitudes (left side) and (right hand side)

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Direct CP- Violation exists through a complex phase in K-M-Quark Mixing2004: 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 interactionK. Kleinknecht, Universitt MainzAverage of all experimentsResults

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Quark Mixing of 6 quarks by weak mixing K-M- matrix relates quark mass eigenstates and weak eigenstates

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Standard parametrization of KM-Matrix has 3 angles connecting generations 12 , 23 , 13, and one phase 13

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Unitarity triangleUnitarity applied to first and third column yields:

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New element:Observation of Bs and Bd mixingMeasurement 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:

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Other CP conserving constraints K decays : Vus=0.2244 0.0022B 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

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CKM Unitarity triangle from CP conserving quantities

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CP violating constraints -- || = (2.2810.020) 10-3 from K decay -- sin2 = 0.687 0.032 from Bd(Bd)KS decay asymmetry (BaBar, Belle) -- =(99 -9+12) degrees from Bd(Bd) , , asymmetries (BaBar, Belle) yield constraints coinciding in upper half of complex plane:

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Unitarity triangle from CP violating processes

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All constraints togetherFit with sin sin sin

and

CP-phase Area of unitarity triangle

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Vertex of triangle from CP conservingand CP violating processes

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ConclusionIn the framework of the KM scheme, measurements of CP invariant quantities allow for the first time the prediction that CP violation exists with two solutionsCP violating observables determine both the same sign of the phase 13CP conserving and violating constraints agree within 2Phase 13 = + 63 4 degrees.

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