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Investigation of Doubly Heavy Tetraquark Systems using Lattice QCD

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 Added by Martin Pflaumer
 Publication date 2020
  fields
and research's language is English




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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.

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We use lattice QCD to investigate the spectrum of the $bar{b} bar{b} u d$ four-quark system with quantum numbers $I(J^P) = 0(1^+)$. We use five different gauge-link ensembles with $2+1$ flavors of domain-wall fermions, including one at the physical pion mass, and treat the heavy $bar{b}$ quark within the framework of lattice nonrelativistic QCD. Our work improves upon previous similar computations by considering in addition to local four-quark interpolators also nonlocal two-meson interpolators and by performing a Luscher analysis to extrapolate our results to infinite volume. We obtain a binding energy of $(-128 pm 24 pm 10) , textrm{MeV}$, corresponding to the mass $(10476 pm 24 pm 10) , textrm{MeV}$, which confirms the existence of a $bar{b} bar{b} u d$ tetraquark that is stable with respect to the strong and electromagnetic interactions.
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.
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 investigate the $D_{s0}^ast(2317)$ meson using lattice QCD and considering correlation functions of several $bar{c} s$ two-quark and $bar{c} s (bar{u} u + bar{d} d)$ four-quark interpolating fields. These interpolating fields generate different structures in color, spin and position space including quark-antiquark pairs, tetraquarks and two-meson scattering states. For our computation we use an ensemble simulated with pion mass $m_pi approx 0.296 , textrm{GeV}$ and spatial volume of extent $2.90 , textrm{fm}$. We find in addition to the expected spectrum of two-meson scattering states another state around $60 , textrm{MeV}$ below the $D K$ threshold, which we interpret as the $D_{s0}^ast(2317)$ meson. This state couples predominantly to a quark-antiquark interpolating field and only weakly to a $D K$ two-meson interpolating field. The coupling to the tetraquark interpolating fields is essentially zero, rendering a tetraquark interpretation of the $D_{s0}^ast(2317)$ meson rather unlikely. Moreover, we perform a scattering analysis using Luschers method and the effective range approximation to determine the $D_{s0}^ast(2317)$ mass for infinite spatial volume. We find this mass $51 , textrm{MeV}$ below the $D K$ threshold, rather close to both our finite volume result and the experimentally observed value.
We revisit the static potential for the $Q Q bar Q bar Q$ system using SU(3) lattice simulations, studying both the colour singlets groundstate and first excited state. We consider geometries where the two static quarks and the two anti-quarks are at the corners of rectangles of different sizes. We analyse the transition between a tetraquark system and a two meson system with a two by two correlator matrix. We compare the potentials computed with quenched QCD and with dynamical quarks. We also compare our simulations with the results of previous studies and analyze quantitatively fits of our results with anzatse inspired in the string flip-flop model and in its possible colour excitations.
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