Heavy Quark Physics. Cracking the Standard Model? Matthias Neubert Cornell University. CTEQ Summer School 2005 Puebla Mexico May 2005

Transcription

1 Heavy Quark Physics Cracking the Standard Model? Matthias Neubert Cornell University CTEQ Summer School 2005 Puebla Mexico May 2005 May 25, 2005 CTEQ Summer School 1

2 Lecture 1 Flavor questions Beyond the Standard Model Precision measurements in the quark sector A bit of QCD May 25, 2005 CTEQ Summer School 2

3 1. Flavor Questions Generations, Hierarchies, CP Violation, Baryogenesis May 25, 2005 CTEQ Summer School 3

4 Problem of generations Gauge forces in SM do not distinguish betw. fermions of different generations: e,µ have same electrical charge Quarks have same color charge All equal, but not quite equal Why generations? Why 3? A new quantum number? May 25, 2005 CTEQ Summer School 4

5 Hierarchies Masses of quarks and leptons Fermion masses and mixings constitute many of the parameters of the SM Neutrino masses may indicate the relevance of a very large mass scale (GUT, see-saw mechanism), or the existence of extra dimensions! May 25, 2005 CTEQ Summer School 5

6 Fermions of different generations can communicate via flavor-changing weak interactions New parameters (mixing angles, phases) (d L,s L,b L ) k W - V ik Cabibbo-Kobayashi-Maskawa matrix element (u L,c L,t L ) i May 25, 2005 CTEQ Summer School 6

7 New hierarchies: V CKM 1 λ 3 λ λ 1 2 λ 3 λ 2 λ 1 small U MNS ε 1 1 Possible explanation of CP violation! Properties of matter CP Properties of antimatter Needs 3 generations! May 25, 2005 CTEQ Summer School 7

8 May 25, 2005 CTEQ Summer School 8

9 The cosmic connection: Baryon asymmetry Matter Antimatter 10,000,000,000 10,000,000,000 Early Universe May 25, 2005 CTEQ Summer School 9

10 The big annihilation Today: us 1 Sakharov criteria: Baryon-number violation CP violation Non-equilibrium May 25, 2005 CTEQ Summer School 10

11 SM satisfies prerequisites for baryogenesis: Baryon-number violation at high temperatures ( B= L) Non-equilibrium during phase transitions (symmetry breaking) CP violation in the quark and lepton sectors However: CKM phase in the quark sector is not sufficient to account for the baryon asymmetry in the Universe Need for additional CP-violating couplings! May 25, 2005 CTEQ Summer School 11

12 2. Beyond the Standard Model Complementarity of High Energy and High Luminosity May 25, 2005 CTEQ Summer School 12

13 Exploring Nature Colliders (Tevatron, LHC, ILC) + Factories (BaBar, Belle, BTeV, LHC-b, Super-B-Factories, Neutrinos, Kaons) new particles new flavor- and CP-violating interactions May 25, 2005 CTEQ Summer School 13

14 Future role of flavor physics Flavor physics can probe effects of New Physics at scales of TeV, far extending beyond the range of LHC and ILC Many flavor- and CP-violating couplings can only be measured at highest luminosity May 25, 2005 CTEQ Summer School 14

15 Examples: top & neutrinos Top-Quark: Direct production proves existence und gives mass and spin Mass predicted using electroweak precision measurements Couplings V ts ~0.04 and V td ~0.01 and CP-violating phase can only be measured in B- and K-physics Neutrinos: Existence known since long, but only discovery of flavorchanging interactions (neutrino oscillations) brought far-reaching discoveries Possibility of CP violation in the lepton sector; leptogenesis Completely different hierarchy as in the quark May 25, 2005 CTEQ Summer School 15

16 Empirical fact Data show no compelling evidence for Physics beyond the Standard Model: Electroweak precision tests Precision measurements in flavor physics Either: New Physics decouples very effectively: SUSY, split SUSY Or: New Physics lives at scales of several TeV (apart from a few possibly lighter particles) Extra dimensions, little Higgs, technicolor May 25, 2005 CTEQ Summer School 16

17 Flavor/CP-violating couplings Generic properties: Many new particles (SUSY partners, Kaluza-Klein partners, new gauge bosons, new fermions, etc.) at the TeV scale Generation-changing couplings of new particles are not diagonal after field redefinitions of SM fields There must be effects in the flavor sector at some level of precision! May 25, 2005 CTEQ Summer School 17

18 3. Precision Measurements in the Quark Sector Cabibbo-Kobayashi-Maskawa Matrix, Unitarity Triangle, Standard Analysis, Future Potential May 25, 2005 CTEQ Summer School 18

19 Wolfenstein parameterization and unitarity triangle CKM matrix can be parameterized in terms of 4 real quantities: b-sector CPV V V V ud cd td V V V us cs ts V V V ub cb tb 2 1 λ 2 = λ 3 Aλ (1 ρ iη) λ=0.22, A=0.84 well determined 2 1 λ 2 2 Aλ 3 Aλ ( ρ iη) 2 4 Aλ + O( λ ) 1 May 25, 2005 CTEQ Summer School 19 λ t-sector CPV Complex couplings CP violation! (ρ,η) are being determined at the B-factories

20 Experimental information on (ρ,η) can be presented as a unitarity triangle : V ud V ub* +V cd V cb* +V td V tb* = 0 (ρ,η) α * ~V ub ub * ~V td td γ (0,0) (1,0) β May 25, 2005 CTEQ Summer School 20

21 The standard analysis 1 m d m s & m d η 0 ε K V ub /V cb sin 2β WA ε K -1 C K M f i t t e r May 25, 2005 CTEQ Summer ρschool 21

22 The standard analysis 1 m d m s & m d η 0 ε K V ub /V cb Determination of V ub in semileptonic B decays sin 2β WA Theoretical uncertainties due to hadronic binding effects ε K l -1 C K M V ub W f i t t e r b -1 0 B May 25, 2005 CTEQ Summer ρ d School 22 u ν π +

23 The standard analysis 1 m d Determination of V td in B 0 -B 0 ε mixing K η Theoretical uncertainties due to hadronic binding effects V tb b W d -1 B 0 t t B 0 d W b * C K M V V f i t t e r td tb V * td 0 V ub /V cb sin 2β WA m s & m d ε K May 25, 2005 CTEQ Summer ρschool 23

24 The standard analysis 1 m d m s & m d η 0-1 ε K V ub /V cb C K M f i t t e r sin 2β WA Determination of Im(V td2 ) in K 0 -K 0 mixing Theoretical uncertainties due ε K to hadronic binding effects s W d K 0 t t K d W 2 s May 25, 2005 CTEQ Summer ρschool Vtd * V 24 V ts V * td ts

25 The standard analysis 1 m d m s & m d η Determination of sin2β in B 0 -B 0 mixing 0-1 ε K V ub /V cb No theoretical uncertainties! sin 2β WA ε K C K M f i t t e r May 25, 2005 CTEQ Summer ρschool 25

26 Measurement of sin2β CP-violating phases can only be probed via quantum-mechanical interference Simplest case: Interference of B decay and B 0 -B 0 mixing for transitions into a CP eigenstate f B 0 B 0 If decay amplitude A has a single CP-violating phase φ A, A A f then: [ ] Γ( B with: 0 ( t) S f ) e t/ τb ( f A [ 1[ ± ] S( f )sin( m t) ] ) =± sin 2( β ϕ ) May 25, 2005 CTEQ Summer School 26 B

27 How does this work? V tb b W d B 0 t t B 0 d W b * V V td V * td tb Schrödinger equation for B 0, B 0 : Time evolution of a state B 0 at time t=0: 2 decay modes: B 0 f (A) and B 0 f (A) May 25, 2005 CTEQ Summer School 27

28 How does this work? Amplitude for decay of this state into final state f after some time t>0: Corresponding decay rate (assume A~e iφ A, A~e -i φ single weak phase): A May 25, 2005 CTEQ Summer School 28

29 A Time-dependent CP asymmetry: CP ( t) Γ( B = Γ( B = S( 0 0 ( t) f ( t) f f )sin( m ) Γ( B ) +Γ( B t) ( t) f ( t) f Direct determination of CP-violating phases, even without knowledge of decay amplitudes! B 0 0 ) ) Golden decay mode: B J/ψ K S B 0 b W d c s Amplitude is real to an excellent approximation, i.e. φ A =0 c J/ψ K S Direct determination on sin2β, practically without theoretical uncertainties (~1%) May 25, 2005 CTEQ Summer School 29

30 CP violation visible with the naked eye! 0 0 a) 0 50 S 0 0 a) B S 0 0 J/ψK 0 a) S tags S B 0 0 c1 0 S tags 0 0 ψ(2s)k 0 c1 B 0 S tags B 0 S 0 χ c1 K S S 0 b) b) 50 0 b) tags B 0 0 tags tags c) 0.5 c) 0.5 c) d) 0 0 L d) B 0 0 J/ψK L d) L 0 tags 25 B 0 tags tags 0 e) e) e) 0 tags 25 B 0 tags tags 0 f) 0.5 f) 0.5 f) t t (ps) t (ps) (ps) BaBar (2001) sin2φ. sin2φ 1. sin( m d t) sin2φ 1. sin( m d t) 1 sin( m d t) Asymmetry Asymmetry Asymmetry (a) (a) Combined (a) Combined Combined (b) (cc)k (b) (cc)k S (ξ f = 1) (b) (cc)k S (ξ f = 1) S (ξ f = 1) (c) (c) J/ψK J/ψK L (ξ f = +1) (c) J/ψK L (ξ f = +1) L (ξ f = +1) (d) (d) Non-CP sample 1 (d) Non-CP Non-CP sample sample f +1 q. f +1. ξ f = +1. f 1 q. f 1. ξ f = May 25, 2005 CTEQ Summer t t (ps) (ps) School 30 t (ps) 1/N 1/N.. 1/N. dn/d( t) Belle (2001) t t (ps) t (ps) (ps) Combined: sin2β=0.73±0.04

31 Combination So far, all measurements are consistent with each other CKM mechanism established as the dominant contribution to flavor-changing interactions Confirmation of CP violation in the t sector of the CKM matrix, i.e., Im(V td ) 0 η ε K V ub /V cb C K M f i t t e r m d sin 2β WA m s & m d ρ ε K May 25, 2005 CTEQ Summer School 31

32 Future potential Probe of new Physics in B s -B s mixing at Tevatron (hopefully ) and/or LHC Expect larger New Physics effects in b s FCNC transitions as compared with b d True for B=2 and B=1 (2nd lecture) May become the most important measurement at the Tevatron! May 25, 2005 CTEQ Summer School 32

33 Future potential Greater precision on V ub : Recent theoretical work using soft-collinear effective theory allows precision determination from inclusive B X u lν decay with theory errors at the 5% level First measurements using this technology have just appeared (April-May 2005), with combined errors of about 10% Comparison with β will test SM with unprecedented precision [Bosch, Lange, MN, Paz] May 25, 2005 CTEQ Summer School 33

34 Impact of precise V ub Realistic: δ V ub : ±7% May 25, 2005 CTEQ Summer School 34

35 4. A bit of QCD Soft-Collinear Factorization in Inclusive B Decays May 25, 2005 CTEQ Summer School 35

36 Basics Separation of scales ( factorization ) is crucial to many applications of QCD Q 2» Λ QCD 2 Wilsonian OPE: integrate out heavy particles or large virtualities (Fermi theory, HQET, correlators at large Q 2 ) Expansion in (Λ QCD2 /Q 2 ) n and α s (Q 2 ) May 25, 2005 CTEQ Summer School 36

37 Basics Complication for jet-light physics: large energies and momenta, but small virtualities e + e - jets, B light particles, Light-cone kinematics How to integrate out short-distance physics in a situation where p µ is large, but p 2 small? May 25, 2005 CTEQ Summer School 37

38 Challenge Construct short-distance expansions for processes involving both soft and energetic light partons B Soft: p soft ~ Λ QCD b Collinear: p 2 col «E 2 col p soft p col ~E col Λ: semi-hard scale lν jet Technology: effective field theory, OPE, RG May 25, 2005 CTEQ Summer School 38

39 Soft-collinear effective theory Effective Lagrangian for this kinematics Systematic power counting in λ=λ QCD /2E jet Operators classified in terms of their scaling with λ More complicated than previous heavy-quark expansions Expansion in non-local string operators integrated over light-like field separation Many degrees of freedom [Bauer, Pirjol,Stewart] May 25, 2005 CTEQ Summer School 39

40 Soft-collinear factorization Separation of short- and long-distance physics order by order in 1/m b : [Korchemsky, Sterman] [Lee, Stewart] [Bosch, MN, Paz] Hard functions (~m b ) Jet functions (~ m b ) Soft functions (~ ) May 25, 2005 CTEQ Summer School 40

41 Scale separation Master formula for inclusive decay B-decay rates: Γ ~ H(µ h ) * U(µ h,µ i ) * J(µ i ) * U(µ i,µ 0 ) * S(µ 0 ) QCD SCET (RG evolution) HQET (RG evolution) Shape Function Perturbation theory Non-perturbative physics May 25, 2005 CTEQ Summer School 41

42 Example: B X s γ decay Photon spectrum: Jet function: May 25, 2005 CTEQ Summer School 42

43 Example: B X s γ decay Hard function: May 25, 2005 CTEQ Summer School 43

44 Nonperturbative input Shape function of B meson (usual parton distribution function) can be measured with good precision in B X s γ decay Use result to predict B X u lν decay spectra Extraction of V ub Other applications: very precise determination of m b from moments of B X s γ photon spectrum: m b SF = (4.68 ± 0.03 th ± 0.07 exp ) GeV May 25, 2005 CTEQ Summer School 44

45 Lecture 2 Rare hadronic B decays Departures from the Standard Model? Conclusions May 25, 2005 CTEQ Summer School 45

46 1. Rare Hadronic B Decays Determination of γ, Topological Amplitudes, Penguin Zoology May 25, 2005 CTEQ Summer School 46

47 Rare exclusive B decays Precise determination of the phase V ub ~e -iγ is difficult ( LHC-b, Super-B-factories) clean measurement à la sin2β possible at LHC (?) Independently, important information can be gained from rare hadronic B M 1 M 2 decays Theoretically challenging, since hadronic binding effects must be controlled Much recent progress! May 25, 2005 CTEQ Summer School 47

48 Flavor topologies Tree: Penguin: Electroweak! b W gz d d u u π - B 0 π + b W t,c,u d u u π - B 0 π + May 25, 2005 CTEQ Summer School 48 d

49 Beware of penguins May 25, 2005 CTEQ Summer School 49

50 Amplitude interference Rates for many charmless B decays are characterized by significant interference of tree and penguin topologies: Amplitude: Α = iδ iγ Te e + Pe + P 1 iδ 2 iδ 3 EW e Rate: Asymmetry: Γ( B f ) +Γ( B f ) ~ cosγ cos( δi δj) Γ( B f ) Γ( B f ) ~ sinγ sin( δi δj) May 25, 2005 CTEQ Summer School 50

51 Reality is far more complicated: b W B 0 π + Until few years ago such nonleptonic decays were believed to be theoretically intractable Recent developments: QCD factorization [Beneke, Buchalla, MN, Sachrajda 1999] Soft-Collinear Effective Theory [Bauer, Fleming, Luke, Pirjol, Stewart 2000; Beneke et al. 2002; Hill, Neubert 2002] Systematic treatment (Λ QCD /m b expansion) d u d u π - May 25, 2005 CTEQ Summer School 51

52 QCD factorization formula First-principles calculation of decay amplitudes and their rescattering phases in heavy-quark limit May 25, 2005 CTEQ Summer School 52

53 How well does it work? Compare theory predictions from 2003 (for fixed set of input parameters) with all available present experimental data Find good global agreement Heavy-quark limit appears to be a good first approximation to the intricate dynamics of these decays May 25, 2005 CTEQ Summer School 53

54 B(B Kπ, ππ, KK) K0 K0 K + K K + K 0 π 0 π 0 π + π π + π 0 K0π0 K + 0 π K + π K 0 π Branching Ratio x 10 6 May 25, 2005 CTEQ Summer School 54

55 B(B Kπ, ππ, KK) K0 K0 K + K K + K 0 π 0 π 0 π + π π + π 0 K0π0 K + 0 π K + π K 0 π Branching Ratio x 10 6 May 25, 2005 CTEQ Summer School 55

56 B(B (η, η )(K ( ), π, ρ)) B(B (K, ρ,ω, φ)(π, K,η, η )) φη φπ 0 φπ + ηk 0 φk 0 ηρ 0 φk + ηπ 0 η π 0 η ρ0 η π + ωπ 0 ωk + ρ 0 π 0 ωπ + ωk0 η K 0 ρ 0 π + ρ + π 0 ηπ + η K + ρ + π ηk + ηρ + ηk 0 η ρ + ηk + K 0 π 0 K + ρ 0 K + π K 0 π + K + π0 K + ρ η K0 η + K K 0 ρ 0 K 0 ρ Branching Ratio x Branching Ratio x 10 6 May 25, 2005 CTEQ Summer School 56

57 B(B (η, η )(K ( ), π, ρ)) B(B (K, ρ,ω, φ)(π, K,η, η )) φη φπ 0 φπ + ηk 0 φk 0 ηρ 0 φk + ηπ 0 η π 0 η ρ0 η π + ωπ 0 ωk + ρ 0 π 0 ωπ + ωk0 η K 0 ρ 0 π + ρ + π 0 ηπ + η K + ρ + π ηk + ηρ + ηk 0 η ρ + ηk + K 0 π 0 K + ρ 0 K + π K 0 π + K + π0 K + ρ η K0 η + K K 0 ρ 0 K 0 ρ Branching Ratio x Branching Ratio x 10 6 May 25, 2005 CTEQ Summer School 57

58 π + π π + K + π + π K + KSKS ρ + ρ 0 K + π π 0 K + K K CP Asymmetry in Charmless B Decays π 0 π 0 K + π 0 π + π 0 η π + η K + ηk + ηρ + ηk 0 φk 0 φk + φk + ωπ + ωk + K + ρ 0 K 0 ρ + K + ρ ρ + π 0 K + π ρ 0 π + ηπ + ηk + K 0 π + K + π sll sγ K γ

59 π + π π + K + π + π K + KSKS ρ + ρ 0 K + π π 0 K + K K CP Asymmetry in Charmless B Decays π 0 π 0 K + π 0 π + π 0 η π + η K + ηk + ηρ + ηk 0 φk 0 φk + φk + ωπ + ωk + K + ρ 0 K 0 ρ + K + ρ ρ + π 0 K + π ρ 0 π + ηπ + ηk + K 0 π + K + π sll sγ K γ

60 Extraction of γ=arg(v ub* ) Decays B ππ, πρ are dominated by tree topologies In limit where penguin amplitudes are neglected, decay amplitudes have phase φ A =-γ, and hence time-dependent CP asymmetries measure sin2(β+γ) Use QCD factorization to estimate penguin pollution May 25, 2005 CTEQ Summer School 60

61 Extraction of γ in B πρ decay [Beneke, MN] B PV modes have smaller penguin contributions than B PP modes Smaller theory uncertain-ties when γ is extracted from timedependent rates in B πρ decays Result: γ = (62 ± 8) o B πρ B ππ Old data New data Old data New data May 25, 2005 CTEQ Summer School 61

62 Impact of precise γ Realistic: δγ: ±8 o (better at LHC-b?) May 25, 2005 CTEQ Summer School 62

63 2. Departures from the Standard Model? Quest for New Physics May 25, 2005 CTEQ Summer School 63

64 Searching for the unknown So far, all measurements in the flavor sector are in agreement with the SM However, there are tantalizing hints of New Physics effects in some rare, penguindominated decays Not in contradiction with anything we know from other processes (e.g., B X s γ) Experimental situation stabilizes, and theory is under good control May 25, 2005 CTEQ Summer School 64

65 CP asymmetry in B ΦK S Interference of mixing and decay: Penguin graph is real to very good approximation! B 0 B 0 ΦK S Phase structure identical to the decay B J/ψ K S Model-independent result: B 0 b W t,c,u g,z d s s s Φ K S S(ΦK S ) - S(J/ψ K S ) = 0.02±0.01 S(ΦK S ) - S(J/ψ K S ) = 0.02±0.01 [Beneke, MN] May 25, 2005 CTEQ Summer School 65

66 It s been a rollercoaster! May 25, 2005 CTEQ Summer School 66

67 Experimental situation: (prior to LP 03) S(ΦK S ) = -0.18±0.51±0.07 BaBar -0.38±0.41 S(ΦK S ) = -0.73±0.64±0.22 Belle S(ΦK S ) - S(J/ψ K S ) = -1.11±0.41 (2.8σ) Constraint from sin2β[φk 0 S] confidence level 1 1 Standard SM fit η CK M f i t t e r ρ May 25, 2005 CTEQ Summer School 67

68 Experimental situation: (after LP 03) S(ΦK S ) =+0.45±0.43±0.07 BaBar -0.15±0.33 S(ΦK S ) = -0.96±0.50±0.10 Belle S(ΦK S ) - S(J/ψ K S ) = -0.88±0.33 (2.7σ) Belle data [press release] Standard Model May 25, 2005 CTEQ Summer School 68

69 Experimental situation: (after ICHEP 04) S(ΦK S ) =+0.50±0.25±0.06 BaBar S(ΦK S ) =+0.06±0.33±0.09 Belle S(ΦK S ) - S(J/ψ K S ) = -0.46±0.25 (1.8σ) 0.27±0.25 But, trends for deviations are also seen in other b s penguin modes, e.g. a 3σ effect for η K S from BaBar! May 25, 2005 CTEQ Summer School 69

70 New Physics? s-penguin average at 2.7σ different from sin2β[cc] (BABAR) Similar difference at 2.4 σ seen by Belle [A. Hoecker, ICHEP 2004] B φk 0 0 B K K K B η K 0 0 B f K B π K May 25, 2005 CTEQ Summer School 70

71 A year later May 25, 2005 CTEQ Summer School 71

72 7 reasons for excitement! Theory Avg.: 0.42±0.08 May 25, 2005 CTEQ Summer School 72

73 Measurements now consistent! Deviation is 3.8σ!!! May 25, 2005 CTEQ Summer School 73

74 In all cases Possible explanation in terms of new, CP-violating flavor-changing neutral currents (FCNC) of the type b sqq, preferrably with (qq) in flavor non-singlet configuration ( trojan penguins ) Predicted in a variety of theories, e.g. SUSY (quark-squark-gluino couplings) and extra dimensions (Kaluza-Klein Z ) [Grossman, Kagan, MN 1999] May 25, 2005 CTEQ Summer School 74

75 Trojan Penguins In the SM, b sqq transitions with q=d,s=u are mediated exclusively by electroweak penguins Extensions of the SM can contain such processes without α EM suppression Sensitivity to large scales: e.g., gluino-squark box graphs in SUSY: M NP 2 = (α s /α EM ) M W 2 New Physics can easily compete with the SM! May 25, 2005 CTEQ Summer School 75 b q ~ D i g ~ ~ g ~ D k s q

76 3. Conclusions Summary and Outlook May 25, 2005 CTEQ Summer School 76

77 Summary Precision measurements in the flavor sector (quarks and leptons) complement the search for New Physics at high energy and are an indispensable part of the exploration of the TeV scale The determination of the CKM matrix and tests of the CKM mechanism have reached a new quality: Discovery of CP violation in both the t and b sectors of the CKM matrix Precise determination of the unitarity triangle May 25, 2005 CTEQ Summer School 77

78 Summary CKM physics is only one of many ways to search for and explore New Physics effects Interesting hints exist for new, CP-violating FCNC interactions of the type b sqq Evidence for New Physics at the TeV scale (?) Possible relevance for cosmology (baryogenesis) When will the SM collapse, and what lies beyond it? The coming years will tell! May 25, 2005 CTEQ Summer School 78