1. B. Golob, Ljubljana Univ.Results from B factories 1HQP School, Dubna, Aug 2008 Boštjan Golob University of Ljubljana, Jožef Stefan Institute & Belle Collaboration Beauty and charm results from B factories University of Ljubljana Jožef Stefan Institute Helmholtz International Summer School Heavy Quark Physics Bogoliubov Laboratory of Theoretical Physics, Dubna, Russia, August 11-21, 2008 JINR

2. B. Golob, Ljubljana Univ.Results from B factories 2HQP School, Dubna, Aug 2008 Outline Part of B-factories lectures with A.J. Bevan; division by topics, not by experiments It is a curious fact that people are never so trivial as when they take themselves seriously. O. Wilde (1854 - 1900) exp. results with some comments on phenomenology

3. B. Golob, Ljubljana Univ.Results from B factories 3HQP School, Dubna, Aug 2008 Introduction Experiments (c c) 1.3 nb (~10 9 X c Y c pairs) continuum production * c c on resonance production e + e - (4S) B 0 B 0, B + B - (BB) 1.1 nb (~0.9x10 9 BB pairs) e + e - (3770) D 0 D 0, D + D - (coherent C=-1 state); ~800 pb -1 of data available at (3770); 2.8x10 6 D 0 D 0 3.5 fb -1 on tape (D 0 ; p t >5.5 GeV,|y|<1) 13 b 50x10 9 D 0 s very diverse exp. conditions We all live with the objective of being happy; our lives are all different and yet the same. Anne Frank (1929 -1945)

4. B. Golob, Ljubljana Univ.Results from B factories 4HQP School, Dubna, Aug 2008 B oscillations diagonal elem.: P 0 P 0 (including decays) non-diagonal elem.: P 0 P 0 P0P0 q1q1 q2q2 q1q1 P0P0 q2q2 P 0 = K 0, B d 0, B s 0 and D 0 Time evolution (also lectures by U. Nierste, A. Pivovarov) flavour states H eff eigenstates: (defined flavour) (defined m 1,2 and 1,2 ) eigenvalues: more

5. B. Golob, Ljubljana Univ.Results from B factories 5HQP School, Dubna, Aug 2008 B oscillations Time evolution for easier notation: t (4S) B 0 B 0 : B meson pair in quantum coherent state; before 1st B decay: B 0 B 0 1st B decay: tag B 0 /B 0 ; mixing clock start, t t decay rates: Decay time distribution of experimentally accessible states P 0, P 0 sensitive to mixing parameters x and y, depending on final state D. Kirkby, Y. Nir, CPV in Meson Decays, in RPP P 1,2 evolve in time according to m 1,2 and 1,2 : |P 0 (t)>, |P 0 (t)> more

6. B. Golob, Ljubljana Univ.Results from B factories 6HQP School, Dubna, Aug 2008 B oscillations Time evolution visually unobservable deviation from pure exponential ~ B s 0 more difficult to observe oscillations within probab. to observe an initially produced X 0 as X 0 after time t ~ D 0

7. B. Golob, Ljubljana Univ.Results from B factories 7HQP School, Dubna, Aug 2008 B oscillations Method similar to CPV, reconstruct flavor specific final states B sig B tag J/ K*0K*0 + - - K+K+ K-K- l-l- fully reconstruct decay to flavor specific final state tag flavor of other B from charges of typical decay products t= z/ c determine time between decays (4S) determined B 0 (B 0 ) B 0 or B 0 signal

8. B. Golob, Ljubljana Univ.Results from B factories 8HQP School, Dubna, Aug 2008 B oscillations Method reconstructed flavour specific decays Belle, PRD71, 072003 (2005), 140 fb -1 E signal region measure t distribution more Method t distribution A f =0, |y|<<1 w: wrong tag probability (reduces ampl. of oscillations) R( t): resolution function - intrinsic detector resolution on position of both B vertices - smearing due to non-primary tracks - smearing due to B meson CMS momentum aver ( t)=1.43 ps more

9. B. Golob, Ljubljana Univ.Results from B factories 9HQP School, Dubna, Aug 2008 B oscillations Results flavour asymmetry Belle, PRD71, 072003 (2005), 140 fb -1 m d =(0.511±0.005±0.006) ps -1 HFAG, http://www.slac.stanford.edu/xorg/hfag/ m d =(0.507±0.005) ps -1 x= m d Bd = 0.776±0.008 largest syst.: D** bkg.

10. B. Golob, Ljubljana Univ.Results from B factories 10HQP School, Dubna, Aug 2008 B oscillations if m i = m j due to CKM unitarity: no mixing d b b d u, c, t W+W+ W-W- B0B0 B0B0 d b b d W+W+ W-W- B0B0 B0B0 V id V jd V jb * V ib * Phenomenology (see also lectures by U. Nierste) P 0 -P 0 transition box diagram at quark level P 0 : any pseudo-scalar meson; specific example of B d 0 considering CKM values and q masses: largest contribution from t quark loop int., CKM unitarity more

11. B. Golob, Ljubljana Univ.Results from B factories 11HQP School, Dubna, Aug 2008 B oscillations calculate M 12, 12 from box diagram; from that calculate m, must be calculated to determine V ij ; theor. uncertainty (LQCD) q: d (B d ) or s (B s ); and m s also measured... Phenomenology A.J. Buras et al., Nucl.Phys.B245, 369 (1984) B Bq : bag parameter, f Bq : decay constant B ( ) : QCD corr. O (1) S 0 (x t ): known kinematic function reduced theor. uncertainty in ratio M. Okamoto, hep-lat/0510113 2

12. B. Golob, Ljubljana Univ.Results from B factories 12HQP School, Dubna, Aug 2008 B oscillations B s amplitude method: instead of m s fit A at different values of m s ; A =1 oscillations at this m s value CDF, PRL97, 242003 (2006) A m s =(17.77±0.10±0.07) ps -1 x= m s Bs = 25.5±0.6 m s / m d uncertainties on ( 2 + 2 ): m d constraint ±13% m d ±1% f Bd B Bd ±12% m s / m d constraint ±6% m s / m d ±1.5% ±5%

13. B. Golob, Ljubljana Univ.Results from B factories 13HQP School, Dubna, Aug 2008 Leptonic B decays B Q q P+P+ l+l+ fPfP V Qq (B + ): (B + ): (B + e + )= 1:4x10 -3 :10 -7 f P meas. V Qq ; H ± ; W+W+ Method fully reconstruct B tag in hadronic decays (K + - + - + ); search for 1/3 tracks from B sig (e - ); no additional energy in EM calorim. (from 0,,...); signal at E ECL ~0 B candidate event EM calorim. (H + )

14. B. Golob, Ljubljana Univ.Results from B factories 14HQP School, Dubna, Aug 2008 BaBar, PRD77, 011107 (2008), 346 fb -1 Leptonic B decays Results Belle, PRL97, 251802 (2006), 414 fb -1 signal bkg. N sig =17 ± 5 3.5 signif. (-2ln L 0 / L max ) largest syst. from signal and bkg. shape semileptonic tag added BaBar: hadronic decays for B tag ; combined with semil. decays: more BaBar, PRD76, 052002 (2007), 346 fb -1 expected signal Br=3x10 -3 HFAG, http://www.slac.stanford.edu/xorg/hfag/ Belle, ICHEP08, 600 fb -1

15. B. Golob, Ljubljana Univ.Results from B factories 15HQP School, Dubna, Aug 2008 Leptonic B decays Phenomenology using f B =(216 ± 22) MeV, |V ub |=(3.9 ± 0.5)x10 -3, B Br SM (B + ) = (1.25 ± 0.41)x10 -4 new physics: to make predictions/measure |V ub | f B (from LQCD) needed; validate LQCD in charm sector (better exp. precision) to be addressed later; established method for decays with large E miss ; to be exploited at SuperB (BK, dark matter) HPQCD, PRL95, 212001 (2005) SuperB 50 ab -1 b u B-B- H+H+ more

16. B. Golob, Ljubljana Univ.Results from B factories 16HQP School, Dubna, Aug 2008 Semileptonic B decays P P l q1q1 q3q3 l+l+ M1M1 q2q2 M2M2 q2q2 in suppressed by m l 2 /m M1 2 negligible for e, ; not for P V l 3 form f. for e, ; 4 for HQS: relations among f.f.s; can be tested; for suppressed f.f.s only by W±,W±, H±H± H ± exchange modified SM Brs for ; in P V only helicity=0 V possible more measurement challenging due to multiple s; skip

17. B. Golob, Ljubljana Univ.Results from B factories 17HQP School, Dubna, Aug 2008 Semileptonic B decays B 0 D* - + method: D* reconstruction; e, B sig : D* and e/ B tag : rest of event control sample: B sig D*, check B tag reconstruction signal sample: requirements on X mis, E vis method: excl. B tag reconstruction e, B sig : D/D* and e/ m mis 2 =p mis 2 MC data B sig D* related to missing mass (>0 for several ); E vis < m( (4S)) D* B sig e/ B tag Belle, PRL99, 191807 (2007), 480 fb -1 BaBar, PRL100, 021801 (2008), 209 fb -1 missing mass (>0 for several );

18. B. Golob, Ljubljana Univ.Results from B factories 18HQP School, Dubna, Aug 2008 Semileptonic B decays B 0 D* - + results bkg. from B 0 D*e (peaking) N sig =60 ±12 6.7 signif. (-2ln L 0 / L max ) main systematics: from signal and bkg shape (MC) B tag reconstr. eff. (control sample) Belle, PRL99, 191807 (2007), 480 fb -1 BaBar, PRL100, 021801 (2008), 209 fb -1 D* - + D - + D - l + D* - l + last uncertainty: normaliz. modes (D l, D* l ) main systematics: from signal and bkg shape (MC) D** contrib.

19. B. Golob, Ljubljana Univ.Results from B factories 19HQP School, Dubna, Aug 2008 Semileptonic B decays B D ( * ) phenomenology limits on H ± ; inclusive B X c predicted Br: (2.30 ±0.25)% sum of D*, D : (2.59 ±0.39)% M. Tanaka, Z.Phys.C67, 321 (1995) Ba/lle average (assuming no correl. and 100% long. polariz.) BaBar A.F.Falk et al., PLB326, 145 (1994) (B D* long. ) (B D* )| SM more

20. B. Golob, Ljubljana Univ.Results from B factories 20HQP School, Dubna, Aug 2008 b s Motivation FCNC process; sensitive to NP in loop; parton level: E m b /2; determ. of m b, Fermi motion needed for V ub determ. from inclusive semil. B decays; Difficulties theory: parameter extraction from partial Br(E >E cut ) extrapolation needed; experiment: measure low E huge bkg. b s W±W± u, c, t V qb V qs b s u, c, t XY H±H± ± b s XY more signal continuum 0 Your background and environment is with you for life. No question about that. S. Connery (1930)

21. B. Golob, Ljubljana Univ.Results from B factories 21HQP School, Dubna, Aug 2008 b s Inclusive measurement (see also lectures by U. Heisch) only reconstructed; bkg. treatment subtract lumin. scaled off-data from on-data (continuum bkg.); veto 0, rest bkg. from MC (control samples); timing info for EM calorim. clusters (overlapping evts.: hadronic + Bhabha) inclusive B 0 X, X samples reconstructed in data (off- data subtraction) and MC; 5%-10% correction to MC bkg. normaliz. on off on scaled off subtracted 80% of remaining bkg. from 0, after vetoing 0, Belle, arXiv:0804.1580, 605 fb -1 more

22. B. Golob, Ljubljana Univ.Results from B factories 22HQP School, Dubna, Aug 2008 b s Inclusive measurement E spectrum Br(B X s ) deconvolution of E (E meas E true ; using radiative di-muon evts); boost to B rest frame; b d contrib. (4%); consistent with 0 above B decay threshold m b 1S /2~2.3 GeV last uncertainty due to boost; largest system.: corr. factors in off-data subtraction; bkg. s from B (other than 0, ) Belle, arXiv:0804.1580,605 fb -1

23. B. Golob, Ljubljana Univ.Results from B factories 23HQP School, Dubna, Aug 2008 b s Seminclusive measurement B reconstructed; (see also lectures by B. Pecjak) sum of exclusive decay modes X s : no S-wave states in BX s 22 final states K -(0) +(1-4) 10 K -(0) + +(0-2) 6 3K -(0) +(0-1) + X s B (better resol.) bgk.: 0, veto, NN from topological variables for continuum; not all final states reconstructed corr. for missing fraction (from MC, checked with data in various final state categories) BaBar, PRD72, 052004, 82 fb -1 peaking bkg.: missing final states reconstructed as one of signal decays; signal decays with some particles exchanged with other B 25% at low M(X s ) from K L at high M(X s ) from K+ 5

24. B. Golob, Ljubljana Univ.Results from B factories 24HQP School, Dubna, Aug 2008 b s Seminclusive measurement fit in bins of M(X s ) Br(M(X s )); E spectrum (E >1.9 GeV); moments of d /dE also determined; m b (and other QCD parameters) determined for use in b u l ; e.g. BaBar, PRD72, 052004, 82 fb -1 K*(892) main systematics: from missing final states more details at HFAG, http://www.slac.stanford.edu/xorg/hfag/ more

25. B. Golob, Ljubljana Univ.Results from B factories 25HQP School, Dubna, Aug 2008 b s Phenomenology average of results: comparison with limits from B : 95% C.L. lower limit on m(H ± ), all tan M. Misiak et al., PRL98, 022002 (2007) HFAG, winter 08, http://www.slac.stanford.edu/xorg/hfag/ first error: stat.+syst. second error: E spectrum (extrapol.) Belle, PRL97, 251802 (2006), 414 fb -1 m(H ± )=300 GeV For my part I know nothing with any certainty, but the sight of the stars makes me dream. V. van Gogh (1853 - 1890)

26. B. Golob, Ljubljana Univ.Results from B factories 26HQP School, Dubna, Aug 2008 b s ll Motivation (see also lectures by E. Lunghi) FCNC process; M expressed in terms C 7,9,10 ; Wilson coeff.s NP modifies C 7,9,10 or/and adds new operators Wilson coeff.s independent of final state (C 7 same for b s and b s ll ); |C 7 | 2 constrained by Br(B X s ); sign not known; b s ll : interference of amplitudes additional information (also sign) on C 7,9,10 b s W±W± u, c, t V qb V qs b s =V qb V* qs C 7 x = perturbative (dependence on M W, m t, M NP ) non-perturbative more

27. B. Golob, Ljubljana Univ.Results from B factories 27HQP School, Dubna, Aug 2008 b s ll exclusive B K* ll K distrib. fraction of long. polarized K* (F L ); l distrib. lepton forward-backward asymmetry (A FB ); prediction for A FB : q 2 =m 2 ( l + l - ) B l+l-l+l- K* K K B l-l- l l+l+ q2q2 SM C 7 = -C 7 SM C 9 C 10 = -C 9 SM C 10 SM C 7 = -C 7 SM C 9 C 10 = -C 9 SM C 10 SM low q 2 high q 2 veto

28. B. Golob, Ljubljana Univ.Results from B factories 28HQP School, Dubna, Aug 2008 b s ll reconstruction e + e -, + - ; K* K, K 0, K s ; M bc fit combinatorial bkg.: e + - ; misid. hadrons: h + - ; peaking bkg.: D(K* ) ( sample only, veto on m(K* )); signal fraction K fit F L free parameter; l fit A FB free parameter; BaBar, arXiv:0804.4412, 350 fb -1 low q 2 high q 2 N s =27.2 ±6.3 N s =36.6 ±9.6

29. B. Golob, Ljubljana Univ.Results from B factories 29HQP School, Dubna, Aug 2008 b s ll results F L ; consistent with SM and -C 7 SM ; A FB ; -C 9 SM C 10 SM disfavored (>3 ); stronger constraints; BaBar, arXiv:0804.4412, 350 fb -1 SM q2q2 average over interval SM C 7 = -C 7 SM C 9 C 10 = -C 9 SM C 10 SM C 7 = -C 7 SM C 9 C 10 = -C 9 SM C 10 SM Belle, PRL96, 251801 (2006), 357 fb -1 C 7 = -C 7 SM more Belle, ICHEP08, 600 fb -1

30. B. Golob, Ljubljana Univ.Results from B factories 30HQP School, Dubna, Aug 2008 b s ll semi-inclusive similar as b s ; e + e -, + - ; K - /K s +(0-4) ~30% missing modes; charmonium sample provides cross-check of bkg.; constraints on NP in C i Br(B X s ), Br(B X s ll ), Br(K ) Br(B s ), no Br(B K* ll ) (large th. uncertainty) Belle PRD72, 092005 (2005), 140 fb -1 N sig =68 ±14 5.4 signif. (-2ln L 0 / L max ) Belle PRD72, 092005 (2005), 140 fb -1 BaBar PRL93, 081802 (2004), 82 fb -1 C 9 C 7 C 9 C 10 J. Kamenik, arXiv:0805.2363

31. B. Golob, Ljubljana Univ.Results from B factories 31HQP School, Dubna, Aug 2008 B oscillations more Time evolution state initially produced as superposition (n.b.: a(0)/b(0) can be 0) will evolve in time as if interested in a(t), b(t): effective Hamiltonian and t-dependent Schrödinger eq.: eigenstates: (well defined m 1,2 and 1,2 ) D. Kirkby, Y. Nir, CPV in Meson Decays, in RPP back

32. B. Golob, Ljubljana Univ.Results from B factories 32HQP School, Dubna, Aug 2008 B oscillations more Time evolution eigenvalues: diagonal elem.: P 0 P 0 (including decays) non-diagonal elem.: P 0 P 0 P 1,2 evolve in time according to m 1,2 and 1,2 :

33. B. Golob, Ljubljana Univ.Results from B factories 33HQP School, Dubna, Aug 2008 B oscillations more Time evolution eigenvalues:

34. B. Golob, Ljubljana Univ.Results from B factories 34HQP School, Dubna, Aug 2008 B oscillations more Time evolution eigenvalues: back

35. B. Golob, Ljubljana Univ.Results from B factories 35HQP School, Dubna, Aug 2008 B oscillations more Time evolution taking into account we arrive at time evolution of P 0, P 0 : back

36. B. Golob, Ljubljana Univ.Results from B factories 36HQP School, Dubna, Aug 2008 B oscillations more Time evolution decay rates: for CP conjugated states: A f A f, A f A f

37. B. Golob, Ljubljana Univ.Results from B factories 37HQP School, Dubna, Aug 2008 B oscillations more CPV |p/q|=1, y<<1 (well fulfilled for B d ) | f |1 |A f /A f |1 CPV in decay |q/p| 1 CPV in mixing I ( f ) 0 CPV in interf. back

38. B. Golob, Ljubljana Univ.Results from B factories 38HQP School, Dubna, Aug 2008 B oscillations more Method reconstructed flavour specific decays; D* l =0 known meas. known meas. known meas. meas. total bkg D** bkg. Belle, PRD71, 072003 (2005), 140 fb -1 back

39. B. Golob, Ljubljana Univ.Results from B factories 39HQP School, Dubna, Aug 2008 B oscillations more Method tagging q=+(-)1 B 0 (B 0 ) r: tag quality H. Kakuno et al., NIM A533, 516 (2004)

40. B. Golob, Ljubljana Univ.Results from B factories 40HQP School, Dubna, Aug 2008 B oscillations more Method tagging single r bin: two r bins: H. Kakuno et al., NIM A533, 516 (2004) back

41. B. Golob, Ljubljana Univ.Results from B factories 41HQP School, Dubna, Aug 2008 B oscillations more Method resolution function H. Tajima et al., NIM A533, 370 (2004) back R ful : vtx of fully reconstructed B meson R asc : vtx of tagging B meson R np : non-primary tracks R k : kinematic smearing

42. B. Golob, Ljubljana Univ.Results from B factories 42HQP School, Dubna, Aug 2008 B oscillations more if m i = m j due to CKM unitarity: no mixing d b b d u, c, t W+W+ W-W- B0B0 B0B0 d b b d W+W+ W-W- B0B0 B0B0 V id V jd V jb * V ib * Phenomenology P 0 -P 0 transition box diagram at quark level simplified treatment based on dimension: O. Nachtmann, Elem. Part. Phys., Springer-Verlag A.J. Buras et al., Nucl.Phys.B245, 369 (1984) for serious treatment see e.g.: P 0 : any pseudo-scalar meson; specific example of B d 0 back

43. B. Golob, Ljubljana Univ.Results from B factories 43HQP School, Dubna, Aug 2008 Leptonic B decays more Systematic checks B sig decay modes check of E ECL, double tagged decays, B sig - D* 0 l -, D* 0 D 0 0 back Belle, PRL97, 251802 (2006), 414 fb -1

44. B. Golob, Ljubljana Univ.Results from B factories 44HQP School, Dubna, Aug 2008 Leptonic B decays more Phenomenology additional Higgs doublet; tan =v 1 /v 2, ratio of vacuum expectation values; H ± coupling m l same factor as helicity SM suppression ratio independent of H ± contribution: back Type II Two Higgs Doublets Models ( 1 gives masses to d-type and charged l ; 2 gives masses to u-type; in Type I models 1 is decoupled and 2 generates all masses) W.S.Hou, PRD48, 2342 (1993) if meas > SM H ± contribution dominant

45. B. Golob, Ljubljana Univ.Results from B factories 45HQP School, Dubna, Aug 2008 Semileptonic B decays more Form factors PP: B(v) B(v): for m b amplitude can only depend on = v·v; for v = v nothing happens, (1)=1; B(v) D(v): for m b, m c same (HQS) back (v·v): Isgur-Wise function relates two in principle independent form factors for P P transition

46. B. Golob, Ljubljana Univ.Results from B factories 46HQP School, Dubna, Aug 2008 Semileptonic B decays more Form factors PV: back q2q2 one more f.f. if m l not small; HQS: relations among f.f.s for P P and P V

47. B. Golob, Ljubljana Univ.Results from B factories 47HQP School, Dubna, Aug 2008 Semileptonic B decays more B D* phenomenology amplitude for W exchange: M =±,0; =±; W =±,0; D*,, W helicity amplitude for H ± exchange: relation among H ±, W exchange amplitudes: H ± : no contribution of transversely polarized D* (H R,L ± =0) back M. Tanaka, Z.Phys.C67, 321 (1995)

48. B. Golob, Ljubljana Univ.Results from B factories 48HQP School, Dubna, Aug 2008 Semileptonic B decays more B D phenomenology update of predictions: U. Nierste et al., PRD78, 015006 (2008) m B 2 /m H 2 tan 2 (in 2HDM-II) back measurement BaBar, PRL100, 021801 (2008), 209 fb -1

49. B. Golob, Ljubljana Univ.Results from B factories 49HQP School, Dubna, Aug 2008 b s more inclusive semil. B decays semil. width: Operator Product Expansion to O (1/m b 2 ): two parameters, 1, 2 : back average p 2 of b in B hyperfine interaction

50. B. Golob, Ljubljana Univ.Results from B factories 50HQP School, Dubna, Aug 2008 b s more inclusive semil. B decays Fermi motion: new parameter same parameters governing moments of various distributions, e.g. mass of hadronic system in semil. decays: or E moments in b s : back A.F.Falk, M.E.Luke, PRD57, 424 (1998) A.Kapustin, Z. Ligeti PLB355, 318 (1995)

51. B. Golob, Ljubljana Univ.Results from B factories 51HQP School, Dubna, Aug 2008 b s more off-data subtraction : lumin. ratio; hadronic,BXs ON,OFF : efficiency of hadronic, signal selection; F N,E : corr. factor due to lower mean E and multiplicity in off-data back

52. B. Golob, Ljubljana Univ.Results from B factories 52HQP School, Dubna, Aug 2008 b s more E resolution inclusive meas.: E measured in EM calorim.; (E ;E =2 GeV) ~ 20 MeV; semi-inclusive meas.: E from (E ) ~ 1-5 MeV; back

53. B. Golob, Ljubljana Univ.Results from B factories 53HQP School, Dubna, Aug 2008 b s ll more OPE, Wilson coeff. example of b cdu almost point-like inter.: series: product of currents expressed as series of local operators (OPE); such expansion valid if q 2 /M W 2 <<1; in this range an effective theory can be constructed, valid up to a cut-off, in the above case up to M W ; back b c d u W BaBar Physics Book, SLAC-R-504

54. B. Golob, Ljubljana Univ.Results from B factories 54HQP School, Dubna, Aug 2008 b s ll more OPE, Wilson coeff. example of b cdu rad. corr. to lowest order: operators receive radiation corr. and must be renormalized; they become dependent on renormalization scale ; physics must be independent of operators receive dependent coefficients in order for H eff to satisfy: back b c d u W g (i,j: color indices) BaBar Physics Book, SLAC-R-504

55. B. Golob, Ljubljana Univ.Results from B factories 55HQP School, Dubna, Aug 2008 b s ll more OPE, Wilson coeff. example of b cdu under renormaliz. set of operators can be enlarged, for the example under consideration there is also H eff is thus C i ( ) are Wilson coeff., containing information on short distance physics down to (arbitrary) scale ; all heavy masses (M>> ) dependence (m t, M W, M NP ) is contained in C i ( ) back b c d u W g (changed color indices) BaBar Physics Book, SLAC-R-504

56. B. Golob, Ljubljana Univ.Results from B factories 56HQP School, Dubna, Aug 2008 b s ll more OPE, Wilson coeff. once O i ( ) dependence is calculated, C i ( ) follow from for b cdu division of energy scales between C i ( ) and local operators can be schematically viewed as Wilson coeff. C i ( ) are independent of external states (f) back C i ( )

57. B. Golob, Ljubljana Univ.Results from B factories 57HQP School, Dubna, Aug 2008 b s ll more OPE, Wilson coeff. Br(b s ll ): A FB, RPV SUSY contrib.: back | 1i3 1i2 *|<4.7x10 -5 Y.-G. Xu et al., PRD74, 114019 (2006) P. Gambino et al., PRL94, 061803 (2005)

58. B. Golob, Ljubljana Univ.Results from B factories 58HQP School, Dubna, Aug 2008 b s ll more back SM C 7 = -C 7 SM C 9 C 10 = -C 9 SM C 10 SM C 7 = -C 7 SM C 9 C 10 = -C 9 SM C 10 SM Belle, PRL96, 251801 (2006), 357 fb -1