1. Studies of Charm Meson Decays at BaBar Kalanand Mishra University of Cincinnati University of Cincinnati On behalf of the BaBar Collaboration DPF 06, Honolulu, October 31, 2006

2. Kalanand Mishra, University of Cincinnati 2/22 Outline Measurements of the ratio of branching fractions for the decays Measurements of the ratio of branching fractions for the decays D +   +  0, K +  0 D +   +  0, K +  0 D 0   -  +  0, K - K +  0 D 0   -  +  0, K - K +  0 Amplitude (Dalitz plot) analysis of the decays Amplitude (Dalitz plot) analysis of the decays D 0  K - K +  0 D 0  K - K +  0 D s +  K + K -  + D s +  K + K -  + hep-ex / 0608009, 2006, submitted to PRD BaBar Preliminary BaBar Preliminary BaBar Preliminary Phys.Rev.D74:011107,2006

3. DPF 06, Honolulu, October 31, 2006 Kalanand Mishra, University of Cincinnati 3/22 - - Use the decay D +  K -  +  + as reference for normalization. - - Reconstruct the decay chain: [ D* +  D +  0 s, D +  h +  0,K -  +  +,  0  ]. - - Reject the events with D + NOT coming from D* + decay (for cleaner signal). P CM (D * ) > 2.9 GeV/c |m D* - m D + | < 155 MeV/c 2 D *+ D+D+  0 soft 00     K + /  + Data Sample = 124 fb -1 B.R. of the Decays D +  +  0, K +  0 B.R. of the Decays D +  +  0, K +  0 1.Measurement of the Cabibbo-suppressed branching ratio D +  +  0. 2.The first measurement of D +  K +  0 branching ratio. Motivation Event Reconstruction Signal Reconstruction Efficiency   D* +  D +  0 soft, D +   +  0 7.8%   D* +  D +  0 soft, D +  K +  0 5.9%   D* +  D +  0 soft, D +  K -  +  + 8.5% The description of charge conjugate decay is implied throughout this presentation unless explicitly stated otherwise.

4. DPF 06, Honolulu, October 31, 2006 Kalanand Mishra, University of Cincinnati 4/22 Signal band Side band m  -  +  + [GeV/c 2 ]  m [GeV/c 2 ] Signal Yield Signal Yield   Divide  M into 2  signal band and >5  side band   Fit D + mass distribution separately (with the same signal pdf)   Subtract side band yield from signal band yield (adjusted by scale factor) Events / (0.5 MeV/c 2 ) D +  K -  +  + signal yield 101380 ± 415 Events / (15 MeV/c 2 ) Events / (5 MeV/c 2 )  m distribution These are D + events NOT coming from D* + decay. [ 1.78 < m K -  +  + < 1.95 GeV/c 2 ]

5. DPF 06, Honolulu, October 31, 2006 Kalanand Mishra, University of Cincinnati 5/22 signal yield 1229 ± 98 m  +  0 [GeV/c 2 ] Signal Yield continued …. Signal Yield continued …. m  +  0 [GeV/c 2 ] First observation of D +   +  0 Background from D s +  K + K s, K s  0  0 events, when we miss one  0. D+  +0D+  +0 D+  +0D+  +0 signal yield 189 ± 35 Events / (10 MeV/c 2 ) Background from a missing  0 in the event, parameterized by an exponential function. Signal events are modeled by bifurcated Gaussian functions. Combinatorial backgrounds are modeled by linear functions.

6. DPF 06, Honolulu, October 31, 2006 Kalanand Mishra, University of Cincinnati 6/22 B(D +   +  0 ) / B (D +  K -  +  + ) = ( 1.33 ± 0.11 (stat) ± 0.09 (sys) ) x 10 -2 B(D +  K +  0 ) / B(D +  K -  +  + ) = ( 2.68 ± 0.50 (stat) ± 0.26 (sys) ) x 10 -3 B(D +   +  0 ) = ( 1.25 ± 0.10 (stat) ± 0.09 (sys) ± 0.04 (ref) ) x 10 -3 using B(D +  K -  +  + ) = ( 9.4 ± 0.3 ) x 10 -2, B(D +  K +  0 ) = ( 2.52 ± 0.47 (stat) ± 0.25 (sys) ± 0.08 (ref) ) x 10 -4 Comparison to the current PDG values : ● ● D +   +  0 world average (2006) B(D +  +  0 ) = (1.28 ± 0.09 ) x 10 -3 ● ● D +  K +  0 world average (2006) B(D +  K +  0 ) < 4.2 x 10 -4 at 90% CL Results and Conclusion This is the first measurement of the doubly Cabibbo-suppressed decay D +  K +  0 [ The CLEO-c collaboration recently made a new measurement which is consistent with our result: ]. hep-ex/0607075 B(D +  K +  0 ) = ( 2.25 ± 0.36 (stat) ± 0.15 (sys) ± 0.07 (ref) ) x 10 -4 ]. hep-ex/0607075 Phys.Rev.D74:011107,2006 Excellent kaon ID has contributed significantly to the sensitivity of this measurement. Preliminary result

7. DPF 06, Honolulu, October 31, 2006 Kalanand Mishra, University of Cincinnati 7/22 B.R. of the Decays D 0   -  +  0, K - K +  0 Event Reconstruction   P CM ( D 0 ) > 2.77 GeV/c   |m D* - m D 0 - 145.5| < 0.6 MeV/c 2 Background Sources   Combinatorial   K  0 reflection in  0 and KK  0 modes Data Sample = 232 fb -1 Use the the Cabibbo-favored decay D 0  K -  +  0 as reference for normalization. Reconstruct the decay chain: [ D* +  D 0  s +, D 0  h - h +  0,  0  ] and c.c. D *+ D0D0  + soft 00   K - /  - K + /  + 1.Precision measurement of the branching ratios of 3-body Cabibbo- suppressed decays of D 0. 2.To investigate the anomaly in the BR of 2- & 3-body CS decays of D 0. Motivation The charge of the  soft determines the charm content of the D 0 meson (i.e., whether it is D 0 or D 0 ). _

8. DPF 06, Honolulu, October 31, 2006 Kalanand Mishra, University of Cincinnati 8/22 Fit for Signal Yield Fit for Signal Yield Signal events are modeled by the sum of 3 Gaussian functions. The means and  ’s of the Gaussians are allowed to vary. Combinatorial backgrounds are modeled by linear functions. The shape of K -  +  0 reflection events in the sidebands of  -  +  0 and K - K +  0 is obtained from MC as described on the next slide. K-+0K-+0K-+0K-+0 -+0-+0-+0-+0 K-K+0K-K+0K-K+0K-K+0 Maximum Likelihood fit for signal yield signal yield 60426 ± 343 signal yield 10773 ± 122 signal yield 505660 ± 750 Events / (2.5 MeV/c 2 ) Events / (625 keV/c 2 ) Events / (5 MeV/c 2 ) Removed D 0  K s 0 [  -  + ]  0 events (~0.5 % of the observed number). BABAR prelim. prelim. BABAR BABAR

9. DPF 06, Honolulu, October 31, 2006 Kalanand Mishra, University of Cincinnati 9/22 Background Events in Monte Carlo -+0-+0-+0-+0 signal Combinatorial Background K -  +  0 reflection K -  +  0 reflection K-K+0K-K+0K-K+0K-K+0 signal ±3 RMS D 0   -  +  0 D 0  K - K +  0 Above: three-body invariant mass distributions of D 0   -  +  0 and D 0  K - K +  0 events in generic cc Monte Carlo (MC). K -  +  0 reflection events peak in the sidebands of  -  +  0, K - K +  0. We take the shape of the reflection from MC and obtain the number of reflection events by fitting their distribution in data. ±3 RMS Combinatorial Background _ Note Log y-scale. BABAR prelim. prelim. BABAR

10. DPF 06, Honolulu, October 31, 2006 Kalanand Mishra, University of Cincinnati 10/22 Reconstruction Efficiency Reconstruction Efficiency -+0-+0-+0-+0 ~ 0.5 % bkg ~ 2 % bkg ~ 5 % bkg K-+0K-+0K-+0K-+0 K-K+0K-K+0K-K+0K-K+0 Reco. Efficiency (%) from Monte Carlo Dalitz plot of events in data m 2 (h +  0 ) [GeV/c 2 ] 2 m 2 (h -  0 ) [GeV/c 2 ] 2 Avg Eff ~10% ~11% ~9% ~9% BABAR BABAR preliminary preliminary

11. DPF 06, Honolulu, October 31, 2006 Kalanand Mishra, University of Cincinnati 11/22 Results and Conclusion Results and Conclusion D 0 decay modeOur Results(%) B(π  π  π 0 )/B(K    π 0 )10.59  0.06  0.13 B(K    π 0 )/B(K    π 0 )2.37  0.03  0.04 PDG-2006 (%) 8.40  3.11 0.95  0.26 The decay rate for each mode  =.  where M = decay matrix element  = phase space factor Roughly consistent with naïve expectations, i.e., sin 2  c = 0.05 Very different from naïve expectations (see the orange box below). ( Naïve expectation = 1.0 ) For 3-body decays: area of the Dalitz plot For 2-body decays: momentum of either daughter in D 0 rest frame. = |M| 2 (π  π  π 0 )/ |M| 2 (K  π  π 0 ) = 0.0668  0.0004  0.0008 |M| 2 (     π 0 )/ |M| 2 (K  π  π 0 ) = 0.0453  0.0006  0.0008 |M| 2 (     π 0 )/ |M| 2 (π  π  π 0 ) = 0.678  0.014  0.021 |M| 2 (π  π  )/ |M| 2 (K  π  ) = 0.034  0.001 |M| 2 (     )/ |M| 2 (K  π  ) = 0.111  0.002 |M| 2 (     )/ |M| 2 (π  π  ) = 3.53  0.12 Using branching ratio values from above table: Using 2-body B.R. values from PDG: hep-ex / 0608009, 2006, submitted to PRD > 5  difference with PDG value. Excellent PID performance has greatly improved the the sensitivity of this measurement.

12. DPF 06, Honolulu, October 31, 2006 Kalanand Mishra, University of Cincinnati 12/22 Amplitude Analysis of D and D s decays

13. DPF 06, Honolulu, October 31, 2006 Kalanand Mishra, University of Cincinnati 13/22 K*(892) - K*(892) +  (1020) f 0 (980) K*(1410) + K*(1410) - K +  0 (s) K -  0 (s) f 2 ’ f 2 ’(1525) - Extract information useful for determination of angle  of the CKM matrix: strong phase difference & relative phase for D 0  K*(892) - K +, K*(892) + K -. - Is there a charged  state ? - Nature of Kπ S-wave below 1.4 GeV/c 2 ? Amplitude Analysis of the Decay D 0  K - K +  0 BABAR prelim. prelim. Motivation Events used to obtain bkg shape ±1  region: ≈ 7000 events, purity ≈ 97 % BaBar Preliminary BaBar Preliminary

14. DPF 06, Honolulu, October 31, 2006 Kalanand Mishra, University of Cincinnati 14/22 Isobar Model Formalism Isobar Model Formalism three-body decay D  ABC decaying through an r=[AB] resonance three-body decay D  ABC decaying through an r=[AB] resonance D decay three-body amplitude Relativistic Breit-Wigner Angular distribution D and r Blatt-Weisskopf form factors NR term (direct 3 body decay) a 0, δ 0, a r, δ r : Free parameters of fit f 0 (980) 11 1 2 2 3 3 3 {12} {13} {23} 1 2 3 2 NR (

15. DPF 06, Honolulu, October 31, 2006 Kalanand Mishra, University of Cincinnati 15/22 – K  S-wave in mass range 0.6–1.4 GeV/c 2 is not well-understood. A possible  state ~ 800 MeV/c 2 has been conjectured, but this has only been reported in the neutral state. – For the K +  0 and K -  0 S-wave amplitudes, we try three models: I=1/2 K  S-wave Parameterization - - Amplitude obtained from LASS K -  +  K -  + scattering. - - K -  + amplitude extracted from a model-independent partial-wave analysis of D +  K -  +  + decay by the E791 collaboration. - - [ coherent sum of  (800) + uniform NR + K* 0 (1430) ]. Normalized to arbitrary scale for m(K  )>1.1 Gev/c 2 for easy comparison. - 80 0 Nucl. Phys. B296, 493 (1988); W. Dunwoodie, web notes. { No evidence in K  elastic scat tering. } Phys. Rev. D73, 032004 (2006)

16. DPF 06, Honolulu, October 31, 2006 Kalanand Mishra, University of Cincinnati 16/22 LASS parameterization for Kπ S-wave Fit Results Fit Results m 2 (K + π 0 ) m 2 (K - π 0 )m 2 (K + K - ) - The best fit is LASS parameterization. - E791 fit worse at low mass. -  model yields mass 870 ± 30 MeV/c 2 mass 870 ± 30 MeV/c 2 width 150 ± 20 MeV/c 2 width 150 ± 20 MeV/c 2 significantly different from the values reported previously for  0. Use the fit model with K  S-wave from E791 for model systematic uncertainty. For K  S-wave These results are preliminary. We are investigating the K  S-wave at lower mass, and contribution of K*(1410).

17. DPF 06, Honolulu, October 31, 2006 Kalanand Mishra, University of Cincinnati 17/22 Each event was weighted by the spherical harmonic Y 0 L (cos  H ) (L=0,1,2,…..). Excellent agreement between data & model.For S- and P- waves in absence of cross-feeds from other channels (also, assuming negligible contributions from D- and higher waves): Analysis of Angular Moments Analysis of Angular Moments Y01Y01 Y00Y00 Y02Y02 Y04Y04 Y06Y06 Y03Y03 Y05Y05 Y07Y07 BABAR prelim. prelim. Significantly large interference between S and P waves. Higher moments above 1 GeV are coming from cross channels.

18. DPF 06, Honolulu, October 31, 2006 Kalanand Mishra, University of Cincinnati 18/22 Strong Phase Difference & Amplitude Ratio Strong Phase Difference & Amplitude Ratio The strong phase difference  D and relative amplitude r D between the decays D 0  K* - K + and D 0  K* + K - are defined, neglecting direct CP violation in D 0 decays, by the equation: r D e i  D = [a K* - K + / a K* + K - ] exp[ i(  K* - K + -  K *- K + ) ] We find  D = -37.9 o ± 2.2 o (stat) ± 0.7 o (exp sys) ± 4.2 o (model sys) r D = 0.64 ± 0.01 (stat) ± 0.01 (exp sys) ± 0.01 (model sys). These measurements are consistent with the previous measurement by CLEO:  D = -28 o ± 8 o (stat) ± 2.9 o (exp sys) ± 10.6 o (model sys) r D = 0.52 ± 0.05 (stat) ± 0.02 (exp sys) ± 0.04 (model sys). These results are preliminary. BaBar Preliminary hep-ex/ 0606045

19. DPF 06, Honolulu, October 31, 2006 Kalanand Mishra, University of Cincinnati 19/22 Amplitude Analysis of D s +  K + K -  + Decay Data Sample = 240 fb -1 - Clean signal obtained with a likelihood selection using vertex separation and p*. - Average reconstruction efficiency ~30 %. Precise measurement of the branching fractions of D s +  + and D s +  K*(892) 0 K +. Motivation BABAR prelim. prelim. BABAR ±2  sig. region: ≈100850 events, purity ≈ 95 % BaBar Preliminary Data Sample = 240 fb -1  (1020) f 0 (980) K*(892) 0 m 2 (K -  + ) / [ GeV 2 /c 4 ] events / 0.02 GeV 2 /c 4 _ _

20. DPF 06, Honolulu, October 31, 2006 Kalanand Mishra, University of Cincinnati 20/22 Fit Results Fit Results Large systematic uncertainty in f 0 (980) amplitude and phase because several different parameterizations were tried. Decay is dominated by D s +  K* 0 K +,  +, and f 0 (980)  + f 0 (980) contribution is large but has large systematic error as well. Higher mass f 0 ’s and D-wave resonances have small contributions. Angular moments : Excellent agreement with data _ Large f 0 (980) contribution BABAR prelim. prelim. Very small interference between S-wave (  (800) ?) and P-wave (K*(892)) => no  (800) contribution found.

21. DPF 06, Honolulu, October 31, 2006 Kalanand Mishra, University of Cincinnati 21/22 The decay D s +  + is frequently used as the D s + reference decay mode for measurement of branching ratios. The previous analysis (E687) of this Dalitz plot was performed with ~ 700 events (vs. 10 5 events in our case). Using Dalitz plot results, we make a precise measurement of the branching ratios of the decays D s +  + and D s +  K*(892) 0 K + integrated over the whole phase space. Branching Ratios Branching Ratios BaBar Preliminary B(D s +  + ) / B(D s +  K + K -  + ) = 0.379 ± 0.002 (stat) ± 0.018 (sys) B(D s +  K*(892) 0 K + ) / B(D s +  K + K -  + ) = 0.487 ± 0.002 (stat) ± 0.016 (sys) where  K + K - and K*(892) 0  K -  +. _ _ _ These results are preliminary.

22. DPF 06, Honolulu, October 31, 2006 Kalanand Mishra, University of Cincinnati 22/22 Precise measurements of singly Cabibbo-suppressed branching ratios: D +  +  0 and D 0  -  +  0, K - K +  0. First measurement of doubly Cabibbo-suppressed branching ratio : D +  K +  0. Amplitude analysis of D 0  K - K +  0 : measure  D & r D for the charge-conjugate dominant decays. with  K + K - and K*(892) 0  K -  + Amplitude analysis D s +  K + K -  + : measure precise branching ratios of D s +  + and D s +  K* 0 (892)K + with  K + K - and K*(892) 0  K -  +. Summary Summary _ _

23. Back up slides

24. DPF 06, Honolulu, October 31, 2006 Kalanand Mishra, University of Cincinnati 24/22 Event Reconstruction  0 reconstruction: have two of them, one from D *+, other from D + :  0 from D *+ is soft, 150 < p  0 < 450 MeV/c  0 from D + has higher mom., p  0 > 200 MeV/c D +  h +  0 reconstruction: 1.7 < m(h +  0 ) < 2.0 GeV/c 2, -0.9 < cos  h < 0.8 (0.7 in case of K +  0 ). K -,  + and  + tracks are fit to a vertex to reconstruct D + candidate for reference mode. P CM (D * ) > 2.9 GeV/c, |m D* - m D + | < 155 MeV/c 2 In case of multiple candidates in an event, select the one with higher D* momentum. D +  +  0, K +  0 p q cos   = p. q D+D+ ++ 00 Helicity angle for  +  0 mode

25. DPF 06, Honolulu, October 31, 2006 Kalanand Mishra, University of Cincinnati 25/22 D 0   -  +  0, K - K +  0 D 0  h - h +  0 Reconstruction   h - and h + tracks are fit to a vertex   Mass of  0 candidate is constrained to m  0 at h - h + vertex   P CM ( D 0 ) > 2.77 GeV/c D* Reconstruction   D *+ candidate is made by fitting the D 0 and the  s + to a vertex constrained in x and y to the measured beam-spot for the run.   |m D* - m D 0 - 145.5| < 0.6 MeV/c 2   Vertex  2 probability > 0.01   Choose a single best candidate with smallest  2 for the whole decay chain ( multiplicity = 1.03 ). Background Sources   Charged track combinatoric   Mis-reconstructed  0   Real D 0, fake  s   K  0 reflection in  0 and KK  0 modes

26. DPF 06, Honolulu, October 31, 2006 Kalanand Mishra, University of Cincinnati 26/22 K - K +  0 branching ratio: CLEO result CLEO CLEO collaboration collaboration K-K+0K-K+0K-K+0K-K+0 signal K -  +  0 reflection Phys. Rev. D54, 4211 (1996) B(D 0  KK  0 )/ B(D 0  KK  0 ) = 0.95 ± 0.26 % Signal yield 151 ± 42 Efficiency 9.2 ± 0.3 % A new cross-check done by the CLEO collaboration shows B(D 0  KK  0 )/ B(D 0  K  0 ) = 2.21 ± 0.14 (stat) %, which is consistent with our measurement. Phys. Rev. D74, 031108 (2006) High pion-to-kaon misidentification rate  contamination from D 0  K -  +  0 events very high. Had to apply various vetoes and the corresponding efficiency corrections. Combinatorial background not fully understood.

27. DPF 06, Honolulu, October 31, 2006 Kalanand Mishra, University of Cincinnati 27/22 Kπ S-wave amplitude is described by the coherent sum of an effective range term and the K* 0 (1430) resonance: S(s) = (√s/ p). sin . e i   = cot -1 [ 1/ap + rp/2 ] + cot -1 [ (m 2 R -s)/(m R  R ) ] Effective Range (NR) term K* 0 (1430) resonance term a = scat. length, r = eff. range, m R = mass of K* 0 (1430),  R = width p = momentum of either daughter in the Kπ rest frame. For Kπ scattering, S-wave is elastic up to K  ' threshold (1.45 GeV). Phase space factor LASS K  S-wave Parameterization

28. DPF 06, Honolulu, October 31, 2006 Kalanand Mishra, University of Cincinnati 28/22 Divide m 2 (K -  + ) into slices Find s – wave amplitude in each slice (two parameters)   Use remainder of Dalitz plot as an interferometer For s-wave: - Interpolate between (c k,  k ). Model P and D waves. [ E791 Collaboration, slide from Brian Meadow’s Moriond 2005 talk ] S (“partial wave”) K  S-wave from D 0  K -  +  + DP

29. DPF 06, Honolulu, October 31, 2006 Kalanand Mishra, University of Cincinnati 29/22 Each event was weighted by the spherical harmonic Y 0 L (cos  H ) (L=0,1,2). Excellent agreement between data & model. Y01Y01 Y00Y00 Y02Y02 Y04Y04 Y06Y06 Y03Y03 Y05Y05 Y07Y07   With cross-feeds or in the presence of D-waves, higher moments ≠ 0.   Wrong fit models tend to give rise to higher moments in the  region, creating disagreement with data. For S- and P- waves in absence of cross-feeds from other channels: Moments Analysis in K - K + channel Moments Analysis in K - K + channel BABAR prelim. prelim.

30. DPF 06, Honolulu, October 31, 2006 Kalanand Mishra, University of Cincinnati 30/22 ±2  sig. region: ≈ 100850 events, purity ≈ 95 % Ds+K+K-+Ds+K+K-+Ds+K+K-+Ds+K+K-+ m = 1969.0± 0.1 MeV/c 2  = 5.8 MeV/c 2 Data Sample = 240 fb -1  Signal events reconstructed from two kaon and a pion charged tracks fitted to a common vertex, with  2 >0.1 %.  Background from D* +  D 0 [K + K - ]  + removed by requiring m(K + K - )<1.85 GeV/c 2.  Removed K -  + mis  + reflection by requiring m(K -  + mis  + ) - m(K -  + mis ) > 0.15 GeV/c 2.  Average event reconstruction efficiency ~ 30 %. Events used to obtain Bkg shape: (-10 , -6  ) and (6 , 10  ).BABAR prelim. prelim.