1. Observation of the  c (2S) in exclusive B  K K S K    decays S.K. Choi, Gyeongsang Univ. & S.L. Olsen, Univ. of Hawaii (For the Belle Collaboration) Introduction A major issue for the charmonium particle system are the two c-cbar states below open charm threshold that are still not well established: the n=2 singlet S state, the  c (2S), and the n=1 singlet P state, the h c (1P); see Fig. 1. The observation of these states and the determination of their masses would provide useful information about the spin-spin part of the c cbar potential. It is expected [1] that the  (2S)-  c (2S) mass splitting is smaller than that for the n=1  c -J/  system by factors corresponding the the reduced value of the wave- function at zero quark separations and the running of the strong coupling constant  s (Q 2 ) between Q = M(J/  ) and M(  (2S)). The expected mass range for the  c (2S) is 3625 < M(  c (2S) )<3645 MeV/c 2. The Crystal Ball group [2] identified an excess of E  = 91 MeV  -rays in the reaction  (2S)   X as evidence for the  c (2S) with mass M(  c (2S))  3594 MeV/c2. This is well below potential model expectations and has not been confirmed by other experiments [3]. B-meson decays to final states containing charmonium particles are relatively common and, thus, the large numbers of B meson decays recorded in the Belle detector provide an excellent opportunity to search for exclusive decays of the type B  K  c (2S). In this experiment we concentrate on the  c (2S)  K S K    decay mode. This a strong decay mode for the  c (Br  1.8%), has low combinatoric background, is strongly suppressed in  (2S) decays, and, since the final state is all charged particles, has good energy resolution in the Belle detector. 1. The charmonium level diagram for ccbar bound states below the M D “open charm” threshold (from the PDG tables [4]). All of the levels in this diagram are experimentally well established except for the  c (2S) and the (unshown) h c ( 1 P 1 ) state. Event Selection We select events with K  K s K    or K s K s K    (inclusion of charge-conjugate modes is implicit). Charged kaons and pions are required to originate near the IP, and identified as such by the combined ACC, TOF and CDC dE/dx measurements. Candidate K s   decays are  pairs from a common vertex that is displaced from the IP and with an invariant mass |M(  –    MeV/c 2 (3  ). We identify B  K K s K    signals by their beam-constrained mass: M bc = [(E cm /2) 2 – p 2 ] 1/2 and cm energy difference:  E = E - E cm /2, where p and E are the total momentum and energy of the K K s K    system. Background Reduction To suppress e + e   q qbar continuum events (q = u, d, s & c), we use a Fisher discriminant of event-shape variables (Fig. 2a) and the cosine of the angle between the B candidate direction and the beam axis (Fig. 2b). Monte Carlo is used to determine signal (L sig, solid histograms) and continuum (L cont, dashed histograms) likelihood functions. We select events with L sig /(L sig + L cont )>0.6, a value that optimizes the B  K  c ;  c  K S K    signal. Backgrounds from B  D(D s )X decays are reduced by vetoing candidates with |M(K  )-M(D)| or |M(K s K)-M(D s )|<10 MeV/c 2. Also, since the decays  c (nS)  K*K are suppressed by a momentum barrier, candidates with |M(K  )-M(K*)|<50 MeV/c 2 are also rejected. 2a 2b 2c Results Figure 5 shows the results of the fits vs M(K s K  ). In addition to the  c signal, the J/  and, possibly, non-resonant B  K K s K  decays, there is a narrow peak at the high mass side that we identify as the  c (2S). The curve in the figure is the result of a fit that includes Breit Wigner shapes to represent the  c and  c (2S), a Gaussian with a negligibly small  and mass fixed at M(J/  ), and a 2 nd -order polynomial to represent the non-resonant contribution. The functions are convolved with a Gaussian resolution function with a MC-determined width of 15 MeV/c 2. The fit results are: Summary In a sample of exclusive B  K K s K  decays, we observe a narrow peak in the K s K  mass spectrum near M(  (2S)). The significance of the signal is greater than 6 . The observed features of this peak lead us to conclude that this is most likely the  c (2S).The measured parameters are:  c (2S) properties M = 3654 ± 6 (stat) ± 8 (syst) MeV/c 2  < 55 MeV/c 2 (90% CL) r (K s K  ) = 0.38 ± 0.12 (stat) ± 0.5 (syst), where r(K s K  ) is the ratio of  c (2S) to  c (1S) product branching fractions: r(KsK  )= Br (B  K  c (2S)) Br (  c (2S))  K s K  ). Br (B  K  c ) Br (  c  K s K  ).  c  c (2S) N evts : 104±14 39±11 Mass (MeV /c 2 ) 2979±2 3654±6 Width (MeV/c 2 ) 11±11 15±24, where only the statistical errors from the fit are listed. The  c mass is in good agreement with the world average value of 2979.8±1.8 MeV/c 2. The  c width value agrees, within errors, both References 1.See, eg, W.Buchmuller and S-H.H. Tye, Phys. Rev. D24, 132 (1981) 2.C.Edwards et al. (Crystal Ball), Phys.Rev. Lett. 48, 70 (1982). 3.T.A.Armstrong et al. (E760), Phys. Rev. D52, 4839 (1985). M. Masuzawa, Northwestern Univ. PhD thesis (1992), unpublished. 4.D.E.Groom et al. (PDG), Eur. Phys. Journ. C15, 1 (2002) 5.A.Abashian et al. (Belle), Nucl. Instr. & Meth A479, 117 (2002) 6.E.Kikutani et al. (KEKB), KEK preprint 2001-157; submitted to Nucl. Instr. & Meth. The Belle Detector The Belle detector [5] at the KEKB e + e  storage ring [6] is a nearly 4  magnetic spectrometer that consists of a three-layer silicon vertex detector (SVD), a 50-layer central drift chamber (CDC), aerogel Cherenkov counters (ACC), time-of-flight scintillators (TOF) and an electromagnetic calorimeter comprised of CsI(Tl) crystals (ECL) located inside a 1.5 T axial magnetic field. The iron flux-return is instrumented to detect K L mesons and identify muons (KLM). with the PDG [4] value of 13.2±3.5MeV/c 2 and a new CLEO result of 26±6 MeV/c 2. The sum of observed events in the three bins centered around the  c (2S) is 56, while the integral of the 2 nd -order polynomial over the same interval is 21±2. The probability for the latter number of events to fluctuate up to 56 is ~10 , which corresponds to a signal significance of greater that 6 . The fitted mass of the candidate  c (2S) is substantially above that of the Crystal Ball value and consistent, within errors, with the upper end of potential model expectations. We repeated the analysis with different bin sizes and bin centers shifted by half a bin width and take the maximum variation in mass, namely 8 MeV/c2, as the systematic error. Changes in the resolution width, the order of the polynomial function, and the inclusion of a possible  c1 contribution have negligible effects on the results. The limited statistics and wide bin size preclude an accurate determination of the width. We set a 90% CL upper limit of  (  c (2S))<55 MeV/c2, from the worst-case result of all the binning combinations that were tried. A MC simulation indicates that the experimental acceptance for the  c and  c (2S) are very nearly the same. Thus the ratio of product branching fractions for the two states is the ratio of observed event yields. Acknowledgement This research was made possible by the strong and dedicated efforts of the KEKB team and the extraordinary performance of the KEKB storage ring. 3. The M bc distributions for 40 MeV/c 2 M(K s K  ) bins. We use Gaussian functions with MC- determined widths for the M bc and  E signals; the areas of the M bc and  E signals are constrained to be equal. For the M bc background, we use a smooth function with a phase-space-like shape near the kinematic endpoint; for  E we use a 2 nd -order polynomial. As an example, Figs. 4(a) & (b)shows the fit to the 3640 MeV/c 2 K s K  mass bin. 4. Simultaneous fits to the M bc (a) &  E (b) plots for the M(K s K  )=3640 MeV/c 2 bin. Fig. 5 Signal Extraction Figures 3(a) through (y) show the M bc projections for events with |  E|<40 MeV for 40 MeV/c 2 bins of M(K s K  ) with central values from 2840 thru 3800 MeV/c 2. An  c signal is apparent around M(K s K  ) = 2980 MeV/c 2. A smaller, but distinct signal is evident near 3660 MeV/c 2, in the expected  c (2S). mass region.We perform simultaneous fits to each M bc plot and its corresponding  E distribution (for events in the same K s K  mass bin and in the 5.27<M bc <5.29 GeV/c 2 signal band) simultaneously.