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D 0 Mixing

D 0 Mixing. B. Golob University of Ljubljana , Jožef Stefan Institute & Belle Collaboration. “Jožef Stefan” Institute. University of Ljubljana. Outline Phenomenology Measurement s A) Experiments B) CP states C) Wrong sign (non-CP) D) t-dependent Dalitz E) y (3770)

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D 0 Mixing

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  1. D0 Mixing B. Golob University of Ljubljana, Jožef Stefan Institute & Belle Collaboration “Jožef Stefan” Institute University of Ljubljana • Outline • Phenomenology • Measurements • A) Experiments • B)CP states • C) Wrong sign (non-CP) • D) t-dependent Dalitz • E)y(3770) • F) Average of results • 3. Prospects & Summary • A) Mixing param. • B) CPV param. • C) Summary

  2. q2 q1 q2 q1 1. Phenomenology P0 P0 P0 = K0, Bd0, Bs0 and D0 Time evolution flavor states ≠ Heff eigenstates: (defined flavour) (defined m1,2 and G1,2) |x|, |y| << 1 Decay time distribution of experimentally accessible states D0, D0 sensitive to mixing parameters x and y, depending on final state coherent production, V→D0D0

  3. 1. Phenomenology x and y d, s, b d, s, b K+ difficult to estimate DCS SU(3) breaking D0 D0 W+ D0 D0 K- W- I.I. Bigi, N. Uraltsev, Nucl. Phys. B592, 92 (2001); A.F. Falk et al., PRD69, 114021 (2004) unique for D0’s: down q’s loop; mixing: 30 years after discovery The duration of passion is proportionate with the original resistance of the woman. H. de Balzac (1799 -1850)

  4. Vus* 1. Phenomenology K+ CP violation Vcs D0 D0: first two quark generations; CKM elements ≈ real; using CKM unitarity: bellow current exp. sensitivity; signals New Physics K- parameterization: RD ≠1: Cabbibo suppression AD ≠0: CPV in decay AM ≠0: CPV in mixing f ≠0 : CPV in interference

  5. 2. Measurements A) Experiments continuum production s(c c)  1.3 nb (~109 XcYc pairs) e+e-→ y(3770) → D0D0, D+D- (coherent C=-1 state); ~800 pb-1 of data available at y(3770) 2.8x106 D0D0 very diverse exp. conditions c g* General B-factories c D*+ →D0ps+ charge of ps flavor of D0; dM=M(D0ps)-M(D0)  background reduction p*(D*) > 2.5 GeV/c eliminates D0 from b → c

  6. S. Bergman et al., PLB486, 418 (2000) 2. Measurements B) Decays to CP eigenstates D0→ K+K- / p+p-, CP even no CPV: CP|D1> = |D1> t=1/G1; K-p+: mixture of CP states t=f(1/G1,1/G2) + = K+K-/p+p- and K-p+ratio Belle, PRL 98, 211803 (2007), 540fb-1 1stevidence for D0 mixing BaBar, arXiv:0712.2249, 384fb-1

  7. 2. Measurements B) Decays to CP eigenstates CPV t-depedent / t-independent method Belle, PRL 98, 211803 (2007), 540fb-1 t-dependent t-independent similar sensitivity BaBar, arXiv:0712.2249, 384fb-1 Belle, arXiv:0807.0148, 540fb-1 BaBar, PRL 100, 061803 (2007), 386fb-1

  8. D*+→ D0pslow+D0 → D0 → K+p- 2. Measurements C) WS decays (non-CP) DCS decays  interference; t-dependence to separate DCS/mixed likelihood contours d: unknown strong phase DCS/CF 1s 3.9s 1stevidence for D0 mixing 3s CDF, PRL 100, 121802 (2008), 1.5fb-1 BaBar, PRL 98, 211802 (2007), 384fb-1 Belle, PRL 96, 151801 (2006), 400fb-1 5s likelihood contours 95% FC confidence region 1s 3.8s 3s

  9. D0→KSp+p- 2. Measurements D)t-dependent Dalitz analyses different types of interm. states; CF: D0→ K*-p+ DCS: D0→ K*+p- CP: D0→r0 KS if f = f  populate same Dalitz plot; relative phases determined (unlike D0→ K+p-); t-dependence: regions of Dalitz plane→ specific t dependence f(x, y); D0→f access directly x, y l1,2=f(x,y); Belle, PRL 99, 131803 (2007), 540fb-1 D0→f D0→KSp+p- most accurate x

  10. Cleo-c, PRD78, 012001 (2008), 281pb-1 2. Measurements E) y(3770) →D0D0 uncorrelated production at threshold D0D0 in C=-1 state  effective Br’s depending on mixing param.: y, RM=(x2+y2)/2, RDcosd S±: CP eigenstates e-: Xen fit to set of single and double Br’s single D0 reconstr. both D0 reconstr. measured from ST rates Br(D0D0→fi/fj) Br(D0→fi)Br(D0→fj) Br(D0D0→fiX) Br(D0→fi) uncorrelated production (RWS=G(K+p-)/G(K-p+))

  11. Cleo-c, PRD78, 012001 (2008), 281pb-1 2. Measurements DT yields E) y(3770) →D0D0 fit to set of single and double Br’s ST yields M [GeV] 1.83 1.89 1.83 1.89 1.83

  12. 2. Measurements K+K- F) Average of results c2 fit including correlations among measured quantities K+p- RM KSp-p+ d uncertainty CPV c2/n.d.f.=25.3/20 http://www.slac.stanford.edu/xorg/hfag/charm/ and HFAG, arXiv:0808.2268 (x,y)≠(0,0): 9.8s; CP even state heavier and shorter lived; no CPV within 1s

  13. 3. Prospects and summary s(√RDcosd) [10-2] charm A) Mixing parameters Cleo-c results improved signif. with higher stat.; (all estimates based on ) x, y related measurements of similar or better accuracy at Super-B with modest lumin.; d already constrained with reasonable accuracy from combination of x’2, y’, x, y meas.; Cleo-c, PRD78, 012001 (2008), 281pb-1 L [fb-1] 0.5 5.0 0.5 5.0 s(RM) [10-3] charm s(x’2) [10-3] B s(y) [%] charm s(yCP) [%] B Prediction is very difficult, especially of the future. s(x) [%] B s(y) [%] B N. Bohr (1885 - 1962) L [fb-1] L [fb-1] L [ab-1] L [ab-1]

  14. 3. Prospects and summary A) Mixing parameters asymmetric factory at y(3770): for same <Dz> as at U(4S) gb~2 (0.42 at Belle), E(e-/e+)=8 GeV/0.45 GeV (8 GeV/3.5 GeV at Belle); resolution: sresD ~ sresB (bgB/bgD) ~0.3 ps ~tD0 N(S+K-p+, S+e-)~1300 @ 281 pb-1 sy~0.1% with 2 ab-1 (stat. only)

  15. 3. Prospects and summary s(AG) [%] B s(|q/p|) B s(f) [rad] B B) CPV parameters various options at y(3770); decays to same sign CP eigenstates: (assuming no direct CPV) suppressed by RM; not feasible; L [ab-1] >>

  16. 3. Prospects and summary B) CPV parameters various options at y(3770); untagged asymmetry: ACP linear in CPV and mixing param., feasible (stat. only); systematics from charge dependent e asymm.? also possible at B-factories L[fb-1] 1400 1000 600 200 current d >> RD, y uncertainty 300 fb-1 0.2 0.5 0.9 sind

  17. 3. Prospects and summary B) CPV parameters D0D0 in C=+1 state (D0D0 g); tagged asymmetry:

  18. 3. Prospects and summary s(AG) [%] B s(|q/p|) B s(f) [rad] B B) CPV parameters various options at y(3770); CPV in mixing: ACP linear in CPV param., feasible (stat. only); systematics from e- spectrum extrapolation (cancels in ACP)? s(AM)~1% with 300 fb-1 sensitivity better than at Super-B; L [ab-1]

  19. 3. Prospects and summary B) CPV parameters s(AD) [%] charm s(AD) [%] B various options at y(3770); direct CPV: ACP linear in CPV param., feasible (stat. only); systematics from e- spectrum extrapolation (cancels in ACP)? sensitivity better than at Super-B; a complete overview of physics cases (for BES-III) can be found in L [fb-1] 0.5 5.0 L [ab-1] K.T. Chao, Y. Wang, editors, arXiv:0809.1869

  20. 3. Prospects and summary C) Summary today: D mixing unambigiously established; x, y ~ O(1%); no CPV asymmetry @ ~0.3%; “tomorrow”: Super-B factory at initial stage s(x), s(y) ~ O( 0.1%) s(ACP) ~ O(0.1%); dKp precisely determined from combination of measurements; RM, y @ charm factory of lower accuracy than @ B factory (unless t-dependent meas. with asymmetric collider); various options for CPV (only few examples shown); several competitive or better, and complementary to B-factory (including D0D0 with C=+1); many other possibilities (Dalitz studies, triple product correlations, T-odd moments, ...)

  21. Systematics bckup Belle, PRL 98, 211803 (2007), 540fb-1 Decays to CP eigenstates scales with MC better detect. (MC) desc. scales with data/MC scales with data/MC scales with data/MC total non-scaling 0.10% 0.06% L0=540 fb-1

  22. Systematics bckup Decays to CP eigenstates s(yCP) [%] s(AG) [%] L [ab-1] L0=540 fb-1

  23. L0=540 fb-1 Systematics bckup t-dependent Dalitz analyses Belle, PRL 99, 131803 (2007), 540fb-1 model dependence [10-4]: Dx                 Dy -10.3           +0.1K*0(1430) DCS/CF -15% + 6.9           -2.5K*2(1430) DCS/CF -30% -1.6 -0.9 K*(1410) DCS & CF -20% -5.1 -4.1G(q2) const. --------------------------------- +10+6        Total model dep. -14-8 experimental: Dx           Dy +7.6         -7.8               p* variation -5.6         -5.7  Dalitz pdf for bkg. from different t bins ----------------------- +9+8 Total experimental-7          -12 better underst. of DCS/CF; arbitrary ½ of uncertainty taken as non-scaling ±8 ± 4.3 model non-scaling scales with data/MC ±6 ±6 exp. non-scaling ±10 ±7 total non-scaling

  24. L0=540 fb-1 Systematics bckup t-dependent Dalitz analyses model dependence: D|q/p|Df [rad] ±0.08 ±0.06 experimental: D|q/p|Df [rad]+0.06 +0.06           p* variation +0.03 -0.05bkg. decay t parameters ±0.08 ±0.06 model non-scaling scales with data/MC scales with data/MC ±0.08 ±0.06 total non-scaling

  25. Systematics bckup t-dependent Dalitz analyses s(x) [%] s(y) [%] s(|q/p|) s(f) [rad] L [ab-1] L0=540 fb-1

  26. L0=400 fb-1 Systematics bckup WS decays (non-CP) Belle, PRL 96, 151801 (2006), 400fb-1 ssyst(1-dim) = 0.75 sstat Dx’2 [sstat]Dy’ [sstat] ±0.44 ±0.44        p* variation ±0.26 ±0.26 fixed decay-t parameters ±0.26 ±0.26st effect on fractions scales with data/MC scales with data scales with data ±0.48 ±0.48 total non-scaling assumed same fraction of scaling/non-scaling systematics as for x’2

  27. Systematics bckup WS decays (non-CP) s(x’2) [10-3] s(y’) [%] L [ab-1] L0=400 fb-1

  28. L0=281 pb-1 Systematics bckup y(3770) →D0D0 Cleo-c, PRD78, 012001 (2008), 281pb-1 assume sensitivity on y is mainly due to S±e- RDcosd is mainly due to S±K-p+ RM is mainly due to K-p+K-p+ calculate fraction of non-scaling syst. on DT yields in total relative error: S±e- (y) s(non-scaling)/s(total)=15% extrap. of e- momentum S±K-p+ (RDcosd) s(non-scaling)/s(total)=15% FSR, sideband subtr. K-p+K-p+ (RM) s(non-scaling)/s(total)=2.4% FSR

  29. d bckup y(3770) →D0D0 • constraints • average • direct meas. • (fit w/o external input) cosd 1.0 0.5 0 -0.5 -1.0 1 0 -1 y’ measured y’=ycosd-xsind [%] d measured 0 1 2 3 4 5 d [rad] 0 1 2 3 4 5 d [rad]

  30. q2 q1 Introduction bckup History observation of K0: 1950 (Caltech) mixing in K0: 1956 (Columbia) observation of Bd0: 1983 (CESR) mixing in Bd0: 1987 (Desy) observation of Bs0: 1992 (LEP) mixing in Bs0: 2006 (Fermilab) observation of D0: 1976 (SLAC) mixing in D0: 2007 (KEK, SLAC) (evidence of) Mixing phenomena in course of life neutral meson P0 can transform into anti-meson P0 P0 = K0, Bd0, Bs0 and D0 6 years 4 years 14 years 31 years c quark t quark mass q2 q1 P0 P0 ???? ????

  31. Introduction bckup Central Drift Chamber e+ 3.5 GeV 3(4) layer Si det. e- 8 GeV Aerogel Cherenkov (n=1.015- 1.030) m and KL Counter (14/15 layers RPC+Fe) 1.5T SC solenoid EM calorimeter CsI (16X0) tracking s(pt)/pt= 0.2% √(pt2+2.5) PID e(K±) ~ 85%e(p±→K±)  10% for p < 3.5 GeV/c

  32. Introduction bckup BaBar detector at SLAC gb=0.56 Integrated luminosity: Ldt  500 fb-1 tracking s(pt)/pt= 0.45%+0.13%pt PID 3.4 s K/p separation for p < 3.5 GeV/c

  33. e- ID Had. ID tracking Introduction bckup Cleo-c detector at CESR e+e-→ y(3770) → D0D0, D+D- (coherent C=-1 state); analogous to B-factory with e+e-→ BB @ U(4S); symmetric; also higher energy, above DD* or DsDs threshold; ~572 pb-1 of data available at y(3770) 2.0x106 D0D0, 1.6x106 D+D- charm-factory; also upgraded BES at BEPCII Cleo-c, hep-ex/0606016 s [GeV]

  34. Intrrduction bckup CDF 3.5 fb-1 on tape s(D0; pt>5.5 GeV,|y|<1)≈13 mb 50x109 D0’s ds(D0)/dpt [nb/GeV]

  35. diagonal elem.: P0 P0 (including decays) non-diagonal elem.: P0 P0 Phenomenology bckup Time evolution eigenvalues: P1,2 evolve in time according to m1,2 and G1,2:

  36. Vuj* Vci* Vcj Vui u c W+ D0 D0 d, s, b d, s, b W- u c K+ D0 D0 K- Phenomenology bckup x and y in SM 2nd order perturb.: short distance: |x| ~ O(10-5) G. Burdman, I. Shipsey, Ann.Rev.Nucl.Sci. 53, 431 (2003) DCS SU(3) breaking absorptive part (real interm. states)  y dispersive part (off-shell interm. states)  x long distance: |x|, |y| ~ O(10-2) I.I. Bigi, N. Uraltsev, Nucl. Phys. B592, 92 (2001); A.F. Falk et al., PRD69, 114021 (2004) D0 mixing: rare process in SM; possible contrib. from NP

  37. Phenomenology bckup Oscillations measurable rates:

  38. Phenomenology bckup probab. to observe an initially produced X0 as X0 after time t probab. to observe an initially produced X0 as X0 after time t Oscillations ~ Bs0 more difficult to observe oscillations within t visually unobservable deviation from pure exponential

  39. PRL96, 151801 (2006), 400 fb-1 x’2 < 0.72 ·10-3 -0.99% < y’ < 0.68% no signif. CPV K+p- bckup 95% C.L. (x’2, y’) contour frequentist, FC ordering Results: RD = (3.64 ± 0.17 ) ·10-3 x’2 = (0.18 ±0.210.23) · 10-3 y’= (0.6 ±4.03.9) · 10-3 AD = (23 ± 47) ·10-3 AM = (670 ± 1200) ·10-3 no CPV CPV • CPV allowed: • separate D0 and D0 tags • (x’2,y’,RD) → (x’±2, y’±,RD±) (0,0) lies on 96.1% C.L. contour largest syst. due to p*(D*) selection

  40. Belle, PRL 99, 131803 (2007), 540fb-1 KSp+p- bckup K*X(1400)+ Dalitz projection of fit K*(892)+ r/w K*(892)- test of S-wave pp contr. (f0, s1,2): K-matrix formalism Results (fit fractions, phases) in agreement with (measurement of f3) PRD73, 112009 (2006)

  41. Belle, PRL 99, 131803 (2007), 540fb-1 KSp+p- bckup D0→ KSp+p- model dependence [10-4]: Dx                 Dy -10.3           +0.1K*0(1430) DCS/CF -15% + 6.9           -2.5K*2(1430) DCS/CF -30% -1.6 -0.9 K*(1410) DCS & CF -20% -5.1 -4.1G(q2) const. --------------------------------- +10+6        Total model dep. -14-8 experimental: Dx           Dy +7.6         -7.8               p* variation -5.6         -5.7  Dalitz pdf for bkg. from different t bins ----------------------- +9+8 Total experimental-7          -12 Largest systematics observed discrepancy from input in MC statistical uncertainty: s(x)=29x10-4 s(y)=24x10-4

  42. Belle, PRL 99, 131803 (2007), 540fb-1 KSp+p- bckup D0→ KSp+p- efficiency and resol. in M(pp) rnd ps bkg.: Prnd [(1-fw) M(m-2,m+2,t) +fwM(m+2,m-2,t)] R(t) fw from fit to Q side band: fw= 0.452 ± 0.005 diff. w.r.t. fw=0.5 in systematic error comb. bkg.: Pcmb  B(m-2,m+2) * ([ d(t) + Exp(t) ]R’(t) parameters from fit to Dalitz and t distrib. of M(KSp+p- ) sideband (systematics: Dalitz distrib. in different t intervals)

  43. K+p-p0 bckup BaBar, arXiv:0807.4567, 384fb-1

  44. K+p-p0 bckup BaBar, arXiv:0807.4567, 384fb-1 D0→K+p-p0 separate WS/RS Dalitz distributions; t-distrib. analogous to D0 →K+ p-; RS t-integrated Dalitz analysis; WS Dalitz analysis; no mixing point 0.8% C.L. BaBar, Lepton Photon 07, 384fb-1 dKpp: unknown strong phase shift DCS/CF

  45. K-p+ K+K-/ p+p- bckup Belle, PRL 98, 211803 (2007), 540fb-1 Fit simultaneous binned likelihood fit to K+K-/K-p+/p+p- decay-t, common free yCP R : ideally each si Gaussian resol. term with fraction fi; : described by 3 Gaussians  event-by-event st trec-tgen/st parameters of R depend slightly on data taking conditions t = 408.7±0.6 fs

  46. K+K-/ p+p- bckup Belle, PRL 98, 211803 (2007), 540fb-1 equal t0 assumption DyCP=t0CP - t0Kp / tKp from MC cocktail, including running periods with slight misalign. of SVD

  47. K+K-/ p+p-CPV bckup Decays to CP eigenstates CPV with adec<<1: Belle, PRL 98, 211803 (2007), 540fb-1 t-dependent BaBar, arXiv:0712.2249, 384fb-1 ACPpp ACPKK t-integrated ACPmeas =Aep + AFB + ACPf Aep: comparison of tagged/untagged (D*+→D0p+),D0→K-p+ AFB: asymmetric f(cosqCMS) BaBar, PRL 100, 061803 (2007), 386fb-1 |cosqCMS| |cosqCMS| AFBpp AFBKK Belle, arXiv:0807.0148, 540fb-1 |cosqCMS| |cosqCMS|

  48. y(3770) →D0D0 bckup D0, D0 in anti-symmetric state

  49. Average bckup Average of results inputs http://www.slac.stanford.edu/xorg/hfag/charm/ and HFAG, arXiv:0808.2268

  50. Average bckup http://www.slac.stanford.edu/xorg/hfag/charm/ and HFAG, arXiv:0808.2268 c2 of fit

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