CKM Status & Prospects

Transcription

1 CKM Status & Prospects Brian K. Heltsley, Cornell University Physics In Collision, June 9, 001 CKM Basics Experimental Status b emphasis CP, B d & B s mixing, b clν, b ulν Novel approach to cb Global fitting CKM, QCD, & CLEO-c Prospects B. Heltsley, CKM Status & Prospects, PIC01 1

2 Cabibbo-Kobayashi-Maskawa Quark Mixing Lagrangian (weak charged current) : g µ L = u γ d W + h. c. W Li ij Lj µ CKM : 3 3, UNITARY ( = I ) + Each ij has a real part + imag phase CKM = ud cd td us cs ts ub cb tb B. Heltsley, CKM Status & Prospects, PIC01 CP 3 gen s & 1 imag phase 0

3 The Unitarity Triangle(s) (UT) The sum for each 0 in I is a triangle in the realcomplex plane ud ud us * ub * us * ub cd cd cs * cs * cb... * cb td td ts * tb * ts * tb = = = Phase convention: ( cd *) cb is real Imag (0,0) ud ub * cd cb * td tb * Real B. Heltsley, CKM Status & Prospects, PIC01 3

4 B. Heltsley, CKM Status & Prospects, PIC01 4 CKM parameterizations Wolfenstein (original). Expand in λ, with λ= sinθ C = 0.. To O(λ 4 ) ~ 10-3 : Buras: slight changes attain O(λ 6 ) ~ 10-4 λ, A, ρ, η J= triangle area CP λ η ρ λ λ λ η ρ λ λ λ λ A i A A i A ) ( ) ( = = 1 1 λ η η λ ρ ρ, λ 5 η ia iaλ 4 η λ η ρ λ λ λ η ρ λ λ λ λ 1 ) (1 1 ) ( A i A A i A

5 SM Unitarity Triangle η * ub * cb ud cd ρ +iη ( ρ, η ) α (φ ) * tb * cb td cd 1-ρ -iη γ (φ 3 ) β (φ 1 ) (0,0) (1,0) ρ B. Heltsley, CKM Status & Prospects, PIC01 5

6 Just 4 parameters?! Just four parameters: λ, A, ρ, η Measure them as fundamental constants of nature metrology Now, semi-leptonic decays & mixing provide best access With a rich diversity of quark decays, can overconstrain them global fit to data Inconsistencies seen at any level means New Physics outside SM BUT, hadrons, not q s, are detected B. Heltsley, CKM Status & Prospects, PIC01 6

7 CKM QCD in (Semi)Leptonic Decay q j ij l Leptonic M q i f M ν Decay constant Small BR s ij l ν Semi-Leptonic M q j q i Incl. vs Excl. Form factor F X (q ) B. Heltsley, CKM Status & Prospects, PIC01 7 X

8 CKM QCD in B d, B s Mixing b t q i B 0 d,s ti tj B 0 d,s tj ti q i t B Q f Q b Bag parameter m d,s sets oscillation rate B. Heltsley, CKM Status & Prospects, PIC01 8

9 ~ ij (accuracy) [*=assumes Unitarity] ud: β-decay 0.1% ± cd: νd lc llx 6% 0.4 ± td: B d mixing 19% D s µν ± us: K πeν 1.1% 0.00±0.005 cs: D Keν, 6% W X c X 0.97 ± 0.06 ts: B s mixing 5%* 0.04 ± 0.01 * ub: b ulν & 17% B π(ρ )lν ± cb: b clν, 7% B Dlν ± tb: t blν 15%* 0.99 ± 0.15 * B. Heltsley, CKM Status & Prospects, PIC01 9

10 Experiment Theory CP-violating parameter from K decay: ε K = ub m d C ε / = B cb C K d λ B = λ d η (b u lν ) /(b c lν) d s d s 6 f [ C1A λ (1 ρ) + C + C3 B d ( ρ A λ + η 6 4 ) (0,0) B d -mixing frequency = mass difference B s -mixing frequency: m m = m m λ ξ [(1 ρ) [(1 ρ) + η m s ] circle@(1,0) B. Heltsley, CKM Status & Prospects, PIC01 10 B + η s f B s A ] hyperbola )] (1,0), ξ = λ 4 f f B B s d B B s d

11 UT Constraints 95% CL allowed From A. Hocker, et al. hep-ph/ B. Heltsley, CKM Status & Prospects, PIC01 11

12 More UT Constraints α, β, γ constrained from -body hadronic B-decays (rare): B ππ, Κπ, ρπ, DΚ, J/ΨΚ Help from (rare) K πνν after 005 Today mixing & semi-leptonic decays provide best precision From A. Hocker, et al. hep-ph/ B. Heltsley, CKM Status & Prospects, PIC01 1

13 sin β 0.34 ± 0.1 BaBar 0.58 ± 0.34 Belle 0.79 ± 0.43 CDF 0.84 ± 0.93 ALEPH 3. ±.0 OPAL World Average: 0.48 ± 0.16 B. Heltsley, CKM Status & Prospects, PIC01 13

14 B d Mixing: m d Measured in two ways: - χ method: t- integrated B 0 B 0 vs B 0 B 0 ; e.g. dileptons -direct, t-dependent observation of B 0 B 0 oscillations by flavor tagging as a fcn of decay lengths % error LEP Working Group m d (ps -1 ) m d 1/τ B B. Heltsley, CKM Status & Prospects, PIC01 14

15 B s Mixing B s too heavy to be ϒ(4S) LEP, SLC, Tevatron Near maximal mixing observed m s >>1/τ unlike B d Oscillations not yet definitively seen due to large frequency; hard to measure Only get lower limit on m s, even when combining all expmts B. Heltsley, CKM Status & Prospects, PIC01 15

16 m s World Average LEP B Oscillations Sensitivity to exclude 1.645σ 1 σ Working Group at 18.1 ps σ 1.645σ (stat only) Yes oscillation No oscillation Amplitude=1 up to 15 ps -1 m s >15 ps -1 Oscillation frequency B. Heltsley, CKM Status & Prospects, PIC01 16

17 Inclusive b clν cb = h(µ, m b ) Γ(b clν) = h(µ, m b ) BR(b clν)/τ b h(µ, m b ) from Heavy Quark Expansion Perturbative & non-perturbative pieces Quark-hadron duality assumption: integrated over enough charm bound states & enough phase space, the inclusive hadronic result will match quark-level No consensus on uncertainty in assumption B. Heltsley, CKM Status & Prospects, PIC01 17

18 Inclusive b clν LEP CLEO cb Incl 41± ± 5%? common theoretical error B. Heltsley, CKM Status & Prospects, PIC01 18

19 Exclusive cb : B D * lν Experiments measure dγ dw = G F 48π 3 g( w) w=(m B + m D* q )/(m B m D* ) = D* boost in B rest-frame 1<w<1.5; g(w) is a known function with g(1)=0 HQET: F(1) 1 for m b ; (1/m b ) n corr ns F D* (1) = : HQET, LQCD ( w) D * cb Nearly linear in w: measure curvature: parameter ρ Extrapolate data to w=1 (where phase space 0) Experimental results usually quoted as F D* (1) cb F Form Factor B. Heltsley, CKM Status & Prospects, PIC01 19

20 w fits: B D * lν examples D *+ lν 1.3<w<1.35 D *0 lν Kinematic variable distinguishing D * lν D * Xlν B. Heltsley, CKM Status & Prospects, PIC01 0

21 cb from B D * lν w msd: σ w (CLEO)= 0.03; σ w (LEP) 0.07 Fit each w-bin for (B D * lν+d * Xlν+bgds) CLEO limit: ε(slow π) LEP limit: D * Xlν level F(1) cb Model of Leibovich, et al. PRD 57, 308 (1997) CLEO measures it, sees less Extrapolation CLEO 001 F(1) cb =(4. ± 1.3 ± 1.8) 10-3 ρ =1.61±0.09 CLEO D *+ lν, D *0 lν 5% total error on F(1) cb B. Heltsley, CKM Status & Prospects, PIC01 1

22 cb Exclusive Averages CLEO fits both a smaller D * Xlν AND a larger ρ than LEP, & both are correlated with F D* (1) cb πl CLEO 4.±1.3 ±1.8 When taking out F(1), LEP WG uses F(1)=0.88±0.05 CLEO uses F(1)=0.913±0.04 7% CL consistency B. Heltsley, CKM Status & Prospects, PIC01

23 b ulν Similar to b clν BUT BR(b ulν ) ~ 10-3! Experimentally: few evts, swamped w/ b clν LEP expmts use inclusive analysis LEP ub avg has 10% statistical error HQE uncertainty (5%) + duality/modeling unc. (1%) Systematics from identifying & separating b u, b c Systematics from non-b u, non-b c suppression CLEO uses ν-recon. for B πlν, ρlν Statistical error of 4% Form-factor model uncertainty of 17% B. Heltsley, CKM Status & Prospects, PIC01 3

24 ub Summary ub LEP: (4.13 ± 0.45 ± 0.5) 10-3 Stat + Detector Theory CLEO: (3.5 ± 0.30 ± 0.55) B. Heltsley, CKM Status & Prospects, PIC01 4

25 Global fits: Simmering tempest Conservative Frequentists A. Hocker, et al., hep-ph/ (BaBar) S. Stone, hep-ph/00116 (Beauty 000) A. Falk, hep-ph/990850, Aug (LepPho 1999) J. Rosner, hep-ph/ , Aug (Beauty 000) Optimistic Bayesians: A. Stocchi, hep-ph/0010 (ICHEP 000), NIM A46 (001) 318 (Beauty 000). F. Parodi (CP 000) M. Ciuchini, et al., hep-ph/ (Moriond 001) Issue: How to treat theoretical QCD predictions (TP s) & associated uncertainties in a global CKM fit? B. Heltsley, CKM Status & Prospects, PIC01 5

26 Central Q s in Tempest What are central values of TP s from HQET, LQCD, NLO? Do we exclude disagreeable or outdated predictions? How to combine several incompatible results? What are the uncertainties on the TP s? How well can they be estimated? Do internal tests give adequate estimates? How does one quantify errors from assumptions; e.g. quarkhadron duality in HQET? Can some or all theoretical errors be treated w/bayesian analysis along with the data, with a preferred central value as a result? B. Heltsley, CKM Status & Prospects, PIC01 6

27 Standard vs 95% CL Scanning Standard method advocates similar treatment of uncertainties for data and TP s with Gaussian (or even flat) PDF s (Bayesian) LQCD is mature enough to trust results Know the sign & rough magnitude of corrections Can assign reasonable σ s: don t throw away information! 95% CL Method advocates cautious approach to TP s by restricting them to a 95% CL interval, with no preferred central value ij : contours or intervals with no preferred ctrs (Frequentist) Even combining flat PDF s is treacherous! In multi-dimensional problems Bayesian treatment unfairly predicts a narrowing of possible results, not a broadening B. Heltsley, CKM Status & Prospects, PIC01 7

28 sinβ CL s in different methods ( 95% scan ) 95% scan From A. Hocker, et al. hep-ph/ Direct sinβ msmts not included B. Heltsley, CKM Status & Prospects, PIC01 8

29 Standard Method Global Fit η m s / m d ε K ρ From M. Ciucini, et al., hep-ph/ No sinβ constraint B. Heltsley, CKM Status & Prospects, PIC01 9

30 95% Scanning Global Fit 95% CL 68% CL No sinβ constraint From A. Hocker, et al. hep-ph/ B. Heltsley, CKM Status & Prospects, PIC01 30

31 95% CL w/sinβ Constraint From A. Hocker, et al. hep-ph/ B. Heltsley, CKM Status & Prospects, PIC01 31

32 CL s in 95% Scan Global Fit No sinβ With ε Κ, sinβ No ε Κ, sinβ From A. Hocker, et al. hep-ph/ B. Heltsley, CKM Status & Prospects, PIC01 3

33 YK Global Fit 95%CL Limits 95% Scanning vs Standard ρ: vs Span: 0.34 vs 0.37 η: vs Span: 0.8 vs 0.16 sin(β): vs Span: 0.4 vs 0.6 Here uses flat PDF s From A. Hocker, et al. hep-ph/ No sinβ constraint From M. Ciucini, et al., hep-ph/ Each quoted with its own choice for QCD params B. Heltsley, CKM Status & Prospects, PIC01 33

34 Global Fitting Conclusions No consensus on QCD uncertainties Not likely to converge without data to pin it down No consensus on Bayesian/Frequentist Merits & difficulties on both sides Different methods will give much different answers as soon as the data are more precise (i.e. in a few weeks) Different answers may have very different implications on whether the SM is found lacking Expect continuing spirited discussion B. Heltsley, CKM Status & Prospects, PIC01 34

35 New cb from Moments HQET OPE: expand in (1/m B ) n cb = Γ(b clν) h(λ, λ 1 ) : ~O(m B -3 ) Λ = Mass of light d.o.f. λ 1 = rms momentum of b quark. Λ, λ 1 determined from Lattice QCD Kronfeld & Simone, hep-ph/ A.Falk, M. Luke, & M. Savage, PRD53 (491) M. Gremm & A. Kapustin, PRD55 (6934) M. oloshin, PRD51 (4934) Measured hadronic spectral moments in b clν Measured photon energy spectrum moments in b sγ New, preliminary CLEO use of technique B. Heltsley, CKM Status & Prospects, PIC01 35

36 CLEO b sγ spectral moments Measure photon spectrum in lab-frame. Convert to B rest frame. MC accounts for smearing Best match m b = 4719±115 Me/c ;p F = 378±150 Me Extract moments (E γ >.0 Ge) ( E γ E ) = 0.01± ± 0.00 Ge γ Weights per 100 Me 50 0 E γ =.345 ±0.030 ±0.010 Ge (1.3%) CLEO Photon Energy (Ge) B. Heltsley, CKM Status & Prospects, PIC01 36

37 B X c lν Hadronic Mass Moments Lepton (p>1.5 Ge) ν-reconstruction: p ν Calculate recoil mass Fit spectrum w/b Dlν, B D * lν, B X H lν (various models for X H ) M X -M D, M D is spinaveraged D, D * mass DATA Fit D * lν Dlν X H lν M M X -M D = 0.87±0.065 Ge X nd moment: 0.63 ±0.17 Ge 4 -M D Second moments give consistent results, but still theoretically shaky. B. Heltsley, CKM Status & Prospects, PIC01 37

38 Λ, λ 1 from b sγ, B X c lν moments Λ = 0.35 ± 0.07 ± 0.10 Ge λ 1= 0.16 ± ± Ge moments 3 1/ M B B. Heltsley, CKM Status & Prospects, PIC01 38

39 CLEO cb from b clν, b sγ Using B(B X c l ν)=(10.39±0.46)% (CLEO, PRL76 (1570) 1996 ) τ ± = (1.548 ±0.03) psec (PDG) τ 0 = (1.653 ±0.08) psec (PDG) f +- /f 00 = 1.04 ± 0.08 (CLEO, hep-ex/000600) Γ(b clν) = ( 0.47 ± 0.00 ) Me cb = (40.5 ± 0.9 ± 0.9 ± 0.8) 10-3 Γ exp (Λ, λ 1 ) exp 1/M B 3 3.7% total error B. Heltsley, CKM Status & Prospects, PIC01 39

40 cb Summary F(1)=0.88 F(1)=0.913 CLEO Exclusive 46.4±.4±.1 CLEO Inclusive 41±± CLEO Moments 001 Prel. LEP Incl+Excl Avg 40.5±1.3 ±0.8 Combine at your peril B. Heltsley, CKM Status & Prospects, PIC01 40

41 What s next? B-factories in 5 years: ~0.5 ab -1 ~1/10 statistical σ s D BR s become limiting to B-decay precision Charm physics could become less precise than b-physics: need better cd & cs Theoretical uncertainties dominate even now But Lattice QCD & models promise big improvements B. Heltsley, CKM Status & Prospects, PIC01 41

42 Just imagine Today % theoretical errors No new data 95% CL region 95% CL region B. Heltsley, CKM Status & Prospects, PIC01 4

43 The Role of CLEO-c Modify CESR for E cm =3-11 Ge: L= High precision charm data Measure D BR s for input to B-decay studies Establish successful precision testing ground of QCD for D s to give credibility to those for B s High precision quarkonia spectroscopy & decay data at ψ & ϒ resonances Provide much needed experimental basis for nonperturbative QCD tests. Glueballs/Hybrids? Searches for non-sm phenomena in D- mixing, CP in D decay, & rare decays B. Heltsley, CKM Status & Prospects, PIC01 43

44 A CLEO-c Program ϒ(1S), ϒ(S), ϒ(3S) ~1- fb -1 each Spectroscopy, Matrix elements, Γ ee :(>10 world) ψ(3770) -- 3 fb -1, 30M events 6M tagged D decays (310 Mark III) ψ(4100) -- 3 fb -1, 1.5M D s D s 0.3M tagged D s decays (480 Mark III, 130 BESII) ψ(3100) -- 1 fb -1, 10 9 J/ ψ decays (170 Mark III, 0 times BES II) B. Heltsley, CKM Status & Prospects, PIC01 44

45 I I Tagging at Threshold D 0 + K + K + K D 0 CLEO-c MC e K + e I I Large σ Low multiplicity Pure DD init. State High recon. eff s ~ 0% D tags D ss tags Almost no bgd Clean ν-reconst. Coherent init state B. Heltsley, CKM Status & Prospects, PIC01 45

46 I I I I Tagged Branching Ratios Candidates / 0.6 Me D Kπ 0 D K tag + 1 fb 1 CLEOc M = 1.3 Me S/B ~ fb -1 σ=1.3 Me Using Particle-Id & 3σ E cut Log Scales Candidates / 0.6 Me Ds K K 1 fb 1 CLEOc = 1.4 Me M D KKπ tag S/B ~ fb -1 σ=1.4 Me M (D) (Ge/c ) 1.88 Set absolute BR s for B D Decay Mode PDG M (D) (Ge/c ) CLEOc (δb/b %) (δb/b %) D 0 Kπ D + Kππ D s φπ B. Heltsley, CKM Status & Prospects, PIC Beam-energy constrained mass.0

47 I I I I Leptonic Decays Candidates / 0.01 (Ge /c 4 ) fb 1 CLEOc 0 Tag: KK, KK,, E extra + E tot cut 3 tags 31 tags 5 other tags D s µν τν Candidates / 0.01 (Ge /c 4 ) fb 1 CLEOc 0 0 Tag: K, K K s, E extra + E tot cut D µν τν K L µν M( ) (Ge /c 4 ) Missing mass squared M( ) (Ge /c 4 ) δf Ds f D s.1% (Now: ±35%) δ f D f D.6% (Now: ±100%) B. Heltsley, CKM Status & Prospects, PIC01 47

48 I I I I I Semi-leptonic Decays D 0 + D 0 K + D 0 K D 0 π l + ν Events / (0.01 Ge) Low Bkg! Form factors: 1% Check theory! U = E miss P miss (Ge) U = E miss -P miss q (Ge ) B. Heltsley, CKM Status & Prospects, PIC01 48

49 Semi-leptonic (cont d) Decay Mode PDG000 CLEOc (δb/b %) (δb/b %) D 0 Klν D 0 πlν D + πlν D s φlν 5.8 Plus vector modes... Systematics limited cd, cs to ~1.5%, ratio to <1% Cancelling systematics B. Heltsley, CKM Status & Prospects, PIC01 49

50 Other Experiments BES/BEPC CESR-c higher luminosity than BEPC I or BEPC II BEPC II/BES III upgrade completion: after 005 Physics priorities in τ-charm region dictate E cm B-factories Charm production not clean like at DD threshold Charm measurements will quickly become systematics limited D, D s branching ratio errors -10 times smaller with CLEO-c than B-factories ery different systematics (a good thing) B. Heltsley, CKM Status & Prospects, PIC01 50

51 CKM Conclusions B-factory appetizers to be followed by full course meal: just wait a few weeks Major improvements in B-decay msmts. Surprises? Treatment of theoretical uncertainties & global fitting techniques are active & important subjects of discussion HQ models, LQCD will confront %-level c & b data in a few years: need accurate f X, F X (w), B X CLEO-c to provide precision c, ψ, ϒ data Better precision in D BR s necessary for B DX Improve cd & cs to the 1% level %-level metrology of CKM & very high sensitivity to new physics attainable in ~5 yrs Whither the SM? It should be fun finding out. B. Heltsley, CKM Status & Prospects, PIC01 51