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Niels Tuning (1) CP violation Lecture 5 N. Tuning
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Diagonalize Yukawa matrix Y ij –Mass terms –Quarks rotate –Off diagonal terms in charged current couplings Niels Tuning (3) Recap uIuI dIdI W u d,s,b W
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Niels Tuning (4) CKM-matrix: where are the phases? u d,s,b W Possibility 1: simply 3 ‘rotations’, and put phase on smallest: Possibility 2: parameterize according to magnitude, in O( λ):
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This was theory, now comes experiment We already saw how the moduli |V ij | are determined Now we will work towards the measurement of the imaginary part –Parameter: η –Equivalent: angles α, β, γ. To measure this, we need the formalism of neutral meson oscillations… Niels Tuning (5)
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Some algebra for the decay P 0 f Interference P0 fP0 fP 0 P 0 f
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Meson Decays Formalism of meson oscillations: Subsequent: decay Interference(‘direct’) Decay Recap osc + decays
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Classification of CP Violating effects 1.CP violation in decay 2.CP violation in mixing 3.CP violation in interference Recap CP violation
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Im( λ f ) 1.CP violation in decay 2.CP violation in mixing 3.CP violation in interference We will investigate λ f for various final states f Recap CP violation
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Niels Tuning (10) CP eigenvalue of final state J/K 0 S CP |J/> = +1 |J/> CP |K 0 S > = +1 |K 0 S > CP |J/K 0 S > = (-1) l |J/K 0 S > ( S( B )=0 L(J/K 0 S )=1 ) Relative minus-sign between state and CP-conjugated state: ( S(J/)=1 )
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λ f contains information on final state f Niels Tuning (11) Recap CP in B Investigated three final states f B 0 J/ψK s B 0 s J/ψφ B 0 s D s K 3.CP violation in interference
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λ f contains information on final state f Niels Tuning (12) B 0 s J/ψφ 3.CP violation in interference Recap CP in B
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β s : B s 0 J/φ : B s 0 analogue of B 0 J/K 0 S Niels Tuning (13) Recap CP in B
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Remember! Necessary ingredients for CP violation: 1)Two (interfering) amplitudes 2)Phase difference between amplitudes –one CP conserving phase (‘strong’ phase) –one CP violating phase (‘weak’ phase) Niels Tuning (14)
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Remember! Niels Tuning (15)
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Basics The basics you know now! 1.CP violation from complex phase in CKM matrix 2.Need 2 interfering amplitudes (B-oscillations come in handy!) 3.Higher order diagrams sensitive to New Physics Next: (Direct) CP violation in decay CP violation in mixing (we already saw this with the kaons: ε≠0, or |q/p|≠1 ) Penguins The unitarity triangle Niels Tuning (16)
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Next: γ Niels Tuning (17)
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Niels Tuning (18) CKM Angle measurements from B d,u decays Sources of phases in B d,u amplitudes* The standard techniques for the angles: *In Wolfenstein phase convention. AmplitudeRel. MagnitudeWeak phase bcbcDominant0 bubuSuppressed γ t d ( x2, mixing)Time dependent 2β2β B 0 mixing + single b c decay B 0 mixing + single b u decay Interfere b c and b u in B ± decay. bubu tdtd
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Niels Tuning (19) Determining the angle From unitarity we have: Must interfere b u ( c d) and b c( u d) Expect b u ( c s) and b c( u s) to have the same phase, with more interference (but less events) 3 2 3 2
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Measure γ : B 0 s D s K -/+ : both λ f and λ f Niels Tuning (20) NB: In addition B s D s K -/+ : both λ f and λ f + Γ( B f)= + Γ( B f )= 2 2
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Niels Tuning (21) Measure γ : B s D s K -/+ --- first one f : D s + K - This time | A f ||A f |, so | λ| 1 ! In fact, not only magnitude, but also phase difference:
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Measure γ : B s D s K -/+ Niels Tuning (22) Need B 0 s D s + K - to disentangle and : B 0 s D s - K + has phase difference ( - ):
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Next 1.CP violation in decay 2.CP violation in mixing 3.CP violation in interference
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Niels Tuning (24) B A B AR CP violation in Decay? (also known as: “direct CPV”) HFAG: hep-ex/0407057 Phys.Rev.Lett.93:131801,2004 4.2 B A B AR First observation of Direct CPV in B decays (2004): A CP = -0.098 ± 0.012
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Niels Tuning (25) LHCbLHCb CP violation in Decay? (also known as: “direct CPV”) LHCb-CONF-2011-011LHCbLHCb First observation of Direct CPV in B decays at LHC (2011):
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Niels Tuning (26) Direct CP violation: Γ( B 0 f) ≠ Γ(B 0 f ) Only different if both δ and γ are ≠0 ! Γ( B 0 f) ≠ Γ(B 0 f ) CP violation if Γ( B 0 f) ≠ Γ(B 0 f ) But: need 2 amplitudes interference Amplitude 1 + Amplitude 2
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Niels Tuning (27) Hint for new physics? B 0 Kπ and B K π 0 Average 3.6 Average Redo the experiment with B instead of B 0 … d or u spectator quark: what’s the difference ?? B0KπB0Kπ B+KπB+Kπ
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Hint for new physics? B 0 Kπ and B K π 0 Niels Tuning (28)
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Hint for new physics? B 0 Kπ and B K π 0 Niels Tuning (29) T (tree) C (color suppressed) P (penguin) B0→K+π-B0→K+π- B+→K+π0B+→K+π0
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Next 1.CP violation in decay 2.CP violation in mixing 3.CP violation in interference
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Niels Tuning (31) CP violation in Mixing? (also known as: “indirect CPV”: ε≠0 in K-system) gV cb * gV cb t=0 t ? Look for like-sign lepton pairs: Decay
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Niels Tuning (32) (limit on) CP violation in B 0 mixing Look for a like-sign asymmetry: As expected, no asymmetry is observed…
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CP violation in B s 0 Mixing?? Niels Tuning (33) D0 Coll., Phys.Rev.D82:032001, 2010. arXiv:1005.2757 b s s b “Box” diagram: ΔB=2 φ s SM ~ 0.004 φ s SM M ~ 0.04
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CP violation from Semi-leptonic decays SM: P(B 0 s → B 0 s ) = P(B 0 s ← B 0 s ) DØ: P(B 0 s → B 0 s ) ≠ P(B 0 s ← B 0 s ) b → Xμ - ν, b → Xμ + ν b → b → Xμ + ν, b → b → Xμ - ν Compare events with like-sign μμ Two methods: Measure asymmetry of events with 1 muon Measure asymmetry of events with 2 muons ? Switching magnet polarity helps in reducing systematics But…: Decays in flight, e.g. K→μ K + /K - asymmetry
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CP violation from Semi-leptonic decays SM: P(B 0 s → B 0 s ) = P(B 0 s ← B 0 s ) DØ: P(B 0 s → B 0 s ) ≠ P(B 0 s ← B 0 s ) ? B 0 s → D s ± X 0 μν
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More β… Niels Tuning (36)
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Niels Tuning (37) Other ways of measuring sin2β Need interference of b c transition and B 0 –B 0 mixing Let’s look at other b c decays to CP eigenstates: All these decay amplitudes have the same phase (in the Wolfenstein parameterization) so they (should) measure the same CP violation
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CP in interference with B φK s Same as B 0 J/ψK s : Interference between B 0 → f CP and B 0 → B 0 → f CP –For example: B 0 → J/ΨK s and B 0 → B 0 → J/ΨK s –For example: B 0 → φ K s and B 0 → B 0 → φ K s Niels Tuning (38) + e -iφ Amplitude 2 Amplitude 1
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CP in interference with B φK s : what is different?? Same as B 0 J/ψK s : Interference between B 0 → f CP and B 0 → B 0 → f CP –For example: B 0 → J/ΨK s and B 0 → B 0 → J/ΨK s –For example: B 0 → φ K s and B 0 → B 0 → φ K s Niels Tuning (39) + e -iφ Amplitude 2 Amplitude 1
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Niels Tuning (40) Penguin diagrams Nucl. Phys. B131:285 1977
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Penguins?? Niels Tuning (41) The original penguin:A real penguin:Our penguin:
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Funny Niels Tuning (42) Super Penguin: Penguin T-shirt: Flying Penguin Dead Penguin
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Niels Tuning (43) The “b-s penguin” B 0 J/ψK S B0φKSB0φKS … unless there is new physics! New particles (also heavy) can show up in loops: –Can affect the branching ratio –And can introduce additional phase and affect the asymmetry Asymmetry in SM b s μ μ “Penguin” diagram: ΔB=1
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Niels Tuning (44) Hint for new physics?? sin2β sin2 β b ccs = 0.68 ± 0.03 sin2β peng B J/ψ KsKs b d c c s d φ KsKs B s b d d s t s ? sin2 β peng = 0.52 ± 0.05 g,b,…? ~~ S.T’Jampens, CKM fitter, Beauty2006
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Niels Tuning (45) Smaller than b ccs in most penguin modes Smaller than b ccs in most penguin modes deviation between b sqq and b ccs disappeared over time… deviation between b sqq and b ccs disappeared over time… Hint for new physics? β with b s Penguins 0.64 ±0.04 0.67 ±0.02
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End Niels Tuning (46)
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