1 D 0 -D 0 Mixing at BaBar Charm 2007 August, 2007 Abe Seiden University of California at Santa Cruz for The BaBar Collaboration

2 Status of Mixing Studies: Mixing among the lightest neutral mesons of each flavor has traditionally provided important information on the electroweak interactions, the CKM matrix, and the possible virtual constituents that can lead to mixing. Among the long-lived mesons, the D meson system exhibits the smallest mixing phenomena. The B- factories have now accumulated sufficient luminosity to observe mixing in the D system and we can expect to see more detailed results as more luminosity is accumulated and additional channels sensitive to mixing are analyzed.

3 BaBar Charm Factory: 1.3 million Charm events per fb -1 BaBar integrated luminosity ~384 fb -1 (Runs 1-5) used for evidence for mixing result I will present. Present integrated luminosity is approximately 500 fb -1. BaBar Detector BaBar is a high acceptance general purpose detector providing excellent tracking, vertexing, particle ID, and neutrals detection.

4 The propagation eigenstates, including the electroweak interactions are: Propagation parameters for the two states are given by: With the observable oscillations determined by the scaled parameters:. In the case of CP conservation the two D eigenstates are the CP even and odd combinations. I will choose D 1 to be the CP even state. The sign choice for the mass and width difference varies among papers, I will use the choice above. Mixing Measureables:

5 Assuming CP conservation, small mixing parameters, and an initial state tagged as a D 0, we can write the time dependence to first order in x and y: Projecting this onto a final state f gives to first order the amplitude for finding f: This leads to a number of ways to measure the effect of mixing, for example: 1)Wrong sign semileptonic decays. Here A f is zero and we measure directly the quantity, after integrating over decay times: R M = (x 2 + y 2 )/2 Limits using this measurement however, are not yet sensitive enough to get down to the level for R M. 2) Cabibbo favored (right sign) hadronic decays (for example K     These are used to measure the average lifetime, with the correction from the term involving x and y usually ignored (provides a correction on O(10 -3 )).

6 3) Singly suppressed decays (for example K  K  or     ). In this case tagging the initial state isn’t necessary. For CP even final states: A f =A f. This provides the most direct way to measure y. With tagging we can also check for CP violation, by looking at the value of y for each tag type. BaBar will be updating this measurement with the full statistics later this summer. The initial measurement was based on 91 fb -1 and gave the result y = 0.8, with statistical and systematic errors each about 0.4, consistent with the published Belle measurement. 4) Doubly suppressed and mixed (wrong sign) decays (for example K    ). Mixing leads to an exponential term multiplied by both a linear and a quadratic term in t. The quadratic term has a universal form depending on R M. For any point in the decay phase space the decay rate is given by: Here y ’ = y cos  – x sin , where  is a strong phase difference between the Cabibbo favored and Doubly suppressed amplitudes. For the K    decay there is just the one phase. For multibody decays the phase  varies over the phase space and the term proportional to t will involve a sum with different phases if we add all events in a given channel.

7 BaBar has analyzed the decay channel K     , with a mass cut that selects mostly K    decays, the largest channel for the Cabibbo allowed amplitude arising from mixing. Based on 230 fb -1, BaBar measures: The parameter  allows for the phase variation over the region summed over. Better would be a fit to the full Dalitz plot. This, however, requires a model for all the resonant and smooth components that contribute to the given channel, which may introduce uncertainites. BaBar is working on such a fit, will be based on approximately 1500 signal events. Another important 3-body channel is the K S     decay channel. This contains: CP-even, CP-odd, and mixed-CP resonances. Must get relative amounts of CP-odd and CP-even contributions correct (including smooth components) to get the correct lifetime difference. Provides the possibility to measure x. BaBar also working on this channel, Belle has published their results.

8 Final general comments: In the Standard Model y and x are due to long-distance effects. They may be comparable in value but this depends on physics that is difficult to model. Also, the sign of x/y provides an important measurement. Long-distance effects control how complete the SU(3) cancellation is, which would make the parameters vanish in the symmetry limit. Depends on SU(3) violations in matrix elements and phase space. One might expect the x and y parameters to be in the range O(10 -3 to ). Thus the present data are consistent with the Standard Model. Searches for CP violation are important goals of the B-factories, since observation at a non-neglible level would signify new physics. I will turn now to the strongest Evidence for D-Mixing from BaBar, using the K  final state. (PRL 98, (2007)) Expectations for Mixing Parameters

9 K  Final State Beam-constrained simul- taneous fit of K, ,  tag (slow pion) tracks as shown in figure. –fit probability > –decay time error < 0.5 ps –-2 < decay time < 4 ps D 0 selection –CMS p* > 2.5 GeV/c –K,  particle identification –DCH hits > 11 –1.81 < M(K  ) < 1.92 GeV/c 2  tag –CMS p* < 0.45 GeV/c –lab p > 0.1 GeV/c –SVT hits > 5 beam spot interaction point x y 0.14 <  M < 0.16 GeV/c 2 Select candidate with greatest fit probability for multiple D* + candidates sharing tracks Event Selection:

10 events/0.1 MeV/c 2 events/1 MeV/c 2 x10 3 RS(top)/WS(bottom) Datasets After Event Selection

11 Analysis Strategy Blind analysis of D* + → D 0 (→K  )   tag –Event selection and fitting methodology determined before looking at the mixing results. Unbinned maximum likelihood fit to the data using four variables per event. – First, correlated fit to the M(K  ),  M = M(K  tag ) – M(K  ) distributions (two of the variables) to establish shapes for different components (signal and backgrounds) of the two dimensional distribution. High- statistics RS and WR data samples fit simultaneously. Fit RS proper-time distribution in the four variables, where the two additional variables are the event-by-event lifetime and its error. Establishes proper-time resolution function for signal and backgrounds. –The WS data are fit using the RS resolution functions. Several WS proper time fits –no mixing –mixing, no CP violation –mixing, CP violation Monte Carlo used to search for systematics and validate statistical significance of results.

12 RS/WS M(K  ),  M Distributions Fit RS/WS M(K  ),  M distributions with signal and three background PDFs, correlation between m and  m in signal events taken into account in PDF. Signal: peaks in M(K  ),  M True D 0 combined with random  tag : peaks in M(K  ) only Misreconstructed D 0 : peaks in  M only Purely combinatoric: non-peaking in either variable

13 Simultaneous Fit to RS/WS Data RS signal: 1,141,500±1200 Events. WS signal: 4030±90 Events.

14 Proper Time Analysis Use M(K  ) and  M PDF shapes from mass fits Fit RS decay time and error distribution to determine signal lifetime and resolution model –Signal, background D 0 PDF: exponential convolved with resolution function, which is the sum of three gaussians with widths proportional to the event-by-event lifetime errors. –Random combinatoric PDF: sum of two gaussians, one of which has a power-law tail. Fix WS resolution and DCS lifetime from RS fit –Signal PDF: theoretical mixed lifetime distribution, which is proportional to: (R D + R D ½ y’ (  t) + (x’ 2 +y’ 2 )(  t) 2 /4) e  t, convolved with the resolution model from RS fit. R D is the ratio of WS to RS D 0 decays. With CP violation function is more complicated.

15 RS Decay Time Fit The D 0 lifetime is consistent with the Particle Data Group value, within the statistical and systematic errors of the measurement. Plot selection: 1.843<m<1.883 GeV/c <  m< GeV/c 2

16 WS Mixing Fit: No CP Violation Varied fit parameters –Mixing parameters –Fit class normalizations –Combinatoric shape Plot selection: 1.843<m<1.883 GeV/c <  m< GeV/c 2 Data – No mixing PDF Mixing – No mixing PDF

17 Variations in functional form of signal and background PDFs. Variations in the fit parameters. Variations in the event selection. Small non-zero mean in the proper-time signal resolution PDF. Systematic Errors Investigated

18 Mixing Contours: No CP Violation Accounting for systematic errors, the no-mixing point is at the 3.9-sigma contour y’, x’ 2 contours computed by change in log likelihood –Best-fit point is in non-physical region x’ 2 < 0, but one-sigma contour is in physical region –correlation: R D : (3.03  0.16  0.06) x x’ 2 : (-0.22  0.30  0.21) x y’: (9.7  4.4  3.1) x 10 -3

19 M(K  ),  M Fits in Decay Time Bins Kinematic fit done independently in five decay time bins R WS independent of any assumptions on resolution model  2 from mixing fit is 1.5; for the no mixing fit  2 is 24.0

20 Time Dependence of Mixed Final States: CP Violation If CP is not conserved, the time distribution for D 0 and D 0 differ Direct CP violation in DCS Decay CP violation in mixing CP violation in interference between decay and mixing: Rewrite time dependence to explictly include asymmetries Define CP violating observables

21 Conclusion: Final Results