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Model-independent Analysis of the CKM Matrix

Model-independent Analysis of the CKM Matrix. Motivation Fit Method Inputs Results Conclusion. G. Eigen, University of Bergen. In collaboration with G. Dubois-Felsmann, D. Hitlin, F. Porter. Super B-Factory Workshop, Hawaii 21-01-2004. MOTIVATION.

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Model-independent Analysis of the CKM Matrix

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  1. Model-independent Analysis of the CKM Matrix • Motivation • Fit Method • Inputs • Results • Conclusion G. Eigen, University of Bergen In collaboration with G. Dubois-Felsmann, D. Hitlin, F. Porter Super B-Factory Workshop, Hawaii 21-01-2004

  2. MOTIVATION • In the hunt for New Physics (Supersymmetry) the Standard Model (SM) has to be scrutinized in various areas • Two very promising areas are CP violation and rare decays, that may reveal first signs of New Physics before the start of LHC • BABAR/Belle have measured different CP asymmetries e.g. sin 2 (Ks) = 0.736±0.049, sin 2 (Ks) = -0.14±0.33 sin 2 () = -0.58±0.2  with present statistics this is in good agreement with SM prediction that CP violation is due to phase of CKM matrix • The phase of the CKM matrix, however, cannot predict the observed baryon-photons ratio: nB/ng 10-20  nB/ng 10-11 9orders of magnitude difference • There are new phases predicted in extension of SM • For example in MSSM 124 new parameters enter of which 44 are new phases G. Eigen, U Bergen

  3. The Cabbibo-Kobayashi-Maskawa Matrix • A convenient representation of the CKM matrix is the small-angle Wolfenstein approximation to order O(6) with and • The unitarity relation that represents a triangle (called Unitarity Triangle) in the - planeinvolvesall 4 independent CKM parameters , A, , and  • =sinc=0.22 is best-measured parameter (1.5%), A.8 (~5%) while -arepoorly known G. Eigen, U Bergen

  4. MOTIVATION • SM tests in the CP sector are conducted by performing maximum likelihood fits of the unitarity triangle • Present inputs are based on measurements of B semi- leptonic decays, md,ms, acp(KS) & |K| to extract • Though many measurements are rather precise already the precision of the UT is limited by non gaussian errors in theoretical quantities th(bu,cl), BK, fBBB,  • CKM tests need to be based on a conservative, robust method with a realistic treatment of uncertainties to reduce the sensitivity to avoid fake conflicts or fluctuations • Only then we can believe that any observed significant conflict is real indicating the presence of New Physics G. Eigen, U Bergen

  5. Global Fit Methods • Different approaches exist: • The scanning method a frequentist approach first developed for the BABAR physics book (M. Schune, S. Plaszynski), extended by Dubois-Felsmann et al • RFIT, a frequentist approach that maps out the theoretical parameter space in a single fit A.Höcker et al, Eur.Phys.J. C21, 225 (2001) • The Bayesian approach that adds experimental & theoretical errors in quadrature M. Ciuchini et al, JHEP 0107, 013 (2001) • A frequentist approach by Dresden group K. Schubert and R. Nogowski • The PDG approachF. Gilman, K. Kleinknecht and D. Renker G. Eigen, U Bergen

  6. Model-independent Analysis of UT • New Physics is expected to affect both BdBd mixing & BsBs mixing introducing new CP-violating phases that differ from SM phase • This is an extension of the scenario discussed by Y. Nir in the BABAR physics book to BsBs mixing and bsss penguins Y. Okada has discussed similar ideas • Yossi considered measurements of Vub/Vcb,mBd, aKs, a, we extend this to mBs, aKs (a’Ks) in addition to K, (DK) • In the presence of new physics: • i) • remain primarily tree level • ia) remains at penguin level • ii) There would be a new contribution to KK mixing • constraint: small (ignore new parameters) • iii) Unitarity of the 3 family CKM matrix is maintained • if there are no new quark generations G. Eigen, U Bergen

  7. Model-independent Analysis of UT • Under these circumstances new physics effects can be described by 4 parameters: rd, d, rs, s • Our observables are sensitive to rd, d, rsinduced by mixing (no s sensitive observable) In addition, we are sensitive to a new phase s’=s-d in bsss transitions • Thus,New Physics parameters modify the parameterization of following observables G. Eigen, U Bergen

  8. The Scanning Method • The scanning method is an unbiased, conservative approach to extract & New Physics parameters from the observables • We have extended the method of the BABAR physics book (M.H. Schune and S. Plaszczynski) to deal with the problem of non-Gassian theoretical uncertainties in a consistent way • We factorize quantities affected by non-Gaussian uncertainties (th) from the measurements • We select specific values for the theoretical parameters & perform a maximum likelihood fit using a frequentist approach G. Eigen, U Bergen

  9. The Scanning Method • A particular set of theoretical parameters we call a “model” M & we perform a 2 minimization to determine • Here <Y> denotes an observable & Y accounts for statistical and systematic error added in quadrature, while F(x) represents the theoretical parameters affected by non-Gaussian errors • For Gaussian error part of the theoretical parameters, we also include specific terms in the 2 • We fit many individual models scanning over the allowed theoretical parameter space for each of these parameters • We consider a model consistent with data, if P(2M)min>5%  For these we determine and plot contours  The contours of various models are overlayed We can also study correlations among theoretical parameters extending their range far beyond that specified by theorists G. Eigen, U Bergen

  10. The 2 Function in Model-independent Analysis G. Eigen, U Bergen

  11. Semileptonic Observables • Presently,consider11 different observables Vcb phase space corrected rate in B D*l extrapolated for w1 excl: branching fraction at (4S) & Z0 incl: affected by non-Gaussian uncertainties Vub branching fraction at (4S) excl: branching fraction at (4S) & Z0 incl: G. Eigen, U Bergen

  12. K0K0 CP-violating & B0B0-mixing Observables theoretical parameters with large non-Gaussian errors K account for correlation of mc in 1 & S0(xc) QCD parameters that have small non Gaussian errors (except 1) mBd mBs New Physics scale parameters rd and rs in BB mixing G. Eigen, U Bergen

  13. CP-violating Observables in BB System sin 2(+d) from KS sin 2(+s) from KS sin 2(-d) from   from D(*)K • Note, that presently no extra strong phases in a are included • In future will include this adding C in the global fits New Physics phases in BB mixing New phase component in bsss G. Eigen, U Bergen

  14. Observables G. Eigen, U Bergen • For other masses and lifetimes use PDG 2003 values

  15. Theoretical Parameters G. Eigen, U Bergen

  16. Super B-Factory >2010 PEP-II, KEKB 2006 2009 Error Projections for CP Asymmetries 1.0 sin(2) K0S Error on ACP D*D* ’K0S,   J/K0S 10-1 10-2 10-2 10-1 1 10 102 now Integrated Luminosity [ab-1] G. Eigen, U Bergen

  17. Present Status of the Unitarity Triangle in SM Fit • SM fit to A, ,  using present data set Contour of individual fit central values from individual fits to models Overlay of 95% CL contours, each represents a “model” • Range of - values resulting from fits to different models G. Eigen, U Bergen

  18. Present Results 0.11 0.020 0.024 0.18 2.6 15.8 3.3 G. Eigen, U Bergen

  19. Present Status of the - Plane • Global fits to presentextended data set including aKs, a & (DK) • The introduction of new parameters rd, d, rs, & s weakens the sin 2 constraint • Weakening of mBd, mBs & sin 2 bounds is not visible due to large errors & impact of Vub/Vcb, K, sin constraints • Negative  region is rejected by sin constraint G. Eigen, U Bergen

  20. Present Status of rd-d Plane & rs/rd-s Plane • Global fits to presentextended data set including aKs, a & (DK) 0.5 d • rd-d plane is consistent with SM • Second region (rd<1, d<0) is rejected by sin  constraint 0. rd -0.5 2.5 0 1 s 1.5 • rs- s plane is consistent with SM for some models • Second region inconsistent with SM is visible 0. rs/rd -1.5 2.5 0 1 G. Eigen, U Bergen

  21. Present Status of the - Plane • Old global fits to presentdata set excluding aKs, a & (DK) fitting only to rd, d • The introduction of new parameters rd, d weakens the sin 2 constraint mBd & mBs biunds • Fits extend into negative  region G. Eigen, U Bergen

  22. Present Status of rd-d Plane & rs/rd-s Plane • Old global fits to presentdata set excluding aKs, a & (DK) fitting only to rd, d 0.5 d • rd-d plane is consistent with SM • Second region (rd<1, d<0) is visible 0. rd -0.5 0 1 G. Eigen, U Bergen

  23. Possible Status of the - Plane in 2011 • Global fits todata set expected in 2011 including aKs, a & (DK) • Reduced errors yield smaller-size contours and a reduced # of accepted models • The sin 2 constraint remains weak, now see also weakening mBs bound G. Eigen, U Bergen

  24. Possible Status of rd-d & rs/rd-s Planes in 2011 • Global fits to data set expected in 2011 including aKs, a & (DK) 0.5 d • rd-d plane is still consistent with SM • Size of contours are reduced substantially 0. rd -0.5 2.0 0 1 0.5 s • rs- s plane now is inconsistent with SM for some models • Second region inconsistent with SM disappears 0. rs/rd -0.5 0 1 2.0 G. Eigen, U Bergen

  25. Comparison of Results • Fit Results for parameterization with rd,d, rs,&s 0.031 0.11 0.006 0.017 0.035 0.022 0.18 0.09 1.8 1.1 6.4 2.0 1.3 2.6 G. Eigen, U Bergen

  26. Possible Status of the - Plane in 2011 • Global fits todata set expected in 2011 including aKs, a, (DK) & a’Ks • Inclusion of a’Ks results in reduced countours G. Eigen, U Bergen

  27. Possible Status of rd-d & rs/rd-s Planes in 2011 • Global fits todata set expected in 2011 including aKs, a,(DK) & a’Ks 0.5 d • rd-d plane is still consistent with SM • Inclusion of a’Ks reduces rd-d contour sizes 0. rd -0.5 0 1 2.5 0.5 s • rs- s plane remains inconsistent with SM for some models • Inclusion of a’Ks reduces rs/rd-s contour sizes 0. rs/rd -0.5 0 1 2.5 G. Eigen, U Bergen

  28. Possible Status of the - Plane after 2011 • Global fits todata set expected in 2011 including aKs, a & (DK) with aKs=-0.96±0.01 & a=-0.95±0.05 • Using Belle central values with small errors changes the picture  obtain 2 separated regions in - plane • Weakening of sin 2, mBd, mBs & sin 2 bounds is apparent now G. Eigen, U Bergen

  29. Possible Status of rd-d & rs/rd-s Planes after 2011 • Global fits todata set expected in 2011 including aKs, a & (DK) with aKs=-0.96±0.01 & a=-0.95±0.05 0.5 d • rd-d plane is shifted to rd>0, d>0 values • Size of contours are reduced substantially • rd-d plane is now inconsistent with SM 0. rd -0.5 0 1 2.0 1.5 s • 2 s>0 regions are favored • rs-s plane now is highly inconsistent with SM 0. rs/rd -1.5 2.0 0 1 G. Eigen, U Bergen

  30. Conclusions • Model-independent analyses will become important in the future • The scanning method provides a conservative, robust procedure with a reasonable treatment of non-gaussian theor. uncertainties This allows to avoid fake conflicts or fluctuations This is crucial for believing that any observed significant discrepancyis real indicating New Physics • Due to the large theoretical uncertainties all measurements are presently consistent with the SM expectation • Deviation of aCP(KS) from aCP(KS) is interesting but not yet significant, similar comment holds for Belle’s S & A results • If errors get reduced as prognosed, - plane will be substantially reduced in 2011 • The fits indicate that the impact of New Physics may be less visible in - plane but show up in rd-d or rs-s planes • In the future we will incorporate other sin 2 measurements and add further parameters for strong phases • It is useful to include sin(2+) from BD(*) modes G. Eigen, U Bergen

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