 Motivation  Fit Method  Inputs  Results  Conclusion

Super B-factory workshop Hawaii, G. Eigen, U Bergen2 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  (  K s ) = 0.736±0.049, sin 2  (  K s ) = -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: n B /n g   n B /n g   9 orders 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

Super B-factory workshop Hawaii, G. Eigen, U Bergen3 The Cabbibo-Kobayashi-Maskawa Matrix   A convenient representation of the CKM matrix is the small-angle Wolfenstein approximation to order O( 6 )   The unitarity relation that represents a triangle (called Unitarity Triangle) in the  -  plane involves all 4 independent CKM parameters, A, , and    =sin  c =0.22 is best-measured parameter (1.5%), A .8 (~5%) while  -  are poorly known with and

Super B-factory workshop Hawaii, G. Eigen, U Bergen4 MOTIVATION   SM tests in the CP sector are conducted by performing maximum likelihood fits of the unitarity triangle   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  significant conflict  Only then we can believe that any observed significant conflict is real indicating the presence of New Physics   Present inputs are based on measurements of B semi- leptonic decays,  m d,  m s, a cp (  K S ) & |  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 ), B K, f B  B B, 

Super B-factory workshop Hawaii, G. Eigen, U Bergen5 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 approach F. Gilman, K. Kleinknecht and D. Renker

Super B-factory workshop Hawaii, G. Eigen, U Bergen6   New Physics is expected to affect both B d B d mixing & B s B s mixing introducing new CP-violating phases that differ from SM phase r r This is an extension of the scenario discussed by Y. Nir in the BABAR physics book to B s B s mixing and b  sss penguins Y. Okada has discussed similar ideas r r Yossi considered measurements of V ub /V cb,  m Bd, a  Ks, a , we extend this to  m Bs, a  Ks (a  ’Ks ) in addition to  K,  (DK) r r 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 Model-independent Analysis of UT

Super B-factory workshop Hawaii, G. Eigen, U Bergen7   Under these circumstances new physics effects can be described by 4 parameters: r d,  d, r s,  s   Our observables are sensitive to r d,  d, r s induced 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 Model-independent Analysis of UT

Super B-factory workshop Hawaii, G. Eigen, U Bergen8 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

Super B-factory workshop Hawaii, G. Eigen, U Bergen9 The Scanning Method   A particular set of theoretical parameters we call a “model” M & we perform a  2 minimization to determine   Here 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(  2 M ) 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

Super B-factory workshop Hawaii, G. Eigen, U Bergen10 The  2 Function in Model-independent Analysis

Super B-factory workshop Hawaii, G. Eigen, U Bergen11 Semileptonic Observables   Presently, consider 11 different observables     V cb affected by non-Gaussian non-Gaussianuncertainties V ub phase space corrected rate in B  D * l extrapolated for w  1 excl: incl: excl: incl: branching fraction at  (4S) & Z 0 branching fraction at  (4S) branching fraction at  (4S) & Z 0

Super B-factory workshop Hawaii, G. Eigen, U Bergen12 K 0 K 0 CP-violating & B 0 B 0 -mixing Observables       theoretical parameters with large non-Gaussian errors account for correlation of m c in  1 & S 0 (x c ) New Physics scale parameters r d and r s in BB mixing  m Bs  m Bd KKKK QCD parameters that have small non Gaussian errors (except  1 )

Super B-factory workshop Hawaii, G. Eigen, U Bergen13 CP-violating Observables in BB System        New Physics phases in BB mixing New phase component in b  sss sin 2(  +  d ) from  K S sin 2(  +  s ) from  K S 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

Super B-factory workshop Hawaii, G. Eigen, U Bergen14 Observables   For other masses and lifetimes use PDG 2003 values ObservablePresent Data Set2011 Data Set Y(4S) B(b  ul ) [10 -3 ]1.95±0.19 exp ±0.31 th 1.85±0.06 exp LEP B(b  ul ) [10 -3 ]1.71±0.48 exp ±0.21 th 1.71±0.48 exp Y(4S) B(b  cl )0.1090± ± LEP B(b  cl )0.1042± Y(4S) B(B  l ) [10 -3 ]2.68±0.43 exp ±0.5 th 3.29±0.14 |V cb |F(1)0.0367± ±  m Bd [ps -1 ]0.502± ±  m Bs [ps -1 ] (20±5) CL  (20±5)25±1 |  K | [10 -3 ]2.282± ± sin 2  from  K s 0.736± ±0.01 sin 2  from  K s (  ’K s )-0.14±0.33 (0.27±0.22)0.6±0.15 sin 2  -0.4± ±0.05 sin  0.7±0.50.7±0.15

Super B-factory workshop Hawaii, G. Eigen, U Bergen15 Theoretical Parameters ParameterPresent ValueExpected Value in 2011 F D* (1)0.87   0.92  (cl ) [ps -1 ]34.1   39.2  (  l ) [ps -1 ]12.0   13.4  (ul ) [ps -1 ]54.6   76.9 BKBK 0.74  1.0  Bk =    Bk =  0.03 f Bd  B Bd [MeV]218  238  fB  BB =   233  fB  BB =  10  1.16  1.26   =  0.05 11 1.0  1.64 2  3  0.51 BB 0.54  0.56

Super B-factory workshop Hawaii, G. Eigen, U Bergen16 Error Projections for CP Asymmetries Integrated Luminosity [ab -1 ] Error on A CP 2006 PEP-II, KEKB Super B-Factory >2010 sin(2  ) K0SK0SK0SK0S D*D*D*D*D*D*D*D*  ’K 0 S,   J/  K 0 S now

Super B-factory workshop Hawaii, G. Eigen, U Bergen17 Present Status of the Unitarity Triangle in SM Fit central values from individual fits to models  Range of  -  values resulting from fits to different models Contour of individual fit Overlay of 95% CL contours, each represents a “model”  SM fit to A, ,  using present data set

Super B-factory workshop Hawaii, G. Eigen, U Bergen18 Present Results ParameterScan Method  ,  =±  ,  =± A ,  =± mcmc ,  =± 0.18  ( ) 0,  =± 7.1  ( ) 0,  =± 5.4  ( ) 0,  =±

Super B-factory workshop Hawaii, G. Eigen, U Bergen19 Present Status of the  -  Plane  Global fits to present extended data set including a  Ks, a  &  (DK)  The introduction of new parameters r d,  d, r s, &  s weakens the sin 2  constraint sin 2  constraint  Weakening of  m Bd,  m Bs & sin 2  bounds is not visible due to large errors & impact of V ub /V cb,  K, sin  constraints large errors & impact of V ub /V cb,  K, sin  constraints  Negative  region is rejected by sin  constraint

Super B-factory workshop Hawaii, G. Eigen, U Bergen20 Present Status of r d -  d Plane & r s /r d -  s Plane rdrdrdrd dddd ssss r s /r d  Global fits to present extended data set including a  Ks, a  &  (DK)  r d -  d plane is consistent with SM SM  Second region (r d <1,  d <0) is rejected by sin  constraint is rejected by sin  constraint  r s -  s plane is consistent with SM for some models SM for some models  Second region inconsistent with SM is visible with SM is visible

Super B-factory workshop Hawaii, G. Eigen, U Bergen21 Present Status of the  -  Plane  Old global fits to present data set excluding a  Ks, a  &  (DK) fitting only to r d,  d fitting only to r d,  d  The introduction of new parameters r d,  d weakens the sin 2  constraint  m Bd &  m Bs biunds sin 2  constraint  m Bd &  m Bs biunds  Fits extend into negative  region

Super B-factory workshop Hawaii, G. Eigen, U Bergen22 Present Status of r d -  d Plane & r s /r d -  s Plane  r d -  d plane is consistent with SM SM  Second region (r d <1,  d <0) is visible is visible rdrdrdrd dddd 1  Old global fits to present data set excluding a  Ks, a  &  (DK) fitting only to r d,  d fitting only to r d,  d

Super B-factory workshop Hawaii, G. Eigen, U Bergen23 Possible Status of the  -  Plane in 2011  Global fits to data set expected in 2011 including a  Ks, a  &  (DK)  Reduced errors yield smaller-size contours and a reduced # of accepted models of accepted models  The sin 2  constraint remains weak, now see also weakening  m Bs bound  m Bs bound

Super B-factory workshop Hawaii, G. Eigen, U Bergen24 Possible Status of r d -  d & r s /r d -  s Planes in 2011 rdrdrdrd ssss  Global fits to data set expected in 2011 including a  Ks, a  &  (DK) r s /r d dddd  r d -  d plane is still consistent with SM with SM  Size of contours are reduced substantially substantially  r s -  s plane now is inconsistent with SM for some models with SM for some models  Second region inconsistent with SM disappears with SM disappears

Super B-factory workshop Hawaii, G. Eigen, U Bergen25 Comparison of Results ParameterPresent ResultsPossible results in 2011  ,  =± ,  =±  ,  =± ,  =± A ,  =± ,  =± mcmc ,  =± ,  =± 0.08  ( ) 0,  =± 3.1 ( ) 0,  =± 1.1  ( ) 0,  =± 5.0 ( ) 0,  =± 1.9  ( ) 0,  =± 4.4 ( ) 0,  =±  Fit Results for parameterization with r d,  d, r s, &  s

Super B-factory workshop Hawaii, G. Eigen, U Bergen26 Possible Status of the  -  Plane in 2011  Global fits to data set expected in 2011 including a  Ks, a ,  (DK) & a  ’Ks  (DK) & a  ’Ks  Inclusion of a  ’Ks results in reduced countours

Super B-factory workshop Hawaii, G. Eigen, U Bergen27 Possible Status of r d -  d & r s /r d -  s Planes in r s /r d  Global fits to data set expected in 2011 including a  Ks, a ,  (DK) & a  ’Ks & a  ’Ks rdrdrdrd dddd ssss  r d -  d plane is still consistent with SM with SM  Inclusion of a  ’Ks reduces r d -  d contour sizes r d -  d contour sizes  r s -  s plane remains inconsistent with SM inconsistent with SM for some models for some models  Inclusion of a  ’Ks reduces r s /r d -  s contour sizes r s /r d -  s contour sizes

Super B-factory workshop Hawaii, G. Eigen, U Bergen28 Possible Status of the  -  Plane after 2011  Global fits to data set expected in 2011 including a  Ks, a  &  (DK) with a  Ks =-0.96±0.01 & a  =-0.95±0.05 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  obtain 2 separated regions in  -  plane  Weakening of sin 2 ,  m Bd,  m Bs & sin 2  bounds is apparent now 

Super B-factory workshop Hawaii, G. Eigen, U Bergen29 Possible Status of r d -  d & r s /r d -  s Planes after 2011 ssss dddd rdrdrdrd r s /r d  Global fits to data set expected in 2011 including a  Ks, a  &  (DK) with a  Ks =-0.96±0.01 & a  =-0.95±0.05 with a  Ks =-0.96±0.01 & a  =-0.95±0.05  r d -  d plane is shifted to r d >0,  d >0 values r d >0,  d >0 values  Size of contours are reduced substantially substantially  r d -  d plane is now inconsistent with SM with SM  2  s >0 regions are favored  r s -  s plane now is highly inconsistent with SM inconsistent with SM

Super B-factory workshop Hawaii, G. Eigen, U Bergen30 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 significant This is crucial for believing that any observed significant discrepancy discrepancy is real indicating New Physics   Due to the large theoretical uncertainties all measurements are presently consistent with the SM expectation   Deviation of a CP (  K S ) from a CP (  K S ) 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 r d -  d or r s -  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