Determination of Unitarity Triangle parameters

Transcription

1 Determination of Unitarity Triangle parameters Achille Stocchi LAL-Orsay Phenomenology Workshop on Heavy Flavours Ringberg Schloss 8 April May 003

2 -Introuction (Unitarity Triangle) -The measurements/theoretical inputs - Statistical metho Comparison (very brief) - Results. Determination of the Unitarity Triangle parameters

3 All these topics extensively iscusse at

4 hep-ph/ will be submitte as CERN-Yellow ook THE CKM MATRIX AND THE UNITARITY TRIANGLE Organise as a coherent ocument (work uring 1 months between the Workshops) 98 authors ~ 46 theorists ~ 5 experimentalists 330 pages

5 (b u)/(b c) ε K m m / m s A CP (J/,K S ) Stanar Moel + + [(1 ) + P] (1 ) + (1 ) + K f sin( ) -, 1,F(1), theories which give the link from quarks to harons OPE /HQET/Lattice QCD. Nee to be teste,m t

6 Short review on the inputs

7 V cb - Inclusive Metho b V cb ν l c Moments of istributions HADRONIC mass, LEPTON Momentum, Photon energy b s γ Γ sl ( b cl ν) = r τ f(µ π, m b,, m c α s, ρ D (or 1/m b3 ) m b Γ sl = (0.434 (1 ±0.018)) MeV ( also name Λ) µ π b sl = V cb (λ 1 Fermi movement) M b,kin (1GeV) = 4.59 ± 0.08 ± 0.01GeV m c,kin. (1GeV) = 1.13 ± 0.13 ± 0.03GeV µ π = 0.31 ± 0.07 ± 0.0GeV ρ D = 0.05 ± 0.04 ± 0.01GeV terms 1/m b3 (uner control?)/small! F % ase on OPE 4.3(mb(mb)) V cb (inclusive)= ( 41.4 ± 0.6 ± 0.7(theo.) ) 10-3 Exp + (µ π, m b,, ρ D.absorbe!) Pert. QCD. α s, terms 1/m 4 b hep-ph/01007 C.auer,Z.Ligeti,M.Luke,A.Manohar hep-ph/010319, M.attaglia et al. (P.Gambino,N.Uraltsev) hep-ph/0306 D. enson,i.igi,t.mannel,n.uralstev

8 V cb -Exclusive Metho ase on HQET Γ = w w = w = m D* v v + m m D* G F 48π. D (*) q m V cb F( w) G( w) At zero recoil (w=1), as M Q F(1) 1 F(1) V cb F(1) V cb = 38.1 ± 1.0 ρ F(1) ~ 0.91 ± 0.04 V cb (exclusive)= ( 4.1± 1.1 ± 1.9 ) 10-3

9 V ub Inclusive methos X u l + ν (En Point) 3 D Fit : q an M X E l b b u u CLEO \\\\ b c AAR ackg. substructe DELPHI b b c u ackgr.

10 Conservative approach syst. fully correlate V ub = ( 4.09 ± 0.46 ± 0.36) 10-3

11 Exclusive methos (π,ρ,ω) l ν Common to all analyses V ub = ( 3.30 ± 0.4 ± 0.46) 10-3 Error : ominate by form factor errors as F(1) in V cb

12 0,s b t,c,u Oscillations in 0 system : m W W +,s t,c,u, s b P 1 t / τ q = e (1 ± cos m t) ( ) q q q q V t V ts ( toay ominate by elle-aar ) m f Vcb λ Vt f λ Vcb ((1 ρ ) + η ) m = 0.50 ± ps -1 LEP/SLD/CDF/-factories Precise measurement (1.%)

13 m s > 14.4 ps -1 at 95% CL Sensitivity at 19.3 ps -1 LEP/SLD/CDF-I Oscillations in 0 s system : m s cb t s V f V f m s s s s ) ) ((1 η ρ λ + s s s f f m m 1/ξ

14 ξ Calculation partially unquenche (N f = or +1) in agreement 1.0±0.0 f f s + 1 s = 1.18 ± 4 0, = 1.00 ± 0.03 ^ f s s ξ = = 1.4 ± 0.04 ± 0.06 f ^ Chiral extrapolation : light quarks simulate typically in a range [m s / - m s ]

15 f ^ Calculation partially unquenche (N f = or +1) in agreement f = 03 ± 7 MeV, = 1.34 ± ^ f = 3 ± 33± 1MeV 1.09±0.06 ( Sum Rules f = 08 ± 7 MeV, = 1.67 ± 0.3) (syst not correlate ~m b ) ^ K ( GeV ) = 0.63 ± 0.04 K = 0.86 ± 0.06 K ^ 1.05±0.15 unquenching factor 1.05±0.05 SU(3) effects factor ^ K = 0.86 ± 0.06 ± 0.14

16 sin β 0 0 mixing ecay A f CP ecay A f CP CP violation comes from interference between ecays with an without mixing f CP a f CP Γ Γ ( t) = Γ +Γ ( 0 ( t) phys fcp) ( 0 ( t) phys fcp) ( 0 ( t) phys fcp) ( 0 ( t) phys fcp) = C cos( m t) + S sin( m t) f f CP ~ η sin β sin( m t) 0 J / ψ K S, L CP sin φ 1 = 0.71± 0.09 sin φ 1 = 0.78 ± 0.17 sin β = ± 0.054

17 Determination of V u, V us K l3 ecays : K π l ν Neutron β ecay β transition of J P =0 + nuclei V u = ± Using unitarity V u +V us +V ub =1, σ(v us ) = 1/λ λ σ(v u ) V us = ± V us = 0.69 ± %.σ iscrepancy Attributing it to an unerstimate of syst. error (theo/exp) or (an unlikely stat. fluctuaction) inflate the error V us = 0.40 ±

18 Treatment of the inputs Ex : K = 0.86 ± 0.06 (Gaus.) ± 0.14 (theo.) Scan Rfit ayesian p..f. from convolution (sum in quarature) Likelihoo summing linearly the two errors Likelihoo Delta Likelihoo Delta Likelihoo [ ] [ ] At 68% CL

19 η FIT COMPARISON-same inputs ρ Quantitative ifferences in the selecte (ρ,η) regions between ayesian an frequentist are small Ratio between sizes of intervals corresponing to a given CL

20 The main origin of the ifference on the output quantities between the ayesian an the Rfit metho comes from the likelihoo associate to the input quantities oth methos use the same likelihoo Conclusion of the CERN Workshop: If same (an any) likelihoo are use the output results are very similar

21 Parameter Value Error(Gaussian) Error(Flat) λ V cb ( 10-3 ) (excl.) V cb ( 10-3 ) (incl.) V ub ( 10-4 ) (excl.) V ub ( 10-4 ) (incl.) m (ps -1 ) m s (ps -1 ) > 14.4 ps -1 at 95% CL m t (GeV) m c (GeV) f ^ (MeV) ξ K sinβ

22 Combination of V cb an V ub incl/excl No correlation between the incl/excl measurements V cb = ( 41.5 ± 0.8) 10-3 V ub = ( 35.7 ± 3.1) 10-4 Differences if : If the theoretical/statistical errors are - Convolute (ayesian) - Linearly (frequentist-rfit) (ifference of 95% C.L.) V cb know at ~% Precision riven by incl. metho V ub know at ~10%

23 Results on Unitarity Triangle parameters uras,ciuchini,franco,lubicz,martinelli,paroi,roueau,silvestrini,stocchi

24 Crucial Test of the SM in the fermion sector sinβ = ± ( ) J/ψ K 0 s sin β = ( ) from sies-only Coherent picture of CP Violation in SM

25 Fit of the Unitarity Triangle in SM ρ = 0.16 ± [0.067 C. L. η = [0.91 C. L. +

26 Inirect etermination of the UT angles : sin, sin an 90 sin α = [ 0.58 C L. sin β = ± [0.631 C. L. γ = (65 ± 7) egree [50.5 C. L. γ > 90 Prob~0.001 Without m s γ > 90 Prob~0.005

27 RED: WITH ALL CONSTRAINTS / LUE: WITHOUT m s y removing the constraint from m s : = (65 ± 7) = (60 ± 9) γ > 90 Prob~0.005

28 Preiction for m s Without limit on m s With limit on m s m = 0.9 ± 4.0 ps s 1 [9.1 C. L. m = 18.6 ± 1.7 ps s 1 [15.6 C. L.

29 Inirect etermination of the non-perturbative QCD parameters f ^ ξ ^ K = [0.51 C. L. f ^ = 1.5 ± 1.0 MeV [ ] 95% C. L. ^ K = 0.86 ± 0.06 ± 0.14 ^ f = 3 ± 33± 1MeV ξ = 1.4 ± 0.04 ± 0.06

30 Using : V ub / V cb m / m s A CP (J/,K S ) So in particular knowing ξ ^ K = [0.51 C. L. f ^ = MeV [180 4] C. L. Using : V ub / V cb A CP (J/,K S ) ^ K = [0.47 C. L. f ^ = MeV [16 78] C. L. You can take this examples to show how the system is starting to be overconsraine

31 Looking for New physics by measuring m s Re lines: ( m s ) = 1.0, 0.5, 0., 0.1 ps -1 lue line: all errors ivie by 3σ 5σ m s > 6ps -1 New Physics at 3σ >30.5ps -1 New Physics at 5σ Almost inepenently of the precision on the measurement of m s If the value measure for m s will fall in the SM region [(1-6)ps -1 ] important theoretical improvements have to be forseen to test the SM inirectirect m s Delta( m s )

32 Looking for New physics by measuring γ Suppose γ can be measure with an error of 10 o γ >100 o New Physics at 3σ with an error of 5 o γ >90 o New Physics at 3σ Re lines: = 0, 15, 10, 5 egrees lue line: all errors ivie by Importance of reucing some theo. errors (ξ, K ) to perform a more powerful test of the SM for ex: if all theo. errors/ γ >80 o New Physics at 3σ

33 Re lines: (sinβ) = 0., 0.1, 0.05, 0.0 lue line: all errors ivie by SM preiction without A(J/ K s ) sinβ = ± [ ] 3σ SM region if σ (sinβ)=0.0 [ ] 3σ SM region if σ (sinβ)=0.05 (toay) Improving the precision on sinβ using A(J/ K s )? Obviously ifficult to fin any iscrepancy with SM

34 SM preiction with A(J/ K s ) sinβ = ± Re lines: (sinβ) = 0.4, 0., 0.1, σ If the experimental error goes own by a factor ( 0.) A( K s ) ~ σ A( K s ) < 0 4σ Measuring sinβ using a ifferent channel K s? A( K s ) = ±.7σ

35 Important progress in the last years V cb ~% V ub ~10% m ~ 1.% m s > 14.4 ps -1 at 95% CL m t ~ 3% sinβ 7% K ~ 15% ^ f ~ 15% ξ-1 ~ 0-5% Success of SM + LQCD/OPE/HQET Stanarissssssimo Next (in a ~year-time scale) hopes : m s, A( K s )

36 ADDITIONAL MATERIAL

37 The ayes Theorem: f(,, x c 1,...,c m ) ~ f j (c,,x) f i (x i ) f o (, ) j=1,m i=1,n f(, c) ~ L (c, ) f o (, ) x x 1,...,x n = m t, K, F. c c 1,...,c m = ε K, m / m s, A CP (J/,K S )