Results from the B-factories (Lecture 1)

Transcription

1 Results from the -factories (Lecture 1) Helmholz International Summer School HEAVY QUARK PHYSICS ogoliubov Laboratory of Theoretical Physics, Dubna, Russia, August 11-21,

2 Introduction Outline These lectures will cover: The factories CKM, mixing, and measuring CP asymmetries Unitarity triangle physics CP violation measurements The angles: (α, β, γ) = (φ 1, φ 2, φ 3 ) Direct CP violation Searching for new physics Side measurements V ub and V cb Measurements of b dγ processes (related to V td / V ts ) Tests of CPT VV decays Testing SM calculations and searching for new physics ostjan Golob will discuss charm physics, mixing, spectroscopy and other new physics searches from the -factories. 2

3 Notes The factories have produced many excellent results. Rather than show the results for both experiments for each measurement, I have selected results from either aar or elle. Where possible I show world average results based on the latest measurements. I choose to use the α, β, γ convention for the Unitarity triangle angle measurements, and the S, C convention for time-dependent CP asymmetry measurements. Experimental references are listed at the end of each lecture. 3

4 The factories 1964: Christensen, Cronin, Fitch and Turlay discover CP violation. 1967: A. Sakharov: 3 conditions required to generate a baryon asymmetry: Period of departure from thermal equilibrium in the early universe. aryon number violation. C and CP violation. 1981: I. igi and A. Sanda propose measuring CP violation in J/ψK 0 decays. 1987: P. Oddone realizes how to measure CP violation: convert the PEP ring into an asymmetric energy e + e - collider. I. igi and A. Sanda Nucl.Phys.193 p85 (1981) Detector Considerations P. Oddone (LL, erkeley) In the Proceedings of Workshop on Conceptual Design of a Test Linear Collider: Possibilities for a Anti- Factory, Los Angeles, California, Jan 1987, pp : aar and elle start to take data. y 2001 CP violation has been established (and confirmed) by measuring sin2β 0 in J/ψK 0 decays. aar Collaboration, PRL 87, (2001); elle Collaboration, PRL 87, (2001). 4

5 How do we make mesons? Collide electrons and positrons at s=10.58 GeV/c 2 σ (e + e - Hadrons)(nb) ϒ(1S) ϒ(2S) ϒ(3S) off-peak Υ(4S) ϒ(4S) Mass (GeV/c 2 ) many types of interaction occur. We re interested in (for physics). Where 5

6 PEP-II and KEK PEP-II 9GeV e - on 3.1GeV e + Υ(4S) boost: βγ=0.56 KEK 8GeV e - on 3.5GeV e + Υ(4S) boost: βγ=

7 AAR and elle AAR IFR SOLENOID EMC e + The differences between the two detectors are small. oth have: Asymmetric design. Central tracking system Particle Identification System Electromagnetic Calorimeter Solenoid Magnet Muon/K 0 L Detection System High operation efficiency e SVT DCH DIRC 7

8 What does an event look like? π 0 π 0 0 August event ππ 8

9 Data Many Interactions produce meson pairs: and produced in equal quantities oth experiments have recorded data while scanning through the region above the Y(4S) 9

10 The CKM matrix Quarks change type in weak interactions: W + V ij qi q j = u, c, t = d, s, b V = We parameterise the couplings V ij in the CKM matrix: V λ /2 λ Aλ ( ρ iη) = λ λ λ Aλ (1 ρ iη ) Aλ 1 λ /2 A O( ) λ ~0.22 A ~0.8 ρ ~ η ~ At the factories we want to measure: ρ ρ λ η η λ 2 2 (1 Adrian /2), evan (1 /2) 10

11 Mixing Neutral mesons oscillate between 0 and 0, The Hamiltonian is u, c, t = W + Long Distance Terms W + u, c, t We study the mass eigenstates: If CPT is conserved z=0 p and q are mixing parameters: Physics depends on mass eigenstate differences in m and Γ: Δ Γ / Γ = (usually set ΔΓ = 0). 11

12 Time-dependent CP asymmetries Ingredients of a time-dependent CP asymmetry measurement: Isolate interesting signal decay: REC. Identify the flavour of the non-signal meson ( TAG ) at the time it decays. Measure the spatial separation between the decay vertices of both mesons: convert to a proper time difference Δt = Δz / βγc; fit for S and C. The time evolution of TAG = 0 ( 0 ) is Note that elle use a convention where C is replaced by A CP = C S is related to CP violation in the interference between mixing and decay. C is related to direct CP violation. η f is the CP eigenvalue of REC. 12

13 Time-dependent CP asymmetries Ingredients of a time-dependent CP asymmetry measurement: Isolate interesting signal decay: REC. Identify the flavour of the non-signal meson ( TAG ) at the time it decays. Measure the spatial separation between the decay vertices of both mesons: convert to a proper time difference Δt = Δz / βγc; fit for S and C. The time evolution of TAG = 0 ( 0 ) is Note that elle use a convention where C is replaced by A CP = C 13

14 Time-dependent CP asymmetries Construct an asymmetry as a function of Δt: f - (Δt) f + (Δt) Experimental effects we need to include: Detector resolution on Δt. Dilution from flavor tagging (see later). With detector resolution With detector resolution and dilution Δt (ps) Δt (ps) 14

15 Time integrated CP asymmetries Charged mesons do not oscillate. Measure a direct CP asymmetry by comparing amplitudes of decay: Event counting exercise! With two (or more) amplitudes see that we need different weak and strong phases to generate. A CP is largest when a 1 = a 2. Need to measure δ! We can use this technique when studying neutral mesons decaying to a self tagging final state. 15

16 Isolating signal events eam energy is known very well at an e + e collider use an energy difference and effective mass to select events: σ(δe)~ MeV (mode dependent) signal M ES σ ~ 3 MeV background 16

17 More background suppression Use the shape of an event to distinguish between Υ(4S) and e + e qq. s=10.58 GeV: compare m = GeV/c 2 with m uu, m dd, m ss ~ few to 100 MeV/c 2 m cc ~ 1.25 GeV/c 2 -pair events decay isotropically continuum (ee qq) events are jetty Analyses combine several event shape variables in a single discriminating variable: either Fisher or artificial Neural Network. This allows for some discrimination between and continuum events Arbitrary Units Signal Fisher Discriminant: u,d,s,c background F = α x i 17 i i

18 Measuring Δt e - e Asymmetric energies produce boosted Υ(4S), decaying into coherent pair π + π Fully reconstruct decay to state or admixture under study ( REC ) 18

19 Measuring Δt π + e - e + Asymmetric energies produce boosted Υ(4S), decaying into coherent pair βγ = 0.56 (aar) = (elle) 0 0 Δz=(βγc)Δt Determine time between decays from vertices π Fully reconstruct decay to state or admixture under study ( REC ) t = t 1 corresponds to the time that TAG decays. t 2 -t 1 = Δt t=t 2 t=t 1 19

20 Measuring Δt e - e + Asymmetric energies produce boosted Υ(4S), decaying into coherent pair βγ = 0.56 (aar) = (elle) 0 0 t = t 1 corresponds to the time that TAG decays. t 2 -t 1 = Δt Determine time between decays from vertices t=t 2 Δz=(βγc)Δt Then fit the Δt distribution to determine the amplitude of sine and cosine terms. t=t 1 π + π Fully reconstruct decay to state or admixture under study ( REC ) Determine flavor and vertex position of other decay ( TAG ) l- K - 20

21 Flavor tagging Decay products of TAG are used to determine its flavor. At Δt=0, the flavor of REC is opposite to that of other TAG. aar s flavor tagging algorithm splits events into mutually exclusive categories ranked by signal purity and mis-tag probability. elle opt to use a continuous variable output. These plots are for the 316fb -1 h + h - data sample. Lepton REC continues to mix until it decays. Different TAG final states have different purities and different mis-tag probabilities. Kaon 1 Can (right) split information by physical category or (below) use a continuous variable to distinguish particle and antiparticle. 0 0 Kaon 2 Kaon-Pion Pion Other 21

22 Flavor tagging Don t always identify TAG flavor correctly: asymmetry diluted by ω is probability for assigning the wrong flavor (mistag probability). Effect is slightly different for 0 and 0 tags: Δω Define an effective tagging efficiency: Use a modified f ± (Δt): 22

23 Flavor tagging Don t always identify TAG flavor correctly: asymmetry diluted by ω is probability for assigning the wrong flavor (mistag probability). Effect is slightly different for 0 and 0 tags: Δω Define an effective tagging efficiency: Use a modified f ± (Δt): Example: The aar tagging algorithm: 23

24 Fitting for CP asymmetries Perform an extended un-binned ML fit in several dimensions (2 to 8). P ji is the probability density functions for the i th event and j th component (type) of event. n j is the event yield of the j th component. N is the total number of events. Usually replicate the likelihood for each tagging category (aar) or include a variable in the fit that incorporates flavor tagging information (elle). In practice we minimize lnl in order to obtain the most probable value of our experimental observables with a 68.3% confidence level (1σ error) using MINUIT. S and C (or A CP ) are observables that are allowed to vary when we fit the data. 24

25 Angles of the Unitarity triangle 25

26 Theoretically clean (SM uncertainties ~10-2 to 10-3 ) tree dominated decays to Charmonium + K 0 final states. b ccs J / ψ K 0 0 L J / ψ K 0 0 S ψ (2 S) K 0 0 S χ K 0 0 1c S η K 0 0 c S J / ψ K 0 *0 0 J / ψπ D D (*) + (*) 0 η K 0 ρk 0 ωk 0 0 π K φk KKK (*)0 f (980) K

27 CP violation: β Need to determine many parameters before we can extract S and C (and the angles of the triangle): ω, Δω, ε TAG, Δε TAG for signal and for background. Use a sample of fully reconstructed decays to flavor specific final states to determine these parameters ( flav ). Sample includes: D 0 (*) + D π ρ 0 (*) + 0 (*) + D a1 0 *0 *0 J / ψ K, K K ackground π + aar sin2β analysis Lepton, pion or kaon π + ν TAG REC = FLAV D π π + π This method to validate the tagging performance is used for all time-dependent CP asymmetry measurements. 27

28 CP violation: β Measure S and C in several modes. b ccs aar sin2β analysis Theoretically clean: Tree level process dominates: 0 Gluonic loop (penguin) is small: 0 b d b d W Calculations suggest C<10-3. g t,c,u Data driven methods constrain C< W c c s d c c s d J/ ψ K 0 J/ψ K 0 η = + 1 f η f eff η f = 1 ~0.5 This mode is a CP admixture with CP even and odd parts that need to be distinguished using an angular analysis. 28

29 CP violation: β CP violating asymmetry is well established in these decays! η = 1 f η =+ 1 f aar sin2β analysis sin 2β = 0.671± aar Collaboration, SLAC-PU-13317, PRL 99, (2007) 29

30 CP violation: β Theoretically clean CP violation measurements consistent with the Standard Model for: J / ψ K 0 0 L 0 0 / ψ S 0 0 ψ (2 S) KS 0 0 χ1 cks 0 0 ηcks 0 *0 J K J / ψ K Four solutions exist in the ρ-η plane as we compute arcsin(2β). Additional measurements provide cos(2β) and help to resolve ambiguities. Established technique for extracting S and C that can be used for other final sates. Measured S=sin2 β provides a reference point to search for New Physics (NP). 30

31 b uud transitions with possible loop contributions. Extract α using SU(2) Isospin relations. SU(3) flavour related processes. b uud ππ ρπ ρρ a1π a1ρ b1π b1 ρ aa

32 CP violation: α Interference between box and tree results in an asymmetry that is sensitive to α in hh decays: h=π, ρ, Loop corrections are not negligible for α. V * td : β +Loops (penguins) Vtd : β Measure S α eff. Need to determine δα=α eff -α [ P/T is different for each final state ] C S hh hh = 0 = sin(2 α) Vub : γ C S sin( δ ) hh This scenario is equivalent to 2 hh = the measurement 1 Chh sin(2 of α eff ) sin2β in Charmonium decays but nature is = P more complicated T than this! δ δ δ 32

33 CP violation: α Interference between box and tree results in an asymmetry that is sensitive to α in hh decays: h=π, ρ, Loop corrections are not negligible for α. V * td : β +Loops (penguins) Vtd : β Vub : γ C hh sin( δ ) C S hh hh = 0 = sin(2 α) S hh = δ = δ δ P 2 1 Chh sin(2 eff ) T α Measure S hh α eff. Need to determine δα=α eff -α [ P/T is different for each final state ] 33

34 ounding penguins Several recipes describe how to bound penguins and measure alpha. These are based on SU(2) or SU(3) symmetry. SU(2) (Isospin analysis) π + π and ρ + ρ Gronau-London Isospin Triangles Use charged and neutral decays to the hh final state to constrain the penguin contribution and measure alpha. π + / ρ / + Lipkin (et al.) Isospin Pentagons Use charged and neutral decays to the ρπ final state to constrain the penguin contribution and measure alpha. Remove any overlapping regions in the Dalitz plot. π + / π / + π 0 Snider-Quinn (et al.) Fit Dalitz plot and extract parameters related to α Regions of the Dalitz plot with intersecting ρ bands are included in this analysis; this helps resolve ambiguities. 34

35 ounding penguins Several recipes describe how to bound penguins and measure alpha. These are based on SU(2) or SU(3) symmetry. SU(3) flavor analysis Fit for T and P amplitudes, as well as phase differences δ TP in related decays Theoretical uncertainties tend to result in weaker constraints than the SU(2) analyses. No choice for decays like a 1 π. Exception exists for ρ + ρ : Use K* 0 ρ + to constrain penguin contribution in ρ + ρ and measure α with better precision than SU(2). 35

36 Isospin analysis S + Consider the simplest case: ππ / ρρ decays. 0 + ( hh) + CC ( hh) + CC ( hh) + CC.. h h A + A = A For ππ & ρρ require: A + A = A δα δα = α eff -α Measuring S in h 0 h 0 provides an additional constraint on this angle. There are SU(2) violating corrections to consider, for example electroweak penguins, but these are much smaller than current experimental accuracy and can be incorporated into the Isospin analysis. 36

37 ππ Easy to isolate signal for π + π and π + π 0 as these modes are relatively clean and have large ~ O( ). elle π + π 0 tagged 0 tagged elle π + π Much harder to isolate π 0 π 0 : ~ C No tracks in the final state to provide vertex information. Have to reconstruct 0 π 0 π 0 γγγγ, which has a large ΔE resolution. S + π π + π π = 0.65 ± 0.07 = 0.38 ± 0.06 Possible to separate flavor tags to measure C 00. This information completes the set of information required for an Isospin analysis. elle π 0 π 0 0 tagged 0 tagged 37

38 ππ Inputs from: 0 π π 0 π π π π Gronau-London Isospin analysis How do I read plots like this? 1-CL = 1: central value reported from measurements, before considering uncertainties. 1-CL = 0: Region excluded by experiment. If we think in terms of Gaussian errors, then 1-CL = 0.317, 0.046, correspond to regions allowed at 1σ, 2σ and 3σ. 38

39 ππ Gronau-London Isospin analysis How do I read plots like this? At 68.3% CL = 1σ for Gaussian errors we have the following allowed regions for α: α < < α < < α < α >

40 ππ If we have measured CP violation in π + π, does this tell us something about α? Yes! CP violation measured as a nonzero value of S is related to α via: Excluded using Additional information. C ππ 0 gives a scale factor. S ππ 0 means there is CP violation in this decay and sin(2α eff ) 0. If α=0, then the unitarity triangle would be flat, so if S 0 we must have α 0. Can use constraints on P from s K + K to remove the solutions near August α= and

41 ρρ This is a decay of a meson to two vector mesons. Requires a (simplified) angular analysis (will come back to this in Lecture 2). Inputs from: 0 + ρ ρ 0 ρ ρ + + ρ ρ We define the fraction of longitudinally polarised events as: fl ~ 1 for ρρ decays: this helps simplify extracting α. Can measure S 00 as well as C 00 to help resolve ambiguities. Finite width of the ρ is ignored in the α determination (see Falk et al.) 41

42 ρρ Obtain a more stringent constraint on α than from ππ decays. aar ρ 0 ρ 0 paper Not including S 00 and C 00. Include C 00, but not S 00. Using all constraints. Some features of this result: Two of the solutions overlap near 90 and 180. Using S 00 and C 00 we see that the solution at 80 is very slightly preferred over the other solutions. There are two regions for α that are excluded: α 45 α

43 Using SU(3) Can relate the penguin contribution in K *+ ρ 0 to that in ρ + ρ : F = 0.9 ± 0.6 aar ρ + ρ paper δ TP < 90 δ TP > 90 If we assume that δ TP < 90 : Relaxing this assumption: Most precise determination of α! 43

44 ρπ (π + π π 0 Dalitz Plot) Analyse a transformed Dalitz Plot to extract parameters related to α. Use the Snyder-Quinn method. ρ + π ρ 0 π 0 (θ 0 =π + π - helicity) ρ π + (m 0 =m π+π- ) Fit the time-dependence of the amplitudes in the Dalitz plot: 26 parameters: i-linear form factor coefficients: U s and I s. 44

45 ρπ (π + π π 0 Dalitz Plot) The amplitudes are written in terms of Us and Is: Which are related to CP conserving and CP violating observables: CP conserving observables CP violating observables elle ρ + π paper Some features of this result: No region is excluded at 3σ significance. A high statistics measurement will help resolve ambiguities in the measured value of α. Results from the Dalitz analysis, and the pentagon analysis (solid) are more stringent than using the Dalitz analysis alone. 45

46 CP violation: α No single mode dominates our knowledge of α. Three comparable inputs from ππ, ρρ, ρπ using SU(2). SU(3) can be used to provide a more stringent constraint for α from ρ + ρ. Many modes are required to try and measure α precisely. Any deviation in measured values of could indicate new physics. α = 97.5 α = SU (2) 5.3 SU (3) π π, π π, π π ρ ρ, ρ ρ, ρ ρ + 0 πππ a1π a ρ 1 46 Shown here Not shown: Need more data than currently available, and use SU(3) to extract α from final states with axial-vector mesons. These are related to hh modes above.

47 b c interfering with b u D K 0 D 0 (*) D 0 (*) (*) (*) DKπ 0 + π ρ + charmless Extract γ using D (*) K (*) final states using: GLW: Use CP eigen-states of D 0. ADS: Interference between doubly suppressed decays. GGSZ: Use the Dalitz structure of D K s h + h decays. Measurements using neutral D mesons ignore D mixing. 47

48 γ: GLW Method D X + + ( + ) GLW Method: Study and X + CP D 0 X + CC.. D 0 K π is a strangeness one meson e.g. a K + or K* +. 0 D CP is a CP eigenstate (use these to extract γ): DCP=+ 1 = K K, ππ DCP= 1 = KSπ, KSω, KSφ Γ( DCP± K ) +Γ( DCP± K ) 2 RCP± = 2 = 1+ r 2 cos cos 0 0 ± r γ δ + + Γ( D K ) +Γ( D K ) A Γ( DCP± K ) Γ( DCP± K ) 2rsinγ sinδ CP± = =± Γ( D K ) +Γ( D K ) RCP± 4 observables 3 unknowns: r, γ and δ The precision on γ is strongly dependent on the value of r. r ~0.1 as this is a ratio of Cabibbo suppressed to Cabibbo allowed decays and also includes a color suppression factor for + D (*) K (*) b u decays. Vcs cosθc = cos0.23 = 0.97 Cabbibo allowed Vcd sinθc = sin 0.23 = 0.23 Cabbibo suppressed Measurement has an 8-fold ambiguity on γ. 48 Gronau, London, Wyler, PL253 p483 (1991).

49 γ: GLW Method aar GLW paper Insufficient data to constrain γ: 149±16 90±13 x ± is related to R CP± and A CP±. We can perform similar measurements using D* CP K: 106±14 129±15 Again: insufficient statistics to perform a precision measurement of γ. 49

50 γ: GLW Method A CP± =± 2rsinγ sinδ R CP± R r r γ δ = ± CP± 2 cos cos All measured A CP and R CP values are compatible with 0 and 1, respectively. 50

51 γ: ADS Method D K ±,0 *0 * ± ADS Method: Study Reconstruct doubly suppressed decays with common final states and extract γ through interference between these amplitudes: D K (*)0 (*) CKM Favoured V cb V us V ub V cs D K (*)0 (*) CKM and Color Suppressed (*)0 D γ extracted using ratios of rates: r (*) r D = = K + π Doubly CKM Suppressed D(*)0 π (*)0 A ( D K ) (*)0 A ( D K ) 0 + AD ( Kπ ) 0 + AD ( Kπ ) W + u c d V cd V us u u s K + W d c s V cs V ud D (*)0 K + u u u (*)0 D K + π CKM Favoured R = r + r + 2r r cosγ cosδ (*) (*)2 2 (*) (*) D D δ (*) = δ (*) + δ D δ (*) is the sum of strong phase differences between the two and D decay amplitudes. r D and r are measured in and charm factories. δ D is measured by CLEO-c 51 π Attwood, Dunietz, Soni, PRL (1997)

52 γ: ADS Method R = r + r + 2r r cosγ cosδ (*) (*)2 2 (*) (*) D D Insufficient precision to extract γ using the ADS method alone. Measurement of R ADS can be used to constrain r. Help when extracting γ using other methods. Full statistics from the factories will not improve the situation significantly. 52

53 γ: GGSZ Method GGSZ ( Dalitz ) Method: Study D (*)0 K (*) using the D (*)0 K s h + h Dalitz structure to constrain γ. (h = π, K) Self tagging: use charge for ± decays or K (*) flavour for 0 mesons. i A ( Khh) ) m f m m r e ± 0 + ± ( S DK f( m+, ) + (, + ) where m m ± ± = 0 S K h ( δ ± γ ) Need a detailed model of the amplitudes in the D meson Dalitz plot. Use a control sample (CLEO-c data or D *+ D 0 π + ) to measure the Dalitz plot. D D π * + 0 D 0 0 S Khh + π + π Control sample plots from aar GGSZ paper K + K 53 Giri, Grossman, Soffer, Zupan, PRD 68, (2003)

54 γ: GGSZ Method DK DK + + Note: axes swapped between Figures (a) and (b). Differences between the two plots contain information on γ. elle GGSZ paper Method has a 2-fold ambiguity on γ. γ γ elle aar ( ) 13 stat 4syst 9mod el = ± ± ( ) 24 stat 5syst 5mod el = ± ± aar GGSZ paper r ~0.16 (elle), and ~0.09 (aar) The elle measurement has a larger value for r, hence a smaller uncertainty on γ. 54

55 CP violation: γ As with α, no single channel dominates the determination of γ. Several methods available. est results come from the GGSZ Dalitz method. LHCb will produce more precise analyses of these decay modes, and will also be able to use U-spin related rare charmless decays to try and measure γ more precisely. The factories have started to measure γ! With β measured to ~1, and α measured to ~7, we can use γ measurements to over-constrain the Unitarity triangle and test the integrity of the CKM mechanism. The CKM mechanism works at this level: ( ) α + β + γ 180 = 10 ± 21 New experiments are needed to test the CKM to a higher accuracy: LHCb, Super, and SuperKEK. 55

56 Next Lecture Direct CP Violation. CP violation: Searching for new physics. Summary of CP violation signals found. Side measurements. VV decays. 56

57 Experimental References Experiments Averages β b ccs α ππ ρρ ρπ γ GGSZ ADS GLW 57