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Register a new userPerfect $DD^*$ molecular prediction matching the $T_{cc}$ observation at LHCb
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In 2012, we investigated the possible molecular states composed of two charmed mesons [Phys.Rev. D 88, 114008 (2013), arXiv:1211.5007 [hep-ph](2012)]. The $D^*D$ system with the quantum numbers of $I(J^P)=0(1^+)$ was found to be a good candidate of the loosely bound molecular state. This state is very close to the $D^*D$ threshold with a binding energy around 0.47 MeV. This prediction was confirmed by the new LHCb observation of $T_{cc}^+$ [see Franz Muheims talk at the European Physical Society conference on high energy physics 2021].
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The isospin breaking effect plays an essential role in generating hadronic molecular states with a very tiny binding energy. Very recently, the LHCb Collaboration observed a very narrow doubly charmed tetraquark $T_{cc}^+$ in the $D^0D^0pi$ mass spectrum, which lies just below the $D^0D^{*+}$ threshold around 273 keV. In this work, we study the $D^0D^{*+}/D^+D^{*0}$ interactions with the one-boson-exchange effective potentials and consider the isospin breaking effect carefully. We not only reproduce the mass of the newly observed $T_{cc}^+$ very well in the doubly charmed molecular tetraquark scenario, but also predict the other doubly charmed partner resonance $T_{cc}^{prime+}$ with $m=3876~text{MeV}$, and $Gamma= 412~text{keV}$. The prime decay modes of the $T_{cc}^{prime+}$ are $D^0D^+gamma$ and $D^+D^0pi^0$.
The mass and coupling of the doubly charmed $J^P=0^{-}$ diquark-antidiquark states $T_{cc;bar{s} bar{s}}^{++}$ and $T_{cc;bar{d} bar{s}}^{++}$ that bear two units of the electric charge are calculated by means of QCD two-point sum rule method. Computations are carried out by taking into account vacuum condensates up to and including terms of tenth dimension. The dominant $S$-wave decays of these tetraquarks to a pair of conventional $ D_{s}^{+}D_{s0}^{ast +}(2317)$ and $D^{+}D_{s0}^{ast +}(2317)$ mesons are explored using QCD three-point sum rule approach, and their widths are found. The obtained results $m_{T}=(4390~pm 150)~mathrm{MeV}$ and $Gamma =(302 pm 113~mathrm{MeV}$) for the mass and width of the state $T_{cc;bar{ s} bar{s}}^{++}$, as well as spectroscopic parameters $widetilde{m} _{T}=(4265pm 140)~mathrm{MeV}$ and $widetilde{Gamma }=(171~pm 52)~ mathrm{MeV}$ of the tetraquark $T_{cc;bar{d} bar{s}}^{++}$ may be useful in experimental studies of exotic resonances.
The doubly charmed exotic state $T_{cc}$ recently discovered by the LHCb Collaboration could well be a $DD^{*}$ molecular state long predicted in various theoretical models, in particular, the $DD^*$ isoscalar axial vector molecular state predicted in the one-boson-exchange model. In this work, we study the $DDD^*$ system in the Gaussian Expansion Method with the $DD^*$ interaction derived from the one-boson-exchange model and constrained by the precise binding energy of $273pm63$ keV of $T_{cc}$ with respect to the $D^{*+}D^0$ threshold. We show the existence of a $DDD^*$ state with a binding energy of a few hundred keV and spin-parity $1^-$. Its main decay modes are $DDDpi$ and $DDDgamma$. The existence of such a state could in principle be confirmed with the upcoming LHC data and will unambiguously determine the nature of the $T_{cc}^+$ state and of the many exotic state of similar kind, thus deepening our understanding of the non-perturbative strong interaction.
On March 26th, 2019, at the Rencontres de Moriond QCD conference, the LHCb Collaboration reported the observation of three new pentaquarks, namely $P_c(4312)$, $P_c(4440)$ and $P_c(4457)$, which are consistent with the loosely bound molecular hidden-charm pentaquark states composed of an S-wave charmed baryon $Sigma_c$ and an S-wave anti-charmed meson ($bar{D}, bar{D}^*$). In this work, we present a direct calculation by the one-boson-exchange (OBE) model and demonstrate explicitly that the $P_c(4312)$, $P_c(4440)$ and $P_c(4457)$ do correspond to the loosely bound $Sigma_cbar{D}$ with $(I=1/2,J^P=1/2^-)$, $Sigma_cbar{D}^*$ with $(I=1/2,J^P=1/2^-)$ and $Sigma_cbar{D}^*$ with $(I=1/2,J^P=3/2^-)$, respectively.
We have studied, using double ratio of QCD (spectral) sum rules, the ratio between the masses of $T_{cc}$ and X(3872) assuming that they are respectively described by the $D-{D}^*$ and $D-bar{D}^*$ molecular currents. We found (within our approximation) that the masses of these two states are almost degenerate. Since the pion exchange interaction between these mesons is exactly the same, we conclude that if the observed X(3872) meson is a $Dbar{D}^*+c.c.$ molecule, then the $DD^*$ molecule should also exist with approximately the same mass. An extension of the analysis to the $b$-quark case leads to the same conclusion. We also study the SU(3) breakings for the $T^s_{QQ}/T_{QQ}$ mass ratios. Motivated by the recent Belle observation of two $Z_b$ states, we revise our determination of $X_b$ by combining results from exponential and FESR sum rules.
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