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Register a new userX(3872) and Y(4140) using diquark-antidiquark operators with lattice QCD
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We discuss a recent lattice study of charmonium-like mesons with $J^{PC}=1^{++}$ and three quark contents $bar ccbar du$, $bar cc(bar uu + bar dd)$ and $bar ccbar ss$, where the latter two can mix with $bar cc$. In this quantum channel, the long known exotic candidate, X(3872), resides. This simulation employs $N_f=2$, $m_pi=266~$MeV and a large basis of $bar cc$, two-meson and diquark-antidiquark interpolating fields, with diquarks in both anti-triplet and sextet color representations. It aims at the possible signatures of four-quark exotic states. Along the way, we discuss the relations between the diquark-antidiquark operators and the two-meson operators via the Fierz transformations.
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We perform a lattice study of charmonium-like mesons with $J^{PC}=1^{++}$ and three quark contents $bar cc bar du$, $bar cc(bar uu+bar dd)$ and $bar cc bar ss$, where the later two can mix with $bar cc$. This simulation with $N_f=2$ and $m_pi=266$ MeV aims at the possible signatures of four-quark exotic states. We utilize a large basis of $bar cc$, two-meson and diquark-antidiquark interpolating fields, with diquarks in both anti-triplet and sextet color representations. A lattice candidate for X(3872) with I=0 is observed very close to the experimental state only if both $bar cc$ and $Dbar D^*$ interpolators are included; the candidate is not found if diquark-antidiquark and $Dbar D^*$ are used in the absence of $bar cc$. No candidate for neutral or charged X(3872), or any other exotic candidates are found in the I=1 channel. We also do not find signatures of exotic $bar ccbar ss$ candidates below 4.3 GeV, such as Y(4140). Possible physics and methodology related reasons for that are discussed. Along the way, we present the diquark-antidiquark operators as linear combinations of the two-meson operators via the Fierz transformations.
We compare two frequently discussed competing structures for a stable $bar b bar b u d$ tetraquark with quantum numbers $I(J^P) = 0(1^+)$ by considering a meson-meson as well as a diquark-antidiquark creation operator. We treat the heavy antiquarks as static with fixed positions and find diquark-antidiquark dominance for $bar b bar b$ separations $r < 0.2 , text{fm}$, while for $r > 0.5 , text{fm}$ the system essentially corresponds to a pair of $B$ mesons. For the meson-meson to diquark-antidiquark ratio of the tetraquark we obtain around $58%/42%$.
In recent years, the existence of a hadronically stable $bar{b} bar{b} u d$ tetraquark with quantum numbers $I(J^P) = 0(1^+)$ was confirmed by first principles lattice QCD computations. In this work we use lattice QCD to compare two frequently discussed competing structures for this tetraquark by considering meson-meson as well as diquark-antidiquark creation operators. We use the static-light approximation, where the two $bar{b}$ quarks are assumed to be infinitely heavy with frozen positions, while the light $u$ and $d$ quarks are fully relativistic. By minimizing effective energies and by solving generalized eigenvalue problems we determine the importance of the meson-meson and the diquark-antidiquark creation operators with respect to the ground state. It turns out, that the diquark-antidiquark structure dominates for $bar{b} bar{b}$ separations $r < 0.25 , text{fm}$, whereas it becomes increasingly more irrelevant for larger separations, where the $I(J^P) = 0(1^+)$ tetraquark is mostly a meson-meson state. We also estimate the meson-meson to diquark-antidiquark ratio of this tetraquark and find around $60% / 40%$.
Using the QCD sum rule approach we investigate the possible four-quark structure of the recently observed charmed scalar mesons $D_0^{0}(2308)$ (BELLE) and $D_0^{0,+}(2405)$ (FOCUS) and also of the very narrow $D_{sJ}^{+}(2317)$, firstly observed by BABAR. We use diquak-antidiquark currents and work to the order of $m_s$ in full QCD, without relying on $1/m_c$ expansion. Our results indicate that a four-quark structure is acceptable for the resonances observed by BELLE and BABAR: $D_0^{0}(2308)$ and $D_{sJ}^{+}(2317)$ respectively, but not for the resonances observed by FOCUS: $D_0^{0,+}(2405)$.
We explore the use of optimized operators, designed to interpolate only a single meson eigenstate, in three-point correlation functions with a vector-current insertion. These operators are constructed as linear combinations in a large basis of meson interpolating fields using a variational analysis of matrices of two-point correlation functions. After performing such a determination at both zero and non-zero momentum, we compute three-point functions and are able to study radiative transition matrix elements featuring excited state mesons. The required two- and three-point correlation functions are efficiently computed using the distillation framework in which there is a factorization between quark propagation and operator construction, allowing for a large number of meson operators of definite momentum to be considered. We illustrate the method with a calculation using anisotopic lattices having three flavors of dynamical quark all tuned to the physical strange quark mass, considering form-factors and transitions of pseudoscalar and vector meson excitations. The dependence on photon virtuality for a number of form-factors and transitions is extracted and some discussion of excited-state phenomenology is presented.
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