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Register a new userThe newly observed state $D_{s0}(2590)^{+}$ and width of $D^*(2007)^0$
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We choose the Reduction Formula, PCAC and Low Energy Theory to reduce the $S$ matrix of a OZI allowed two-body strong decay involving a light pseudoscalar, the covariant transition amplitude formula with relativistic wave functions as input is derived. After confirm this method by the decay $D^*(2010)to Dpi$, we study the state $D^*(2007)$, and the full width $Gamma_{rm{th}}(D^*(2007))=53.8pm0.7$ keV is obtained. Supposing the newly observed $D_{s0}(2590)^{+}$ to be the state $D_s(2^1S_0)^+$, we find its decay width $Gamma$ is highly sensitive to the $D_{s0}(2590)^{+}$ mass, which result in the meaningless comparison of widths by different models with various input masses. Instead of width, we introduce a model independent quantity $X$ and the ratio $Gamma/{|{vec P_f}|^3}$, which are almost mass independent, to give us useful information. The results show that, all the existing theoretical predictions $X_{D_s(2S) to D^*K}=0.25sim 0.41$ and $Gamma/{|{vec P_f}|^3}=0.81sim1.77$ MeV$^{-2}$ are much smaller than experimental data $0.585^{+0.015}_{-0.035}$ and $4.54^{+0.25}_{-0.52}$ MeV$^{-2}$. Further compared with $X^{ex}_{D^*(2010) to Dpi}=0.58$, the current data $X^{ex}_{D_s(2S) to D^*K}=0.585^{+0.015}_{-0.035}$ is too big to be an reasonable value, so to confirm $D_{s0}(2590)^{+}$ as the state $D_s(2^1S_0)^+$, more experimental studies are needed.
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The recently discovered $D_{s0}(2590)$ state by the LHCb collaboration was regarded as the first excited state of $^1S_{0}$ charmed-strange meson. Its mass is, however, lower than the Godfrey-Isgur quark model prediction by about 80 MeV. In this work, we take into account the $D^{ast}K$ contribution to the bare $cbar{s}$ state, and show that the coupled-channel interaction induces an 88 MeV shift with respect to the conventional quark model $cbar{s}$ state, which is much closer to the experimental mass. Our study shows that in addition to $S$-wave, $P$-wave coupled-channel interactions also play a role for hadrons located close to two-hadron thresholds. We further scrutinize the unquenched quark model results with a model independent approach. It is shown that the two-body $D^*K$ decay width is proportional to the weight of the $D^*K$ component. To saturate the experimental total decay width with the $D^*K$ partial decay width we need a weight of about 60% while to reproduce the unquenched quark model result a weight of about 5% is needed. Therefore, we encourage future experimental studies on the two-body $D^*K$ partial decay of $D_{s0}(2590)$.
The scalar meson $D_{s0}^*(2317)$ is found 37(17)MeV below DK threshold in a lattice simulation of the $J^P=0^+$ channel using, for the first time, both DK as well as $bar sc$ interpolating fields. The simulation is done on $N_f=2+1$ gauge configurations with $m_pisimeq 156 $MeV, and the resulting $M_{D_{s0}^*}-tfrac{1}{4}(M_{D_s}+3M_{D_s^*})=266(16)$ MeV is close to the experimental value 241.5(0.8)MeV. The energy level related to the scalar meson is accompanied by additional discrete levels due to DK scattering states. The levels near threshold lead to the negative DK scattering length $a_0=-1.33(20)$ fm that indicates the presence of a state below threshold.
Lately, the LHCb Collaboration reported the discovery of two new states in the $B^+rightarrow D^+D^- K^+$ decay, i.e., $X_0(2866)$ and $X_1(2904)$. In the present work, we study whether these states can be understood as $D^*bar{K}^*$ molecules from the perspective of their two-body strong decays into $D^-K^+$ via triangle diagrams and three-body decays into $D^*bar{K}pi$. The coupling of the two states to $D^*bar{K}^*$ are determined from the Weinberg compositeness condition, while the other relevant couplings are well known. The obtained strong decay width for the $X_0(2866)$, in marginal agreement with the experimental value within the uncertainty of the model, hints at a large $D^*bar{K}^*$ component in its wave function. On the other hand, the strong decay width for the $X_1(2904)$, much smaller than its experimental counterpart, effectively rules out its assignment as a $D^*bar{K}^*$ molecule.
After the discovery of the new $Omega^{*}$ state, the ratio of the branching fractions of $Omega(2012)to bar{K}piXi$ relative to $bar{K}Xi$ decay channel was investigated by the Belle Collaboration recently. The measured $11.9%$ up limit on this ratio is in sharp tension with the $S$-wave $bar{K}Xi(1530)$ molecule interpretation for $Omega(2012)$ which indicates the dominant $bar{K}piXi$ three-body decay. In the present work, we try to explore the possibility of the $P$-wave molecule assignments for $Omega(2012)$ (where $Omega(2012)$ has positive parity). It is found that the latest experimental measurements are compatible with the $1/2^+$ and $3/2^+$ $bar{K}Xi(1530)$ molecular pictures, while the $5/2^+$ $bar{K}Xi(1530)$ molecule shows the larger $bar{K}piXi$ three-body decay compared with the $bar{K}Xi$ decay as the case of $S$-wave molecule. Thus, the newly observed $Omega(2012)$ can be interpreted as the $1/2^+$ or $3/2^+$ $bar{K}Xi(1530)$ molecule state according to current experiment data.
We report improved measurements of the product branching fractions ${mathcal B}(B^+rightarrowbar{D}^0 D_{s0}^{*+} (2317))times{mathcal B}( D_{s0} ^{*+}(2317)rightarrow D_s^{+}pi^0) =(8.0^{+1.3}_{-1.2} pm 1.1 pm 0.4)times 10^{-4}$ and ${mathcal B}(B^0rightarrow D^- D_{s0} ^{*+}(2317))times{mathcal B}(D_{s0}^{*+}(2317)rightarrow D_s^{+}pi^0) =(10.2^{+1.3}_{-1.2} pm 1.0 pm 0.4)times 10^{-4}$, where the first errors are statistical, the second are systematic and the third are from $D$ and $D_s$ branching fractions. In addition, we report negative results from a search for hypothesized neutral ($Z^0$) and doubly charged ($Z^{++}$) isospin partners of the $D_{s0}^{*+}(2317)$ and provide upper limits on the product branching fractions ${mathcal B}(B^0 rightarrow D^0 z^0)times{mathcal B}(z^0rightarrow D_s^{+}pi^-)$ and ${mathcal B}(B^+rightarrow D^- z^{++})times{mathcal B}(z^{++}rightarrow D_s^{+}pi^+)$ that are more than an order of magnitude smaller than theoretical expectations for the hypotheses that the $D_{s0} ^{*+}(2317)$ is a member of an isospin triplet. The analysis uses a 711 fb$^{-1}$ data sample containing 772 million $Bbar{B}$ meson pairs collected at the $Upsilon(4S)$ resonance in the Belle detector at the KEKB collider.
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