CKM Matrix I. V ud V us V ub d. d s b

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1 s = V u V us V u V c V cs V c s V t V ts V t flavour CKM matrix mass 18 parameters (9 complex elements) -5 relative quark phases (unoservale) -9 unitarity conitions - = 4 inepenent parameters 3 Euler angles an 1 Phase CKM Matrix I 4 funamental Stanar Moel Parameters (out of 28) Stephanie Hansmann-Menzemer p.1/24

2 Lagrangian insensitive to phases of left-hane fiels: possile reefinition: u L e iφ(u) u L c L e iφ(c) c L t L e iφ(t) t L L e iφ() L s L e iφ(s) s L L e iφ() L φ(q): real numers CKM Matrix II V = e iφ(u) 0 0 V u V us V u e iφ() e iφ(c) 0 V c V cs V c 0 e iφ(s) e iφ(t) V t V ts V t 0 0 e iφ() 5 unoservale phase ifferences. Stephanie Hansmann-Menzemer p.2/24

3 CKM Matrix III u c t u c t s s Diagonal elements of CKM matrix are close to one. Only small of iagonal contriutions. Mixing etween quark families is CKM suppresse. Stephanie Hansmann-Menzemer p.3/24

4 Unitarity Triangle I Wolfenstein Parameterization: λ, A, ρ, η; (λ 0.22) V CKM = V CKM = V u V us V u V c V cs V c V t V ts V t 1 λ2 2 λ Aλ 3 (ρ iη) λ 1 λ2 2 Aλ 2 + O(λ4 ) Aλ 3 (1 ρ iη) Aλ 2 1 Only very small complexe contriutions, up to thir orer in λ ( 0.5%) only in V u an V t Stephanie Hansmann-Menzemer p.4/24

5 Unitarity Triangle I Stephanie Hansmann-Menzemer p.5/24

6 Unitarity Triangle II Stephanie Hansmann-Menzemer p.6/24

7 Unitarity Triangle III η 0.6 Summer exclue area has CL > 0.95 γ sin2β ε K m α m s & m ε K sol. w/ cos2β < 0 (excl. at CL > 0.95) α CKM f i t t e r γ 0.1 γ V α u β Current status of knowlege on the CKM triangle. Sofar all measurements consistent with each other. ρ Stephanie Hansmann-Menzemer p.7/24

8 Phenomenology of Mixing I B s s V V t ts t t V V ts t s B s B s s V V t t V t ts V ts t s B s Schröinger equation: i t B0 B0 = H = H 11 H 21 B 0 B 0 H 12 H 22 B 0 ) = (M i2 Γ B0 = m 11 i 2 Γ 11 m 21 i 2 Γ 21 B 0 m 12 i 2 Γ 12 m 22 i 2 Γ 22 B0 B0 B 0 CPT theorem: m 11 = m 22 = m(b 0 ) = m( B 0 ) Γ 11 = Γ 22 = Γ = 1 τ(b 0 ) = 1 τ( B 0 ) off-iagonal elements mixing M, Γ hermetic: m 12 = m 21, Γ 12 = Γ 21 Stephanie Hansmann-Menzemer p.8/24

9 Phenomenology of Mixing II Diagonalizing of (M 2 i Γ) mass eigen states: B L >= p B 0 > +q B 0 >, B L (t) >= B L > e Γ L 2 t e im Lt B H >= p B 0 > q B 0 >, B H (t) >= B H > e Γ H 2 t e im Ht p 2 + q 2 = 1 complex coefficients Flavour eigenstates: B 0 >= 1 2p ( B L > + B H >) B 0 >= 1 2q ( B L > B H >) m H,L = m ± Re H 12 H 21 Γ H,L = Γ 2Im H 12 H 21 m = m H m L = 2Re H 12 H 21 Γ = Γ H Γ L = 4Im H 12 H 21 Stephanie Hansmann-Menzemer p.9/24

10 Phenomenology of Mixing III CPT conversation! P(B 0 B 0 ) = P( B 0 B 0 ) = ( e ΓLt + e ΓHt + 2e (Γ L+Γ H )t/2 cos( mt) 1 4 P(B 0 B ) 0 ) = 1 4 q p (e 2 ΓLt + e ΓHt 2e (Γ L+Γ H )t/2 cos mt P( B ) 0 B 0 ) = 1 4 p q (e 2 ΓLt + e ΓHt 2e (Γ L+Γ H )t/2 cos mt CP violation in mixing: P(B 0 B 0 ) P( B 0 B 0 ) q p 1 CP violation in mixing negligile in B /s system. (This is not true in the neutral kaon system) ) Stephanie Hansmann-Menzemer p.10/24

11 Stephanie Hansmann-Menzemer p.11/24

12 Baar & CDF proaility ensity total unmixe mixe ecay time, ps asymmetry A = #unmixe #mixe #unmixe + #mixe ecay time, ps B 0 Fitte Amplitue CDF Run II Preliminary ata cosine with A= L = 1.0 f Decay Time Moulo 2π/ m s [ps] B 0 s B 0 s 2006 Stephanie Hansmann-Menzemer p.12/24

13 CP Transformation & Weak Interaction Stephanie Hansmann-Menzemer p.13/24

14 CP Violation CP violation: A(B f) 2 A( B f) 2 Within weak interaction, moving from particle to antiparticle, system amplitues are complex conjugate. No CP violation if: There is only one amplitue contriuting to the ecay: A 2 = A 2 The sum of two amplitues, where oth are complex conjugate when moving from particle to antiparticle system: A 1 + A 2 2 = (A 1 + A 2 )(A 1 + A 2 ) = A 1 + A 2 2 For CP violation one nees two complex amplitues, where one of them is complex conjugate an one not when moving from particle to antiparticle system. Stephanie Hansmann-Menzemer p.14/24

15 CP Violation B A 1 = A 1 e iφ 1 e iδ 1 f B A 1 = A 1 e iφ 1 e iδ 1 f A 2 = A 2 e iφ 2 e iδ 2 CP A 2 = A 2 e iφ 2 e iδ 2 A 2 = A A A 1A 2 cos( φ + δ) A 2 = A A A 1A 2 cos( φ + δ) A 1 an A 2 nee to have ifferent weak phases φ an ifferent CP invariant (e.g. strong) phases δ. Stephanie Hansmann-Menzemer p.15/24

16 CP Violation 3 Types of CP violation: 1) CP violation in mixing (not present in B system) 2) CP violation in ecay (sometimes calle irect CPV): Different ecay amplitues contriuting to the same finals state 3) CP violation in interference: Same final state can e reache irectly via ecay an as well through mixing an then ecay. Stephanie Hansmann-Menzemer p.16/24

17 CP Violation in Decay s B 0 W u u K π + A 1 e i arg(v uv us ) e iδ 1 B 0 K + π W s u K + A 2 e i arg(v tv ts ) e iδ 2 0 B g u π CP Asymmetrie: Ā 2 A 2 = 2 A 1 A 2 [cos(arg(v t V ts) + δ) cos(arg(v t V ts) δ)] Stephanie Hansmann-Menzemer p.17/24

18 CP Violation in Decay Stephanie Hansmann-Menzemer p.18/24

19 CP Violation in Interference Same final state through ecay & mixing + ecay c c J /ψ c c J/ψ s K s s K s A 1 = A mix (B 0 B 0 ) A ecay (B 0 J/ΨK s ) = cos( mt 2 ) A eiω A 2 = A mix (B 0 B 0 ) A ecay ( B 0 J/ΨK s ) = isin( mt 2 ) e+iφ A e iω φ = φ 2ω (assume no CP violation in mixing an in ecay) δ = π/2 mixing introuces secon phase ifference Stephanie Hansmann-Menzemer p.19/24

20 B J/ψK s c c s A symmetrie (t) = J /ψ K s Γ( B J/ψK s )(t) Γ(B J/ψK s )(t) Γ( B J/ψK s )(t) + Γ(B J/ψK s )(t) = ξ sin(φ mix 2ω) sin( m t) c c s J/ψ K s CP J/ψK s > = ξ J/ψK s > = -1 J/ψK s > φ mix = arg((v t V t )2 ) = 2β ω = arg((v c V cs)(v us V u )) = 0 V CKM = 0 1 V u V us V u V c V cs V C c A = V t V ts V t λ λ Aλ 2 3 (ρ iη) λ 1 λ2 Aλ 2 2 C A + O(λ4 ) Aλ 3 (1 ρ iη) Aλ 2 1 Stephanie Hansmann-Menzemer p.20/24

21 B J/ψK s A symmetrie (t) = -sin(2β) sin( m t) Baar: sin(2β) = ± ± Belle: sin(2β) = ± ± η f i t t e r 0.6 Summer exclue area has CL > 0.95 γ sin2β ε K m α m s & m ε K sol. w/ cos2β < 0 (excl. at CL > 0.95) α CKM γ 0.1 γ V α u β ρ Stephanie Hansmann-Menzemer p.21/24

22 Matter-Antimatter Asymmetrie We have a clear overhang of matter in our worl, however same amount of matter an antimatter where prouce in the early universe CP Violation! CPV introuce y the CKM matrix is to small to explain material overlap in universe To e honest: even aitional phases in the quark sector introuce y new physics will not e ale to explain this huge iscrepancy. Still CPV is interesting place to check for hints of New Physics. Stephanie Hansmann-Menzemer p.22/24

23 Summary CPV Requirement for CP violation: one weak phase ifference an one CP invariant phase ifference! In B physics, mainly two type of CP violation: CPV in ecays an in interference etween ecay an mixing+ecay. CKM mechanism is the only source of CP violation in the SM! (it s the only phase which flip sign uner CP transformation) CKM sector & weak IA theo. est escrie part of SM In asymmetries uncert. cancel (e.g. strong IA). u c Large statistics availale experimental clean measurements precision test of SM Stephanie Hansmann-Menzemer p.23/24

24 Esher s View on CPV P transformation C transformation Stephanie Hansmann-Menzemer p.24/24