Recent CP violation measurements. Advanced topics in Particle Physics: LHC physics, 2011 Jeroen van Tilburg 1/38

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1 Recent CP violation measurements Advanced topics in Particle Physics: LHC physics, 2011 Jeroen van Tilburg 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. CKM relates the quarks in the mass eigenbase with the weak eigenbase. CKM has one complex phase which is responsible for CP violation. All current CP-violating measurements are consistent with this single phase. Advanced topics in Particle Physics: LHC physics, 2011 Jeroen van Tilburg 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 = us, A = cb / λ 2 and ρ, η. (# & i" ) 2 3 $ % 1 &! / 2! A! ' ( = ' &! 1 &! / 2 A! ( + O! ' 3 2 A! ( 1& # & i" ) & A! 1 ( ) * ( ) CKM = & $ $ $ % ud cd td us cs ts ub cb tb #!!! " λ ~ 0.22 (sinus of Cabibbo angle) A ~ 1 (actually 0.80) ρ ~ 0.14 η ~ 0.34 Advanced topics in Particle Physics: LHC physics, 2011 Jeroen van Tilburg 3/38

4 Mixing of neutral mesons (recap) x y B 0 meson # m $ " #" $ 2"! 0.7! 0 B s meson # m x $ " #" y $ 2"! 26! 0.1 The 4 different neutral meson systems have very different mixing properties. B s system: very fast mixing K 0 meson $ m x % # $# y % 2# " 1 "! 1 D 0 meson # m x $ " #" y $ 2"! 0.01! 0.01 Kaon system: large decay time difference. Charm system: very slow mixing Advanced topics in Particle Physics: LHC physics, 2011 Jeroen van Tilburg 4/38

5 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: td versus 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. Advanced topics in Particle Physics: LHC physics, 2011 Jeroen van Tilburg 5/38

6 Measurement of Δm s (B s -B s mixing frequency) Beautiful example of oscillations. B s meson Keep in mind this very fast oscillation in the B s system: x y $ $ # m " #" 2"! 26! 0.1 This oscillation was first observed at the Tevatron in 2006 at the Tevatron: Δm s =17.77 ± 0.10(stat) ± 0.07 (sys) ps 1 Fourier spectrum Advanced topics in Particle Physics: LHC physics, 2011 Jeroen van Tilburg 6/38

7 Measurement of Δm s (B s -B s mixing frequency) Now this measurement has been repeated with much better precision by LHCb: B s decayed as B s B s changed into B s Advanced topics in Particle Physics: LHC physics, 2011 Jeroen van Tilburg 7/38

8 Measurement of Δm s (B s -B s mixing frequency) What is needed to measure m s? Main ingredients for measuring m s : Resolve the fast B s oscillations. Average decay time resolution ~45 fs Decays into flavour specific final state: B s D s π High branching ratio (~0.3%) Tag the B s flavour at production. High efficiency and low mistag rate. Tagging power: ~5%. Advanced topics in Particle Physics: LHC physics, 2011 Jeroen van Tilburg 8/38

9 Flavour tagging Tagging of production flavour (B or B) Important for mixing & CP analyses. Performance calibrated using control channels such as B + J/ψ K + Tagging power: ε(1-2ω) 2 = (3.2 ± 0.8) % (opposite-side tag) (1.3 ± 0.4) % (same-side tag) from B s D s π mixing analysis. D In a perfect detector, why is the OS mistag rate not 0%? Advanced topics in Particle Physics: LHC physics, 2011 Jeroen van Tilburg 9/38

10 Advanced topics in Particle Physics: LHC physics, 2011 Jeroen van Tilburg 10/38 Measurement of Measurement of Δm s B s oscillations oscillations Dilution of mixing amplitude from tagging and proper time [LHCb-CONF ] Define mixing asymmetry : ) ( ) ( ) ( ) ( ) ( mix! + +!! + +! " + " "! " = # # # # s s s s s s s s D B N D B N D B N D B N t A Why is the amplitude not 1?

11 Measurement of Δm s m s extracted from unbinned ML fit to B s D s π candidates Uses mass, decay time and flavour tagging Method includes now same side tagging (cf 2010 fit) [LHCb-CONF ] Preliminary Δm s = ± 0.041(stat) ± (sys) ps 1 Most precise measurement of Δm s Dominant systematics uncertainty: z-scale and momentum scale Analysis done with 341 pb -1. (3x more data now available) SM: Δm s =17.3 ± 2.6 ps 1 Advanced topics in Particle Physics: LHC physics, 2011 Jeroen van Tilburg 11/38

12 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? Advanced topics in Particle Physics: LHC physics, 2011 Jeroen van Tilburg 12/38

13 Types of CP violation Phenomenologically, there are 3 types of CP violation: Advanced topics in Particle Physics: LHC physics, 2011 Jeroen van Tilburg 13/38

14 Types of CP violation Phenomenologically, there are 3 types of CP violation: 1. CP in mixing 2. CP in decay 3. CP in the interference between mixing and decay Advanced topics in Particle Physics: LHC physics, 2011 Jeroen van Tilburg 14/38

15 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: In the B d and B s systems Γ 12 is small Small CP violation in mixing. Advanced topics in Particle Physics: LHC physics, 2011 Jeroen van Tilburg 15/38

16 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) Advanced topics in Particle Physics: LHC physics, 2011 Jeroen van Tilburg 16/38

17 Example of CP in mixing: kaon system A + $ ( ) ( $ + ) L! " e L! " e 0 ( ) ( 0 ) L! " e L! " e R K % e $ R K % e 1 $ q/ p & = = 4' # 4 R K % e + R K % e 1 + q/ p +$ + $ $ + CPLEAR, Phys.Rep. 374(2003) AT! 3 ( t) = ( 6.6 ± 1.6) 10 " q p = ± # 1 CP violation in mixing small in SM: (due to cancellations) K 0 system: Order 1% D 0 system: Order 10-5 B d system: Order 5x10-4 Not yet observed B s system: Order 10-5 Advanced topics in Particle Physics: LHC physics, 2011 Jeroen van Tilburg 17/38

18 Hints for New Physics? Semileptonic measurement of CP in B mixing from D0 (Tevatron) CP in B s mixing Discrepancy of central value too large for New Physics. CP in B d mixing Advanced topics in Particle Physics: LHC physics, 2011 Jeroen van Tilburg 18/38

19 Hints for New Physics? Semileptonic measurement of CP in B mixing from D0 (Tevatron) CP in B s mixing High on agenda LHCb: Estimated uncertainty for measurement from LHCb (expected this Winter) Stay tuned CP in B d mixing Advanced topics in Particle Physics: LHC physics, 2011 Jeroen van Tilburg 19/38

20 2. CP violation in decay We define the decay amplitudes as: CP violation in decay means: In other words: Г(B 0 f ) Г(B 0 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 Advanced topics in Particle Physics: LHC physics, 2011 Jeroen van Tilburg 20/38

21 2. CP violation in decay B f B 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 No CP violation Advanced topics in Particle Physics: LHC physics, 2011 Jeroen van Tilburg 21/38

22 2. CP violation in decay B f B 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) 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. Advanced topics in Particle Physics: LHC physics, 2011 Jeroen van Tilburg 22/38

23 Example: CP violation in decay Charmless charged two-body B decays Tree B 0 K K + + B 0 π - Penguin a 1 a 2 π - Direct CP violation possible due to treepenguin interference in B d,s K π decays. Advanced topics in Particle Physics: LHC physics, 2011 Jeroen van Tilburg 23/38

24 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 ] Advanced topics in Particle Physics: LHC physics, 2011 Jeroen van Tilburg 24/38

25 Example: CP violation in decay Definition of asymmetry (time-integrated): Note that this does not require flavour tagging: we want to know flavour at decay. LHCb s s measurement for A CP Preliminary [LHCb-CONF ] A CP ( B 0 " K# ) =! ± 0.011± WA:! ! Most precise, and first 5σ observation of CP violation in hadronic machine. A ( B! K) = 0.27 ± 0.08 ± 0.02 CP s " first 3σ evidence of CP violation in B s 0 πk Caveat: strong phases and T/P unknown, so difficult to extract the weak phase. Advanced topics in Particle Physics: LHC physics, 2011 Jeroen van Tilburg 25/38

26 Another Example: CP violation in decay " A ΔA CP in D 0 h + h - (CP in decay) CP = A Preliminary [LHCb-CONF ] 0 +! 0 +! dir ind CP( D # K K )! ACP( D # $ $ ) = " acp! 0.1aCP New result! Only presented 3 weeks ago at HCP Measurement (2011 only; 580 pb -1 ): Signifance 3.5σ First evidence of CP violation in charm sector! Advanced topics in Particle Physics: LHC physics, 2011 Jeroen van Tilburg 26/38

27 3. CP in interference mixing&decay Now you have seen two examples of CP violation: 1. CP in mixing (interference between M 12 and Γ 12 ) 2. CP 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. CP in the interference between mixing and decay Advanced topics in Particle Physics: LHC physics, 2011 Jeroen van Tilburg 27/38

28 3. CP in interference mixing&decay 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: Advanced topics in Particle Physics: LHC physics, 2011 Jeroen van Tilburg 28/38

29 3. CP in interference mixing&decay Now let s just write down the full time-dependent decay rate: Compared to plain B mixing: Two new interference terms where: and: Advanced topics in Particle Physics: LHC physics, 2011 Jeroen van Tilburg 29/38

30 3. CP in interference mixing&decay This beast simplifies a lot when assuming no CP in decay and no CP in mixing: 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/ψ K 0 S this amplitude equals: CKM phase β directly observable! Advanced topics in Particle Physics: LHC physics, 2011 Jeroen van Tilburg 30/38

31 Example: Measurement of sin2β The golden decay B 0 J/ψ K 0 S (final state is CP eigenstate) B d φ D J/ψ K 0 S φ M B d φ D Mixing (box) diagram: Decay diagrams: Advanced topics in Particle Physics: LHC physics, 2011 Jeroen van Tilburg 31/38

32 Advanced topics in Particle Physics: LHC physics, 2011 Jeroen van Tilburg 32/38 Example: Measurement of sin2 Example: Measurement of sin2β sin2β well determined by B-factories (BaBar and Belle) using the golden decay B 0 J/ψ K 0 S :!!! " # $ $ $ % & ' ' ' ' =!!! " # $ $ $ % & = ' ' ' 1 ~ ~ 2 / 1 ~ 2 / CKM s i i i tb ts td cb cs cd ub us ud e e A e ( ( ) * * * * * * * * sin2β = 0.679±0.020

33 Example: Measurement of sin(2β s ) Measure CP asymmetry in B s J/ψ φ B s counterpart of B d J/ψ K 0. Can simultaneously extract ΔΓ s Small SM prediction: 2β s = 0.036± β s : interference phase between B s mixing and b ccs decay: CKM & $ = $ $ % ud cd td us cs ts ub cb tb #!!! " 2 & 1' * / 2 $ = $ ' * $ 3 ' i( % ~ * e * 2 1' * 2 ~ '* e / 2 ' i( s 3 ~ * e 2 A* 1 ' i) #!!! " Definition: φ s = -2β s Advanced topics in Particle Physics: LHC physics, 2011 Jeroen van Tilburg 33/38

34 Example: Measurement of sin(2β s ) Two decay modes B s J/ψ φ LHCb-CONF-049 B s J/ψ f 0 (980) LHCb-CONF-051 Narrow φ resonance (clean) ector-vector final state (requires angular analysis) First seen by LHCb last winter CP odd final state (no angular analysis) BR about 20% of B s J/ψ φ Advanced topics in Particle Physics: LHC physics, 2011 Jeroen van Tilburg 34/38

35 Example: Measurement of sin(2β s ) Combined fit Comparison with Tevatron Preliminary LHCb-CONF φ s = ± 0.16(stat) ± 0.07 (sys) SM: φ s = ± Two solutions: PDF insensitive to Next steps: Included more data (2.5 times more data recorded) Include same-side tagging (~1.5x more tagging power) Expect ~2x smaller statistical error. Advanced topics in Particle Physics: LHC physics, 2011 Jeroen van Tilburg 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 Af are caused by a single complex parameter δ in the CKM matrix! 2. CP viola3on in decay ( direct CP viola3on):! A f Tree Penguin 3. CP viola3on in the interference: arg! + arg! " 0 f f Advanced topics in Particle Physics: LHC physics, 2011 Jeroen van Tilburg 36/38

37 Advanced topics in Particle Physics: LHC physics, 2011 Jeroen van Tilburg 37/38

38 Backup slides Advanced topics in Particle Physics: LHC physics, 2011 Jeroen van Tilburg 38/38

39 Measurement of Δm s The D s decays as D s K + K π (largest hadronic BR) Intermediate resonances used for this analysis: D s φ π D s K * K D s K + K π (non-resonant) Event selection based on kaon ID, track IP and vertex χ 2 Event yield in 340 pb 1 0!! + 0! *! + B s " D s ($# )# Bs " Ds ( K K )# B 0 s!! +! + " Ds ( K K # )# Advanced topics in Particle Physics: LHC physics, 2011 Jeroen van Tilburg 39/38

40 Example: measurement of φ s Angular analysis of B s J/ψ φ B s J/ψ φ has vector-vector final state: Mixture of CP-odd and CP-even decay amplitudes Even and odd amplitudes can be disentangled using decay angles. Decay amplitudes used in fit: Transversity angles P wave S wave (non resonant K + K - ) Advanced topics in Particle Physics: LHC physics, 2011 Jeroen van Tilburg 40/38

41 Example: measurement of φ s Angular analysis of B s J/ψ φ PDF of unbinned ML fit described as: Complicated PDF: 3 independent implementations in LHCb Advanced topics in Particle Physics: LHC physics, 2011 Jeroen van Tilburg 41/38

42 Example: measurement of φ s Angular analysis of B s J/ψ φ Time and angular distributions Main systematic errors from uncertainties in the description of angular and decay time acceptance and background angular distribution. Advanced topics in Particle Physics: LHC physics, 2011 Jeroen van Tilburg 42/38

43 Example: Measurement of sin(2β s ) Result of the two fits B s J/ψ φ B s J/ψ f 0 (980) CL contours obtained using Γ s from J/ψφ. Two solutions: PDF insensitive to CP-odd final state, cannot determine Γ s and ΔΓ s simultaneously. When using both Γ s and ΔΓ s from B s J/ψφ: φ s =-0.44±0.44(stat)±0.02(syst) Advanced topics in Particle Physics: LHC physics, 2011 Jeroen van Tilburg 43/38