Recent CP violation measurements

Transcription

1 Recent CP violation measurements 1/38

2 Recap of last week What we have learned last week: Indirect searches (CP violation and rare decays) are good places to search for effects from new, unknown particles. Example from past: GIM mechanism Symmetries are a very important concept in physics Lead to conservation laws, new theories, etc. P (parity) and C (charge conjugation) are completely broken in weak interactions CPT is still an exact symmetry (required by field theory). Weak interaction shows a small CP violation. Not enough to explain baryon asymmetry in the Universe. Fermion masses and the CKM matrix originate from the Yukawa couplings with the Higgs. V CKM relates the quarks in the mass eigenbase with the weak eigenbase. V CKM has one complex phase which is responsible for CP violation. All current CP-violating measurements are consistent with this single phase. 2/38

3 Wolfenstein Parametrization (recap) Makes use of the fact that the off-diagonal elements are small compared to the diagonal elements. Expansion in λ = V us, A = V cb / λ 2 and ρ, η. " $ $ V = $ $! V CKM = " 1 λ 2 / 2 λ Aλ 3 ( ρ iη) λ 1 λ 2 / 2 Aλ 2 ( ) Aλ 2 1 Aλ 3 1 ρ iη V ud V us V ub V cd V cs V cb V td V ts V tb $ % % ' ' ' ' +O( λ 4 ) λ ~ 0.22 (sinus of Cabibbo angle) A ~ 1 (actually 0.80) ρ ~ 0.14 η ~ /38

4 CKM angles and unitarity triangle Writing the complex elements explicitly:! V CKM = " V ud V us V ub V cd V cs V cb V td V ts V tb $! = % " 1 λ 2 / 2 λ ~ λ 3 e iγ λ 1 λ 2 / 2 Aλ 2 ~ λ 3 e iβ ~ λ 2 e iβ s 1 $ +O(λ 4 ) % Definition of the angles: α arg V V * td tb % * ( $ V ud V ub ' β arg V V * cd cb % * ( $ V td V tb ' γ arg V V * ud tb % * ( $ V cd V cb ' β s arg V * tsv tb % * ( $ V cs V cb ' Using one of the 9 unitarity relations: V CKM V CKM =1 Multiply first d column with last b column: V ud V ub * γ α V cd V cb * V td V tb * β 4/38

5 Progress in UT /38

6 Mixing of neutral mesons (recap) B 0 meson x Δm Γ 0.7 y ΔΓ 2Γ 0 B s meson x Δm Γ 26 y ΔΓ 2Γ 0.1 The 4 different neutral meson systems have very different mixing properties. B s system: very fast mixing K 0 meson x Δm Γ 1 y ΔΓ 2Γ 1 D 0 meson Kaon system: large decay time difference. x Δm Γ 0.01 y ΔΓ 2Γ 0.01 Charm system: very slow mixing 6/38

7 The weak box diagram These two diagrams contribute to mixing in B d,s system: The (heavy) top quark dominates the internal loop. No GIM cancellation (if u,c,t would have the same mass these diagrams would cancel) Why is are the oscillations in the B s system so much faster than in B d? Why is the mixing in the D system so small? Oscillations in B d versus B s system: V td versus V ts Order λ 3 Order λ 2 Much faster oscillation in B s system (less Cabbibo suppression). In the D system, the d,s,b quarks in internal loop (no top): small mixing. 7/38

8 candidates / 0.2 ps 400 LHCb preliminary -1 s=7 TeV, 1 fb -3 Recent measurements:!10 0 two extremes B s mixing: very fast 2. Fit WS sample with 7 signal shape fixed 6.5 to RS and bkg shape 6 free to float 5.5 Tagged mixed R Tagged unmixed 3. Calculate Fit mixed WS/RS ratio from measured M (D 0 s) + [GeV/c 2 ] Fit unmixed LHCb preliminary yields 3.5 LHCb s=7 TeV, 1 fb OST+SSKT 3.5 LHCb Table 1: Results 0 of the 2 time-dependent 4 6 fit to the data. 20 The uncer 0 and systematic sources; ndf 3 indicates the number t/ of degrees of decay time [ps] Fit type Parameter Fit result t/ Correlat ( 2 /ndf) (10 3 ) R D timeδm distributions s = for± events 0.041(stat) tagged as ± mixed (red) (sys) andps unmixed (blue) Mixing in a signal R D 3.52 ± Bs 0 mass. Overlayed is the decay time projection of the fitted PDF. Plots (9.5/10) are shown y 7.2 ± 2.4 x10-3 ly the SSKT (upper plot), only the OST (middle plot) and the combination of SSKT x ± 0.13 ot). No mixing R D 4.25 ± 0.04 (98.1/12) C / R 0.2 Data 5 Mixing fit 0 No-mixing D 0 mixing: fit very slow -5! Both measurements very challenging -3 R(t) = Pseudo-data Mixing fit No-mixing fit WS N RS (t) = R D + Candidates/(0.1 MeV/c 2 / R ] 8/38

9 CP violation So we just learned that neutral mesons mix, that we can actually measure the oscillations, but what has this to do with CP violation? 9/38

10 Types of CP violation Phenomenologically, there are 3 types of CP violation: 10/38

11 Types of CP violation Phenomenologically, there are 3 types of CP violation: 1. CPV in mixing 2. CPV in decay 3. CPV in the interference between mixing and decay 11/38

12 1. CP violation in mixing We had already the probability that an initially pure B 0 or B 0 oscillates into B 0 or B 0 : Not the same if One can see that in case the oscillation probability P(B 0 B 0 ) is different from the CP conjugate process P(B 0 B 0 ). Remember that:! H = " M M 12 * M 12 M $ i! 2 % " Γ Γ 12 * Γ 12 Γ $ % In the B d and B s systems Γ 12 is small è Small CP violation in mixing. (do you remember why Γ 12 is small?) 12/38

13 1. CP violation in mixing Remember that: Requirements for CP violation in mixing, i.e. M 12 and Γ 12 must be non-negligible. M 12 and Γ 12 must have a phase difference. CP violation in mixing is due to the interference between the amplitudes M 12 and Γ 12. (between off-shell and on-shell mixing amplitudes) 13/38

14 Example of CPV in mixing: kaon system A + ( ) R K 0 L e π + ν e ( ) + R K 0 L e π + ν e R K L 0 e + π ν e R K L 0 e + π ν e ( ) ( ) = 1 q/p 4 1+ q/p 4 = 4Rε Flavour-specific final state: K 0 e + π ν e CPLEAR, Phys.Rep. 374(2003) A T ( t) = ( 6.6 ±1.6)10 3 q p = ± K 0 e π + ν e CP violation in mixing small in SM: K 0 system: Order 1% D 0 system: Order 10-5 B d system: Order 5x10-4 Not yet observed B s system: Order /38

15 Searches for mixing CPV in B d,s Asymmetry for B d : a d sl = Γ(B0 D µ + ) Γ(B 0 D + µ ) Γ(B 0 D µ + )+ Γ(B 0 D + µ ) = 1 (q / p)4 1+ (q / p) 4 Standard Model for B Asymmetry for B s : (substitute dà s) a s sl = Γ(B 0 s D s µ + ) Γ(B 0 s D s+ µ ) Γ(B 0 s D s µ + )+ Γ(B 0 s D s+ µ ) = 1 (q / p)4 1+ (q / p) 4 Very similar to kaon system 15/38

16 Possible measurements Searches for mixing CPV in B d,s Dimuon analysis: A b sl = Γ(µ + µ + ) Γ(µ µ ) Γ(µ + µ + )+ Γ(µ µ ) = C da d s sl + C s a sl Y µ + B 0 B 0 B 0 µ + X Consider that muons from two B decays can be like-sign: one mixes and the other not. contains contribution from both B d and B s Untagged analysis: Γ(D (s) µ + ) Γ(D + (s) µ ) Γ(D (s) µ + )+ Γ(D + (s) µ ) a sl 2 Dilutes sensitivity by 50% (compared to 3% from flavour tagging) need to measure production asymmetry and detection asymmetry 16/38

17 a sl according to D0 3 from SM CPV in B s mixing SM Discrepancy of central value even too large for New Physics. CPV in B d mixing 17/38

18 B s 0 D s + ( φπ + )µ LHCb s measurement of a sl s Effect of B s production asymmetry is reduced to negligible level by rapid mixing oscillations Calibration samples (J/ψ, D *+ ) used to measure detector trigger, track muon ID biases Magnet down: Events / ( 3 MeV ) LHCb 4 10 Preliminary 3 10 (a) D+ D s + Events / ( 3 MeV ) LHCb 4 10 Preliminary 3 10 (b) D D s m(k K + ) (MeV) m(k + K - - ) (MeV) D! s µ + D + s µ! Magnet UP Magnet Down 40,945±285 55,755±278 39,849±239 56,447±294 18/38

19 a sl according to rest of world Consistent with SM 19/38

20 Outlook Semileptonic measurement of CPV in B mixing CPV in B s mixing Sensitivity LHCb in 2017 LHCb will pin this discrepancy down. CPV in B d mixing 20/38

21 2. CP violation in decay We define the decay amplitudes as: CP violation in decay means: In other words: Г(B f ) Г(B f ) This only occurs when there are different decay amplitudes (Feynman diagrams) to the same final state with different weak phases and different strong phases: Weak phase changes sign under CP transformation Strong phase invariant under CP transformation CP violation in decay is also called direct CP violation 21/38

22 2. CP violation in decay Bà f Bà f A=a 1 +a 2 A=a 1 +a 2 A a 2 +φ a 1 a 1 A a 2 -φ No strong phase difference è No CP violation 22/38

23 2. CP violation in decay Bà f Bà f A=a 1 +a 2 A=a 1 +a 2 A a 2 +φ a 1 a 1 δ A -φ δ a2 Strong phase difference (δ not zero) è CP violation in decay due to interference between strong and weak phase difference. CP violation in decay does not require mixing: can also occur in charged hadrons decays Problem: strong phases unknown, so difficult to extract the weak phase. 23/38

24 Example: CP violation in decay Charmless charged two-body B decays Tree B 0 K + K + B 0 Penguin a 1 a Direct CP violation possible due to treepenguin interference in B d,s K decays. 24/38

25 Example: CP violation in decay B d,s Κ + π - : Clear asymmetry in raw distributions B 0 K + π - B 0 K - π + B s π + K - B s π - K + [LHCb-CONF ] Nice example of CPV in decay, but strong phases unknown, so difficult to extract the weak phase. 25/38

26 Another Example: CP violation in decay ΔA CP in D 0 h + h - (CPV in decay) ΔA CP = A CP (D 0 K + K ) A CP (D 0 π + π ) = Δa dir ind CP 0.1a CP LHCb measurement (2011 only; 0.6 fb -1 ): Theory predictions: ~0.1% Signifance 3.5 [LHCb-PAPER ] First evidence of CP violation in charm sector! News flash: Updates with more data push result much closer to zero. 26/38

27 Another example: measurement of γ Direct CP violation in interference between two subsequent weak decays. ADS method Colour suppressed D 0 K + B + Colour favoured D 0 K + Cabibbo favoured (K π + )K + Doubly Cabibbo suppressed Diagrams with b c and b u transitions are sensitive to γ. Clean extraction of γ : strong phases can be measured. First measurement of CKM angle γ from LHCb! (including ADS, GLW, GGSZ methods) = ( ) ± Is becoming competitive with B factories. 1-CL % 95% LHCb Preliminary [ ] [LHCb-CONF ] 27/38

28 3. CPV in interference mixingdecay Now you have seen two examples of CP violation: 1. CPV in mixing (interference between M 12 and Γ 12 ) 2. CPV in decay (interference between strong and weak phases) And both are due to interference. Now the obvious third type of CP violation (and most beautiful) is: 3. CPV in the interference between mixing and decay 28/38

29 3. CPV in interference mixingdecay We have seen already the time-dependence of flavour of a initially pure B 0 or B 0 : with But what we are actually interested in is the decay rate of a B into a final state f So, we define the decay amplitudes as: 29/38

30 3. CPV in interference mixingdecay Now let s just write down the full time-dependent decay rate: Compared to plain mixing: Two new interference terms where: and: 30/38

31 3. CPV in interference mixingdecay This beast simplifies a lot when assuming no CPV in decay, no CPV in mixing and f is CP eigenstate: Then defining the CP asymmetry as: If amplitude non-zero: The asymmetry is oscillating with Δm and amplitude Im(λ). Experimentally, you simply need to measure this amplitude to access directly the phases of the CKM matrix (time-dependent + flavour tagging) For example, for the golden decay B 0 J/ K 0 S this amplitude equals: CKM phase β directly observable! 31/38

32 Example: Measurement of sin2β The golden decay B 0 J/ K 0 S B d D M B d Mixing (box) diagram: J/ K 0 S D (final state is CP eigenstate)! V ud V us V $! ub 1 λ 2 / 2 λ ~ λ 3 e iγ V cd V cs V cb = λ 1 λ 2 / 2 Aλ 2 " V td V ts V tb ~ λ 3 e iβ ~ λ 2 e iβ s 1 % " $ % Decay diagrams: 32/38

33 Example: Measurement of sin2β! V CKM = " V ud V us V ub V cd V cs V cb V td V ts V tb $! = % " 1 λ 2 / 2 λ ~ λ 3 e iγ λ 1 λ 2 / 2 Aλ 2 ~ λ 3 e iβ ~ λ 2 e iβ s 1 $ % sin2β well determined by B-factories (BaBar and Belle) using the golden decay B 0 J/ K 0 S : sin2β = 0.679±0.020 Recent measurement from LHCb: sin2β = 0.73±0.07(stat)±0.04(syst) 33/38

34 Example: Measurement of sin2β s! V CKM = " V ud V us V ub V cd V cs V cb V td V ts V tb $! = % " 1 λ 2 / 2 λ ~ λ 3 e iγ λ 1 λ 2 / 2 Aλ 2 ~ λ 3 e iβ ~ λ 2 e iβ s 1 $ % Measure CP asymmetry in B s J/ B s counterpart of B d J/ K 0. Can simultaneously extract ΔΓ s Small SM prediction: 2β s = 0.036±0.002 J Narrow resonance (clean) L Vector-vector final state (requires angular analysis) J CP odd final state (no angular analysis) L BR about 20% of B s J/ 34/38

35 Example: Measurement of sin2β s B s J/ and B s J/ ππ time-dependent analysis Using 1.0 fb 1 [LHCb-CONF ] [Phys. Lett. B 713 (2012) ] Γ s = ± (stat.)± (syst.) ΔΓ s = ± 0.018(stat.) ± 0.006(syst.) s = ± 0.083(stat.) ± 0.027(syst.) Definition: s = -2β s In good agreement with Standard Model 35/38

36 Overview: Types of CP violation Three types of CP viola3on (always two amplitudes!): 1. CP viola3on in mixing ( indirect CP viola3on): q p 1 Note that in the SM all these effects are caused by a single complex parameter δ in the CKM matrix! 2. CP viola3on in decay ( direct CP viola3on): A f A f Tree Penguin 3. CP viola3on in the interference: arg λ f + arg λ f 0 36/38

37 CPT violation? Question 1: Answer 1 + 2: A K L an anti-k S particle! The mass difference between K L and K S : Δm = 3.5 x 10-6 ev => CPT violation? Question 2: How come the lifetime of K S = ns while the lifetime of the K L = 51.7 ns? Question 3: BaBar measures decay rate B J/ψ K S and B J/ψ K S. Clearly not the same: how can it be? Answer 3: Partial decay rate total decay rate! However, the sum over all partial rates (>200 or so) is the same for B and B. (Amazing! at least to me) 37/38

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