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Register a new userExistence and Non-Existence of Doubly Heavy Tetraquark Bound States
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In this work we investigate the existence of bound states for doubly heavy tetraquark systems $ bar{Q}bar{Q}qq $ in a full lattice-QCD computation, where heavy bottom quarks are treated in the framework of non-relativistic QCD. We focus on three systems with quark content $ bar{b}bar{b}ud $, $ bar{b}bar{b}us $ and $ bar{b}bar{c}ud $. We show evidence for the existence of $ bar{b}bar{b}ud $ and $ bar{b}bar{b}us $ bound states, while no binding appears to be present for $ bar{b}bar{c}ud $. For the bound four-quark states we also discuss the importance of various creation operators and give an estimate of the meson-meson and diquark-antidiquark percentages.
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Spectrum of the doubly heavy tetraquarks, $bbbar qbar q$, is studied in a constituent quark model. Four-body problem is solved in a variational method where the real scaling technique is used to identify resonant states above the fall-apart decay thresholds. In addition to the two bound states that were reported in the previous study we have found several narrow resonant states above the $BB^*$ and $B^*B^*$ thresholds. Their structures are studied and are interpreted by the quark dynamics. A narrow resonance with spin-parity $J^P=1^+$ is found to be a mixed state of a compact tetraquark and a $B^*B^*$ scattering state. This is driven by a strong color Coulombic attraction between the $bb$ quarks. Negative-parity excited resonances with $J^P=0^-$, $1^-$ and $2^-$ form a triplet under the heavy-quark spin symmetry. It turns out that they share a similar structure to the $lambda$-mode of a singly heavy baryon as a result of the strongly attractive correlation for the doubly heavy diquark.
We search for possibly existent bound states in the heavy-light tetraquark channels with quark content $ bar{b}bar{b}ud $, $ bar{b}bar{b}us $ and $ bar{b}bar{c}ud $ using lattice QCD. We carry out calculations on several gauge link ensembles with $ N_f=2+1 $ flavours of domain-wall fermions and consider a basis of local and non-local interpolators. Besides extracting the energy spectrum from the correlation matrices, we also perform a Luscher analysis to extrapolate our results to infinite volume.
In the framework of an extended chromomagnetic model, we systematically study the mass spectrum of the $S$-wave $qQbar{Q}bar{Q}$ tetraquarks. Their mass spectra are mainly determined by the color interaction. For the $qcbar{c}bar{c}$, $qbbar{c}bar{c}$ and $qbbar{b}bar{b}$ tetraquarks, the color interaction favors the color-sextet $ket{(qQ)^{6_{c}}(bar{Q}bar{Q})^{bar{6}_{c}}}$ configuration over the color-triplet $ket{(qQ)^{bar{3}_{c}}(bar{Q}bar{Q})^{3_{c}}}$ one. But for the $qcbar{b}bar{b}$ tetraquarks, the color-triplet configuration is favored. We find no stable states which lie below the thresholds of two pseudoscalar mesons. The lowest axial-vector states with the $qQbar{b}bar{b}$ flavor configuration may be narrow. They lie just above the thresholds of two pseudoscalar mesons, but cannot decay into these channels because of the conservation of the angular momentum and parity.
Recently, the authors of the current paper established in [9] the existence of a ground-state solution to the following bi-harmonic equation with the constant potential or Rabinowitz potential: begin{equation} (-Delta)^{2}u+V(x)u=f(u) text{in} mathbb{R}^{4}, end{equation} when the nonlinearity has the special form $f(t)=t(exp(t^2)-1)$ and $V(x)geq c>0$ is a constant or the Rabinowitz potential. One of the crucial elements used in [9] is the Fourier rearrangement argument. However, this argument is not applicable if $f(t)$ is not an odd function. Thus, it still remains open whether the above equation with the general critical exponential nonlinearity $f(u)$ admits a ground-state solution even when $V(x)$ is a positive constant. The first purpose of this paper is to develop a Fourier rearrangement-free approach to solve the above problem. More precisely, we will prove that there is a threshold $gamma^{*}$ such that for any $gammain (0,gamma^*)$, the above equation with the constant potential $V(x)=gamma>0$ admits a ground-state solution, while does not admit any ground-state solution for any $gammain (gamma^{*},+infty)$. The second purpose of this paper is to establish the existence of a ground-state solution to the above equation with any degenerate Rabinowitz potential $V$ vanishing on some bounded open set. Among other techniques, the proof also relies on a critical Adams inequality involving the degenerate potential which is of its own interest.
We prove that every entire solution of the minimal graph equation that is bounded from below and has at most linear growth must be constant on a complete Riemannian manifold $M$ with only one end if $M$ has asymptotically non-negative sectional curvature. On the other hand, we prove the existence of bounded non-constant minimal graphic and $p$-harmonic functions on rotationally symmetric Cartan-Hadamard manifolds under optimal assumptions on the sectional curvatures.
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