1. Evidence for Narrow D s  0 and D s   0 states Jianchun Wang 05/09/03 Directly involved: Dave Cinabro Selina Li Sheldon Stone Jon Urheim Jianchun Wang Committee: R. Briere, S. Stone

2. 05/09/03Jianchun (JC) Wang2 BABAR Discovery  BABAR observed a narrow D s  0 resonance at 2.317 GeV, possibly the 0 + state (hep-ex/0304021). They reconstructed 1267  53 events, with P(D s  0 ) > 3.5 GeV using 91 fb  data.  They also noticed a peak at 2.46 GeV. “This mass corresponds to the overlap region of the D s *  D s  and D s (2317)  D s  0 signal bands that, because of the small width of both mesons, produces a narrow peak in the D s +    mass distribution that survives a D s * selection” M( D s   0 ) M( D s   0 ) BABAR

3. 05/09/03Jianchun (JC) Wang3 Theory  D s ** predicted J p : 0 +, 1 +, 1 + & 2 +. One 1 + & 2 + seen. Others predicted to be above DK threshold and have large ~200 MeV widths, but this state is way below DK threshold.  The D s  o decay from an initial cs state violates isospin, this suppresses the decay width and makes it narrow. So the low mass ensures the narrow width.  Many theoretical explanations appeared (see references in our paper); One claims a DK molecule.  Bardeen, Eichten and Hill (hep-ph/0305049) couple chiral perturbation theory with a quark model representing HQET. They infer that D s *(2317) is the 0 + state. The theory also predict the existence of the 1 + partner of this state, and has mass splitting identical to that of D s *(2112) and D s ( M(1 + )  M(0 + ) = M(1  )  M(0  ) ). The branching fraction of other possible modes are also calculated.

4. 05/09/03Jianchun (JC) Wang4 The D s *  0 Final State Fit result N = 53.3  9.7  = 6.1  1.0 MeV  M = 350.6  1.2 MeV  2 /ndof = 98.3/78 Brief Selection criteria  All CLEO II and II.V data  P(D s *  0 ) > 3.5 GeV  D s   ,   K  K   |cos   | > 0.3  Invariant mass cuts ~ 2.5   Photons in good barrel D s * sideband D s * signal !?

5. 05/09/03Jianchun (JC) Wang5 D s *  0 Monte Carlo Simulations D s (2461)  D s *  0 Signal MC  = 6.7  0.5 MeV D s (2317)  D s  0 Signal + Random   = 15.0  3.0 MeV Thus D s (2317) does “feed up” to the D s (2460) by attaching to a random . However, the probability is low, only 12%, and the width is 15 MeV rather than 6.7.

6. 05/09/03Jianchun (JC) Wang6 Feed Down: D s (2460) Signal, Reconstructed as D s (2317) All events in the D s *  0 mass spectrum are used to show the D s (2460) signal “feed down” to the D s (2317) spectrum.

7. 05/09/03Jianchun (JC) Wang7 Reconstruction of D s  0 Signal Fit result N = 160.2  19.0  = 8.7  0.9 MeV  M = 350.3  1.1 MeV  2 /ndof = 93.5/78 It is different from Selina’s study as endcap photons are not included here, to be consistent with D s *  0 reconstruction.

8. 05/09/03Jianchun (JC) Wang8 Reconstruct D s  0 from MC D s (2320)  D s  0 Signal  = 6.5  0.3 MeV D s (2461)  D s *  0 signal reconstructed as D s  0  = 14.9  1.0 MeV D s (2460) also “feed down” to D s (2317) with very large probability, 1/0.75. The width is 14.9 MeV rather than 6.5.

9. 05/09/03Jianchun (JC) Wang9 Basic Ideas  We are dealing with two narrow resonances which can reflect (or feed) into one another.  From the data and the MC we can calculate the amount of cross feed and thus extract the “true” signals in the data.

10. 05/09/03Jianchun (JC) Wang10 Calculation of Rates R0  reconstructed D sJ *(2317)  D s  0 excluding feed-down. R1  reconstructed D sJ *(2461)  D s *  0 excluding feed-up. N0  number of events extracted from fit to D s  0 mass spectrum. (160.2  19.0) N1  number of events extracted from fit to D s *  0 mass spectrum (53.3  9.7)   the probability that the photon from a D s * is reconstructed. (0.75±0.08)  the probability that a D s pickup a random  to form D s *. (0.120±0.025) N0 = R0 + feed-down = R0 + R1 /  N1 = R1 + feed-up = R1 + R0   R0 = 104.6  28.6 R1 = 40.7  10.6

11. 05/09/03Jianchun (JC) Wang11 Alternative Way to Estimate Feed-up Sideband subtraction Conventional method Number of events40.8 ± 11.340.7 ± 10.6 ( 53.3 ± 9.7) M(D s *  0 )  M(D s *) MeV 351.6 ± 1.7350.6 ± 1.2 sigma (MeV)5.3 ± 1.26.1 ± 1.0 The D s * side band spectrum should pickup as much feed-up as in D s * “signal”. We did sideband subtraction and fit the spectrum.

12. 05/09/03Jianchun (JC) Wang12 Alternative Way to Estimate Feed-down  We can fit the spectrum using double Gaussian functions for the peak. One for the signal with narrow width and the other for reflection which is broad.  The fit confirms the existence of the contribution of broad distribution.  The amount of reflection in the fit is consistent within error with calculation.  The reflection not only broadens the peak, but also shifts the center position. With this fit we can extract more precise mass. Narrow Width Broad width Single Gaussian Data 5.5  1.315.3  4.18.4  1.2 MC 6.4  0.414.9  1.0 Selina’s cuts & analysis

13. 05/09/03Jianchun (JC) Wang13 Summary  We observed a narrow resonance at mass 2.46 GeV in the D s *  0 final state, with 40.7  10.6 events and mass – M Ds (351.6  1.2  1.0) MeV.  The state is possibly the 1 + cs meson.  We confirm the D s (2317).  Cross-feed exists between 2.46 and 2.32 states. We estimated the cross-feed contributions and establish that they both are real signals.