Study The χ_cJ�'φφ Decays

ψ(2S) is the heaviest charmonium state below the DD mass threshold, which decays radia-tively into charge-parity even charmnonia, such as ηc(2S) and χcJ·As one of the important members of charmonium family, χcJ is very important for us to understand the underlying structure of the triplet P-wave state and its decay mechanism, such as the helicity selec-tion rule(HSR). For a charmonium decay to two light hadrons, the HSR require the sum of the helicities of hadrons equal to zero, otherwise, the branching fraction will be suppressed. χc1�'ΦΦ is highly suppressed due to the HSR. However, the BESIII collaboration has ob-served for the decay of χc1 to a vector-meson pair VV (VV= ΦΦ) with branching fraction at the same order as Xc0 decays, Br[χc1�'ΦΦ]= (4.1 ± 0.3 0.4) × 10-4. Using the～450 million decays collected with the BESIII, we analyze the χcJ�'ΦΦ decays and the measured results include:1. Branching fraction of χcJ�'ΦΦBr[χc0�'ΦΦ]= (7.81 ± 0.18(sta) ± 0.67(sys)) × 10-4,Br[χc1�'ΦΦ]= (3.93 ± 0.11(sta) ± 0.22(sys)) × 10-4,Br[χc2�'ΦΦ]= (11.61 ± 0.20(sta) ± 0.67(sys)) × 10-4. These measurements refresh the accuracy of the world average values. In particular, the precision of Br[χc1�'ΦΦ] is improved by a factor 2. These measurements are helpful for us to understand the charmonium structure and hadronic decay mechanisms.2. The mass and width of χc0:M(χc0)= 3415.26 ± 0.24(sta) ±0.10(sys) MeV/c2,г(χc0)= 11.85 ± 0.47(sta) ± 1.40(sys) MeV/c2. The mass of χco is the most accurate measurement in the world now.3. We measure the polarization parameters of the Φ meson for the first time by analyzing the joint angular distribution in the cascade decay e+e- �'φ (2S)�'λχcJ�'λΦΦ�' λ2(K+K-).The variables x measures fraction of transverse over longitudinal polarization of Φ meson in χc0�'ΦΦ decay:The variables u measure fractions of transverse over longitudinal polarization of Φ meson in χc2�'ΦΦ decay: these measurements of polarization parameters of a vector-meson pair VV have played a crucial role in the understanding of perturbative QCD and the quark-pair-creation model, and they are helpful for us to understand the evasion of HSR.