Results from the B-factories (Lecture 2)

Transcription

1 Results from the B-factories (Lecture 2) Helmholz International Summer School HEAVY QUARK PHYSICS Bogoliubov Laboratory of Theoretical Physics, Dubna, Russia, August 11-21, 28 1

2 Previous lecture b c interfering with b u B D K B B B (*) (*) DKπ D (*) D (*) + π ρ + charmless b uud B aπ B ππ B a1ρ B ρπ B b1π B ρρ B b1 ρ B aa ( ) α + β + γ 18 = 1 ± b ccs B J / ψ K L B J / ψ K B B B S ψ (2 S) K S χ K 1c S η K c S B J / ψ K * B J / ψπ B D D (*) + (*) B η K B ρk B ωk B π K B φk B KKK (*) B f (98) K 2

3 This lecture Direct CP violation Searching for New Physics Alternate measurements of angles: ΔS Sides of the Unitarity Triangle: Over-constraining the SM CPT Tests B VV decays (and related channels) 3

4 CP violation: Direct CP violation Recap from Lecture 1: Number counting exercise: Requires at least two amplitudes to interfere. Amplitudes have to have different weak and strong phases. We are comparing A f with A f. Predictive power will be limited by our knowledge of weak phases and of the strong phase differences. But there are many possible measurements that we can compare! 4

5 B CP violation: Direct CP violation K ± π : Tree and gluonic penguin contributions Compute time integrated asymmetry A ± K π = ± Experimental results from Belle, BaBar, and CDF have significant weight in the world average of this CP violation parameter. Direct CP violation present in B decays. 1856±52 K π + Belle Kπ analysis 2241±57 K + π Unknown strong phase differences between amplitudes, means we can t use this to measure weak phases! 5

6 B + + CP violation: Direct CP violation K π : Color suppressed tree and gluonic penguin contributions Many theory calculations indicate that. K + π K + π Experimentally measure: Belle Kπ analysis AK π A + =.5 ±.25 A Difference between B + and B asymmetries: AK π Difference could be an indication of new physics, however: Theory calculations assume that only T+P contribute to K + π, and C+P contribute to K + π. Δ = ± (>5σ from zero) The C contribution is larger than originally expected in K + π. For example, see G. Hou arxiv: and references therein. 6

7 Direct CP violation searches CP A = = no CP violation Observed signal of direct CP violation in B meson decay This is a small sub-set of decays where we have searched for direct CP violation. 2 observed signals (> 5σ): K + π and π + π ; five possible effects (> 3σ): ρ K +, ηk *, ρ + π D (*) K (*), and D CP K. 7

8 CP violation: Searching for new physics sin2β has been measured to O(1 ) accuracy in decays. Can use this to search for signs of New Physics (NP) if: Identify a rare decay sensitive to sin2β (loop dominated process). Measure S precisely in that mode (S eff ). Control the theoretical uncertainty on the Standard Model pollution (ΔS SM ). Compute. In the presence of NP: ΔS NP B b d W uct,, g Many tests have been performed in: B d processes. B s processes. s s s d φ, η,( KK) CP K S b ccs Unknown heavy particles can introduce new amplitudes that can affect physical observables of loop dominated processes. Observables that might be affected include branching fractions, CP asymmetries, forward backward asymmetries and so on. A successful search requires that we understand Standard Model contributions well! 8

9 SM uncertainties on ΔS To find NP we need to understand the SM contributions to a process. Leading order term is expected to be the same as a SM weak phase. Higher order terms including re-scattering, suppressed amplitudes, final state radiation and so on can modify our expectations. Some channels are better understood than others. Sign of ΔS correction is mode dependent. Most precise ΔS correction is for B η K, where ΔS theory ~ ±.1. Concentrate efforts on well understood channels.?? QCDF Beneke, PLB62, 143 (25) SCET/QCDF, Williamson and Zupan, PRD74, 143 (26) QCDF Cheng, Chua and Soni, PRD72, 146 (25) SU(3) Gronau, Rosner and Zupan, PRD74, 933 (26) 9

10 B η K Loop dominated b s decay. B b d S C η K η K W uct,, g s s s d =.6 ±.7 =.4 ±.5 η K Possible to measure S and C for both B B η K S η KL (CP odd) (CP even) These asymmetries can be compared with the Charmonium reference measurement to calculate ΔS. B tagged B tagged Δ = ± ± S η K.7.7exp.1theory CP violation has been established in this decay channel by the B factories. Need at least 5 ab -1 of data to do a precision search for NP at the level of current theoretical uncertainties. Belle η K analysis 1

11 B J/ψπ Tree and penguin contributions: can be sensitive to NP. Alternatively, can be used to constrain SM uncertainties in the Charmonium β measurement. B tagged B tagged CP even final state: S C J / ψπ J / ψπ Tree S = S ccs J / ψπ CP violation observed in this decay. =.93±.15 =.1 ±.13 Δ S =.23±.15 J / ψπ exp BaBar J/ψπ analysis Require a dataset of ~22ab -1 to make a 1% ΔS measurement in this channel. 11

12 Overview of ΔS measurements Comparing sin2β in different physical processes, we see good agreement with the b ccs reference point. (reference point) Most of the b s penguin channels have sin2β eff < sin2β. Could this be an indication of NP? Insufficient statistics to tell. Need to perform a mode-by-mode precision measurement in order to properly decouple Standard Model uncertainties from possible signals of NP. We need at least 5ab -1 to start performing measurements that will have comparable experimental and theoretical uncertainties in b s penguin processes. Need ~22ab -1 to do the same for b d. Can start to do the same with α and γ once we have a precision measurement from one mode. b s-penguin processes b d 12

13 Summary of CP violation signals found We have discovered CP violation in the following channels: Indirect CP violation measurement: related to a weak phase in the Standard Model. These modes measure either β or α. Direct CP violation measurement: related to weak phase differences and strong phase differences in the Standard Model. Can be used to constrain weak phases using model dependent analysis of charmless rare B meson decays. All of our measurements have been consistent with the SM (so far). 13

14 Sides of the Unitarity Triangle 14

15 Sides of the Unitarity Triangle b ulν B πlν B Xl u ν B ρlν B ωlν Use theory to relate partial branching fractions to V ub for a given region of phase space. Several theoretical schemes available. 15

16 Side measurements: V ub V ub B(B X u lν) in a limited region of phase space. Reconstruct both B mesons in an event. Study the B recoil to measure V ub. Measure B as a function of q 2, m, m or E lν X MISS l and use theory to convert these results into V ub. Can study modes exclusively or inclusively. Several models available to estimate V ub The resulting values of V ub have a significant model uncertainty. 16

17 Exclusively reconstructed b ulν If we fully reconstruct one B meson in an event, then with a single ν in the event, we can infer P μ and recontruct the ν. Clean signals! Low efficiency! Study B decays to: B B B B B + π l ν + ρ l ν π l ν ρ l ν ωl ν Fully reconstruct B RECO Extract yields from m 2 MISS q < 8( GeV) < q < 16( GeV) q 2 2 > 16( GeV) 2 2 (reduces form factor dependence) Then compute V ub. Fully Reconstructed B RECO decay Lepton B B X ν Semi-leptonic b ulν decay Use the beam energy to constrain P μ to effectively reconstruct ν from the missing energy-momentum: m MISS m ν =. 17 Belle: See W. Dungel, ICHEP 8 for more details

18 V ub : Using q 2 distribution Use B πlν decays B ( B π l ν) = (1.34 ±.6 ±.5) dγ( B πν l ) dq G 24π 2 F = 2 3 V ub p f( q ) π Light cone sum rules: PRD71, 1415 (25) Unquenched LQCD: PRD73, 7452 (26) Unquenched LQCD: Nucl.Phys.Proc.Suppl. 14, p461 (25) Quenched LQCD:NPB619, p565 (2) σ(v ub ) EXPT ~ 5% σ(v ub ) THEORY ~ 11 to 17% Experiments have also studied higher mass meson l ν decays 18

19 V ub : Using M X distribution High background from c lν decays. Kinematic cuts are used to suppress background. Use Operator Product Expansions to translate measured branching fractions to V ub. B X c lν background All D* D D** X u Measure branching fraction in different kinematic regions. BLNP: PRD72, 736 (25) DGE: JHEP 61:97 (26) GGOU: JHEP 71:58 (27) ADFR: arxiv: BLL: PRD64, 1134 (21) 19

20 Sides of the Unitarity Triangle Use theory to relate partial branching fractions to V cb for a given region of phase space. b clν (*) B D lν B DXlν ** B D lν 2

21 Side measurements: V cb Use the differential decay rates of B D * lν to determine V cb : * dγ( B D l ν ) dωdcosθ dcosθ dχ l V F ( ωθ,, θ, χ) V 2 2 l V cb F is a form factor. Need theoretical input to relate the differential rate measurement to V cb. Δ m= m m Kππ Kπ Reconstruct * B D e ν e * D Dπ BaBar D*eν paper D Measurement is not statistically limited, so use clean signal mode for D Kπ decay only. K + π Extract signal yield, F(1) V cb and ρ from 3D binned fit to data. 21

22 Side measurements: V cb Use the differential decay rates of B D * lν to determine V cb : * dγ( B D l ν ) dωdcosθ dcosθ dχ l V F ( ωθ,, θ, χ) V 2 2 l V cb F is a form factor. Need theoretical input to relate the differential rate measurement to V cb. Δ m= m m Kππ Kπ B * ( B D e ν ) = (5.56 ±.8 ±.41)% F(1) V cb = (35.9 ±.6 ± 1.4) 1 3 BaBar D*eν paper = (39. ±.6 ± 2.) 1 V cb Using F(1)=.919 ±.33 from Hashimoto et al., PRD (22). 3 22

23 Side measurements: V cb Use the differential decay rates of B Dlν to determine V cb : dγ( B Dl ν ) dωdcosθ dcosθ dχ l V G ( ω) V 2 2 cb G is a form factor. Need theoretical input to relate the differential rate measurement to V cb. Use a sample of fully reconstructed tag B mesons, then look for the signal. Improves background rejection, at the cost of signal efficiency. Fully Reconstructed B RECO decay B B D ν Lepton Semi-leptonic b Dlν decay Use the beam energy to constrain P μ to effectively reconstruct ν from the missing energy-momentum: m MISS m ν =. D Reconstruct the following D decay channels: K K K K K K K π + + S + Sπ ππ Sπ K KK ππ + π ππ + + ππ + + ππ S S D K K K K + S + Sππ + + K K K K K S S ππ π ππ + + π + π + + π ππ 23

24 Side measurements: V cb Use the differential decay rates of B Dlν to determine V cb : dγ( B Dl ν ) dωdcosθ dcosθ dχ l V G ( ω) V 2 2 cb G is a form factor. Need theoretical input to relate the differential rate measurement to V cb. ω is related to q 2 of the B meson to the D 24

25 Side measurements: V cb Use the differential decay rates of B Dlν to determine V cb : dγ( B Dl ν ) dωdcosθ dcosθ dχ l V G ( ω) V 2 2 cb G is a form factor. Need theoretical input to relate the differential rate measurement to V cb. Results of a combined fit to D and D ± modes gives: G(1) V = (43. ± 1.9 ± 1.4) 1 cb V = (39.8 ± 1.8 ± 1.3 ±.9 ) 1 cb 3 stat syst FF 3 Using G(1) from Okamoto et al., NPPS (25) and correcting by 1.7 for QED effects. 25

26 V cb B Dlν B * D lν G(1) V = (42 ± 1.6) 1 cb 3 V = (39.7 ± 1.4 ±.9 ) 1 cb exp theory Using G(1)=1.74 ±.18±.16 from Okamoto et al., NPPS 14, 461 (25). 3 F(1) V = (35.97 ±.53) 1 cb exp theory 3 V = (38.7 ±.6 ±.9 ) 1 cb Using F(1)=.924 ±.12±.19 from Laiho, arxiv: [hep-lat]. 26 3

27 Sides of the Unitarity Triangle Use inclusive measurements of b dγ and b sγ to measure the ratio V td / V ts. Able to compare results with Bs mixing results from the TeVatron. b dγ B X d γ 27

28 B X d γ FCNC process (same topology as B X s γ). Leading order contribution: electroweak penguin. sensitive to NP b γ, Z d Challenging analysis with large backgrounds at high m X. Signal suppressed by V td. Extract signal from a 2D Fit in m ES and ΔE. X d γ signal X d γ signal Convert B(dγ) / B(sγ) into a measurement of V td / V ts using Ali, Asatrian, and Greub PLB (1998) BaBar dγ paper top :.6 < mx < 1. GeV / c d bottomaugust :1. < m28 < 1.8 GeV / c X d

29 B X d γ Exclusive analysis of b dγ recently performed by Belle Converting results to V td / V ts obtain Vtd V ts =.195 (exp) ±.15(th) [ Belle] =.177 ±.43(exp) ±.1(th) [ BaBar] Belle dγ paper Mainly from neglecting annihilation topologies. N.B. Errors from fragmentation etc included in the quoted experimental error. 29

30 Tests of CPT 3

31 CPT Discrete symmetry conserved in Lorentz invariant local QFT. i.e. the SM and popular extensions. Expect CPT to be conserved based on prejudice that we have not seen it violated. But we have seen that the same prejudice had to be given up for P, C, and CP symmetries in Weak decay. Possible to construct a theory that violates CPT. Don t expect to see CPT violation, but we must look for it! Experimentally test CPT at the B factories via: Measurements of the τ + / τ lifetime. Measuring z in B decays (recall mass eigen-states): If CPT is conserved particles and antiparticles have: The same mass and lifetime. Symmetric electric charge. Opposite magentic dipole moments (or gyro-magnetic ratios for point like leptons) using samples of Hadronic B decays Di-lepton events. 31

32 CPT Discrete symmetry conserved in Lorentz invariant local QFT. i.e. the SM and popular extensions. Expect CPT to be conserved based on prejudice that we have not seen it violated. But we have seen that the same prejudice had to be given up for P, C, and CP symmetries in Weak decay. Possible to construct a theory that violates CPT. Don t expect to see CPT violation, but we must look for it! Experimentally test CPT at the B factories via: Measurements of the τ + / τ lifetime. Measuring z in B decays (recall mass eigen-states): z = i ( M M ) ( Γ Γ ) Δm ΔΓ i 2 32

33 CPT: Using hadronic B decays Similar selection of events as used for the ccs sin2β analysis (*) * * + BFlav decays: B D π ( ρ, a1 ), B J / ψk ( K K π ) CP modes: B J / ψk, ψ(2 S) KS, χ1 cks + (*) + (*) Charged B control samples: B D π, J / ψk, ψ(2 S) K, χ ck 1 compatible with CPT, CP and T conservation. 33 BaBar Collaboration, PRD 7, 127 (24)

34 CPT: Using di-lepton events Reconstruct BB pairs where both B mesons decay via b Xlν Sample includes direct b l events: lepton charge tags the B flavor. ν Lepton X B B X ν Lepton Δt = t 1 t 2 = proper time difference between the decays of the two B mesons. As B mesons mix we can have ++,, and + charge combinations for the two leptons: measure N ++, N, and N +. We can measure two asymmetries: A CPT CP SM 3 A T / CP ~1 / sensitive to ΔΓ Re( z) 34

35 CPT: Using di-lepton events Can also study variations as a function of sidereal time. 1 d sidereal z depends on the 4-momentum of the B candidate: d solar Results are compatible with CPT conservation. Results shown are from BaBar s di-lepton CPT papers Compatible with z= at 2.8σ 35

36 B VV decays (and related channels) 36

37 Angular analysis With sufficient statistics one can perform a full angular analysis: J P : B VV We define the fraction of longitudinally polarised events as: 3 d Γ dcosθ dcosθ dφ 1 2 HY ( θ, Φ) Y ( θ, Φ) m= 1,,1 m 1, m 1 1, m 2 where the H m are helicity amplitudes sin θ1sin θ2( H+ 1 + H 1 ) + cos θ1cos θ2 H * * + 2 sin θ1sin θ2[cos 2 ΦR( H+ 1H 1) sin 2 ΦI( H+ 1H 1)] sin2θ sin2 [cos ΦR ( + ) sin ΦI( * * * 1 θ2 H+ 1H H 1H H+ 1H H H * )]

38 Angular analysis Consider the tree contribution for B ρ + ρ Spin Initial state s b s d In the transversity basis we have three CP eigen-states: A = H 1 A = H + H 2 1 A = H H 2 ( ) ( ) Spectator quark has indefinite spin CP even CP odd Spin flip s are helicity suppressed: : m V m V A A : A O(1) : O : O mb mb 2 s d s u s u s d h= h= state preferred over h=+1 (overall J = ) With sufficient statistics we can measure S and C for each of these three components. If f L ~1 we just measure S and C for the longitudinal polarisation. f L m 2 V 1 2 mb = Neglecting motion within the mesons only H is allowed. Relative quark motion in the mesons gives rise to the H +1 and H -1 contributions. H +1/-1 require 1 and 2 spin flips, respectively. Ali, Kagan, Kramer, Dunietz et al., Suzuki 38

39 B VV decays B ρρ decays fit the pattern: f L f L is large for: m = K + ωρ φk 2 V 1 2 mb K * * * 2 * + ρ K f L ~.5 for some penguin dominated modes: notably φk*. What mechanism(s) result in the observed behaviour? 39

40 B φk* BaBar φk* analysis Able to simultaneously measure f L, f (and f ). K * (892) K * (143) 2 φ VV φk* has f L ~.5 and f ~.2. Doesn t fit naïve picture very well. K * (892) φ VT φk* has f L ~.9 and f ~.. Fits naïve picture. f << f in the SM. This ratio could be inverted in the presence of right handed currents. Important to study other similar decays! cos θ 1 cos θ 2 cosθ 1 S/T Kπ cosθ 2 S/T Kπ 4

41 B ωk * Belle ωk* analysis When we don t have a large signal, it is not possible to do a full angular analysis. Fit for the fraction of longitudinally polarised events (as with the ρρ α analysis from Lecture 1). Signal yield is extracted from a fit to mes, ΔE, m Kπ, and m 3π in bins of helicity angle. Perform a χ 2 fit only varying f L to extract polarisation information. Signal significance: 3. σ ( ).2 B = 1.8 ±

42 B ωk * Belle ωk* analysis When we don t have a large signal, it is not possible to do a full angular analysis. Fit for the fraction of longitudinally polarised events (as with the ρρ α analysis from Lecture 1). f L =.56 ±

43 B φρ, φφ Rare decays: φφ OZI suppressed. φρ ±, Electroweak penguin processes. Could be sensitive to new physics. Different enhancements for different scenarios: RPV SUSY/2HDM/MSUGRA BR ~ 1-9. φρ + could be enhanced by φ-ω mixing up to O(1-7 ); what about φρ? What do we use for f L when fitting the data if there is insufficient signal? i) Use prejudice from a theory calculation [OK if they agree]. ii) Scan for signal for different f L and take the largest upper limit/most significant result. Signal Yield Note: ε = ε(f L ); Fit for f L eff with a known R = ε L /ε T So: 1 For each value of f L compute the value of Nsig and its error, as well as the significance of the result, branching fraction and 9% CL upper limit. f L 43

44 Rare decays: B φρ, φφ φφ OZI suppressed. φρ ±, Electroweak penguin processes. φφ BaBar φφ, φρ analysis Could be sensitive to new physics. Different enhancements for different scenarios: RPV SUSY/2HDM/MSUGRA φρ + BR ~ 1-9. φρ + could be enhanced by φ-ω mixing up to O(1-7 ); what about φρ? φρ No signal observed. 44

45 B VV decays Have searched for a number of rare B VV decays. Many rare penguin processes are suppressed to B ~ O(1-9 ). These could be sensitive probes of NP! Also searched for B AV: a 1 ρ [< ] b 1 +/ ρ /+ [< ] Babar b 1 ρ analysis Recent theory prediction gave B(b 1 +/ ρ /+ ) ~ 15 to We have a lot to learn from VV & AV decays! 45

46 Summary The B-factories have tested the CKM mechanism to an unprecedented level: σ ρ ~ 16%, σ η ~ 4.7% ( ) ( ) CKM works at this level. Still not enough CP violation to explain the universal matter-antimatter asymmetry! Is there NP in weak interactions with (s)quarks to make up the shortfall? CPT has been experimentally tested by the B-factories. Need more precise searches for new physics and possible deviations from CKM. Rare B decays to final states with V and A are not fully understood (from experimental or theoretical perspectives). Next generations of B factories will start to build on the knowledge of BaBar and Belle soon. 46

47 Outlook BaBar has finished taking data: 467 million B pairs recorded at the Y(4S) Recorded 3fb -1 at the Y(3S) and 14.5fb -1 at the Y(2S) Performed an energy scan above the Y(4S) Belle Will record 1ab -1 at the Y(4S) Has data at the Y(1S), Y(5S) and above the Y(5S) Will be upgraded to ~1 35 (SuperKEKB) LHC-b Should start taking data in September 28. We can look forward to results soon after! SuperB Could start taking data as early as 215. Would aim to record 75 ab -1 in the first 6 years of data taking. 47

48 Alternate β and CPT Experimental References CPT Direct CP Asymmetries B Kπ B ρπ Sides V ub (Also see the HFAG web site: Semi-leptonic group page for older publications) b dγ V cb B VV decays + arxiv: , arxiv: , PRD (26), (Also see α: ρρ Refs. for Lecture 1) 48