1. Paolo Gambino Daphne-2004 7/6//2004 1 Status of the CKM matrix Paolo Gambino INFN Torino

2. Paolo Gambino Daphne-2004 7/6//2004 2 Why CKM? For a complete overview, see the Proceedings of the 2002 and 2003 CKM workshops: CKM1: Yellow Book Cern-2003-002-corr ( hep-ph/0304132 ) CKM2: eConf C0304052 (2003) http://ckm-workshop.web.cern.ch CKM3 will take place in San Diego, march 2005 Many thanks to M. Bona, G.Isidori, V.Lubicz, M. Pierini,N.Uraltsev and to all UTfitters. Observed Flavor Violation is surprisingly close to SM prediction >>> the flavor problem Strong interactions make CKM studies hard. Learning slowly but steadily. Theory errors dominate almost everywhere.

3. Paolo Gambino Daphne-2004 7/6//2004 3 The CKM matrix Wolfenstein parameterization describes Flavor Violation in the SM 3 angles and 1 phase with strong hierarchy:  0.22 sine of Cabibbo angle, A, ,  =O(1) At present accuracy,Wolfenstein par must be improved _ , 

4. Paolo Gambino Daphne-2004 7/6//2004 4 The Cabibbo angle Historically, universality of charged currents O(10 -5 ) Comparison between V ud,V us determinations of tests unitarity of the first line of V CKM could also be measured from 2nd line, V cd (DIS) at 10%, W decays at LEP constrains Σ ij |V ij | 2 at 1.3%  V cs at 1.3%

5. Paolo Gambino Daphne-2004 7/6//2004 5 from V ud from V ud Superallowed Fermi transitions (0 + ->0 + β decay) extremely precise, 9 expts, δV ud ~0.0005 dominated by RC and nuclear structure neutron β decay δV ud ~0.0015, will be improved at PERKEO, Heidelberg π + decay to  0 e th cleanest, promising in long term but BR=10 -8 PIBETA at PSI already at δV ud ~0.005 PDG : V ud =0.9738±0.0005 = 0.2274±0.0021

6. Paolo Gambino Daphne-2004 7/6//2004 6 2σ discrepancy! Semileptonic K l3 (K->πlν) E865 K + disagrees 2.3σ from older exp new KLOE (prelim) K S and KTeV K L agree with new result K + from KLOE, NA48 should come soon. th error? New results are con- sistent with unitarity AG theorem: easily calculable ? Discarding old results and using Leutwyler & Roos: |V us | Kl3 = 0.2255 ±0.0021 Next frontier: LQCD & measure slopes for K μ3 (Dalitz plot) to constrain  PT from V us (K l3 ) New lattice result: Becirevic et al at 1% (see Lubicz talk) E865 KLOE,K S prelim KTeV, K L both e,μ

7. Paolo Gambino Daphne-2004 7/6//2004 7 New ideas τ decay (V us ) Jamin et al. m s from sum rules or LQCD as input, may become competitive with B-factory results. At present δV us ~0.0045, low values Hyperon decays (V us ) Cabibbo et al. have revisited the subject focussing on vector form fact. δV us ~0.0027 (exp) but O(1%) or more SU(3) breaking effects NOT included, lattice? using f  /f K from lattice Marciano (2004): R.C. Use LQCD for f  /f K. Present MILC result 1.201(8)(15) Staggered fermions, partially unquenched. From there we get = 0.2238 ± 0.0003 (exp) ± 0.0004 (rc) ± 0.0030 (lattice) Compatible with other determinations. MILC error debated. Great potential for improvement

8. Paolo Gambino Daphne-2004 7/6//2004 8 EXCLUSIVE Determination of A V CKM A can be determined using |V cb | or |V ts | Two roads to |V cb | INCLUSIVE

9. Paolo Gambino Daphne-2004 7/6//2004 9 The advantage of being inclusive Λ QCD «m b : inclusive decays admit systematic expansion in Λ QCD /m b Non-pert corrections are generally small and can be controlled Hadronization probability =1 because we sum over all states Approximately insensitive to details of meson structure as Λ QCD «m b (as long as one is far from perturbative singularities) α s and can be expressed as double series in α s and Λ QCD /m b (OPE) with parton model as leading term No 1/m b correction!

10. Paolo Gambino Daphne-2004 7/6//2004 10 Leptonic and hadronic spectra Total rate gives CKM elmnts; shape tells us about B structure OPE predictions can be compared to exp only after SMEARING and away from endpoints: they have no LOCAL meaning

11. Paolo Gambino Daphne-2004 7/6//2004 11 State of the art Known corrections up to 1/m b 3 : OPE/HQE predictions are only functions of possible cuts and of Perturbative Corrections: full O( α s ) and O(β 0 α s 2 ) available For hadronic moments thanks to NEW calculations Trott,Uraltsev BLM to hadr moments not yet used in fits Recent implementation for moments of lept and hadronic spectra including a cut on the lepton energy Bauer et al.,Uraltsev & PG Leptonic momts measured more precisely but less sensitive to higher dim parmtrs than hadr momts 1, 2 Gremm,Kapustin... 1,21,2

12. Paolo Gambino Daphne-2004 7/6//2004 12 Which masses? Which scheme? m q (pole) is ill-defined, cannot be determined better than ~100MeV, and induces large uncontrolled higher orders |V cb | ~ k 0 [1-0.66 (m b -4.6) +0.39 (m c -1.15)+ +0.01 (   2 -0.4) +0.05(  G 2 -0.35)+0.09(ρ D 3 -0.2)...] Need short distance masses: m b kin (μ) and m b 1S Exploit correlations (most moments depend on the same combination of m c,m b as width) Avoid unnecessary parameters Define carefully   2 =- 1 +...  G 2 = 3 2 +... Theoretical uncertainties: missing 1/m b 4, missing pert and mixed effects. Need a recipe to estimate them... More work ahead Traditionally m Q reexpressed using Non linear ops: T 1-4 M B,D 1/m c expansion

13. Paolo Gambino Daphne-2004 7/6//2004 13 Babar fit to | V cb |, BR sl, HQE paramts Pioneer work by CLEO & Delphi employed less precise/complete data, some external constraints, and CLEO a different scheme Problems with 1S scheme: a cloud? Not all points included No external constraint

14. Paolo Gambino Daphne-2004 7/6//2004 14 No sign of deterioration for higher cuts Kinetic scheme: Small pert corrections Minimal set of parmts No 1/m c expansion Uraltsev & PG

15. Paolo Gambino Daphne-2004 7/6//2004 15 Comparison with other determinations A real step forward: non-pert parameters are everywhere in B physics

16. Paolo Gambino Daphne-2004 7/6//2004 16  +unquenching

17. Paolo Gambino Daphne-2004 7/6//2004 17 Testing parton-hadron duality What is it? What is it? For all practical purposes: the OPE. No OPE, no duality Do we expect violations? Do we expect violations? Yes, Problems prevalently arise because OPE must be continued analytically. there are effects that cannot be described by the OPE, like hadronic thresholds. Can we constrain them effectively? Can we constrain them effectively? in a self-consistent way:just check the OPE predictions. Models may give hints of how it works Caveats? Caveats? HQE depends on many parameters and we know only a few terms of the double expansion in α s and Λ/m b.

18. Paolo Gambino Daphne-2004 7/6//2004 18 The photon spectrum of B->X s γ Motion of b quark inside B and gluon radiation smear the spike at m b /2 Belle NEW: lower cut at 1.8GeV (in the  rest frame) The photon spectrum is very insensitive to new physics, can be used to study the B meson structure = m b /2 +... var =μ п 2 /12+... Importance of extending to E γ (min) ~ 1.8 GeV or less for the determination of both the BR AND the B parameters (Bigi Uraltsev) Preliminary study found Belle results compatible with Babar fit

19. Paolo Gambino Daphne-2004 7/6//2004 19 |V cb | from B  D * l At zero recoil, where rate vanishes. Despite extrapolation, exp error ~ 2% Main problem is form factor F(1) The non-pert quantities relevant for excl decays cannot be experimentally determined Must be calculated but HQET helps. No new calculation since CKM1: F(1) = 0.91 +0.03 -0.04 Sum rules give consistent results Needs checking and unquenching F B →D * (1) = η A [1 - O(1/m b,1/m c ) 2 ] B  Dl gives consistent but less precise results δV cb /V cb ~ 5% and agrees with inclusive det, despite contradictory exps

20. Paolo Gambino Daphne-2004 7/6//2004 20 The unitarity triangle Unitarity determines several triangles in complex plane |V ub /V cb | describes a circle in the ( ,  ) plane V td cannot be accessed directly: we resort to loop transitions FCNC sensitive to new physics O( 3 ) area= measure of CPV

21. Paolo Gambino Daphne-2004 7/6//2004 21 |V ub | (not so much) inclusive |V ub | can be determined from total BR(b  ul ) almost exactly like incl |V cb | but we need kinematic cuts to avoid the ~100x larger b  cl background: m X (M B 2 -M D 2 )/2M B q 2 > (M B -M D ) 2 or combined (m X,q 2 ) cuts The cuts destroy convergence of the OPE, supposed to work only away from pert singularities Rate becomes sensitive to “local” b-quark wave function properties (like Fermi motion >>> SHAPE function)

22. Paolo Gambino Daphne-2004 7/6//2004 22 Each strategy has pros and cons Luke, CKM workshop 2003

23. Paolo Gambino Daphne-2004 7/6//2004 23 V ub incl. and exclusive exclusive Intense theoretical activity: subleading shape functions optimization of cuts (P +,P - etc) weak annihilation contribs. Resum. pert. effects relation to b  s  spectrum SCET insight A lot can be learned from exp (on WA, better constraints on s.f., subleading effects from cut dependence, b  s ...) REQUIRES MANY COMPLEMENTARY MEASUREMENTS (affected by different uncert.) Exclusive modes: LCSR and LQCD complement each other, but ~20% error. Waiting for unquenching… New Babar M X 4.62(38)(49) New Belle (q 2,M X ) 4.66(28)(40)(58) But th error probably overestimated WE ARE ALREADY AT 10%

24. Paolo Gambino Daphne-2004 7/6//2004 24 ε K, ΔM d,ΔM s : hoping for new physics at the mercy of lattice QCD To use ε K and Δm Bd,s to extract CKM parameters, we need 3 quantities from lattice: B K, B Bq f 2 Bq and Typical errors for quenched results: 10-17%, less for ξ

25. Paolo Gambino Daphne-2004 7/6//2004 25 Progress in LQCD Despite folklore, there has been progress B physics simulations are multiscale: present lattices can resolve neither b (too heavy) nor light q (too light) 3 main sources of systematics:  Discretization (different complementary approach)  Chiral extrapolation (needs lighter quarks)  Quenching (getting there: many new unquenched results) Example of difficulties: ξ parameter Chiral extrapolation done using ChPT but at NLO large logs appear (+10-20%) can we trust ChPT in regime of simulations? (chiral logs are not observed in that range) Waiting for lower m q, a 10% effect maybe safe ξ=1.18(4)( +12 -0 ) Lellouch ξ=1.21(5)(1) Becirevic quenched Quench. Appr.

26. Paolo Gambino Daphne-2004 7/6//2004 26 Two alternative routes to |V td | A good measurement of BR(K +  + ), O( 10 -10 ), will provide an excellent clean deter mination of |V td |. BR(K L  0 )~3x 10 -11, determines  Both very useful, but theory must be improved,exp is still far and prospects at NA48, CKM,JHF,KOPIO unclear B  /B  K*  can give a determination of V td. New Belle result (first observation of b  d) : BR(B  ( ,ω)  )=(1.8±0.6±0.1)x10 -6 R( B  /B  K *  )=(4.2±1.3)% Ali et al. extract from this 0.16<|V td /V ts |<0.29 at 1σ, in agreement with fits, but less precise. Form factors from LC sum-rules. Exploratory calculations on the lattice confirm LCSR: their improvement is essential

27. Paolo Gambino Daphne-2004 7/6//2004 27 Global fit results ρ = 0.204 ± 0.045 η = 0.341 ± 0.027 http://www.utfit.org

28. Paolo Gambino Daphne-2004 7/6//2004 28 Global fit results (II) http://ckmfitter.in2p3.fr = 0.189±0.078 =0.358±0.044 slightly different inputs

29. Paolo Gambino Daphne-2004 7/6//2004 29 Fitting methods: a matter of taste Differ in treatment of theory error. Two main groups: Bayesian (UTfit) Non gaussian errors (th & exp) are assigned a flat pdf, to be convoluted with gaussian pdfs Pro : conceptually clean, easy for Δm s. Con: does not provide a  2 test Rfit (CKMfitter) Non gaussian parameters have flat likelihood, not pdf Pro: more conservative (beware of theorists guessing errors!) Con: CL is at least x% Difference important especially when theory (non-gaussian) error dominates. The 99% CL ranges of global fit are quite similar with SAME INPUTS. see CKM Yellow book DO NOT TAKE 1σ RANGES TOO SERIOUSLY

30. Paolo Gambino Daphne-2004 7/6//2004 30 CP violation in the B and K sectors Using only the sides of the UT (CP conserving) Sin2 β J /ψ K s = 0.734 ± 0.054 Sin2 β UT = 0.706 ± 0.048 (without direct meas.)

31. Paolo Gambino Daphne-2004 7/6//2004 31 Prediction of Δm s DIRECT MEASUREMENT: Δm s > 14.5 @ 95 % C.L. Δm s > 14.5 @ 95 % C.L. Δm s = 21.0 ± 3.3 ps -1 (Δm s not used) Δm s = 18.5 ± 1.7 ps -1 (with all constraints) In the absence of new physics Tevatron should measure it soon

32. Paolo Gambino Daphne-2004 7/6//2004 32 At 95%CL [ 42-78.5 ] Prediction of  and  new Belle B  DK sin2 

33. Paolo Gambino Daphne-2004 7/6//2004 33 Fitting non-pert parameters LATTICE QCDUT FIT fB√BBfB√BB 223  33  12 MeV217  12 MeV BKBK 0.86  0.06  0.14 0.71  0.11 UTfit

34. Paolo Gambino Daphne-2004 7/6//2004 34 B K = 0.86 ± 0.06 ± 0.14 ξ = 1.24 ± 0.04 ± 0.06 f Bs √B Bs = 276 ± 38 MeV 14 sin2β = 0.734 ± 0.054 21 The near (?) future? Δρ = 24% → 15% Δη = 7% → 4.6% A direct measurement of Δm s will also have a significant effect

35. Paolo Gambino Daphne-2004 7/6//2004 35 Summary  CKM describes well a host of data. Present errors are dominantly theoretical: LQCD best hope, but theory control can be improved by new data at B-Factories,Cleo-c,Tevatron...  New |V cb | inclusive/momnts analysis by Babar: duality verified at % level, better determination of non-pert B parameters  First row universality problem seems resolved by new K l3 data  Progress in LQCD: learning to unquench etc  Excellent agreement so far with direct angle measurmnt (pending scrutiny of B  K S )...nevertheless, still room for new physics (we have tested only a few FCNC) (we have tested only a few FCNC)

36. Paolo Gambino Daphne-2004 7/6//2004 36 comparison