CP violation lectures

Transcription

1 CP violation lectures MARCELLA BONA University of London Intercollegiate Postgraduate Course in Elementary Particle Physics Lecture 3

2 Outline recap on three types of CP violation recap on angles direct CP violation sides of the Unitarity Triangle extraction of the CKM parameters the LHC experiments D system 2

3 3 kinds of CP violation (recap) 1. Direct CP violation. P( B0 f ) P( B0 f ) t=0 mixing Cartoon shows the decay of a B0 or B0 into a CP eigenstate fcp. B0 B Af CP ay dec 0 t f Af t 2. Indirect CP violation (CPV in mixing). P( B0 B0 ) P( B0 B0 ) 3. CPV in the interference between mixing and decay. Need more than one amplitude to have a non zero CP violation: interference 3

4 sin2 in golden b ccs modes (recap) V*cbVcs branching fraction: (10 3) the colour suppressed tree dominates and the t penguin has the same weak phase of the tree theoretical uncertainty: S ~ sin2 C~0 model independent data driven estimation from J/ 0 data: SJ/ K0 = SJ/ K0 sin2 = ± model dependent estimates of the u and c penguin biases SJ/ K0 = SJ/ K0 sin2 ~ (10 3) H.Li, S.Mishima 4 JHEP 0703:009 (2007) SJ/ K0 = SJ/ K0 sin2 ~ (10 ) H.Boos et al. Phys. Rev. D73, (2006) 4

5 CP violation: (recap) Interference between box and tree results in an asymmetry that is sensitive to in B hh decays: h =,, Loop corrections are not negligible for Vtd* : + Loops (penguins) Vub : Vtd : Chh 0 Shh sin(2 ) Chh sin( ) 2 S hh 1 Chh sin(2 eff ) P T Measure S eff Need to determine = eff [P/T is different for each final state] 5

6 CP violation: (recap) Combining all the modes to maximize our knowledge of.. evidence of CP violation bayesian analysis: the quantity plotted is now the Probability Density Function (PDF) no CP violation observed SM = (92 ± 7) 6

7 and DK trees (recap) D(*)K(*) decays: from BRs and BR ratios, no time dependent analysis, just rates the phase is measured exploiting interferences: two amplitudes leading to the same final states some rates can be really small: ~ 10 7 Vcb (~ 2) Theoretically clean (no penguins neglecting the D0 mixing) Vub= Vub e i (~ 3) 7

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9 Time integrated CP asymmetries Charged B 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 it. We can use this technique when studying neutral B mesons decaying to a self tagging final state. limited by our knowledge of weak phases and of the strong phase differences. But there are many possible measurements that we can compare! 9

10 Direct CP violation (recap) both neutral and charged B's tagging not always necessary (charged and "self tagging" modes) higher efficiency interference between (at least) two amplitudes contributing to the same final state i: strong phase CP even i: weak phase CP odd the measured asymmetry becomes: ACP interesting interesting modes: modes: K K :: penguin+tree penguin+tree K K :: pure pure penguin penguin 10

11 Direct CP violation B0 K : Tree and gluonic penguin contributions d d Compute time integrated asymmetry = ± Experimental results from Belle, BaBar, and CDF have significant weight in the world average of this CP violation parameter. 6.1 Direct CP violation present in B decays. Unknown strong phase differences between amplitudes, means we can t use this to measure weak phases! 11

12 Direct CP violation B+ K : Color suppressed tree and gluonic penguin contributions s Experimentally measure: s + K K+ A(K ) = ± Difference between B+ and B0 asymmetries: A(K ) = ± Difference claimed to be an indication of new physics, however: Theory calculations assume that only T+P contribute to K, and C+P contribute to K. The C contribution is larger than originally expected in K. Belle K analysis For example, see G. Hou arxiv: and references therein. 12

13 Is there a k puzzle? Only SCET includes a non factorizable O( QCD/mb) charming penguin All these approaches neglect the CKM suppressed O( QCD/mb) corrections 13

14 The k amplitudes CKM enhanced CKM suppressed A(B0 K = Vts Vtb* P1(c) Vus Vub* {E1 P1GIM(u c)} A(B+ K = Vts Vtb* P1(c) + Vus Vub* {A1 P1GIM(u c)} 2 A(B+ K = Vts Vtb* P1(c) 2 A(B0 K = Vts Vtb* P1(c) Charming Penguin ~ Vus Vub* {E1+E2+A1 P1GIM(u c)} Vus Vub* {E2+P1GIM(u c)} 2 Vus Vub* ~ 4 The ingredients: The elements of the CKM matrix (from the UT analysis) Color Allowed (E1) and Color suppressed (E2) tree level emissions Charming (P1) and GIM (P1GIM) penguins Annihilation (A1) 14

15 The k amplitudes CKM enhanced CKM suppressed A(B0 K = Vts Vtb* P1(c) Vus Vub* {E1 P1GIM(u c)} A(B+ K = Vts Vtb* P1(c) + Vus Vub* {A1 P1GIM(u c)} 2 A(B+ K = Vts Vtb* P1(c) 2 A(B0 K = Vts Vtb* P1(c) Charming Penguin ~ Vus Vub* {E1+E2+A1 P1GIM(u c)} Vus Vub* {E2+P1GIM(u c)} 2 Vus Vub* ~ 4 15

16 Direct CP violation searches ACP 0 no CP violation This is a small sub set of decays where we have searched for direct CP violation. 2 observed signals (> 5 ): K and ; possible effects (> 3 ): K+, hk*0, K*0,, D(*)0K(*), and D0CPK. 16

17 CP violation: Searching for new physics sin2 has been measured to O(1 ) accuracy in b ccs decays. Can use this to search for signs of New Physics (NP) if: Identify a rare decay sensitive to sin2 (loop dominated process). Measure S precisely in that mode (Seff). Control the theoretical uncertainty on the Standard Model pollution ( SSM). Compute. In the presence of NP: SNP 0 W u,c, t s,,( KK ) b CP s 0 g B d s 0 K d S Many tests have been performed in: B d processes. B s processes. 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! 17

18 SM uncertainties on S 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 S correction is mode dependent. Most precise S correction is for B0 K0, where Stheory ~ Concentrate efforts on well understood channels. QCDF Beneke, PLB620, 143 (2005) SCET/QCDF, Williamson and Zupan, PRD74, (2006) QCDF Cheng, Chua and Soni, PRD72, (2005) SU(3) Gronau, Rosner and Zupan, PRD74, M.Bona CP violation lecture (2006) 18

19 Overview of S measurements Comparing sin2 in different physical processes, we see good agreement with the b ccs reference point. (reference point) Most of the b s penguin channels have sin2 eff < sin2. 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 50ab 1 to start performing measurements that will have comparable experimental and theoretical uncertainties in b s penguin processes. Can start to do the same with and once we have a precision measurement from one mode. 19

20 Sides of the Unitarity Triangle 20

21 Sides of the Unitarity Triangle Use theory to relate partial branching fractions to Vub for a given region of phase space. Several theoretical schemes available. 21

22 Sides of the Unitarity Triangle Use theory to relate partial branching fractions to Vcb for a given region of phase space. 22

23 Side measurements: Vcb and Vub Vub BR(B Xul ) in a limited region of phase space. similarly for Vcb F is a form factor. Need theoretical input to relate the differential rate measurement to Vcb. Reconstruct both B mesons in an event. Study the Brecoil to measure Vub. Measure BR as a function of ql2, mx, mmiss or El and use theory to convert these results into Vub. Can study modes exclusively or inclusively. Several models available to estimate Vub and Vcb The resulting values have a significant model uncertainty. 23

24 Vcb and Vub in 2015 exclusive result inclusive result inclusive result exclusive result LCHb ratio result 24

25 Unitarity Triangle analysis 25

26 Unitarity Triangle analysis in the SM SM UT analysis: provide the best determination of CKM parameters test the consistency of the SM ( direct vs indirect determinations) provide predictions for future experiments (ex. sin2, ms,...) analysis from M. Bona et al. (UTfit) JHEP0507:028,

27 the method and the inputs Bayes Theorem } } Standard Model + OPE/HQET/ Lattice QCD to go mt from quarks to hadrons M. Bona et al. (UTfit Collaboration) JHEP 0507:028,2005 hep ph/ M. Bona et al. (UTfit Collaboration) JHEP 0603:080,2006 hep ph/

28 Unitarity Triangle analysis in the SM Vcb/Vub K ms/ md md B

29 Unitarity Triangle analysis in the SM Observables Accuracy Vub/Vcb ~ 13% K ~ 0.5% md ~ 1% md/ ms ~ 1% sin2 ~ 3% cos2 ~ 15% ~ 7% ~ 11% BR(B ) ~ 19% 29

30 Unitarity Triangle analysis in the SM 95% Prob = ± = ± analysis from M. Bona et al. (UTfit) JHEP0507:028,

31 Angles vs the others = ± = ± % Prob = ± = ±

32 Compatibility plots A way to measure the agreement of a single measurement with the indirect determination from the fit using all the other inputs: test for the SM description of the flavour physics Color code: agreement between the predicted values and the measurements at better than 1, 2,...n exp = (68.3 ± 7.5) UTfit = (68.6 ± 3.7) The cross has the coordinates (x,y)=(central value, error) of the direct measurement exp = (92.2 ± 6.2) UTfit = (87.3 ± 3.9) 32

33 tensions sin2 exp = ± sin2 UTfit = ± ~1.5 Vubexp = (3.75 ± 0.46) 10 3 VubUTfit = (3.63 ± 0.13)

34 tensions Vub (excl) Vub (incl) sin2 exp = ± sin2 UTfit = ± ~1.5 Vubexp = (3.75 ± 0.46) 10 3 VubUTfit = (3.63 ± 0.13)

35 Unitarity Triangle analysis in the SM obtained excluding the given constraint from the fit Pull (# ) Observables Measurement Prediction sin ± ± ~ ± ± 3.7 < ± ± 3.9 <1 Vub ± ± 0.13 <1 Vub 103 (incl) 4.40 ± 0.31 ~ 2.3 Vub 103 (excl) 3.42 ± 0.22 <1 Vcb ± ± 0.7 <1 BK ± ± <1 BR(B )[10-4] 1.14 ± ± 0.07 ~ 1.3 BR(Bs ll)[10-9] 2.8 ± ± 0.15 ~ 1.4 BR(Bd ll)[10-9] 0.39 ± ± ~ 1.7 ASLs ± ± <1 A ± ± 0.02 ~

36 standard model predictions: B BR(B ) = (1.14 ± 0.22) 10 4 SM prediction enhanced or reduced by factor rh: ~1.4 indirect determinations from UT BR(B ) = (0.81 ± 0.07) 10 4 M.Bona et al, [hep ph] 36

37 more standard model predictions from CMS+LHCb from CMS+LHCb BR(Bs ) = (2.8 ± 0.7) 10 9 ~1.4 indirect determinations from UT BR(Bs ll) = (3.88 ± 0.15) 10 9 time integration included, but no corrections BR(Bd ) = (3.9 ± 1.6) ~1.7 BR(Bd ll) = (1.13 ± 0.07)

38 Unitarity triangle fit beyond the SM 1. fit simultaneously for the CKM and the NP parameters (generalized UT fit) add most general loop NP to all sectors use all available experimental info find out NP contributions to ΔF=2 transitions 2. perform a ΔF=2 EFT analysis to put bounds on the NP scale consider different choices of the FV and CPV couplings 38

39 generic NP parameterization: SM Bd and Bs mixing amplitudes (2+2 real parameters): Aq =C B e 2i B q q A SM q e 2i CB e 2i B s SM q = 1 ANP q A SM q s = e B s H NP mq /K =C B / m mq/ K SM K =C KSM A Bd J / K S CP Bs SM A 2i NP =1 SM q A NP e A SM e 2i s SM 2i q e assume NP only in loop K =sin 2 B AqSL =Im q12 / Aq SM eff 2i q q Observables: q NP B s H eff H eff B s d A Bs J / CP ~sin 2 s B s q / mq =Re q12 / Aq 39

40 NP analysis results = ± = ± degeneracy of broken by ASL SM is = ± = ±

41 NP parameter results K system dark: 68% light: 95% SM: red cross C K = 1.07 ± 0.16 Aq=C B e q CBd = 1.08 ± 0.16 Bd = ( 2.1 ± 3.2) 2i ϕ B q A SM q e SM 2i ϕ q CBs vs Bs CBs = 1.06 ± 0.08 CBd vs Bd Bs = (1.4 ± 2.0) 41

42 NP parameter results ( Aq = 1+ NP Aq A SM q e NP SM ) 2i(ϕq ϕq ) SM q A e SM 2i ϕq dark: 68% light: 95% SM: red cross The ratio of NP/SM amplitudes is: < prob. in Bd mixing < prob. in Bs mixing 42

43 Testing the new physics scale At the high scale new physics enters according to its specific features At the low scale use OPE to write the most general effective Hamiltonian. the operators have different chiralities than the SM NP effects are in the Wilson Coefficients C NP effects are enhanced up to a factor 10 by the values of the matrix elements especially for transitions among quarks of different chiralities up to a factor 8 by RGE M. M. Bona Bona et et al. al. (UTfit) (UTfit) JHEP JHEP 0803:049, :049,2008 arxiv: arxiv:

44 Effective BSM Hamiltonian for F=2 transitions The Wilson coefficients Ci have in general the form Putting bounds on the Wilson coefficients give insights into the NP scale in different NP scenarios that enter through Fi and Li Fi: function of the NP flavour couplings Li: loop factor (in NP models with no tree level FCNC) : NP scale (typical mass of new particles mediating F=2 transitions) 44

45 Contribution to the mixing amplitutes analytic expression for the contribution to the mixing amplitudes arxiv: : for magic numbers a,b and c, = S( )/ S(mt) analogously for the K system to obtain the p.d.f. for the Wilson coefficients Ci( ) at the new physics scale, we switch on one coefficient at a time in each sector and calculate its value from the result of the NP analysis. 45

46 Testing the TeV scale The dependence of C on changes on flavour structure. we can consider different flavour scenarios: Generic: C( ) = / 2 Fi~1, arbitrary phase NMFV: C( ) = FSM / 2 Fi~ FSM, arbitrary phase MFV: C( ) = FSM / 2 F1~ FSM, Fi 1~0, SM phase (Li) is the coupling among NP and SM ~ 1 for strongly coupled NP ~ W ( S) in case of loop coupling through weak (strong) interactions If no NP effect is seen lower bound on NP scale if NP is seen upper bound on NP scale FSM is the combination of CKM factors for the considered process 46

47 lower bounds on the scale Generic: C( ) = / 2, Fi~1, arbitrary phase ~ 1 for strongly coupled NP To obtain the lower bound for loop mediated contributions, one simply multiplies the bounds by s ( 0.1) or by W ( 0.03). ~ W in case of loop coupling through weak interactions Lower bounds on NP scale (in TeV at 95% prob.) Non perturbative NP > TeV NP in W loops > TeV 47

48 lower bound on the scale NMFV: C( ) = FSM / 2, Fi~ FSM, arbitrary phase ~ 1 for strongly coupled NP To obtain the lower bound for loop mediated contributions, one simply multiplies the bounds by s ( 0.1) or by W ( 0.03). ~ W in case of loop coupling through weak interactions Lower bounds on NP scale (in TeV at 95% prob.) NP in W loops > 2.9 TeV Non perturbative NP > 96 TeV 48

49 B Physics beyond the B Factories This naturally splits into two categories of experiment (with overlapping physics reach): B Physics experiments at the LHC Amongst other physics, ATLAS and CMS will study B mesons (as long as the muon triggers have low enough threshold) LHCb dedicated B physics experiment. B Physics experiments not at the LHC a e+e Super B Factory work in progress Super KEK B in Japan 49

50 B Physics Experiments at the LHC There are 3 B physics experiments at the LHC: LHCb is a dedicated forward arm spectrometer (a specialised detector with the aim of doing a fantastic job at studying B physics from pp collisions). The pp beams are defocused near the interaction point of LHCb, so the luminosity of collisions is a lot lower than at the GPDs. ATLAS and CMS are general purpose detectors. The cross section for B hadron production is very large, and the luminosity of the pp collisions at these detectors is the same as for the rest of the GPD physics programme for these two experiments

51 LHCb Detector Single arm spectrometer design. UK Groups: Bristol Cambridge Edinburgh Imperial College Liverpool Glasgow Oxford RAL running at a reduced luminosity as the beams are locally defocused: design luminosity (already reached) cm 2s 1 51

52 ATLAS and CMS detectors Both of these GPDs have almost a 4 coverage Very forward b jets are lost down the beam pipe Good identification of b quarks is essential for tagging in new physics searches (e.g. the H bb search). The physics programmes of both experiments will be dominated by direct new physic searches, but they will also be in a position to play an important role in searching for rare B decays, and furthering our understanding of B physics. 52

53 Possible Future Experiments Planned future experiment: Super KEK B, KEK, Japan: aim to collect a factor of times the data of BaBar and Belle. The detector technology choice is similar to BaBar and Belle (with upgrades to deal with the expected increase in data rate). Accelerator R&D is underway in order to move a step closer to realising the luminosity increase required to have a SuperB factory. KEK: incremental upgrades to KEK B are being tested 53

54 CP violation in the D system B factories have measured the D mixing (2007) The time integrated CP asymmetry have contributions from both direct CP violation (in the decays) and indirect CP violation (in the mixing or in interference) In the SM, indirect CP violation in charm is expected to be very small and universal between CP eigenstates: predictions of about O(10 3) for CPV parameters Direct CP violation can be larger in SM: it depends on final state (on the specific amplitudes contributing) negligible in Cabibbo favoured modes (SM tree dominates everything) In singly Cabibbo suppressed modes: up to O( ) plausible Both can be enhanced by NP, in principle up to O(%) 54

55 Where to look for direct CP violation Remember: need (at least) two contributing amplitudes with different strong and weak phases to get CPV. D0 K+K and D0 + decays: Singly Cabibbo suppressed modes with gluonic penguin diagrams Several classes of NP can contribute... but also non negligible SM contribution 55

56 No CP violation measured so far 56

57 s and s measurement from Bs J/ The time evolution of the meson BS and BS is described by the superposition of BH and BL states, with masses ms ± ms/2 and lifetimes S ± S /2. These states deviate from defined values CP = ± 1, as described in the SM by the mixing phase S ( S = 2 S), SM prediction (fit): S = ± rad S = ± ps 1 New Physics can contribute to S, and change the ratio S / ms. In general, the decay to a final state that is coupled to BS and/or BS, exhibits fast oscillations driven by ms. Interference between amplitudes for both states generates CP violation, and conveys information on S. If B/B flavour at production is not determined (not tagged), the fast oscillations cannot be observed, but interference terms remain if the final state is described by a superposition of amplitudes of different CP values. 57

58 angular analysis in Bs J/ In the decay BS(BS) J/ l+l K+K different components in the angular distributions amplitudes correspond to CP = +1 or 1 The transversity angles are used to describe the angular distributions 58

59 angular analysis in Bs J/ Angular analysis as a function of proper time and b tagging Similar to Bd measurement in Bd J/ K* Additional sensitivity from the s terms (negligible for Bd) Dunietz et al. Phys.Rev.D63:114015,2001 Ambiguities for s s, s s, cos( ) cos( ) transversity basis: W(,, ) and : direction of the + from J/ decay : between the decay planes of J/ and 59

60 angular analysis in Bs J/ 60

61 Look at the future ( ) ~ 0.9 (Vcb) ~ 1.1% (Vub) ~ 2.2% errors from tree only fit on and : ( ) = [currently 0.051] ( ) = [currently 0.050] errors predicted from Belle II + LHCb upgrade ( ) ~ 0.2 (BK) ~ 0.1% (fb BB) ~ 0.5% errors from 5 constraint fit on and : ( ) = [currently 0.034] ( ) = [currently 0.015] 61

62 Summary Points to consider to measure a CP violating asymmetry. Need more than one amplitude (more than one Feynman diagram) to have a non zero CP violation signal. Neutral mesons can be used to measure the weak phase cleanly (usually). Charged mesons can be used to measure direct CP violation. Knowledge of strong phases limits how you can interpret these measurements in terms of the weak phases. Need a model, and many measurements to say anything sensible. Even then you will have a large theoretical uncertainty. You can count the CKM vertex factors in the Feynman diagrams to tell you relative sizes of decays that you expect (This works for tree level processes. You need to consider colour / Zweig supression for more detailed guesses). 62

63 Summary (II) The B factories have tested the CKM mechanism to an unprecedented level: ~ 16%, 15% CKM works at this level. ~ 4.7% 3% Still not enough CP violation to explain the universal matter antimatter asymmetry! Need more precise searches for new physics and possible deviations from CKM. the unitarity triangle fit is an useful tool to exploit all the flavour physics contributions to extract SM and NP parameters and also insight on the NP scale. LHCb and the next generation B factory will start to build on the knowledge of BaBar and Belle soon. 63

64 Conclusions The study of CP violation is a fundamental part of particle physics, and cosmology. It revolves around EPR experiments with correlated B, D, K, mesons, and quantum interference studies. We don t really understand it. The CKM mechanism works well but it is incomplete. It is only a small part of the story. We don t know if CP violation in leptons, or some new physics scenario really explains the matter antimatter asymmetry questions arising from the Big Bang. Eventually we hope to understand the reason behind this conundrum, and in doing so we will either find new particle physics, or new cosmological effects. Given that its very hard to have an asymmetry in the big bang that doesn t get washed out by inflation the money is on new physics effects/particles to be discovered! 64

65 backup 65

66 Side measurements: Vub Vub BR(B Xul ) in a limited region of phase space. Reconstruct both B mesons in an event. Study the Brecoil to measure Vub. Measure BR as a function of ql2, mx, mmiss or El and use theory to convert these results into Vub. Can study modes exclusively or inclusively. Several models available to estimate Vub The resulting values of Vub have a significant model uncertainty. 66

67 Exclusively reconstructed b ul If we fully reconstruct one B meson in an event, then Study B decays to: Fully reconstruct BRECO Extract yields from m2miss q 2 8(GeV ) 2 with a single in the event, we can infer P and reconstruct the. 8 q 2 16(GeV ) 2 q 2 16(GeV ) 2 (reduces form factor dependence) Clean signals but low efficiency Fully Reconstructed BRECO decay Then compute Vub. Lepton B0 X B0 Semi-leptonic b ul decay Use the beam energy to constrain P to effectively reconstruct from the missing energy momentum: mmiss m = 0. 67

68 Vub: Using q2 distribution Use B l decays BR(B0 l ) = Light cone sum rules Unquenched LQCD Unquenched LQCD: (Vub)EXPT ~ 5% (Vub)THEORY ~ 11 to 17% Experiments have also studied higher mass meson l decays 68

69 Vub: Using MX distribution High background from cl decays. Kinematic cuts are used to suppress background. Use Operator Product Expansions to translate measured branching fractions to Vub. Measure branching fraction in different kinematic regions. B Xcℓ background All D* D D** Xu 69

70 Side measurements: Vcb Use the differential decay rates of B D*l to determine Vcb : F is a form factor. Need theoretical input to relate the differential rate measurement to Vcb. Reconstruct BaBar D*e paper m mk mk Measurement is not statistically limited, so use clean signal mode for D K decay only. Extract signal yield, F(1) Vcb and from 3D binned fit to data. 70

71 Side measurements: Vcb Use the differential decay rates of B Dl to determine Vcb : G is a form factor. Need theoretical input to relate the differential rate measurement to Vcb. Use a sample of fully reconstructed tag B mesons, then look for the signal. Improves background rejection, at the cost of signal efficiency. Reconstruct the following D decay channels: is related to q2 of the B meson to the D 71

72 Vcb B Dl G(1) Vcb =( ) 10 3 Vcb =( ) 10 3 Using G(1)= from Okamoto et al., NPPS 140, 461 (2005). B D*l F(1) Vcb =( ) 10 3 Vcb =( ) 10 3 Using F(1)= from Laiho, arxiv: [hep lat]. 72