Search For The X(1812) And Branching Fraction Measurement In B~±�'K~± ωφ Decay

We perform a search for X(1812) in the decay modes of B^±→K^±ωφbased on 604 fb^-1 ofdata sample at theÎ¥(4S) state collected with Belle detector in KEKB asymmetric energy e⁺e^-collider. X(1812) is a new possible particle state observed by BES collaboration in 2006 in theanalysis on the decay channel J/ψ→γωφ. Due to its strange production and decay mechanismobserved in the J/ψ→γωφ, X(1812) is speculated to be tetraquark state, hybrids, glueball,a mesonic molecule or just a threshold cusp attracting a resonance. Theorist proposed manydifferent models and discussion.We reconstruct B mesons from B^±→K^±ωφ,ω→π⁺Ï€^-Ï€⁰ andφ→K⁺K^-. To identifyB candidates, two widely used kinematic variables are calculated in the center-of-mass system:the beam-energy constrained mass (M_bc≡(?)) and the energy difference (ΔE≡E_B-E_beam), where E_beam is the beam energy, P_B and E_B are the reconstructed momentumand energy of the B^±candidate. We select B candidates within the range -0.2 GeV＜ΔE＜0.2 GeV and 5.27 GeV/c²ï¼œM_bc＜5.29 GeV/c² for final analysis.Because the branch ratio of B^±→K^±ωφis expected to be very small (in the order of10^-6), how to suppress the big background from different sources is critical for this analysis.We produced a large signal Monte Carlo (MC) sample to improve the reconstruction efficiencyand event selection criteria. For suppressing the combination background ofω, we required themomentum in the laboratory frame (?)＞0.38 GeV/c. In addition, because in the final state,there are 3 kaons, one directly from the B-meson decay and the other two from theφdecay,in order to distinguish the two kinds of kaons effectively and reduce multiple candidates, werequire kaons from theφto have momenta p_K±＜1.5 GeV/c in the CM frame.To study the background source, a huge amount of MC samples are used. The dominantbackground comes from random combinations of particles in continuum e⁺e^-→q(?) events (q=u,d,s,c). We combine shape variables, which is spherical for B(?) events and jet-like for q(?)continuum events in the (?)(4S) rest frame, into a Fisher discriminant to suppress this kindof background. For further continuum background, B flavor tagging technique is used also.Finally, We preserve 57.9% of the signal while rejecting 98.6% of the continuum background.Additionally, We also use mass veto to exclude BB background from D_s and D⁰ decays.The signal yield is extracted by performing an 4-Dimension unbinned extended maximumlikelihood fit to theΔE,M_bc,M_ωand M_φdistribution of candidate events. Before the data fit,large Toy and full MC samples are used to check the correctness of the whole analysis processand the statistical and systematic behavior of the result. After making sure that all the analysisis right, We fit to data and obtain a signal yield of 22.1_-7.2^+8.3 events with a statistical significanceof 2.8σ. As the significance is less than 3σfor the B^±→K^±ωφdecay mode, we derive anupper limit on the yield at 90% confidence level by a frequentist method using ensembles ofpseudo-experiments. The upper limit of three-body decay branch fraction at the 90% confidence level is obtained: BR(B^±→K^±ωφ＜1.9×10^-6) (90% C.L.). To search for X(1812), wecarefully studied theωφspectrum. No significant signals are observed. An upper limit was setfor BR(B^±→K^±(1812),X(1812)→ωφ)＜3.2×10^-7) (90% C.L.).