B. Golob, BelleD 0 Mixing 1Lepton Photon ‘07, Daegu B. Golob University of Ljubljana Belle Collaboration Outline 1.Introduction 2.Phenomenology 3.Measurements K + K - /  +  - K S  +  + CPV 4. Prospects & Summary Recent results on D 0 mixing from Belle Lepton Photon Interactions 2007

Introduction Dual role of charm - experimental tests of theor. predictions (most notably of (L)QCD); improve precision of CKM measurements (B physics); - standalone field of SM tests and search for new phenomena (SM and/or NP) → D 0 -D 0 Mixing E. Golowich et al., arXiv: different NP models: 17 of those → constraints in parameter space from established D 0 mixing rate <~10 -4 example: 4th fermion family (severly constrained from other measurements as well) mixing ampl. |V ub’ V cb’ | m b’ =500 GeV m b’ =200 GeV B. Golob, BelleD 0 Mixing 2Lepton Photon ‘07, Daegu  (c c)  1.3 nb (Belle luminos.:~850·10 6 X c Y c pairs)  (4S):

Introduction 3(4) layer Si det. Central Drift Chamber Aerogel Cherenkov (n= ) 1.5T SC solenoid e - 8 GeV e GeV EM calorimeter CsI (16X 0 )  and K L Counter (14/15 layers RPC+Fe)  L dt fb -1  t /  (D 0 )  t /  (D 0 )=1/3  (K ± ) ~ 85%  (  ± →K ± )  10% for p < 3.5 GeV/c /  (D 0 ) ~ 1/2 D 0 → K -  + B. Golob, BelleD 0 Mixing 3Lepton Photon ‘07, Daegu D* + → D 0  + slow, D 0 → K -  +  M=M(K  slow )-M(K  )

D 0 - D 0 Phenomenology Mixing phenomena X 0 = K 0, B d 0, B s 0 and D 0 t-dependent Schrödinger eq.: mass eigenstates: decay time evolution: X0X0 q1q1 q2q2 q2q2 q1q1 X0X0 CP eigenstates if q/p=1; propagate in t according to distinct eigenvalues; Decay time distribution of experimentally accessible states X 0, X 0 sensitive to mixing parameters B. Golob, BelleD 0 Mixing 4Lepton Photon ‘07, Daegu I.I. Bigi, N. Uraltsev, Nucl. Phys. B592, 92 (2001); A.F. Falk et al., PRD69, (2004) |x|, |y| < O (10 -2 ) ~

Belle measurements - semileptonic decays, D 0 → K ( * ) l n - hadronic decays to non-CP final state D 0 → K +  - - hadronic decays to multi-body final state, D 0 → K S  +  - - decays to CP final state, D 0 → K + K - /  +  - Measurements arXiv: , 540 fb -1, subm. to PRL common: D* + →D 0  s + charge of  s tags the flavor of initially produced D 0 ; p*(D*) > 2.5 GeV/c eliminates D meson production from b → c selection determined “blindly” PRL 98, (2007), 540fb -1 PRD72, (2005), 253 fb -1 PRL96, (2006), 400 fb -1 B. Golob, BelleD 0 Mixing 5Lepton Photon ‘07, Daegu

Measurements K + K - /  +  - PRL 98, (2007), 540fb -1 D 0 → K + K - /  +  - CP even final state; in the limit of no CPV: CP|D 1 > = |D 1 >  measure 1/  1 S. Bergman et al., PLB486, 418 (2000) A M,  : CPV in mixing and interference Signal side band M(K + K - ), Q=M(K + K -  s )- M(K + K - )- M(  ),  t, selection optimized on MC K+K-K+K- K-+K-+ +-+- N sig 111x x x10 3 P98%99%92% B. Golob, BelleD 0 Mixing 6Lepton Photon ‘07, Daegu

Measurements K + K - /  +  - Fit simultaneous binned likelihood fit to K + K - /K -  + /  +  - decay-t, common free y CP  = 408.7±0.6 fs event-by-event  t K-+K-+ parameters of R depend slightly on data taking conditions PRL 98, (2007), 540fb -1 B. Golob, BelleD 0 Mixing 7Lepton Photon ‘07, Daegu  PDG =410.1 ± 1.5 fs constructed using event-by-event  t M sideband

Measurements K + K - /  +  - Result K + K - /  +  - and K -  + ratio difference of lifetimes visually observable evidence for D 0 mixing (regardless of possible CPV) 3.2  from zero (4.1  stat. only)  2 /ndf=1.084 (ndf=289) + negligible CPV, y CP =y PRL 98, (2007), 540fb -1 B. Golob, BelleD 0 Mixing 8Lepton Photon ‘07, Daegu ± 1 

Measurements K S  +  - arXiv: , 540 fb -1, subm. to PRL t-dependent Dalitz analysis different decays identified through Dalitz analysis; CF: D 0 → K* -  + DCS: D 0 → K* +  - CP: D 0 →  0 K S their relative phases determined (unlike D 0 → K +  - ); t-dependence: 1,2 = f (x,y); n.b.: K +  - :x’ 2, y’ m ± 2 = m 2 (K S  ± ) M = analogous sum of intermediate states B. Golob, BelleD 0 Mixing 9Lepton Photon ‘07, Daegu

Measurements K S  +  - arXiv: , 540 fb -1, subm. to PRL fit M (m - 2,m + 2,t) to data distribution  x, y Fit no CPV: M(K S  +  - ) and Q= M(K S  +  -  s )- M(K S  +  - )- M(  ); 3  signal region in M, Q Signal N sig = (534.4 ± 0.8)x10 3 P  95% Dalitz model 13 BW resonances, non-resonant contr.; comb. bkg.: from M sideband t M signal rnd slow p combin. B. Golob, BelleD 0 Mixing 10Lepton Photon ‘07, Daegu

Measurements K S  +  - arXiv: , 540 fb -1, subm. to PRL Dalitz projection of fit K*(892) + K* X (1400) + K*(892) -  test of S-wave  contr. (f 0,  1,2 ): K-matrix formalism Results (fit fractions, phases) in agreement with (measurement of  3 ) PRD73, (2006) B. Golob, BelleD 0 Mixing 11Lepton Photon ‘07, Daegu

Measurements K S  +  - arXiv: , 540 fb -1, subm. to PRL Decay-t projection of fit t [fs]  = 409.9±0.9 fs most sensitive meas. of x; Cleo, PRD72, (2005) x = 1.8 ± 3.4 ± 0.6% y = -1.4 ± 2.5 ± 0.9 %  PDG =410.1 ± 1.5 fs comb. bkg. PRD72, (2005), 253 fb -1 D 0 → K ( * ) l PRL96, (2006), 400 fb -1 D 0 → K +  - 2-d 68% C.L. region B. Golob, BelleD 0 Mixing 12Lepton Photon ‘07, Daegu 2-d 68% C.L. region D 0 → K + K - /  +  - PRL 98, (2007), 540fb -1

Measurements CPV CPV in D 0 system first two generations involved: t distributions depend also on CPV parameters; x, y at upper limit of SM expectation → search for CPV; at current level of sensitivity positive signal clear indication of NP; Wolfenstein parameter. CPV in decay: (singly Cabibbo supp. decays only) CPV in mixing: CPV expected to be small in SM CPV in interf. mix./decay: B. Golob, BelleD 0 Mixing 13Lepton Photon ‘07, Daegu

Measurements CPV CPV in D 0 → K + K - /  +  - CPV in D 0 → K S  +  - include |q/p| (A M ) and  as additional free param. separate  for D 0, D 0 95% C.L. B. Golob, BelleD 0 Mixing 14Lepton Photon ‘07, Daegu

Measurements CPV CPV in D 0 →  +  -  0 B. Golob, BelleD 0 Mixing 15Lepton Photon ‘07, Daegu CPV in decay, integrated over t and Dalitz space D 0 →  +  -  fb -1, preliminary Cleo, PRD 72, (2005) Belle preliminary

Measurements average Combination, no CPV all available meas.; observables (y CP, x,...) → x, y,  K , R D sum of likelihood curves, non-Gaussian shapes accounted for HFAG charm, B. Golob, BelleD 0 Mixing 16Lepton Photon ‘07, Daegu

Measurements average Combination, CPV observables (A , x,...) → |q/p|, , A D, x, y, R D,  K   2 minimization, non-Gaussian shapes not accounted for HFAG charm, B. Golob, BelleD 0 Mixing 17Lepton Photon ‘07, Daegu

Prospects & Summary Super-B factory extrapolation of existing Belle results L = 5 ab -1 L = 50 ab -1  (x) 0.1% 0.07%  (y) 0.1% 0.07%  (A M )  0.1 rad 0.07 rad Summary  2007: D 0 mixing established (slowest of all neutral mesons)  Belle presented first evidence for D 0 mixing (y CP ), most precise x meas.; confirmation in D 0 → K + K -, K S  +  -, other sensitive modes? (esp. x, from Dalitz analyses, sign)?  combination of existing D 0 mixing results: established at ~5  ; x,y ~ O (10 -2 );  (x,y) ~ 0.3%;  observed mixing may (not) be arising from SM → important CPV search  existing facilities: any CPV indication of NP  Super-B: allows to test CP asymmetries to few (SM expectations) B. Golob, BelleD 0 Mixing 18Lepton Photon ‘07, Daegu LHCb, 10 fb -1 (5 y):  (x’ 2 )~6x10 -5,  (y’)~0.9x10 -3  (y CP )~0.05%

Introduction (bckup) Physics of c-hadrons increased interest at B-factories in recent years Dual role of charm standalone field of SM tests and search for new phenomena (SM and/or NP) experimental tests of theor. predictions (most notably of (L)QCD); improve precision of CKM measurements (B physics); √s = M(  (4S))c 2 = GeV B-factory, c-factory  (B B)  1.1 nb (~750·10 6 BB pairs)  (c c)  1.3 nb (~850·10 6 X c Y c pairs) → D 0 -D 0 Mixing B. Golob, BelleD 0 Mixing 19Lepton Photon ‘07, Daegu

Phenomenology bckup Mixing phenomena in course of life neutral meson X 0 can transform into anti-meson X 0 X 0 = K 0, B d 0, B s 0 and D 0 t-dependent Schrödinger eq.: mass eigenstates: eigenvalues: X0X0 q1q1 q2q2 q2q2 q1q1 X0X0 CP eigenstates if q/p=1 B. Golob, BelleD 0 Mixing 20Lepton Photon ‘07, Daegu

D 0 - D 0 Phenomenology (bckup) Mixing description observation of K 0 : 1950 (Caletch) mixing in K 0 : 1956 (Columbia) observation of B d 0 : 1983 (CESR) mixing in B d 0 : 1987 (Desy) observation of B s 0 : 1992 (LEP) mixing in B s 0 : 2006 (Fermilab) observation of D 0 : 1976 (SLAC) mixing in D 0 : 2007 (KEK, SLAC) (evidence of) c u u c d, s, b W+W+ W-W- D0D0 D0D0 V ci * V cj V uj * V ui 6 years 4 years 14 years 31 years if m i = m j  due to CKM unitarity: no D 0 D 0 mixing |V cb *V ub |<< |V cs *V us |, |V cd *V ud | mainly d,s contrib.; m d ~ m s  mixing small (as opposed to B d 0, where term with m t 2 |V tb * V td | 2 dominates) d-like quarks in loop B. Golob, BelleD 0 Mixing 21Lepton Photon ‘07, Daegu

D 0 - D 0 Phenomenology (bckup) c u u c d, s, b W+W+ W-W- D0D0 D0D0 V ci * V cj V uj * V ui x and y in SM 2nd order perturb.: short distance: DCS SU(3) breaking G. Burdman, I. Shipsey, Ann.Rev.Nucl.Sci. 53, 431 (2003) |x| ~ O (10 -5 ) long distance: absorptive part (real interm. states)  y dispersive part (off-shell interm. states)  x D0D0 D0D0 K+K+ K-K- I.I. Bigi, N. Uraltsev, Nucl. Phys. B592, 92 (2001); A.F. Falk et al., PRD69, (2004) |x|, |y| ~ O (10 -2 ) D 0 mixing: rare process in SM; possible contrib. from NP B. Golob, BelleD 0 Mixing 22Lepton Photon ‘07, Daegu

D 0 - D 0 Phenomenology (bckup) Oscillations visually unobservable deviation from pure exponential ~ B s 0 more difficult to observe oscillations within  B. Golob, BelleD 0 Mixing 23Lepton Photon ‘07, Daegu

right sign (RS) Semileptonic (bckup) PRD72, (2005), 253 fb -1 Semileptonic decays Wrong charge combinations (WS): D* + → D 0  slow + D 0 → D 0 → K ( * )+ e - no “DCS” decays  N WS /N RS = R M  (x 2 +y 2 )/2 Reconstruct : missing momentum with kinematic constraints Signal:  M = M(Ke  slow ) - M(Ke ) N RS = ( ± 0.69) ·10 3 B. Golob, BelleD 0 Mixing 24Lepton Photon ‘07, Daegu

Semileptonic (bckup) PRD72, (2005), 253 fb -1 Result: R M = (0.20 ± 0.47 ± 0.14) ·10 -3 R M < 1.2 · % C.L. dominating systematics from limited bkg. statistics (embedded  slow ) Decay time: reduce bkg., increase sensitivity; (bkg., RS) (mix. signal) 6 bins in 1 < t < 10 allowed B. Golob, BelleD 0 Mixing 25Lepton Photon ‘07, Daegu

K +  - (bckup) D* + → D 0  slow + D 0 → D 0 → K +  - DCS decays  interference Wrong charge combinations (WS): Signal: M= M(K  ) Q = M(K  slow ) - M(K  ) - M(  ) 2D M-Q fit: N WS = 4024 ± 88 3  M interval WS PRL96, (2006), 400 fb -1 3  Q interval t-dependence to separate DCS/mixed B. Golob, BelleD 0 Mixing 26Lepton Photon ‘07, Daegu

K +  - (bckup) PRL96, (2006), 400 fb -1 Decay time: resol. function from RS  (D 0 ) = ± 0.7 fs x’ 2, y’, R D free parameters Results: R D = (3.64 ± 0.17 ) ·10 -3 x’ 2 = (0.18 ± ) · y’ = (0.6 ± ) · % C.L. (x’ 2, y’) contour frequentist, FC ordering WS t dist. B. Golob, BelleD 0 Mixing 27Lepton Photon ‘07, Daegu

Measurements K +  - bckup PRL96, (2006), 400 fb -1 R D = (3.64 ± 0.17 ) ·10 -3 x’ 2 = (0.18 ± ) · y’ = (0.6 ± ) · A D = (23 ± 47) ·10 -3 A M = (670 ± 1200) ·10 -3 Results: no CPV CPV CPV allowed: separate D 0 and D 0 tags (x’ 2,y’,R D ) → (x’ ±2, y’ ±,R D ± ) 95% C.L. (x’ 2, y’) contour frequentist, FC ordering (0,0) lies on 96.1% C.L. contour x’ 2 < 0.72 · % < y’ < 0.68% no signif. CPV largest syst. due to p*(D*) selection B. Golob, BelleD 0 Mixing 28Lepton Photon ‘07, Daegu

K +  - BaBar comp. (bckup) BaBar, hep-ex/ , 384fb -1, acc. to PRL Result R D = (3.03 ± 0.19) ·10 -3 x’ 2 = (-0.22 ± 0.37 ) · y’ = (9.7 ± 5.4 ) · including sys. error 1  2  3  3.9  Comparison consistent evidence for (x,y)  (0,0) B. Golob, BelleD 0 Mixing 29Lepton Photon ‘07, Daegu

Prospects bckup perspective (1 ab -1 ) 1  3  x, y at upper limit of SM expectation  search for CPV; at current level of sensitivity positive signal clear indication of NP;  (x) ~ ± 0.21%  (y) ~ ± 0.17% B. Golob, BelleD 0 Mixing 30Lepton Photon ‘07, Daegu

K S  +  - syst. (bckup) D 0 → K S  +  - arXiv: M(K S  +  - ) and Q= M(K S  +  -  s )- M(K S  +  - )- M(  ); 3  signal region in M, Q B. Golob, BelleD 0 Mixing 31Lepton Photon ‘07, Daegu

K S  +  - syst. (bckup) D 0 → K S  +  - Largest systematics arXiv: model dependence [10 -4 ]:  x  y K* 0 (1430) DCS/CF -15% K* 2 (1430) DCS/CF -30% K*(1410) DCS & CF -20%  (q 2 ) const Total model dep experimental:  x  y p* variation Dalitz pdf for bkg. from different t bins Total experimental observed discrepancy from input in MC statistical uncertainty:  (x)=29x10 -4  (y)=24x10 -4 B. Golob, BelleD 0 Mixing 32Lepton Photon ‘07, Daegu

K S  +  - syst. (bckup) D 0 → K S  +  - Largest systematics arXiv: model dependence [10 -4 ]:  x  y K* 0 (1430) DCS/CF -15% K* 2 (1430) DCS/CF fixed to K*(892) K*(1410) DCS & CF fixed to K*(892) Total model dep B. Golob, BelleD 0 Mixing 33Lepton Photon ‘07, Daegu

K S  +  - param. (bckup) D 0 → K S  +  - parameterization arXiv: B. Golob, BelleD 0 Mixing 34Lepton Photon ‘07, Daegu

K S  +  - param. (bckup) D 0 → K S  +  - arXiv: CP=+1 states Cleo, PRD 63, (2001) parameterization as in B. Golob, BelleD 0 Mixing 35Lepton Photon ‘07, Daegu

K S  +  - param. (bckup) D 0 → K S  +  - arXiv: CP= -1 states Cleo, PRD 63, (2001) parameterization as in B. Golob, BelleD 0 Mixing 36Lepton Photon ‘07, Daegu

K S  +  - K-matrix (bckup) D 0 → K S  +  - scalar  arXiv: BW formalism: M(  1 ) = 527 ± 6 MeV/c 2  (  1 ) = 442 ± 10 MeV M(  2 ) = 1031 ± 11 MeV/c 2  (  2 ) = 94 ± 6 MeV K-matrix formalism: unit. relat. for 2-body scatt. trans. operator: T: N ch xN ch matrix for N ch coupled chann.;  : density of final states product. process (init. state non-interacting with channel j); trans. ampl. unitarity: satisf. by defining unitarity satisf. if product. ampl.: V.V. Anisovich, A.V. Sarantev, Eur.Phys.J. A16, 229 (2003) BaBar, hep-ex/ parameters taken from: B. Golob, BelleD 0 Mixing 37Lepton Photon ‘07, Daegu

K S  +  - eff., resol. (bckup) D 0 → K S  +  - efficiency and resol. in M(  arXiv: rnd  s bkg.: P rnd  [(1-f w ) M (m - 2,m + 2,t) +f w M (m + 2,m - 2,t)]  R (t) f w from fit to Q side band: f w = ± diff. w.r.t. f w =0.5 in systematic error comb. bkg.: P cmb  B(m - 2,m + 2 ) * ([  (t) + Exp(t) ]  R ’(t) parameters from fit to Dalitz and t distrib. of M(K S  +  - ) sideband (systematics: Dalitz distrib. in different t intervals) B. Golob, BelleD 0 Mixing 38Lepton Photon ‘07, Daegu

K S  +  - toy MC (bckup) D 0 → K S  +  - arXiv: MC tests, correct reconstruction of input; t-projection; P sig  M (m - 2,m + 2,t)  R (t) P rnd  [(1-f w ) M (m - 2,m + 2,t) +f w M (m + 2,m - 2,t)]  R (t) P cmb  M sideband (m - 2,m + 2,t) * [  (t) + Exp(t) ]  R ’(t) B. Golob, BelleD 0 Mixing 39Lepton Photon ‘07, Daegu

K + K - /  +  -, M, Q (bckup) M [GeV/c 2 ] D 0 → K + K - /  +  - hep-ex/ v2 B. Golob, BelleD 0 Mixing 40Lepton Photon ‘07, Daegu

K + K - /  +  -, systematics (bckup) D 0 → K + K - /  +  - systematics hep-ex/ v2 B. Golob, BelleD 0 Mixing 41Lepton Photon ‘07, Daegu K + K - only: y CP =(1.25 ± 0.39)% A  =(0.15 ± 0.35)%  +  - only: y CP =(1.44 ± 0.57)% A  =(-0.28 ± 0.52)%

K + K - /  +  - resolution (bckup) Fit simultaneous binned likelihood fit to K + K - /K -  + /  +  - decay-t, common free y CP R : ideally each  i Gaussian resol. term with fraction f i ; : described by 3 Gaussians   = 408.7±0.6 fs event-by-event  t K-+K-+ parameters of R depend slightly on data taking conditions t rec -t gen /  t PRL 98, (2007), 540fb -1 B. Golob, BelleD 0 Mixing 42Lepton Photon ‘07, Daegu  PDG =410.1 ± 1.5 fs

K + K - /  +  -, t fit (bckup) D 0 → K + K - /  +  - running periods w/ diff. conditions fitted t 0 of R for K  robust to resol. f. shape; R(t): single Gauss →  =3.5%,  y CP =0.01%; no bias, reweigted MC: y CP (out) - y CP (in) < 0.04%; background P=98% (KK), 99% (K  ), 92% (  ); changing data side band/MC signal,  y CP = -0.04%; bkg. subtracted / no bkg. subtraction,  y CP = -0.07%; bkg. subtracted / MC signal subtr.,  y CP = -0.03%; systematic checks hep-ex/ v2 B. Golob, BelleD 0 Mixing 43Lepton Photon ‘07, Daegu

K + K - /  +  -, t 0 (bckup) D 0 → K + K - /  +  - fitted t 0 of R in diff. run periods and diff. decay modes hep-ex/ v2 B. Golob, BelleD 0 Mixing 44Lepton Photon ‘07, Daegu

K + K - /  +  -, t 0 (bckup) D 0 → K + K - /  +  - equal t 0 assumption  y CP =t 0 CP - t 0 K  /  K  from MC cocktail, including running periods with slight misalign. of SVD hep-ex/ v2 B. Golob, BelleD 0 Mixing 45Lepton Photon ‘07, Daegu

K + K - /  +  -, bkg t distr. (bckup) D 0 → K + K - /  +  - background comparison small tail of signal present in side band, only visible in K  sample; fraction of rnd  s negligible: 0.3%, 0.3%, 0.2% KK K   hep-ex/ v2 B. Golob, BelleD 0 Mixing 46Lepton Photon ‘07, Daegu

K + K - /  +  -, K S  +  - comparison (bckup) K S  +  - : (x,y)=(0,0) has C.L. 2.6% K + K - /  +  - : y=0 has C.L. 6x10 -4 Results B. Golob, BelleD 0 Mixing 47Lepton Photon ‘07, Daegu

Measurements average (bckup) Combination, no CPV sum of likelihood curves, non-Gaussian shapes accounted y CP x HFAG charm, B. Golob, BelleD 0 Mixing 48Lepton Photon ‘07, Daegu

Measurements average (bckup) Combination, no CPV sum of likelihood curves, non-Gaussian shapes accounted y HFAG charm, B. Golob, BelleD 0 Mixing 49Lepton Photon ‘07, Daegu KK

Measurements average (bckup) Combination, no CPV sum of likelihood curves, non-Gaussian shapes accounted y HFAG charm, B. Golob, BelleD 0 Mixing 50Lepton Photon ‘07, Daegu x D 0 → K +  - x’ 2 y’ CPV: A D = (-0.76 ± 3.10)%

Measurements average (bckup)  HFAG charm, B. Golob, BelleD 0 Mixing 51Lepton Photon ‘07, Daegu Combination, CPV observables (A , x,...) → |q/p|, , A D, x, y, R D,  K   2 minimization, non-Gaussian shapes not accounted for |q/p| overall fit:  2 /ndf = 14.4 / 7

Measurements Combination 1996 FNAL E791 R M = ( − −0.014 )%FNAL E CLEO II.V R M = (0.16 ± 0.29 ± 0.29 )%CLEO II.V 2004 BaBar R M = (0.23 ± 0.12 ± 0.04 )%BaBar 2005 Belle R M = (0.020 ± ± )Belle 1999 FNAL E791 ΔΓ = (0.04 ± 0.14 ± 0.05 ) ps −1 (y CP = (0.8 ± 3.1)%)FNAL E FOCUS y CP = (3.42 ± 1.39 ± 0.74 )%FOCUS 2002 CLEO II.V y CP = (−1.2 ± 2.5 ± 1.4 )%CLEO II.V 2003 BaBar y CP = (0.8 ± −0.4 )%BaBar 2002 Belle y CP = (−0.5 ± −0.8 )%Belle 2007 Belle y CP = (1.31 ± 0.32 ± 0.25 )%Belle 2006 Belle x' 2 = ( −0.023 )% y' = ( −0.39 )%Belle 2007 BaBar x' 2 = (−0.022 ± ± 0.021)% y' = (0.97 ± 0.44 ± 0.31)%BaBar 2006 BaBar K + π − π 0 R M = ( −0.014 ± 0.004)%BaBar 2006 BaBar K + π − π + π − R M = ( −0.015 ± 0.002)%BaBar 2005/2007 CLEO II.V x = ( −3.3 ± 0.4 ± 0.4)% y = (−1.4 ± 2.4 ± 0.8 ± 0.4)%CLEO II.V 2007 Belle x = (0.80 ± 0.29 ± 0.17)% y = (0.33 ± 0.24 ± 0.15)%Belle 2006 CLEO-c R M = (0.17 ± 0.15)% y = (−5.8 ± 6.6)% cos δ K π = 1.09 ± 0.66CLEO-c R M semil. y CP x’ 2, y’ R M Kn  x, y Cleo-c B. Golob, BelleD 0 Mixing 52Lepton Photon ‘07, Daegu

Measurements average Average fit to individual measurements with x, y,  free assuming Gaussian p.d.f.’s; correlation for K +  - ; illustration! B. Golob, BelleD 0 Mixing 53Lepton Photon ‘07, Daegu

Prospects bckup Combination numbers very preliminary  (y CP ) ~ 0.15%,  (A  /y CP ) ~ 0.10  (x) ~  (y) ~ 0.15%,  (|q/p|) ~  (  ) ~ 0.10  (x’ 2 ) ~ 0.12x10 -3,  (y’) ~ 0.20%  (x) ~  (y) ~ 0.10%  (cos  ) ~ 0.07  (|q/p|) ~ 0.09,  (  ) ~0.05 rad D 0 → K + K - /  +  - D 0 → K S  +  - D 0 → K +  - combined approximate projections to 5 ab -1 B. Golob, BelleD 0 Mixing 54Lepton Photon ‘07, Daegu