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CP Violation and the CKM Matrix —————— Assessing the impact of the asymmetric B Factories

CP Violation and the CKM Matrix —————— Assessing the impact of the asymmetric B Factories. Andreas Höcker (LAL, Orsay) for the CKMfitter Group. SLAC Experimental Seminar, May 09, 2005. http://www.slac.stanford.edu/xorg/ckmfitter / and http://ckmfitter.in2p3.fr/. hoecker@lal.in2p3.fr.

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CP Violation and the CKM Matrix —————— Assessing the impact of the asymmetric B Factories

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  1. CP Violation and the CKM Matrix —————— Assessing the impact of the asymmetric B Factories Andreas Höcker (LAL, Orsay) for the CKMfitter Group SLAC Experimental Seminar, May 09, 2005 http://www.slac.stanford.edu/xorg/ckmfitter/ and http://ckmfitter.in2p3.fr/ hoecker@lal.in2p3.fr A. Höcker – CP Violation and the CKM Matrix …

  2. Outline Introductory disclaimer: this seminar mainly addresses B-physics experts it discusses/condenses parts of the 2004 publication from the CKMfitter Group Charles et al., EPJ C41, 1–131 (2005) [hep-ph/0406184] Höcker-Lacker-Laplace-Le Diberder, EPJ C21, 225 (2001) Themes : • CKM phase invariance and unitarity • Statistical issues • CKM metrology • the traditional inputs • deep B physics :, ,  • a new star : B+  + • the global CKM fit • Related topics • phenomenological discussion of B  K decays • Preparing the future A. Höcker – CP Violation and the CKM Matrix …

  3. (if there’s too many transparencies in this talk, why must we start with this one ?) • The Universe is empty* ! • The Universe is almost empty* ! Bigi, Sanda, « CP Violation » (2000) • Initial condition ? • Dynamically generated ? Sakharov rules (1967) to explain Baryogenesis • Baryon number violation • CP violation • No thermic equilibrium (non-stationary system) • So, if we believe to have understood CPV in the quark sector, what does it signify ? • A sheer accident of nature ? • and … (less important, but puzzling) is the new physics minimal flavor violating ? If so, why ??? A. Höcker – CP Violation and the CKM Matrix …

  4. Im Im Im Q q W– Q CP Violation (Im[...]  0) VqQ q  J/2 J/2   Re Re Re Jarlskog invariant J = 0  no VCP Jarlskog, PRL 55, 1039 (1985) phase invariant : The CKM Matrix and the Unitarity Triangle d s b u c t    A. Höcker – CP Violation and the CKM Matrix …

  5. If one wishes (not necessary for the analysis), one can Taylor expand in  and finds : The Unitary Wolfenstein Parameterization • The standard parameterization uses Euler angles and one CPV phase  unitary ! • Now, define • And insert into V V is still unitary ! With this one finds (to all orders in ) : where: Buras et al., PRD 50, 3433 (1994) A. Höcker – CP Violation and the CKM Matrix …

  6. The CKMfitter Project • Started development in 2000 with Standard CKM fit – first publication in 2001 • Since then, many additional implementations : • B , ,  isospin analyses, and Dalitz interpretation • B , K, KK isospin + SU(3) analyses • full QCD Factorization (BBNS) for B PP, PV • B D(*)K(*)(ADS, GLW and Dalitz) interpretation • rare B decays: B  () and B  (K*) • CPV and mixing in Bs decays • rare kaon decays: K   • dilepton CP asymmetries • new physics analyses • Features 3 statistical approaches : • Rfit(frequentist) • 90% CL scan method (frequentist) • Bayesian • Code :~ 42k lines at present (40k F vs. 2k C++) – re-foundation meeting in June, 2005 to take future technology decision: full rewrite in C++/Root, or with Mathematica The European Physical Journal C - Publisher: Springer-Verlag GmbH ISSN: 1434-6044 (Paper) 1434-6052 (Online) DOI: 10.1140/epjc/s2005-02169-1 Issue: Volume 41, Number 1 Date:  May 2005 Pages: 1 - 131 CKMfitter Group: from 4 (2000) to 15 (2005) members, mostly experimentalists including BABAR, Belle, LHCb Code is publicly available : • under CVS (still needs BABAR account – will eventually move to sourceforge), • on the web: http://www.slac.stanford.edu/xorg/ckmfitter/ A. Höcker – CP Violation and the CKM Matrix …

  7. Fitting Approach Constraints on theoretical parameters Measurement xexp ytheo = (A,,,,mt,, …) Theoretical predictions = (BK,fB,BBd, …) Xtheo(ymodel= ytheo ,yQCD) yQCD Define: “2” = – 2 lnL(ymodel) L(ymodel) =Lexp[– xtheo(ymodel)]Ltheo(yQCD) xexp « Guesstimates » • experimental likelihood • if not available: Gaussian errors • asymmetric errors • correlations between xexp’s Frequentist:Rfit Bayesian Uniform likelihoods: “allowed ranges” Probabilities A. Höcker – CP Violation and the CKM Matrix …

  8. Three Step CKM Analysis using Rfit Probing the SM Metrology Test New Physics • Define: ymod = {a; µ} = {, , A,,yQCD,...} • Set Confidence Levels in {a} space, irrespective of the µvalues • Fit with respect to {µ} ²min;µ(a) = minµ{²(a, µ) } • ²(a)=²min;µ(a)–²min;ymod CL(a) = 1 –Prob(²(a), Ndof) (or toy MC) • If CL(SM) good Obtain limits on New Physics parameters • If CL(SM) bad Try some other model • Test of “Goodness-of-fit” • Evaluate global minimum ²min;ymod(ymod-opt) • Create perfect data set : xexp-opt = xtheo(ymod-opt) generate xexp usingLexp • Perform many toy fits:²min-toy(ymod-opt)  F(²min-toy) AH-Lacker-Laplace-Le Diberder EPJ C21 (2001) 225, [hep-ph/0104062] A. Höcker – CP Violation and the CKM Matrix …

  9. Statistics : Popular Misconceptions See also R. Faccini’s plenary talk at BABAR Collaboration meeting February, 2005 • Use and misuse of Bayesian statistics : • Bayes’ theorem tells us about the convolution of probability densities (the “priors”) • Bayes did not tell us that we should assign probabilities to all quantities in this world • Addresses the problem of Finetuning : • Leaving all ymodel parameters free to vary in the fit (within defined ranges) is certainly conservative, but does not apply any hierarchy between the solutions • If one wishes to introduce a hierarchy to increase the information budget, one has to take care about the origin of the ymodel parameters : The yQCD parameters have prior information: all yQCD may hit at their bounds  finetuning scenario ? The ytheo parameters are unknown:  no finetuning scenario use of PDFs for yQCD suppresses these solutions in a controlled way: • arbitrary suppression strength • not conservative use of PDFs for ytheo suppresses (and enh.) solutions in an uncontrolled way: • arbitrary results (biased) • not conservative A. Höcker – CP Violation and the CKM Matrix …

  10. Popular Misconceptions: Examples (I) • Famous illustrative example: consider observable T with theory prediction a Bayesian approach with a priori PDFs G(yi), generates the a posteriori PDF and using uniform priors for all xi leads to : • Illustration for N=3 and Δ=3 : • Rfit is not weighed within : • Biasian strongly weighs see plot see appendix in: hep-ph/0104062 A. Höcker – CP Violation and the CKM Matrix …

  11. Bayesian: flat priors Bayesian: flat priors Popular Misconceptions: Examples (II) • B  Gronau-London isospin analysis: • there are 8 mirror solutions for   [0,], i.e., 8 different values of  give sameOi • if penguins  0 : two sets of 4 solutions merge with 2 solutions left • nature cannot distinguish between these solutions ! (because the corresp. observables are degenerate) • independent of the param. (polar, cartesian, …) • The Rfit analysis (2 fit) reproduces degenerate 2min() at the mirror solutions • When using PDFs for the ytheo, the Bayesian analysis cannot in general reproduce the mathematical property of the isospin analysis, since it applies arbitrary input weights A. Höcker – CP Violation and the CKM Matrix …

  12. Concluding Remarks • Is the frequentist analysis without approximations ? In principle yes, but not in practice : • Often use Gaussian CL = 1– Prob(Δ2,Ndof) approximation for simplicity • full approach would be toy Monte Carlo analysis to determine CL • Prob(…) is mostly conservative (tested for sin(2+) and B  analyses) • What about the definition of the estimator ? Is this arbitrary ? Source of bias ? • the choice of the estimator is arbitrary; in Gaussian case, maximum likelihood is optimal • using a bad estimator does not create a bias; however, it will give bad constraints • using an optimized estimator is just like optimizing a BABAR data analysis: there is nothing wrong with cut & count, it’s just not optimal M U C H L E S S T E X T F R O M N O W ON ! • Other comments to Bayesian analyses : • In many applications (like, e.g.,  from B DK) there is no obvious (mathematical) way to see the bias from priors • however, in most cases it can still be significant • Does the prior dependence reduces when the measurement is significant ? • not true in general (see example for  from B ) • A serious Bayesian analysis would use priors when there is prior information, and leave parameters free, when there is not digression:Concluding Remarks • Is the frequentist analysis without approximations ? In principle yes, but not in practice : • Often use Gaussian CL = 1– Prob(Δ2,Ndof) approximation for simplicity • full approach would be toy Monte Carlo analysis to determine CL • Prob(…) is mostly conservative (tested for sin(2+) and B  analyses) • What about the definition of the estimator ? Is this arbitrary ? Source of bias ? • the choice of the estimator is arbitrary; in Gaussian case, maximum likelihood is optimal • using a bad estimator does not create a bias; however, it will give bad constraints • using an optimized estimator is just like optimizing a BABAR data analysis: there is nothing wrong with cut & count, it’s just not optimal • Other comments to Bayesian analyses : • In many applications (like, e.g.,  from B DK) there is no obvious (mathematical) way to see the bias from priors • however, in most cases it can still be significant • Does the prior dependence reduce when the measurement is significant ? • not true in general (see  from B ) • The Bayesian analysis should use priors when there is prior information, and leave parameters free, when there is not A. Höcker – CP Violation and the CKM Matrix …

  13. m e t r o l o g y Inputs to the Global CKM Fit • |Vud| and |Vus| [not discussed here] • |Vub| and |Vcb| • CPV in K0 mixing • Bd and Bs mixing • sin2 •  : • B • B • B •  : • ADS, GLW • Dalitz • B+  + A. Höcker – CP Violation and the CKM Matrix …

  14. |Vub /Vcb | sin2 |Vcb| and |Vub| • For|Vcb|and|Vub|existexclusive and inclusive semileptonic approaches d s b exclusive inclusive B Xu ℓ B  ℓ b u u b c c B D* ℓ B Xc ℓ dominant uncertainties t Form factor OPE (|Vcb,ub|) and shape function (|Vub|) • |Vub| ( 2 +2) is crucial for the SM prediction of sin(2 ) • |Vcb| ( A) is important in the kaon system (K, BR(K ), …) A. Höcker – CP Violation and the CKM Matrix …

  15. (|Vub|) = 5% (|Vcb|) = 5% |Vcb| and |Vub| • Inclusive approaches most appealing at present nonperturbative corrections free quark decay • |Vcb| : moments analyses have 1.5–2% precision ! CKM-05 • |Vub| : reduced conflict between excl. and incl. • SF params. from bcl , OPE from Bosch et al. • reduction of central value 4.6  4.110–3 • ℓ result goes up with Lattice FF (unquenched) our average A. Höcker – CP Violation and the CKM Matrix …

  16. no |Vcb| inclusive CPV in the Kaon System effective matrix element • Neutral kaon mixing mediated by box diagrams • Most precise results from amplitude ratio of KL to KS decays to +– and 00 • ij from perturbative QCD • significant improvement on BK from Lattice QCD reported at CKM-05 : 0.79 ± 0.04 ± 0.09 • Direct CPV (י) theory not yet mature for use in CKM fit ( same problem in B physics) A. Höcker – CP Violation and the CKM Matrix …

  17. B0 Mixing • Effective FCNC Processes (CP conserving –– top loop dominates in box diagram): [B=2] [B=2] + Perturbative QCD CKM Matrix Elements Non-perturbative: Lattice (eff. 4 fermion operator) Loop integral (top loop dominates) • Dominant theoretical uncertainties : consider in fit that Lattice results are correlated ! • Improved error indirect via ms : [SU(3) breaking correction] A. Höcker – CP Violation and the CKM Matrix …

  18. No signal yet for Δmsupper limit : Δms > 14.5 ps–1 at 95% CL [ CDF: WA sensitivity 18.1  18.6 ps–1 ] CKM fit predicts : Δmd = 18.3 ps–1 + 6.5 – 2.3 Δms measured B0 Mixing • Δmd = (0.510 ± 0.005) ps–1 [ CKM constraint dominated by theory error ] CKM fit predicts : Δmd = 0.47 ps–1 HFAG – Winter 2005 + 0.23 – 0.12 A. Höcker – CP Violation and the CKM Matrix …

  19. S I N 2  I S N O T A G O L D E N M O D E ! Mannel at CKM 2005 • Conflict with sin2efffrom s-penguin modes ? WG4 at CKM 2005 I T ‘ S P L A T I N U M ! (*) (*)Thomas Mannel at CKM-05 sin(2)eff[s-penguin] careful with this average ! sin2[ first UT input that is not theory limited ! ] • “The” raison d’être of the B factories : Theory uncertainty ? HFAG – Winter 2005 A. Höcker – CP Violation and the CKM Matrix …

  20. Principal modes : Tree : dominant Penguin : competitive ? Not a CP eigenstate  [ next UT input that is not theory limited ]  A. Höcker – CP Violation and the CKM Matrix …

  21. ! Charmless b u Decays : realistic case • “T” and “P” are of the same order of magnitude : [Note that T and P are complex amplitudes !] Direct CP violation can occur : where is the relative strong phase • Time-dependent CP observable : realistic scenario A. Höcker – CP Violation and the CKM Matrix …

  22. digression: what is the meaning of “T” and “P” ? • Example : U - convention unitarity C - convention T - convention “Tree” “Penguin” The “tree” in the (most popular) C - and T - conventions has penguin contributions ! A. Höcker – CP Violation and the CKM Matrix …

  23. Isospin Analysis for B,  Unknowns Observables Constraints Account , T+–, P+–, T+0, P+0, T00, P00 B+–, S , C B+0, ACP B00, (S00),C00 2 isospin triangles and one common side 13unknowns – 7 observ. – 5 constraints – 1 glob. phase = 0  Assumptions: • neglect EW penguins (shifts  by ~ +2o)penguins • neglect SU(2) breaking • in ρρ: Q2B approx. (neglect interference)  can be resolved up to an 8-fold ambiguity within [0,] Refs. for SU(2) analyses : Gronau-London, PRL, 65, 3381 (1990), Lipkin et al., PRD 44, 1454 (1991), a.o. A. Höcker – CP Violation and the CKM Matrix …

  24. digression: Electroweak (EW) Penguins • EW penguins canmediate I = 3/2 transitionsand henceviolatetheSU(2) relations • Use “Fiertz” trick : the effective weak Hamiltonian of the decay B  reads: whereO1andO2are(V–A)(V–A)treeoperators andO7-10 EW penguinsoperators O7andO8have Lorentz structure (V–A)(V+A)whileO9andO10are(V–A)(V–A) but: c7,c8 c9,c10so that one can Fiertz-relatetheEW O9, O10to thetree O1, O2 : Neubert-Rosner, PLB 441, 403 (1998) PRL 81, 5076 (1998) • Hence, if f(…) real, ACP(+0)not sensitive to PEW ! A. Höcker – CP Violation and the CKM Matrix …

  25. CP Results for B0+– • Results for the time-dependent analysis : BABAR, hep-ex/0501071 Belle, hep-ex/0502035 Mediocre (but improved) agreement : 2 = 7.9 (CL = 0.019  2.3σ) A. Höcker – CP Violation and the CKM Matrix …

  26. BABAR & Belle BABAR & Belle note yet updated with new result from Belle σ(S+–)= σ(C+–)~0.01 penguin / tree • Study decay dynamics ... B Isospin Analysis • 2 fit of isospin relations to observables: BABAR A. Höcker – CP Violation and the CKM Matrix …

  27. A “surprise” : B • Nature’s great present : longitudinal polarization dominates  almost no CP dilution • Branching fractions for the B  system : BABAR, hep-ex/0412067 B+– = (30 ± 6)10–6 , B+0 = (26.4 )10–6 ,B00 < 1.110–6 at 90% CL • Small B00/B+0 ratio requires small penguins ! • But: P+– = 0 would mean that : B+-/B+0 2 • Test : input  from CKM fit, and solve isospin analysis without B+0in fit : 8 10–6 <B+0 < 29 10–6 [ 1 region ] A. Höcker – CP Violation and the CKM Matrix …

  28. BABAR toy smaller errors at 1 no difference at >2 1 2 B Isospin Analysis • Results from CP fit : BABAR, hep-ex/0503049 • Isospin analysis : full toy of which 11o is due to penguins penguin / tree As expected: much smaller than in B  A. Höcker – CP Violation and the CKM Matrix …

  29. CP mixing The B System • Dominant mode ρ+– is not a CP eigenstate Aleksan et al, NP B361, 141 (1991) • Q2B Isospin analysis requires to constrain pentagon Lipkin et al., PRD 44, 1454 (1991) • 13 observables vs 12 unknowns  • needs statistics of Super-B  [systematics?] • Better: exploit amplitude interference in Dalitz plot Snyder-Quinn, PRD 48, 2139 (1993) • simultaneous fit of  and strong phases • BABAR determines 16 (27) FF coefficients • correlated 2 fit to determine physics quantities BABAR 00 +– –+ BABAR, hep-ex/0408099 A. Höcker – CP Violation and the CKM Matrix …

  30. Results of B0()0 +–0 Dalitz analysis • From the 16 FF coefficients one determines the physical parameters : Parameters : , |T+–|,T–+,T00,P+–,P–+ Direct CP violation ? Scan in  using the bilinears : Δχ2(no direct CPV) = 14.5 (CL = 0.00070  3.4σ) A+– no direct CPV BABAR A–+ BABAR, hep-ex/0408099 A. Höcker – CP Violation and the CKM Matrix …

  31. similar precision as CKM fit : CKM fit (no ,  in fit) Combination of, ,  : first measurement of  • Combining the three analyses (B   best single measurement) : mirror solution disfavored for the SM solution we find : A. Höcker – CP Violation and the CKM Matrix …

  32. digression : “Color-Suppressed” Amplitudes Famous modes : • The color of the quarks emitted by the virtual W must correspond to the external quark lines to produce color-singlets  suppressionby ~1/Nc(naïve!) [ Suppression  verified in B(B0  D00)/B(B0  D–+) = (1/10.4)exp  (1/Nc)2 ] important non-factorizable contributions when large penguins ? Large u-penguins ? A. Höcker – CP Violation and the CKM Matrix …

  33.  [ next UT input that is not theory limited ] • GLW : D0 decays into CP eigenstate • ADS : D0 decays to K–+ (favored) and K+– (suppressed) • GGSZ : D0 decays to KS+– (interference in Dalitz plot) • All methods fit simultaneously: , rB and  the million dollar Q: Gronau-London, PL B253, 483 (1991); Gronau-Wyler, PL B265, 172 (1991) Atwood-Dunietz-Soni, PRL 78, 3257 (1997) Giri et al, PRD 68, 054018 (2003) No Penguins  relative CKM phase :  Tree: dominant Tree: color-suppressed A. Höcker – CP Violation and the CKM Matrix …

  34. “ADS+GLW” : Constraint on  • BABAR and Belle have measured the observables for GLW and ADS in the modesB– D0K–, D*0K–, D0K*– not yes used • No significant measurement of suppressed amplitude yet  limit : rB(*) 0.2 BABAR, hep-ex/0408082, hep-ex/0408060 hep-ex/0408069, hep-ex/0408028 Belle, Belle-CONF-0443, hep-ex/0307074 hep-ex/0408129 for the SM solution : not yet competitive with CKM fit A. Höcker – CP Violation and the CKM Matrix …

  35. Measurement of amplitude ratio: [ no improved constraint when adding  from CKM fit ] “GGSZ” : Constraint on  • Promising : Increase B decay interference through D decay Dalitz plot with D0 KS+– • huge number of resonances to model: K*(892), (770), (782), f0(980,1370), K0*(1430), ...  • amplitudes of Dalitz plot measured in charm control sample  A. Höcker – CP Violation and the CKM Matrix …

  36. Similarly: golden  mode at LHCb “sin(2 + )” Tree: dominant Tree: doubly CKM-suppressed • Relative weak phase 2 +  but :  dependence of the order of O(10–4) full toys Huge statistics, but small CP asymmetry Unknowns : rB0,  and   needs external input Use SU(3) to estimate rB0(*) (theory error: 30%) therefore not used in global CKM fit BABAR, hep-ex/0408038, hep-ex/0408059 Belle, hep-ex/0408106, PRL 93 (2004) 031802; Erratum-ibid. 93 (2004) 059901 A. Höcker – CP Violation and the CKM Matrix …

  37. B+ + • A new star at the horizon; helicity-suppressed annihilation decay sensitive to fB|Vub| • Powerful together with Δmd : removesfBdependence • Sensitive to charged Higgs replacing the W propagator not to be used as a measurement of fB ! • Best current limit from BABAR : Datta, SLAC seminar 2005 • Prediction from global CKM fit : A. Höcker – CP Violation and the CKM Matrix …

  38. Putting it all together t h e g l o b a l C K M f i t Inputs: Perfect agreement … if it weren’t for the s-penguin decays A. Höcker – CP Violation and the CKM Matrix …

  39. 2nd solution Putting it all together the impact of the unitarity triangle angles  The angle measurements dominate ! A. Höcker – CP Violation and the CKM Matrix …

  40. Consistent Predictions of all CKM-related Observables FOR UPTODATE RESULTS CHECK THE CKMFITTER WEB numerical results at: http://www.slac.stanford.edu/xorg/ckmfitter/ and http://ckmfitter.in2p3.fr/ (mirror) A. Höcker – CP Violation and the CKM Matrix …

  41. What Else ? Other CKM-related topic not discussed in this seminar : • super rare kaon decays : K  • charged decay already seen by E787, E949) • radiative decays : B , B K*, b  s, … • model-independent analysis of new physics in mixing and decay E787, PRL 88, 041803 (2002) E949, PRL 93, 031801 (2004) Charles et al., EPJ C41, 1–131 (2005) [hep-ph/0406184] Dynamical analysis of B , K, KK decays under different hypotheses Most simple charmless B decays; theory understanding must start here • SU(2)  done for , not fruitful for K at present • SU(3) • QCD Factorization next pages Puzzle ? A. Höcker – CP Violation and the CKM Matrix …

  42. “” from B  00, K00, K+K– • interesting combined constraint in (,) plane • “” from B  +–, K+–, K+K– • Global analyses: • at present: 13 parameters vs. 19 observables • when everything is measured (incl. Bs) : 15 par. vs. ~ 50 obs. Puzzling B, K, KK Decays : SU(3) • Many analyses use assumptions beyond SU(3) • are annihilationgraphs and PEW,C negligible ? Silva-Wolfenstein, 1993 Buras et al. (BFRS), EPJ C32, 45 (2003) Chiang et al, PRD D70, 034020 (2004) Wu-Zhou, hep-ph/0503077 Charles et al., EPJ C21, 225 (2001) Charles-Malclès-Ocariz-AH, in preparation … apologies to the many other interesting works ! • Are there puzzles ? • there is a puzzle: why are “color-suppressed” terms so large ? • there isnoK puzzleusing SU(2) [quadrilateral system not constraining enough – 9 params vs. 9 obs] • there seems to beaK puzzleusing SU(3) when neglecting annihilation terms and PEW,C • Our analysis: add annihilation and PEW,C(via Fierz) • the only analysis so far in strict SU(3) limit A. Höcker – CP Violation and the CKM Matrix …

  43. Puzzling B, K, KK Decays : QCDF • Several theoretical tools exist for nonleptonic B decays. All are based on the concept of Factorization • QCD FA • pQCD • SCET including the treatment of charming penguins by Ciuchini et al. Beneke et al, PRL 83, 1914 (1999); NP B675, 333 (03) Keum et al, PLB 504, 6 (2001); PRD 67, 054009 (03) Bauer et al, PRD 63, 114020 (2001) “Color Transparency” • With conservative error treatment, only a data-driven fit is predictive Is there a puzzle ? A. Höcker – CP Violation and the CKM Matrix …

  44. Zfitter I N S P I R E D CKMfitter MNSfitter Sfitter GUTfitter HEPfitter COSMOfitter instead of conclusions … D R E A M S NA48 t h a n k y o u A. Höcker – CP Violation and the CKM Matrix …

  45. a p p e n d i x n o n e A. Höcker – CP Violation and the CKM Matrix …

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