Recent results charmonium decays at BES-III

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Nuclear Physics B (Proc. Suppl.) 225–227 (2012) 97–101 www.elsevier.com/locate/npbps

Recent results charmonium decays at BES-III P. Wang Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, China

Abstract The recent results of charmonium decays are presented. These are: ψ decaying to γP where P is a pseudoscalar meson π0 , η, η , χcJ decaying to γV and VV, where V is a vector meson ρ, ω, φ. Keywords: charmonium decays, χcJ decays 1. Introduction BEPC-II/BES-III has accumulated 106 million ψ(2S ) in a short period of 2 months. In this presetation, the analysis of ψ decaying to γP where P is a pseudoscalar meson π0 , η, η , as well as χcJ decaying to γV and VV, where V is a vector meson ρ, ω, φ, are reported.

Table 1: The measured branching fractions for ψ → γπ0 , γη, γη . The branching fractions for J/ψ decays are from the PDG.

mode γπ0 γη γη R1/2

B(ψ )[×10−6] 1.58 ± 0.42 1.38 ± 0.49 126 ± 9 (1.10 ± 0.39)%

B(J/ψ)[×10−4] 0.35 ± 0.03 11.04 ± 0.34 52.8 ± 1.5 (20.9 ± 0.9)%

Q = B(ψ )/B(J/ψ) (4.5 ± 1.3)% (0.13 ± 0.04)% (2.4 ± 0.2)% -

2. The decay ψ → γπ0 , γη The study of vector charmonium decay to a photon and neutral pseudoscalar meson P = (π0 , η, η ) provides experimental constraints on the relevant QCD predictions, such as the vector meson dominance model(VDM), two-gluon couplings to qq¯ states, mixing  of ηc − η( ) . The ratio Rn ≡ B(ψ(nS ) → γη)/B(ψ(nS ) →  γη ) is predicted by first order perturbation theory, and R1 ≈ R2 is also expected [1]. However, CLEO-c reported measurements for the decays of J/ψ, ψ and ψ to γP, and no evidence for ψ → γη or γπ0 was found [2]. Therefore, they obtained R2 << R1 with R2 < 1.8% at 90% CL. Such a small R2 is unanticipated, and it poses a significant challenge to our understanding of the c¯ c bound states. Do other processes contribute? Is this related to the ρπ puzzle [3]? With 106M ψ events, BESIII observed ψ → γπ0 and ψ → γη and ψ → γη , where η is reconstructed from η → π+ π− π0 and π0 π0 π0 , and η is reconstructed from η → π+ π− η and η → γπ+ π− [4], as shown in 0920-5632/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.nuclphysbps.2012.02.022

Fig. 1. The measured branching fractions are summarize in Table. 1. The R2 is about 20 times smaller than →γP) R1 . Q ≡ B(ψ B(ψ →γP) for each decay mode is also shown in the table, which is much smaller than 12%. 3. The decay χ cJ → γV χcJ events make significant contributions to the radiative decays of ψ . The decay of the P wave χcJ to γV provides a good chance to validate theoretical predictions and search for glueballs [5]. CLEO-c found [6] a surprisingly large χcJ → γV branching fraction, an order of magnitude higher than the pQCD prediction [7]. With 106M ψ events, BESIII studied the decays χcJ → γV, with V representing ρ0 , ω and φ [8]. Figure 2 shows the K + K − , π+ π− , and π+ π− π0 invariant mass distributions for the candidate events. The

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curves show the best fit to the mass spectra using a sdependent Breit-Wigner function for signal and a polynomial for background. Events with |MK + K − − Mφ | ≤ 0.01 GeV/c2 , |Mπ+ π− − Mρ | ≤ 0.2GeV/c2 , and |Mπ+ π− π0 − Mω | ≤ 0.035GeV/c2 are taken as φ, ρ0 , and ω candidates, respectively. Here Mφ , Mρ , and Mω are the nominal masses of these vector mesons. The sideband regions are defined as 1.05 ≤ MK + K − ≤ 1.07GeV/c2 , 1.25 ≤ Mπ+ π− ≤ 1.65GeV/c2 , and (0.68 ≤ Mπ+ π− π0 ≤ 0.71GeV/c2 and 0.85 ≤ Mπ+ π− π0 ≤ 0.88GeV/c2 ) for the φ, ρ0 , and ω, respectively.

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Figure 2: Invariant mass distributions of (a) K + K − , (b) π+ π− , and (c) π+ π− π0 . Dots with error bars are data; dashed lines are signal shapes; and dotted lines are the polynomial background contributions. The signal regions and sideband regions are indicated with the solid and dashed arrows respectively.

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Figure 1: Mass distributions of the pseudoscalar meson candidates in ψ → γP: (a) γπ0 , (b) γη(π+ π− π0 ); (c) γη(3π0 ); (d) γη [π+ π− η(γγ)]; and (e) γη (γπ+ π− ).

The invariant mass distributions of γh V, where V = φ, ρ0 , ω, respectively, are shown in Figs. 3(a)-3(c). There are clear χc1 signals in all decay modes, while χc0 and χc2 signals are not evident. In order to extract the signal yields from the mass spectra, we first obtain signal shapes for each χcJ → γV mode (9 decay modes in total) using MC simulations. Each of the distributions in Fig. 3 is fitted with a background shape composed of the vector meson mass sideband distribution plus a 2nd order polynomial function and three χcJ resonances as the signal shapes. Parameters of the polynomial function and the normalization for each of the χcJ resonances are

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Table 2: Compare the χcJ → γV branching fraction of pQCD calculations, with measurements from CLEO-c and BESIII.

mode χc0 → γρ0 χc1 → γρ0 χc2 → γρ0 χc0 → γω χc1 → γω χc2 → γω χc0 → γφ χc1 → γφ χc2 → γφ

pQCD 1.2 14 4.4 0.13 1.6 0.5 0.46 3.6 1.1

CLEO-c < 9.6 243 ± 19 ± 22 < 50 < 8.8 83 ± 15 ± 12 < 7.0 < 6.4 < 26 < 13

BESIII < 10.5 228 ± 13 ± 16 < 20.8 < 12.9 69.7 ± 7.2 ± 5.6 < 6.1 < 16.2 25.8 ± 5.2 ± 2.0 < 8.1

Evts/(10MeV/c2) Evts/(5MeV/c2) Evts/(10MeV/c2)

allowed to float in the fit. The fitted yields are summarized in Table 2. χc1 → γρ and γω are observed with a statistical significance larger than 10σ, and the significance for χc1 →  γφ is 6.4σ. Here, the significance is determined from −2log(L0 /Lmax ), where Lmax is the maximum likelihood value, and L0 is the likelihood for a fit with the signal contribution set to zero. Branching fractions are calculated after considering the signal efficiency, as listed in Table 2, and the upper limits at the 90% C.L on the branching factions of χc0 and χc2 decays are estimated by a Bayesian method.The effects of both the statistical and systematic uncertainties to the upper limits are taken into account. The results are listed in Table 2, where the decay χc1 → γφ is the first observation. The results provide tight constraints on QCD. 30

Figure 4: The left column shows scatterplots for events within the χcJ mass region. The boxes indicate the signal region (without label) and sideband regions labeled as A and B. The plots in the right column are the one-dimensional projections of the system recoiling against a selected φ or ω resonance. Plots (a) and (b) are for the γ2(K + K − ) mode; (c) and (d) for the 5γ2(π+ π− ) mode; and (e) and (f) for the 3γK + K − π+ π− mode.

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Figure 3: Invariant mass distributions of (a) γφ, (b) γρ0 , and (c) γω. Dots with error bars are data; histograms are the best fit; dashed histograms are signal shapes; and the gray-shaded histograms are the sum of the sideband background and the background polynomial.

Decays of the χcJ (J = 0, 1, 2) P-wave charmonium states are considered to be an ideal laboratory to test QCD theory. The initial theoretical calculations of χcJ exclusive decays into light hadrons predicted branching fractions that were smaller than the experimental measurements [9]. With the inclusion of the coloroctet mechanism [10], calculations of χcJ decays into pairs of pseudoscalar mesons and pairs of baryons came into reasonable agreement with the experimental measurements, indicating the importance of the color-octet mechanism. In the case of χcJ decays into pairs of vector (J PC = −− 1 ) mesons VV, where V is an ω or φ, the branching fractions for χc0/2 decays to φφ and ωω have been measured to be at the 10−3 level [11, 12], which is much larger than predictions based on perturbative QCD cal-

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Table 3: Summary of the branching fractions (B) for χcJ → φφ, ωω, and ωφ. Here Nnet is the number of signal events,  is the detection efficiency. The upper limit is estimated at the 90% C.L.

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Figure 5: Invariant mass of VV for (a) φφ mode in the γ2(K + K − ) final state, (b) φφ mode in the γπ+ π− π0 K + K − final state, (c) ωω mode in the γ2(π+ π− π0 ) final state, and (d) ωφ mode in the γπ+ π− π0 K + K − final state. The points with error bars are the data; the solid lines are the fit results; and dotted lines represent the signal components. The shaded and open histograms in (a,b) and (c), respectively, are peaking backgrounds. In (c), the shaded histogram denotes the nonχcJ backgrounds. In (d) the long dash line is background normalized by a simultaneous fit to ωφ sidebands, and the dash-dot line is non-χcJ background.

culations [13]. Decays of the χc1 into φφ, ωω and ωφ violate the helicity selection rule (HSR) and are expected to be highly suppressed [14]. In addition, the decays χcJ → ωφ are doubly OZI suppressed and have yet to be observed. Recently, long-distance effects in χc1 decays [15, 16] have been proposed to account for the HSR violation. Precise measurements of χc1 → VV decays will help clarify the influence of long distance effects in this energy region. Vector pair decay modes are measured at BESIII [17]. The final states of interest are γ2(K + K − ), 5γ2(π+ π− ), and 3γK + K − π+ π− . Event candidates are required to have four well reconstructed charged tracks with net charge zero, and at least one, five, or three good photons, for φφ, ωω, and ωφ, respectively. In the analysis, χcJ candidates are reconstructed with φφ, ωω and ωφ, respectively. A scatterplot of masses for one K + K − pair versus the other K + K − pair is shown in Fig. 4(a), where a clear φφ signal can be seen. The MK + K − distribution, after requiring that the other two kaons are consistent

Mode Nnet χc0 → φφ 433 ± 23 χc1 → φφ 254 ± 17 χc2 → φφ 630 ± 26 → 2(K + K − ) χc0 → φφ 179 ± 16 χc1 → φφ 112 ± 12 χc2 → φφ 219 ± 16 → K + K − π+ π− π0 Combined: χc0 → φφ — χc1 → φφ — χc2 → φφ — χc0 → ωω 991 ± 38 χc1 → ωω 597 ± 29 χc2 → ωω 762 ± 31 → 2(π+ π− π0 ) χc0 → ωφ 76 ± 11 χc1 → ωφ 15 ± 4 χc2 → ωφ < 13 → K + K − π+ π− π0

 (%) 22.4 26.4 26.1

B(×10−4 ) 7.8 ± 0.4 ± 0.8 4.1 ± 0.3 ± 0.4 10.7 ± 0.4 ± 1.1

12.8 15.3 14.9

9.2 ± 0.7 ± 1.0 5.0 ± 0.5 ± 0.6 10.7 ± 0.7 ± 1.2

— — — 13.1 13.2 11.9

8.0 ± 0.3 ± 0.8 4.4 ± 0.3 ± 0.5 10.7 ± 0.3 ± 1.2 9.5 ± 0.3 ± 1.1 6.0 ± 0.3 ± 0.7 8.9 ± 0.3 ± 1.1

14.7 16.2 15.7

1.2 ± 0.1 ± 0.2 0.22 ± 0.06 ± 0.02 < 0.2

with being a φ, is shown in Fig. 4(b). A φ peak is clearly seen with very low background. The φφ invariant mass distribution for the selected events is shown in Fig. 5 (a), where χcJ signals are clearly observed. A scatterplot of the mass for one π+ π− π0 pair versus the other π+ π− π0 pair is shown in Fig. 4(c), and the Mπ+ π− π0 distribution for the three pions recoiling against an ω candidate is plotted in Fig. 4(d). The ωω mass spectrum is shown in Fig. 5 (c), where χcJ signals are prominent. A scatterplot of masses for K + K − pairs versus that for π+ π− π0 pairs is shown in Fig. 4(e), and the Mπ+ π− π0 distribution for events satisfying φ → K + K − is shown in Fig. 4(f), where the ω → π+ π− π0 and φ → π+ π− π0 signals are clearly seen. The φφ and ωφ mass spectra are shown in Figs. 5 (b) and 5 (d), respectively. The numbers of observed events are obtained by fitting the MVV distributions. The fit results are shown in Fig. 5 and the numbers of signal events are listed in Table 3. The helicity selection rule suppressed decays χc1 → φφ/ωω are observed for the first time and there is an evidence of the doubly OZI suppressed decay χc1 → ωφ with a significance of 4.1σ.

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5. Search for η c (2S) → VV decays BESIII searched for ηc (2S ) → VV decays using 106M ψ events, where VV represents ρ0 ρ0 , K ∗0 K ∗0 and φφ [18]. They found no evidence for ηc (2S ) → VV signal, and determined 90% limits on the branching fractions, which are lower than the theoretical predictions [19]. 6. Summary With 106 million ψ(2S ) collected by BES-III, ψ decaying to γP where P is a pseudoscalar meson π0 , η, η , as well as χcJ decaying to γV and VV, where V is a vector meson ρ, ω, φ have been measured. These will be important to our understanding of strong interactions and QCD.

7. Acknowledgment This work is supported in part by the Ministry of Science and Technology of China under Contract No. 2009CB825200; References [1] V. L. Chernyak, A. R. Zhitnitsky, Phys. Rept. 112, 173 (1984). [2] T. K. Pedlar et al. [CLEO Collaboration], Phys. Rev. D 79, 111101 (2009). [3] T. Appelquist and H. D. Politzer, Phys. Rev. Lett. 34, 43 (1975). [4] M. Ablikim et al., Phys. Rev. Lett. 105, 261801 (2010). [5] C. Amsler and F. E. Close, Phys. Rev. D 53, 295 (1996). [6] J. V. Bennett et al. [CLEO Collaboration], Phys. Rev. Lett. 101, 151801 (2008). [7] Y. J. Gao, Y. J. Zhang and K. T. Chao, Chin. Phys. Lett. 23, 2376 (2006). [8] M. Ablikim et al. [BESIII Collaboration], Phys. Rev. D 83, 112005 (2011). [9] A. Duncan, A. Mueller, Phys. Lett. B 93, 119 (1980); H. F. Jones, J. Wyndham, Nucl. Phys. B 195, 222 (1982); M. Anselmino, F. Murgia, Phys. Rev. D 47, 3977 (1993). [10] J. Bolz, P. Kroll and G. A. Schuler, Eur. Phys. J. C 2, 705 (1998); S. M. H. Wong, Eur. Phys. J. C 14, 643 (2000). [11] M. Ablikim et al. (BES Collaboration), Phys. Lett. B 642, 197 (2006). [12] M. Ablikim et al. (BES Collaboration), Phys. Lett. B 630, 7 (2005). [13] H. Q. Zhou, R. G. Ping and B. S. Zou, Phys. Lett. B 611, 123 (2005). [14] S. J. Brodsky, G. P. Lepage, Phys. Rev. D 24, 2848 (1981). [15] Xiao-Hai Liu and Qiang Zhao, Phys. Rev. D 81, 014017 (2010). [16] Dian-Yong Chen, Jun He, Xue-Qian Li and Xiang Liu, Phys. Rev. D 81, 074006 (2010). [17] M. Ablikim et al., Phys. Rev. Lett. 107, 092001 (2011). [18] T. B. Collaboration, arXiv:1110.0949 [hep-ex]. [19] Q. Wang, X. H. Liu and Q. Zhao, arXiv:1010.1343 [hep-ph].

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