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Status of the CKM matrix

Status of the CKM matrix. Paolo Gambino INFN Torino. Why CKM?. 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.

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Status of the CKM matrix

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

  2. Why CKM? 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. 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. Paolo Gambino Daphne-2004 7/6//2004

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

  4. O(10-5) The Cabibbo angle Historically, universality of charged currents Comparison between Vud,Vus determinations of tests unitarity of the first line of VCKM  could also be measured from 2nd line, Vcd (DIS) at 10%, W decays at LEP constrains Σij|Vij|2at 1.3%Vcs at 1.3% Paolo Gambino Daphne-2004 7/6//2004

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

  6. ? AG theorem: easily calculable Semileptonic Kl3 (K->πlν) E865 K+ disagrees 2.3σ from older exp new KLOE (prelim) KS and KTeV KL agree with new result New lattice result: Becirevic et al at 1% (see Lubicz talk) KTeV, KL both e,μ K+ from KLOE, NA48 should come soon. th error? New results are con-sistent with unitarity E865 KLOE,KS prelim  from Vus (Kl3) 2σ discrepancy! Discarding old results and using Leutwyler & Roos: |Vus|Kl3= 0.2255 ±0.0021 Next frontier: LQCD & measure slopes for Kμ3(Dalitz plot) to constrain PT Paolo Gambino Daphne-2004 7/6//2004

  7.  using f/fK from lattice Marciano (2004): Use LQCD for f/fK . 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 R.C. New ideas Hyperon decays(Vus) Cabibbo et al. have revisitedthe subject focussing on vector form fact.δVus~0.0027 (exp) but O(1%) or more SU(3) breaking effects NOT included, lattice? τdecay(Vus) Jamin et al. ms from sum rules or LQCD as input, may become competitive with B-factory results. At present δVus~0.0045, low values Paolo Gambino Daphne-2004 7/6//2004

  8. VCKM Determination of A A can be determined using |Vcb|or |Vts| Two roads to |Vcb| INCLUSIVE EXCLUSIVE Paolo Gambino Daphne-2004 7/6//2004

  9. can be expressed as double series in αs and ΛQCD/mb (OPE) with parton model as leading termNo 1/mb correction! The advantage of being inclusive ΛQCD«mb : inclusive decays admit systematic expansion in ΛQCD/mbNon-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 ΛQCD«mb (as long as one is far from perturbative singularities) Paolo Gambino Daphne-2004 7/6//2004

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

  11. 1,2 1,2 Gremm,Kapustin... Recent implementation for moments of lept and hadronic spectra including a cut on the lepton energy Bauer et al.,Uraltsev & PG Perturbative Corrections: full O(αs) and O(β0αs2) available For hadronic moments thanks to NEW calculations Trott,Uraltsev BLM to hadr moments not yet used in fits Leptonic momts measured more precisely but less sensitive to higher dim parmtrs than hadr momts State of the art Known corrections up to 1/mb3: OPE/HQE predictions are only functions of possible cuts and of Paolo Gambino Daphne-2004 7/6//2004

  12. MB,D 1/mc expansion Non linear ops: T1-4 Which masses? Which scheme? mq(pole) is ill-defined, cannot be determined better than ~100MeV, and induces large uncontrolled higher orders |Vcb| ~ k0 [1-0.66 (mb-4.6) +0.39 (mc-1.15)+ +0.01 (2 -0.4) +0.05(G2-0.35)+0.09(ρD3-0.2)...] • Need short distance masses: mbkin(μ) and mb1S • Exploit correlations (most moments depend on the same combination of mc,mb as width) • Avoid unnecessary parameters • Define carefully 2=-1+... G2= 32+... • Theoretical uncertainties: missing 1/mb4, missing pert and mixed effects. Need a recipe to estimate them... More work ahead Traditionally mQ reexpressed using Paolo Gambino Daphne-2004 7/6//2004

  13. Not all points included No external constraint Babar fit to|Vcb|,BRsl,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? Paolo Gambino Daphne-2004 7/6//2004

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

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

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

  17. Testing parton-hadron duality • What is it?For all practical purposes: the OPE. No OPE, no duality • 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? in a self-consistent way:just check the OPE predictions. Models may give hints of how it works • Caveats?HQE depends on many parameters andwe know only a few terms of the double expansion in αs and Λ/mb. Paolo Gambino Daphne-2004 7/6//2004

  18. The photon spectrum of B->Xsγ Motion of b quark inside B and gluon radiation smear the spike at mb/2 The photon spectrum is very insensitive to new physics, can be used to study the B meson structure <Eγ> = mb/2+ ...var<Eγ> =μп2/12+... Importance of extending to Eγ(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 Belle NEW: lower cut at 1.8GeV (in the  rest frame) Paolo Gambino Daphne-2004 7/6//2004

  19. FB→D*(1) = ηA [1 - O(1/mb,1/mc)2] |Vcb| 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 δVcb/Vcb~ 5% and agrees with inclusive det, despite contradictory exps BDl gives consistent but less precise results Paolo Gambino Daphne-2004 7/6//2004

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

  21. |Vub| (not so much) inclusive |Vub| can be determined from total BR(bul) almost exactly like incl |Vcb| but we need kinematic cuts to avoid the ~100x larger bcl background: mX < MD El > (MB2-MD2)/2MB q2 > (MB-MD)2 or combined (mX,q2) 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) Paolo Gambino Daphne-2004 7/6//2004

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

  23. exclusive Vub incl. and 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 MX 4.62(38)(49) New Belle (q2,MX) 4.66(28)(40)(58) But th error probably overestimated WE ARE ALREADY AT 10% Paolo Gambino Daphne-2004 7/6//2004

  24. εK, ΔMd,ΔMs: hoping for new physics at the mercy of lattice QCD To use εK and ΔmBd,s to extract CKM parameters, we need 3 quantities from lattice: BK , BBqf2Bq and Typical errors for quenched results: 10-17%, less for ξ Paolo Gambino Daphne-2004 7/6//2004

  25. quenched Quench. Appr. 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 mq, a 10% effect maybe safe ξ=1.18(4)(+12-0) Lellouchξ=1.21(5)(1) Becirevic Paolo Gambino Daphne-2004 7/6//2004

  26. Two alternative routes to |Vtd| • A good measurement of BR(K++), O(10-10), will provide an excellent clean deter mination of |Vtd|. • BR(KL0)~3x10-11, 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 Vtd. New Belle result (first observation of b d) : BR(B (,ω) )=(1.8±0.6±0.1)x10-6R(B/BK*)=(4.2±1.3)% Ali et al. extract from this 0.16<|Vtd/Vts|<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 Paolo Gambino Daphne-2004 7/6//2004

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

  28. slightly different inputs =0.358±0.044 = 0.189±0.078 Global fit results (II) http://ckmfitter.in2p3.fr 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 Δms. 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 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) Sin2βUT= 0.706 ± 0.048 (without direct meas.) Sin2βJ/ψKs= 0.734 ± 0.054 Paolo Gambino Daphne-2004 7/6//2004

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

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

  33. Fitting non-pert parameters UTfit Paolo Gambino Daphne-2004 7/6//2004

  34. 14 BK = 0.86 ± 0.06 ± 0.14 fBs√BBs = 276 ± 38 MeV 21 sin2β = 0.734 ± 0.054 ξ = 1.24 ± 0.04 ± 0.06 The near (?) future? A direct measurement of Δms will also have a significant effect Δρ = 24% →15%Δη = 7% →4.6% 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 |Vcb| inclusive/momnts analysis by Babar: duality verified at % level, better determination of non-pert B parameters • First row universality problem seems resolved by new Kl3 data • Progress in LQCD: learning to unquench etc • Excellent agreement so far with direct angle measurmnt (pending scrutiny of BKS) ...nevertheless, still room for new physics (we have tested only a few FCNC) Paolo Gambino Daphne-2004 7/6//2004

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

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