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Register a new userStrong decays of $bar{D}^{*}K^{*}$ molecules and the newly observed $X_{0,1}$ states
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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.
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We revisit, improve and complete some recent estimates of the $0^{+}$ and $1^-$ open charm $(bar c bar d)(us)$ tetraquarks and the corresponding molecules masses and decay constants from QCD spectral sum rules (QSSR) by using QCD Laplace sum rule (LSR) within stability criteria where the factorised perturbative NLO corrections and the contributions of quark and gluon condensates up to dimension-6 in the OPE are included. We confront our results with the $D^-K^+$ invariant mass recently reported by LHCb from $B^+to D^+(D^-K^+)$ decays. We expect that the bump near the $D^-K^+$ threshold can be originated from the $0^{++}(D^-K^+)$ molecule and/or $D^-K^+$ scattering. The prominent $X_{0}$(2900) scalar peak and the bump $X_J(3150)$ (if $J=0$) can emerge from a {it minimal mixing model}, with a tiny mixing angle $theta_0simeq (5.2pm 1.9)^0$, between a scalar {it Tetramole} (${cal T_M}_0$) (superposition of nearly degenerated hypothetical molecules and compact tetraquarks states with the same quantum numbers) having a mass $M_{{cal T_M}_0}$=2743(18) MeV and the first radial excitation of the $D^-K^+$ molecule with mass $M_{(DK)_1}=3678(310)$ MeV. In an analogous way, the $X_1$(2900) and the $X_J(3350)$ (if $J=1$) could be a mixture between the vector {it Tetramole} $({cal T_M}_1)$ with a mass $M_{{cal T_M}_1}=2656(20)$ MeV and its first radial excitation having a mass $M_{({cal T_M}_1)_1}=4592(141)$ MeV with an angle $theta_1simeq (9.1pm 0.6)^0$. A (non)-confirmation of the previous {it minimal mixing models} requires an experimental identification of the quantum numbers of the bumps at 3150 and 3350 MeV.
We systematically study the mass spectrum and strong decays of the S-wave $bar cbar s q q$ states in the compact tetraquark scenario with the quark model. The key ingredients of the model are the Coulomb, the linear confinement, and the hyperfine interactions. The hyperfine potential leads to the mixing between different color configurations, as well as the large mass splitting between the two ground states with $I(J^P)=0(0^+)$ and $I(J^P)=1(0^+)$. We calculate their strong decay amplitudes into the $bar D^{(*)}K^{(*)}$ channels with the wave functions from the mass spectrum calculation and the quark interchange method. We examine the interpretation of the recently observed $X_0(2900)$ as a tetraquark state. The mass and decay width of the $I(J^P)=1(0^+)$ state are $M=2941$ MeV and $Gamma_X=26.6$ MeV, respectively, which indicates that it might be a good candidate for the $X_0(2900)$. Meanwhile, we also obtain an isospin partner state $I(J^P)=0(0^+)$ with $M=2649$ MeV and $Gamma_{Xrightarrow bar D K}=48.1$ MeV, respectively. Future experimental search for $X(2649)$ will be very helpful.
With the advent of the LHC, we will be able to probe New Physics (NP) up to energy scales almost one order of magnitude larger than it has been possible with present accelerator facilities. While direct detection of new particles will be the main avenue to establish the presence of NP at the LHC, indirect searches will provide precious complementary information, since most probably it will not be possible to measure the full spectrum of new particles and their couplings through direct production. In particular, precision measurements and computations in the realm of flavour physics are expected to play a key role in constraining the unknown parameters of the Lagrangian of any NP model emerging from direct searches at the LHC. The aim of Working Group 2 was twofold: on one hand, to provide a coherent, up-to-date picture of the status of flavour physics before the start of the LHC; on the other hand, to initiate activities on the path towards integrating information on NP from high-pT and flavour data.
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.
The newly observed $Xi(1620)^0$ by the Belle Collaboration inspires our interest in performing a systematic study on the interaction of an anti-strange meson $(bar{K}^{(*)})$ with a strange or doubly strange ground octet baryon $mathcal{B}$ ($Lambda$, $Sigma$, and $Xi$), where the spin-orbit force and the recoil correction are considered in the adopted one-boson-exchange model. Our results indicate that $Xi(1620)^0$ can be explained as a $bar{K}Lambda$ molecular state with $I(J^P)=1/2(1/2^-)$ and the intermediate force from $sigma$ exchange plays an important role. Additionally, we also predict several other possible molecular candidates, i.e., the $bar{K}Sigma$ molecular state with $I(J^P)=1/2(1/2^-)$ and the triply strange $bar{K}Xi$ molecular state with $I(J^P)=0(1/2^-)$.
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