1. B. Golob, Belle D 0 Mixing 1 KEK Seminar, May 2007 B. Golob University of Ljubljana Belle Collaboration Outline 1.Introduction 2.Phenomenology 3.Measurements semileptonic K +  - K S  +  - K + K -/  +  - CPV 4. Prospects 5. Summary Evidence for D 0 -D 0 Mixing at Belle KEK Physics Seminar

2. B-factory, c-factory Introduction √s = M(  (4S))c 2 = 10.58 GeV  (B B)  1.1 nb (~750·10 6 BB pairs)  (c c)  1.3 nb (~850·10 6 X c Y c pairs) Physics of c-hadrons increased interest at B-factories in recent years B. Golob, Belle D 0 Mixing 2 KEK Seminar, May 2007 FacilityN rec int. lumin. [fb -1 ] Belle2.5x10 6 1000 P  99% Super KEKB13x10 6 5000 c-factory0.4x10 6 20coherent CDF/D00.5x10 6 0.35 benchmark: D* 0 → D 0  + slow ; D 0 → K -  +

3. Introduction B. Golob, Belle D 0 Mixing 3 KEK Seminar, May 2007 3(4) layer Si det. Central Drift Chamber Aerogel Cherenkov (n=1.015-1.030) 1.5T SC solenoid e - 8 GeV e + 3.5 GeV EM calorimeter CsI (16X 0 )  and K L Counter (14/15 layers RPC+Fe)  L dt 2007 2000 700 fb -1  t /  (D 0 )  (D 0 )/3  (K ± ) ~ 85%  (  ± →K ± )  10% for p < 3.5 GeV/c /  (D 0 ) ~ 1/2 D0→D0→

4. D 0 - D 0 Phenomenology 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: decay time evolution: B. Golob, Belle D 0 Mixing 4 KEK Seminar, May 2007 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

5. D 0 - D 0 Phenomenology 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 B. Golob, Belle D 0 Mixing 5 KEK Seminar, May 2007 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

6. D 0 - D 0 Phenomenology c u u c d, s, b W+W+ W-W- D0D0 D0D0 V ci * V cj V uj * V ui B. Golob, Belle D 0 Mixing 6 KEK Seminar, May 2007 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, 114021 (2004) |x|, |y| ~ O (10 -2 ) D 0 mixing: rare process in SM; possible contrib. from NP

7. D 0 - D 0 Phenomenology B. Golob, Belle D 0 Mixing 7 KEK Seminar, May 2007 Oscillations visually unobservable deviation from pure exponential ~ B s 0 more difficult to observe oscillations within 

8. 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: 0704.1000, 540 fb -1 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 B. Golob, Belle D 0 Mixing 8 KEK Seminar, May 2007 hep-ex/0703036v2, 540fb -1, acc. to PRL PRD72, 071101 (2005), 253 fb -1 PRL96, 151801 (2006), 400 fb -1

9. right sign (RS) Measurements semileptonic B. Golob, Belle D 0 Mixing 9 KEK Seminar, May 2007 PRD72, 071101 (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 = (229.45 ± 0.69) ·10 3 x,y << 1 D 0 → K ( * )- e +

10. Measurements semileptonic B. Golob, Belle D 0 Mixing 10 KEK Seminar, May 2007 PRD72, 071101 (2005), 253 fb -1 Result: R M = (0.20 ± 0.47 ± 0.14) ·10 -3 R M < 1.2 · 10 -3 95% 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

11. Measurements K +  - B. Golob, Belle D 0 Mixing 11 KEK Seminar, May 2007 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, 151801 (2006), 400 fb -1 3  Q interval t-dependence to separate DCS/mixed N RS  10 6

12. Measurements K +  - B. Golob, Belle D 0 Mixing 12 KEK Seminar, May 2007 PRL96, 151801 (2006), 400 fb -1 Decay time: resol. function from RS  (D 0 ) = 409.9 ± 0.7 fs x’ 2, y’, R D free parameters Results: R D = (3.64 ± 0.17 ) ·10 -3 x’ 2 = (0.18 ± 0.21 0.23 ) · 10 -3 y’ = (0.6 ± 4.0 3.9 ) · 10 -3 95% C.L. (x’ 2, y’) contour frequentist, FC ordering WS t dist.  PDG =410.1 ± 1.5 fs ( x’ 2, y’) =(0,0) C.L. 3.9%

13. Measurements K S  +  - B. Golob, Belle D 0 Mixing 13 KEK Seminar, May 2007 arXiv: 0704.1000, 540 fb -1 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 : Dalitz variables analogous for M = sum of intermediate states

14. Measurements K S  +  - arXiv: 0704.1000, 540 fb -1 fit M (m - 2,m + 2,t) to data distribution  x, y B. Golob, Belle D 0 Mixing 14 KEK Seminar, May 2007 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.; t M signal rnd slow  combin.

15. Measurements K S  +  - arXiv: 0704.1000, 540 fb -1 B. Golob, Belle D 0 Mixing 15 KEK Seminar, May 2007 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, 112009 (2006)

16. Measurements K S  +  - arXiv: 0704.1000, 540 fb -1 B. Golob, Belle D 0 Mixing 16 KEK Seminar, May 2007 Decay-t projection of fit t [fs] x = (0.80 ± 0.29 ± 0.13 0.16 )% y = (0.33 ± 0.24 ± 0.10 0.14 )%  = 409.9±0.9 fs most sensitive meas. of x; Cleo, PRD72, 012001 (2005) x = 1.8 ± 3.4 ± 0.6% y = -1.4 ± 2.5 ± 0.9 %  PDG =410.1 ± 1.5 fs comb. bkg.

17. Measurements K + K - /  +  - B. Golob, Belle D 0 Mixing 17 KEK Seminar, May 2007 hep-ex/0703036v2, 540fb -1, acc. to PRL D 0 → K + K - /  +  - CP even final state; in the limit of no CPV: CP|D 2 > = |D 2 >  measure 1/  2 S. Bergman et al., PLB486, 418 (2000) A M,  : CPV in mixing and interference Signal side band M, Q,  t selection optimized in MC K+K-K+K- K-+K-+ +-+- N sig 111x10 3 1.22x10 6 49x10 3 P98%99%92%

18. Measurements K + K - /  +  - B. Golob, Belle D 0 Mixing 18 KEK Seminar, May 2007 hep-ex/0703036v2, 540fb -1, acc. to PRL 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 (M sideband) MC each  i → 3 Gauss

19. Measurements K + K - /  +  - B. Golob, Belle D 0 Mixing 19 KEK Seminar, May 2007 hep-ex/0703036v2, 540fb -1, acc. to PRL Result K + K - /  +  - and K -  + ratio difference of lifetimes visually observable y CP = (1.31 ± 0.32 ± 0.25) % 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

20. Measurements K +  - B. Golob, Belle D 0 Mixing 20 KEK Seminar, May 2007 BaBar, hep-ex/0703020, 384fb -1, acc. to PRL Signal: M= M(K  )  M = M(K  slow ) - M(K  ) N WS = 4030 ± 90 Reminder Fit

21. Measurements K +  - B. Golob, Belle D 0 Mixing 21 KEK Seminar, May 2007 BaBar, hep-ex/0703020, 384fb -1, acc. to PRL Result R D = (3.03 ± 0.19) ·10 -3 x’ 2 = (-0.22 ± 0.37 ) · 10 -3 y’ = (9.7 ± 5.4 ) · 10 -3 including sys. error 1  2  3  3.9  Comparison consistent evidence for (x,y)  (0,0)

22. Measurements B. Golob, Belle D 0 Mixing 22 KEK Seminar, May 2007 K S  +  - : (x,y)=(0,0) has C.L. 2.6% K + K - /  +  - : y=0 has C.L. 6x10 -4 Results

23. Measurements B. Golob, Belle D 0 Mixing 23 KEK Seminar, May 2007 Combination 1996 FNAL E791 R M = (0.11 +0.30 −0.27 +0.00 −0.014 )%FNAL E791 2005 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 ± 0.047 ± 0.014 )Belle 1999 FNAL E791 ΔΓ = (0.04 ± 0.14 ± 0.05 ) ps −1 (y CP = (0.8 ± 3.1)%)FNAL E791 2000 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 +0.5 −0.4 )%BaBar 2002 Belle y CP = (−0.5 ± 1.0 +0.7 −0.8 )%Belle 2007 Belle y CP = (1.31 ± 0.32 ± 0.25 )%Belle 2006 Belle x' 2 = (0.018 +0.021 −0.023 )% y' = (0.06 +0.40 −0.39 )%Belle 2007 BaBar x' 2 = (−0.022 ± 0.030 ± 0.021)% y' = (0.97 ± 0.44 ± 0.31)%BaBar 2006 BaBar K + π − π 0 R M = (0.023 +0.018 −0.014 ± 0.004)%BaBar 2006 BaBar K + π − π + π − R M = (0.019 +0.016 −0.015 ± 0.002)%BaBar 2005/2007 CLEO II.V x = (1.9 +3.2 −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

24. Measurements average B. Golob, Belle D 0 Mixing 24 KEK Seminar, May 2007 Average fit to individual measurements with x, y,  free assuming Gaussian p.d.f.’s; correlation for K +  - ; x = (0.94 ± 0.36 )% y = (0.68 ± 0.21 )%  =21 o ± 19 o unofficial! x, y ~ 1%, significantly deviating from 0

25. Measurements CPV B. Golob, Belle D 0 Mixing 25 KEK Seminar, May 2007 CPV in D 0 system first two generations involved; Wolfenstein param., CPV in D 0 very small,  10 -3 ; parameterization: D 0 → K +  -,K + K - /  +  -,K S  +  - 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;

26. Measurements CPV B. Golob, Belle D 0 Mixing 26 KEK Seminar, May 2007 CPV in D 0 → K +  - CPV allowed fit: separate D 0 and D 0 tags (x’ 2,y’,R D ) → (x’ ±2, y’ ±,R D ± ) A D = (23 ± 47) ·10 -3 A M = (670 ± 1200) ·10 -3 CPV in D 0 → K + K - /  +  - A  = (0.01 ± 0.30 ± 0.15) % direct CPV indirect CPV CPV allowed indirect CPV hep-ex/0703036v2, 540fb -1, acc. to PRL PRL96, 151801 (2006), 400 fb -1

27. Prospects B. Golob, Belle D 0 Mixing 27 KEK Seminar, May 2007 CPV in D 0 → K S  +  - preliminary study:  (|q/p|  1 + A M /2) ~ 0.30,  (  ) ~ 0.3 rad Prospects near future: 1 ab -1 1  3   (x) ~ ± 0.25%  (y) ~ ± 0.17% individual meas. test CPV with sensitivity ~ O (0.3) no evidence so far arXiv: 0704.1000, 540 fb -1

28. Prospects B. Golob, Belle D 0 Mixing 28 KEK Seminar, May 2007 Super-B rough expectations, 5 ab -1 possible CPV - New Physics - tested with ~ O (5) better sensitivity; (several extensions of SM predict CPV ~ O (1%)) combination of results  (x) ~  (y) ~ 0.10% mixing  (|q/p|) ~ 0.09,  (  ) ~0.05 CPV Y. Grossman et al., hep-ph/0609178

29. Summary B. Golob, Belle D 0 Mixing 29 KEK Seminar, May 2007  Belle and BaBar presented evidence for D 0 mixing x = (0.94 ± 0.36)% y = (0.68 ± 0.21 )%  Values of mixing parameters at upper end of SM expectations; new measurements to further constrain x, y (and hope for more accurate predictions?)  Search for CPV = NP search; Super-B factory would allow for sensitive searches in reasonable extensions of SM