Motivation Fit Method Inputs Results Conclusion

Transcription

1 Motivation Fit Method Inputs Results Conclusion

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 (K s ) = 0.736±0.049, sin (K s ) = -0.14±0.33 sin () = -0.58±0. 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 10-0 n B /n g orders of magnitude difference There are new phases predicted in extension of SM For example in MSSM 14 new parameters enter of which 44 are new phases Super B-factory workshop Hawaii, 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 ) A 3 ( i) V CKM = + A 5 ( 1 i) A 4 A + O( 6 ) A 3 (1 i ) A + A 4 ( 1 i) 1 1 A 4 with = (1 1 ) and = (1 1 ) The unitarity relation V ud V * ub + V cd V * cb + V td V * tb = 0 that represents a triangle (called Unitarity Triangle) in the - plane involves all 4 independent CKM parameters, A,, and =sin c =0. is best-measured parameter (1.5%), A.8 (~5%) while - are poorly known Super B-factory workshop Hawaii, G. Eigen, U Bergen 3

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 semileptonic decays, m d, m s, a cp (K S ) & K to extract A,, Though many measurements are rather precise already the precision of the UT is limited by non gaussian errors in theoretical quantities th (bu,cl), B K, f B B B, 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 Super B-factory workshop Hawaii, G. Eigen, U Bergen 4

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. C1, 5 (001) The Bayesian approach that adds experimental & theoretical errors in quadrature M. Ciuchini et al, JHEP 0107, 013 (001) 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 Bergen 5

6 Model-independent Analysis of UT 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 This is an extension of the scenario discussed by Y. Nir in the BABAR physics book to B s B s mixing and bsss penguins Y. Okada has discussed similar ideas 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) In the presence of new physics: i) b uu d : a =a CP ( + ) b cc s : a Ks =a CP (K s 0 ) remain primarily tree level ia) remains at penguin level b ss s : a Ks =a CP (K s 0 ) ii) There would be a new contribution to KK mixing constraint: small K (ignore new parameters) iii) Unitarity of the 3 family CKM matrix is maintained if there are no new quark generations Super B-factory workshop Hawaii, G. Eigen, U Bergen 6

7 Model-independent Analysis of UT Under these circumstances new physics effects can be described by 4 parameters: r d, d, r s, s 0 B d,s H full 0 eff B d,s 0 B d,s H SM 0 eff B = (r d,s ei d,s ) d,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 bsss transitions Thus, New Physics parameters modify the parameterization of following observables a K s 0 = sin ( + d ) a + = sin ( - d ) m Bd = C t R t r d a K s 0 = sin ( + s ) m Bs = C t R t r s Super B-factory workshop Hawaii, G. Eigen, U Bergen 7

8 The Scanning Method The scanning method is an unbiased, conservative approach to extract A,, & 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 th (B l), th (b ul), th (b cl), F D * (1), B K, f B B B, & perform a maximum likelihood fit using a frequentist approach Super B-factory workshop Hawaii, G. Eigen, U Bergen 8

9 The Scanning Method A particular set of theoretical parameters we call a model M & we perform a minimization to determine A,,, r d, d, r s, s M (A,, ) = Y Y M (A,,,r d, d,r s, s ) F(x) Y 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 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( M ) min >5% For these we determine A,,, r d, d, r s, s 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 Bergen 9

10 The Function in Model-independent Analysis M (A,, ) = m B d m Bd (A,,,r d ) mbd + B l r l A 6 B ( + ) Bl + a K s sin(,, d ) sin + a 'K s sin(,, s ) sin + B K BK B K + m W m W MW + b b b V cb F(1) A 4 F(1) ) Vcb F(1) + B ul Z Z Super B-factory workshop Hawaii, G. Eigen, U Bergen 10 r ul A 6 b ( + ) Bul m Bs m Bs (A,,,r s /r d ) mbs + a sin(,, d ) f B B B f B B B fb + + f Z B 0,+ fb 0,+ B B Z f B 0,+ sin + B 0 B 0 B 0 + f Z B s + fbs Z f Bs + B cl r cl Bcl A 4 b + K K (A,, ) + a K s sin(,, s ) sin + a DK sin(, ) sin + m t m t mt + B + B + B + + f f B 0,+ B 0,+ fb 0,+ + m c m c mc + B s Bs B s

11 Semileptonic Observables Presently, consider 11 different observables V cb excl: R( = 1) = V cb excl F D* (1) phase space corrected rate in B D * l extrapolated for w1w incl: B(B X c l) = V cb th incl b branching fraction at (4S) & Z 0 V ub excl: B(B l) = V ub th excl B 0 affected by non-gaussian uncertainties branching fraction at (4S) incl: B(B X u l) = V ub th incl b branching fraction at (4S) & Z 0 Super B-factory workshop Hawaii, G. Eigen, U Bergen 11

12 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 ) [ ] A 4 1 K K (A,, ) = C B K A 6 1 S 0 (x c ) 3 S 0 (x c,x t ) G m Bd m Bd (A,, ) = r F d 6 Bm Bd m W S 0 (x t )f Bd B Bd A 6 1 ( ) S 0 (x t ) { } QCD parameters that have small non Gaussian errors (except 1 ) [( ) + ] m Bs m Bs (A,, ) = r s G F r d 6 Bm Bs m W S 0 (x t ) f Bd B Bd A 4 New Physics scale parameters r d and r s in BB mixing Super B-factory workshop Hawaii, G. Eigen, U Bergen 1

13 CP-violating Observables in BB System sin (+ d ) from K S sin (+ s ) from K S sin (- d ) from sin(, ) = sin(, ) = sin(, ) = ( 1 ) ( 1 ) + [ ] ( 1 ) ( 1 ) + [ ] ( + ( 1) ) ( + ) 1 [( ) + ] from D (*) K sin(, ) = + ( ) New Physics phases in BB mixing New phase component in bsssb 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 Bergen 13

14 Observable Y(4S) B(bul) [10-3 ] LEP B(bul) [10-3 ] Y(4S) B(bcl) LEP B(bcl) Y(4S) B(Bl) [10-3 ] V cb F(1) m Bd [ps -1 ] m Bs [ps -1 ] K [10-3 ] sin from K s sin from K s ( K s ) sin sin Observables Present Data Set 1.95±0.19 exp ±0.31 th 1.71±0.48 exp ±0.1 th ± ± ±0.43 exp ±0.5 th ± ±0.007 CL (0±5).8± ± ± ±0.33 (0.7±0.) -0.4± ± Data Set 1.85±0.06 exp 1.71±0.48 exp ± ± ± ± ± ±1.8± ± ± ± ± ±0.15 For other masses and lifetimes use PDG 003 values Super B-factory workshop Hawaii, G. Eigen, U Bergen 14

15 Theoretical Parameters Parameter F D* (1) (cl) [ps -1 ] (l) [ps -1 ] (ul) [ps -1 ] B K Present Value Bk =±0.06 Expected Value in Bk =±0.03 f Bd B Bd [MeV] fbbb =± fbbb =± =± =± B Super B-factory workshop Hawaii, G. Eigen, U Bergen 15

16 Error Projections for CP Asymmetries PEP-II, KEKB Super B-Factory >010 Error on A CP sin(+ +) K 0 S D * D * K 0 S, J/K 0 S now Integrated Luminosity [ab -1 ] Super B-factory workshop Hawaii, G. Eigen, U Bergen 16

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 Range of - values resulting from fits to different models Overlay of 95% CL contours, each represents a model Super B-factory workshop Hawaii, G. Eigen, U Bergen 17

18 Present Results Parameter A m c Scan Method , =± , =± , =± , =± ( ) 0, =± ( )0, =±5.4 ( ) 0, =± Super B-factory workshop Hawaii, G. Eigen, U Bergen 18

19 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 constraint Weakening of m Bd, m Bs & sin bounds is not visible due to 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 Bergen 19

20 Present Status of r d - d Plane & r s /r d - s Plane Global fits to present extended data set including a Ks, a & (DK) d r d - d plane is consistent with SM Second region (r d <1, d <0) is rejected by sin constraint r d r s - s plane is consistent with SM for some models 1.5 s Second region inconsistent with SM is visible 0. r s /r d Super B-factory workshop Hawaii, G. Eigen, U Bergen 0

21 Present Status of the - Plane Old global fits to present data set excluding a Ks, a & (DK) fitting only to r d, d The introduction of new parameters r d, d weakens the sin constraint m Bd & m Bs biunds Fits extend into negative region Super B-factory workshop Hawaii, G. Eigen, U Bergen 1

22 Present Status of r d -θ d Plane & r s /r d -θ s Plane Old global fits to present data set excluding a φks, a ππ & γ(dk) fitting only to r d, θ d θ d r d -θ d plane is consistent with SM Second region (r d <1, θ d <0) is visible r d Super B-factory workshop Hawaii, G. Eigen, U Bergen 1

23 Possible Status of the - Plane in 011 Global fits to data set expected in 011 including a Ks, a & (DK) Reduced errors yield smaller-size contours and a reduced # of accepted models The sin constraint remains weak, now see also weakening Bs bound m Bs Super B-factory workshop Hawaii, G. Eigen, U Bergen 3

24 Possible Status of r d - d & r s /r d - s Planes in 011 Global fits to data set expected in 011 including a Ks, a & (DK) 0.5 d r d - d plane is still consistent with SM 0. Size of contours are reduced substantially r d r s - s plane now is inconsistent with SM for some models 0.5 s Second region inconsistent with SM disappears 0. r s /r d Super B-factory workshop Hawaii, G. Eigen, U Bergen 1.0 4

25 Comparison of Results Fit Results for parameterization with r d, d, r s, & s Parameter A m c Present Results , =± , =± , =± , =± 0.16 ( ) 0, =± ( ) 0, =± 5.0 ( ) 0, =± Possible results in , =± , =± , =± , =± ( ) 0, =± 1.1 ( ) 0, =± 1.9 ( ) 0, =± Super B-factory workshop Hawaii, G. Eigen, U Bergen 5

26 Possible Status of the - Plane in 011 Global fits to data set expected in 011 including a Ks, a (DK) & a Ks, Inclusion of a Ks results in reduced countours Super B-factory workshop Hawaii, G. Eigen, U Bergen 6

27 Possible Status of r d - d & r s /r d - s Planes in 011 Global fits to data set expected in 011 including a Ks, a,(dk) & a Ks 0.5 d r d - d plane is still consistent with SM r d.5 Inclusion of a Ks reduces r d - d contour sizes r s - s plane remains inconsistent with SM for some models Inclusion of a Ks reduces r s /r d - s contour sizes r s /r d Super B-factory workshop Hawaii, G. Eigen, U Bergen 7.5 s

28 Possible Status of the - Plane after 011 Global fits to data set expected in 011 including a Ks, a & (DK) with a Ks Ks=-0.96± & a =-0.95± Using Belle central values with small errors changes the picture obtain separated regions in - plane Weakening of sin, m Bd, m Bs & sin bounds is apparent now Super B-factory workshop Hawaii, G. Eigen, U Bergen 8

29 Possible Status of r d - d & r s /r d - s Planes after 011 Global fits to data set expected in 011 including a Ks, a & (DK) with a Ks Ks=-0.96± & a =-0.95± d r d - d plane is shifted to r d >0, d >0 values s >0 regions are favored r s - s plane now is highly inconsistent with SM 1 r d Size of contours are reduced substantially r d - d plane is now inconsistent with SM s r s /r d -1.5 Super B-factory workshop Hawaii, G. Eigen, U Bergen 1 9.0

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 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 011 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 measurements and add further parameters for strong phases It is useful to include sin(+) from BD (*) modes Super B-factory workshop Hawaii, G. Eigen, U Bergen 30