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Heavy-strange meson molecules and possible candidates $D^*_{s0}(2317)$, $D_{s1}(2460)$, and $X_0(2900)$

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 Added by Jun He Prof.
 Publication date 2021
  fields
and research's language is English




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In this work, we systematically investigate the heavy-strange meson systems, $D^{(*)}K^{(*)}/bar{B}^{(*)}K^{(*)}$ and $bar{D}^{(*)}K^{(*)}/B^{(*)}K^{(*)}$, to study possible molecules in a quasipotenial Bethe-Salpter equation approach together with the one-boson-exchange model. The potential is achieved with the help of the hidden-gau ge Lagrangians. Molecular states are found from all six S-wave isoscalar interactions of $D^{(*)}K^{(*)}/bar{B}^{(*)}K^{(*)}$. The charmed-strange mesons $D^*_{s0}(2317)$ and $D_{s1}(2460)$ can be related to the ${D}K$ and $D^*K$ states with spin parities $0^+$ and $1^+$, respectively. The recent observed $B_{sJ}(6158)$ may be assigned as a $bar{B}K^*$ molecular state with $1^+$. Four molecular states are produced from the interactions of $bar{D}^{(*)}K^{(*)}/B^{(*)}K^{(*)}$, among which the $bar{D}^*{K}^*$ molecular state with $0^+$ can be related to the $X_0(2900)$. No isovector molecular states are found in the interactions considered. The current results are helpful to understand the internal structure of $D^*_{s0}(2317)$, $D_{s1}(2460)$, $X_0(2900)$, and new $B_{sJ}$ states. The experimental research for more heavy-strange meson molecules are suggested.



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In this article, we assume that there exist the pseudoscalar $Dbar{D}_{s0}^*(2317)$ and $D^*bar{D}_{s1}^*(2460)$ molecular states $Z_{1,2}$ and construct the color singlet-singlet molecule-type interpolating currents to study their masses with the QCD sum rules. In calculations, we consider the contributions of the vacuum condensates up to dimension-10 and use the formula $mu=sqrt{M_{X/Y/Z}^{2}-left(2{mathbb{M}}_{c}right)^{2}}$ to determine the energy scales of the QCD spectral densities. The numerical results, $M_{Z_1}=4.61_{-0.08}^{+0.11},text{GeV}$ and $M_{Z_2}=4.60_{-0.06}^{+0.07},text{GeV}$, which lie above the $Dbar{D}_{s0}^*(2317)$ and $D^*bar{D}_{s1}^*(2460)$ thresholds respectively, indicate that the $Dbar{D}_{s0}^*(2317)$ and $D^*bar{D}_{s1}^*(2460)$ are difficult to form bound state molecular states, the $Z_{1,2}$ are probably resonance states.
In this talk I present the results obtained using effective field theories in a finite volume from a reanalysis of lattice data on the $KD^{(*)}$ systems, where bound states of $KD$ and $KD^*$ are found and associated with the states $D^*_{s0}(2317)$ and $D^*_{s1}(2460)$, respectively. We confirm the presence of such states on the lattice data and determine the weight of the $KD$ channel in the wave function of $D^*_{s0}(2317)$ and that of $KD^*$ in the wave function of $D^*_{s1}(2460)$. Our results indicate a large meson-meson component in both cases.
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.
We perform a high statistics study of the $J^{P}=0^{+}$ and $1^{+}$ charmed-strange mesons, $D_{s0}^*(2317)$ and $D_{s1}(2460)$, respectively. The effects of the nearby $DK$ and $D^{*}K$ thresholds are taken into account by employing the corresponding four quark operators. Six ensembles with $N_f=2$ non-perturbatively ${cal O}(a)$ improved clover Wilson sea quarks at $a=0.07$ fm are employed, covering different spatial volumes and pion masses: linear lattice extents $L/a=24,32,40,64$, equivalent to 1.7 fm to 4.5 fm, are realised for $m_{pi}=290$ MeV and $L/a=48,64$ or 3.4 fm and 4.5 fm for an almost physical pion mass of $150$ MeV. Through a phase shift analysis and the effective range approximation we determine the scattering lengths, couplings to the thresholds and the infinite volume masses. Differences relative to the experimental values are observed for these masses, however, this is likely to be due to discretisation effects as spin-averaged quantities and splittings are reasonably compatible with experiment. We also compute the weak decay constants of the scalar and axialvector and find $f_V^{0^+}=114(2)(0)(+5)(10)$ MeV and $f_A^{1^+}=194(3)(4)(+5)(10)$ MeV, where the errors are due to statistics, renormalisation, finite volume and lattice spacing effects.
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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