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D 0 -D 0 Mixing

D 0 -D 0 Mixing.

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D 0 -D 0 Mixing

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  1. D0-D0 Mixing The oscillation in time of neutral D mesons into their antiparticles, and vice versa, commonly called D0-D0 mixing, has been observed by several experiments in a variety of channels during the past year. While K0-K0 mixing and B0-B0 mixing are (relatively) well understood in the Standard Model of particle physics, observations of D0-D0 mixing indicate that the physical eigenstates have decay rate differences and/or mass differences greater than expected most naively. In this talk I will discuss recent experimental results and the extent to which mixing measurements can probe non-perturbative QCD and physics beyond the Standard Model. Michael D. Sokoloff University of Cincinnati

  2. Strong Nuclear Interactions of Quarks and Gluons Each quark carries one of three strong charges, and each antiquark carries an anticharge. For convenience, we call these colors: • Quarks are never observed as free particles. • Mesons consist of quark-antiquark pairs with canceling color-anticolor charges

  3. Weak Charged Current Interactions charm decay neutrino scattering f ~ f As a first approximation, the weak charged current interaction couples fermions of the same generation. The Standard Model explains couplings between quark generations in terms of the Cabibbo-Kobayashi-Maskawa (CKM) matirx.

  4. b = f1; a = f2; g = f3 Weak Phases in the Standard Model

  5. Charm Meson Mixing Why is observing charm mixing interesting? It completes the picture of quark mixing already seen in the K, Bd, and Bs systems. K — PR 103, 1901 (1956); PR 103, 1904 (1956). Bd— PL B186, 247 (1987); PL B192, 245 (1987). Bs — PRL 97, 021802 (2006); PRL 97, 242003 (2006). In the Standard Model, it relates to processes with down-type quarks in the mixing loop diagram. Mixing,itself, could indicate new physics. It is a significant step toward observation of CP violation in the charm sector, a clear indication of new physics

  6. D1, D2 have masses M1, M2 and widths 1, 2 Mixing occurs when there is a non-zero mass or lifetime difference For convenience define, xand y where and define the mixing rate Neutral D mesons are produced as flavor eigenstatesD0 and D0 and decay via as mass, lifetime eigenstatesD1, D2 where and Mixing Phenomenology ( < 5 x 10-4)

  7. How Mixing is Calculated

  8. Standard Model Mixing Predictions • Box diagram SM charm mixing rate naively expected to be very low (RM~10-10) (Datta & Kumbhakar) • Z.Phys. C27, 515 (1985) • CKM suppression → |VubV*cb|2 • GIM suppression → (m2s-m2d)/m2W • Di-penguin mixing, RM~10-10 • Phys. Rev. D 56, 1685 (1997) • Enhanced rate SM calculations generally due to long-distance contributions: • first discussion, L. Wolfenstein • Phys. Lett. B 164, 170 (1985)

  9. Standard Model Mixing Predictions • Box diagram SM charm mixing rate naively expected to be very low (RM~10-10) (Datta & Kumbhakar) • Z.Phys. C27, 515 (1985) • CKM suppression → |VubV*cb|2 • GIM suppression → (m2s-m2d)/m2W • Di-penguin mixing, RM~10-10 • Phys. Rev. D 56, 1685 (1997) • Enhanced rate SM calculations generally due to long-distance contributions: • first discussion, L. Wolfenstein • Phys. Lett. B 164, 170 (1985) Partial History of Long-Distance Calculations • Early SM calculations indicated long distance contributions produce x<<10-2: • x~10-3 (dispersive sector) • PRD 33, 179 (1986) • x~10-5 (HQET) • Phys. Lett. B 297, 353 (1992) • Nucl. Phys. B403, 605 (1993) • More recent SM predictions can accommodate x, y ~1% [of opposite sign] (Falk et al.) • x,y≈ sin2 qC x [SU(3) breaking]2 • Phys.Rev. D 65, 054034 (2002) • Phys.Rev. D 69, 114021 (2004)

  10. New Physics Mixing Predictions • Possible enhancements to mixing due to new particles and interactions in new physics models • Most new physics predictions for x • Extended Higgs, tree-level FCNC • Fourth generation down-type quarks • Supersymmetry: gluinos, squarks • Lepto-quarks • Large possible SM contributions to mixing require observation of either a CP-violating signal or | x | >> | y | to establish presence of NP • A recent survey (Phys. Rev. D76, 095009 (2007), arXiv:0705.3650) summarizes models and constraints: and more Heavy weak iso-singlet quarks

  11. DCS K+- D0 CF MIX D0 Time-Evolution of D0K Decays RS = CF WS = DCS DCS and mixing amplitudes interfere to give a “quadratic” WS decay rate (x, y << 1): where and  is the phase difference between DCS and CF decays.

  12. 384 fb-1 e+e-c,c Slow pion charge tags neutral D production flavor D0K Reconstruction Beam spot: x≈ 100 m y≈ 7 m

  13. Full Fit Procedure Unbinned maximum likelihood fit in several steps (fitting 1+ million events takes a long time) Fit to m(Kp) and Dm distribution: • RS and WS samples fit simultaneously • Signal and some background parameters shared • All parameters determined in fit to data, not MC Fit RS decay time distribution: • Determines D0 lifetime and resolution function • Include event-by-event decay time error dt in resolution • Use m(Kp) and Dm to separate signal/bkgd (fixed shapes) Fit WS decay time distribution: • Use D0 lifetime and resolution function from RS fit • Compare fit with and without mixing (and CP violation)

  14. Simplified Fit Strategy & Validation Fit m(K) and m in bins of time: • If no mixing, ratio of WS to RS signal should be constant • No assumptions made on time evolution of background • Each time bin is fit independently Time bins: WS (0.75<t<2.5 ps) WS (0.75<t<2.5 ps) Dm m(K+p–)

  15. Simplified Fit Strategy & Validation Rate of WS events clearly increases with time: (stat. only) WS/RS (%)

  16. Simplified Fit Strategy & Validation Rate of WS events clearly increases with time: (stat. only) WS/RS (%) Inconsistent with no-mixing hypothesis: 2=24

  17. Simplified Fit Strategy & Validation Rate of WS events clearly increases with time: Consistent with prediction from full likelihood fit 2=1.5 (stat. only) WS/RS (%) Inconsistent with no-mixing hypothesis: 2=24

  18. Full Fit Procedure Unbinned maximum likelihood fit in several steps (fitting 1+ million events takes a long time) Fit to m(Kp) and Dm distribution: • RS and WS samples fit simultaneously • Signal and some background parameters shared • All parameters determined in fit to data, not MC Fit RS decay time distribution: • Determines D0 lifetime and resolution function • Include event-by-event decay time error dt in resolution • Use m(Kp) and Dm to separate signal/bkgd (fixed shapes) Fit WS decay time distribution: • Use D0 lifetime and resolution function from RS fit • Compare fit with and without mixing (and CP violation)

  19. m(Kp)-m Fit Results Signal = 1 141 500 ± 1 200 Signal = 4 030 ± 90

  20. Full Fit Procedure Unbinned maximum likelihood fit in several steps (fitting 1+ million events takes a long time) Fit to m(Kp) and Dm distribution: • RS and WS samples fit simultaneously • Signal and some background parameters shared • All parameters determined in fit to data, not MC Fit RS decay time distribution: • Determines D0 lifetime and resolution function • Include event-by-event decay time error dt in resolution • Use m(Kp) and Dm to separate signal/bkgd (fixed shapes) Fit WS decay time distribution: • Use D0 lifetime and resolution function from RS fit • Compare fit with and without mixing (and CP violation)

  21. Decay Time Resolution Average D0 flight length is twice average resolution • Resolution function described by sum of 3 Gaussians • Resolution widths scales with t • Mean of core Gaussian allowed to be non-zero • Observed core Gaussian shifted 3.6±0.6fs = For combinatorial background, use Gaussians and power-law “tail” for small long-lived component

  22. plot signal region: 1.843<m<1.883 GeV/c2 0.1445<m< 0.1465 GeV/c2 RS Decay Time Fit RS decay time, signal region D0 lifetime and resolution function fitted in RS sample: 410.3±0.6 (stat.) fs Consistent with PDG (410.1±1.5 fs) NB: Shifted core Gaussian dominates systematic uncertainties

  23. Full Fit Procedure Unbinned maximum likelihood fit in several steps (fitting 1+ million events takes a long time) Fit to m(Kp) and Dm distribution: • RS and WS samples fit simultaneously • Signal and some background parameters shared • All parameters determined in fit to data, not MC Fit RS decay time distribution: • Determines D0 lifetime and resolution function • Include event-by-event decay time error dt in resolution • Use m(Kp) and Dm to separate signal/bkgd (fixed shapes) Fit WS decay time distribution: • Use D0 lifetime and resolution function from RS fit • Compare fit with and without mixing (and CP violation)

  24. plot signal region: 1.843<m<1.883 GeV/c2 0.1445<m< 0.1465 GeV/c2 WS Fit with no Mixing WS decay time, signal region data - no mix PDF Fit result assuming no mixing: RD: (3.53±0.08±0.04)x10-3

  25. plot signal region: 1.843<m<1.883 GeV/c2 0.1445<m< 0.1465 GeV/c2 WS Fit with no Mixing WS decay time, signal region data - no mix PDF poor fit Fit result assuming no mixing: RD: (3.53±0.08±0.04)x10-3

  26. plot signal region: 1.843<m<1.883 GeV/c2 0.1445<m< 0.1465 GeV/c2 WS Fit with Mixing WS decay time, signal region Fit results allowing mixing: data - no mix PDF RD: (3.03±0.16±0.10)x10-3 x’2: (-0.22±0.30±0.21)x10-3 y’: (9.7±4.4±3.1)x10-3 fine fit

  27. Signal Significance Significance calculated from change in log likelihood: (stat. only) Best fit 1s 2s 3s 4s 5s No mixing

  28. Signal Significance Significance calculated from change in log likelihood: (stat. only) Best fit 1s 2s Corresponds to 4.5s (with 2 parameters) 3s 4s 5s No mixing

  29. Signal Significance Best fit is in unphysical region (x'2<0) (stat. only) (stat. only) Best fit Physical solution (y'=6.4x10-3) 1s 2s Corresponds to 4.5s (with 2 parameters) 3s 4s 5s No mixing

  30. Best fit Fit is inconsistent with no-mixing at 3.9s No mixing Signal Significance with Systematics Including systematics (~ 0.7 x stat) decreases signal significance [ PRL. 98, 211802 (2007) ] 1s 2s 3s 4s 5s

  31. BaBar 1 BaBar 2 BaBar 3 Belle 2 statistical Kp Analysis from Belle Last year Belle published analysis of K decays: Results consistent within 2: 400 fb-1 PRL 96,151801 stat. only no-mixing excluded at 2 (0,0)

  32. Average Kp Mixing Results Heavy flavor averaging group (HFAG) provides “official” averages Combine BaBar and Belle likelihoods in 3 dimensions (RD, x'2,y') May 2007 Averages: RD: (3.30 ) x 10-3 x’2: (-0.01±0.20) x 10-3 y’ : (5.5) x 10-3 +0.14 -0.12 1s y' 2s 3s No mixing excluded > 4 4s 5s +2.8 -3.7 x'2

  33. Preliminary Kπ Mixing Results from CDF[arXiv:0712.1567] • Best fit for mixing parameters • (uncertainties are combined • stat. and systematic) • Fit  = 19.2 for 17 dof • 3.8  from Null Hypothesis RD: (3.04 ± 0.55 ) x 10-3 x’2: (-0.12 ± 0.35) x 10-3 y’ : (8.5 ± 7.6) x 10-3

  34.  in D0 → h+h- [ PRL. 91, 121801 (2003) ]

  35. BaBar’s Early  in D0 → h+h- [ PRL. 91, 121801 (2003) ] 91 fb-1

  36. Belle’s Recent  in D0 → h+h- [ PRL. 98, 211803 (2007) ] 540 fb-1 Ave (1.12 ± 0.32)%

  37. BaBar’s Preliminary  D0 → h+h- 

  38. D0 → h+h-: Results Babar’s preliminary384 fb-1 results Combining KK and  results gives yCP = (1.24 ± 0.39 ± 0.13)% CP violation consistent with zero.

  39. Mixing in D0 → KSπ+π-

  40. Mixing in D0 → KSπ+π- X: (0.80 ± 0.35 ± 0.15)% y : (0.33 ± 0.24 ± 0.14)% (assuming no CP violation) 95% CL contours

  41. Time-Dependence in D0 → KSπ+π- box size is “capped” linear box size is logarithmic  plots illustrate the average decay time as a function of position in the Dalitz plot for (x,y) = (0.8%, 0.3%). The sizes of the boxes reflect the number of entries, and the colors reflect the average decay time.

  42. Mixing in D0 → K+p-p0 1483 ± 56 signal events “Wrong-sign” decay rate varies across the Dalitz plot: DCS term Resonance phase Interference term CF (mixed) term Phase between RS and WS Subscript D indicates dependence on position in the Dalitz plot. Yields from 384 fb-1 Bad charm Combinatorics

  43. D0 → K+p-p0 : Results No mixing is excluded at the 99% confidence level. Stat+syst x’’: (2.39 ± 0.61 ± 0.32) % Y’’ : (-0.14 ± 0.60 ± 0.40)% RM: (2.9 ± 1.6) x 10-4 68.3% 95.0% 99.0% 99.9%

  44. 20 Years Ago

  45. 10 Years Ago RM < 0.92% , no int. RM < 3.6%, int allowed RM < 0.50% , semi-lep RM < 0.85%, CPV allowed in int. RDCSD = (0.68 ± 0.34 ±0.07) % RDCSD = (0.77 ± 0.25 ±0.25) % y = (0.5 ±1.5 ± syst.) % results on the way

  46. Today HFAG D0 → Kπ RD: (3.30 ) x 10-3 x’2: (-0.01±0.20) x 10-3 y’ : (5.5) x 10-3 +0.14 -0.12 y' No mixing excluded > 4 +2.8 -3.7 CDF x'2 D0 → K+π-π0 D0 → KSπ+π- Stat+syst Belle  in D0 → h+h- BaBar + Belle (1.10 ± 0.27)% 68.3% 95.0% 99.0% 99.9% 95% CL contours

  47. 10 Years From Now ?? My guesstimates of measurement precision, assuming 100 fb-1 from LHCb and 50 ab-1 from SuperB, in units of 10-4 BES III should be able to measure cos ±  SuperB and BES III will measure relevant branching fractions with 5% fractional precision, constraining Standard Model contributions to x & y. Altogether,D0-D0 mixing measurements, and measurements of CP-violation in mixing, will provide insights into physics beyond the SM that will complement direct observations made at the LHC.

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