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We investigate BB̅ systems by computing potentials of two static quarks in the presence of two quarks of finite mass using lattice QCD. By solving the Schrodinger equation we check whether these potentials are sufficiently attractive to host bound states. Particular focus is put on the experimentally most promising bottomonium-like tetraquark candidate Zb± with quantum numbers I(JP) = 1(1+).
We compute potentials of two static antiquarks in the presence of two quarks qq of finite mass using lattice QCD. In a second step we solve the Schrödinger equation, to determine, whether the resulting potentials are sufficiently attractive to host a bound state, which would indicate the existence of a stable qqb¯b¯ tetraquark. We find a bound state for qq=(ud−du)/2–√ with corresponding quantum numbers I(JP)=0(1+) and evidence against the existence of bound states with isospin I=1 or qq∈{cc,ss}.
We present SU(3) lattice Yang-Mills data for hybrid static potentials from five ensembles with different small lattice spacings and the corresponding parametrizations for quark-antiquark separations 0.08fm≤r≤1.12fm. We remove lattice discretization errors at tree level of perturbation theory and partly at order a2 as well as the a-dependent self energy. In particular the tree-level improvement of static potentials is discussed in detail and two methods are compared. The resulting parametrizations are expected to represent continuum limit results for hybrid static potentials within statistical errors.
Pflaumer, Martin ; Alexandrou, Constantia ; Finkenrath, Jacob ; Leontiou, Theodoros ; Meinel, Stefan ; Wagner, Marc
We present our recent results on antiheavy-antiheavy-light-light tetraquark systems using lattice QCD. Our study of the b¯b¯us four-quark system with quantum numbers JP=1+ and the b¯c¯ud four-quark systems with I(JP)=0(0+) and I(JP)=0(1+) utilizes scattering operators at the sink to improve the extraction of the low-lying energy levels. We found a bound state for b¯b¯us with Ebind,b¯b¯us=(−86±22±10)MeV, but no indication for a bound state in both b¯c¯ud channels. Moreover, we show preliminary results for b¯b¯ud with I(JP)=0(1+), where we used scattering operators both at the sink and the source. We found a bound state and determined its infinite-volume binding energy with a scattering analysis, resulting in Ebind,b¯b¯ud=(−103±8)MeV.
In this work we investigate the existence of bound states for doubly heavy tetraquark systems Q¯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 b¯b¯ud, b¯b¯us and b¯c¯ud. We show evidence for the existence of b¯b¯ud and b¯b¯us bound states, while no binding appears to be present for b¯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.
Wagner, Marc ; Alexandrou, Constantia ; Finkenrath, Jacob ; Leontiou, Theodoros ; Meinel, Stefan ; Pflaumer, Martin
We present first results of a recently started lattice QCD investigation of antiheavy-antiheavy-light-light tetraquark systems including scattering interpolating operators in correlation functions both at the source and at the sink. In particular, we discuss the importance of such scattering interpolating operators for a precise computation of the low-lying energy levels. We focus on the b¯b¯ud four-quark system with quantum numbers I(JP)=0(1+), which has a ground state below the lowest meson-meson threshold. We carry out a scattering analysis using Lüscher's method to extrapolate the binding energy of the corresponding QCD-stable tetraquark to infinite spatial volume. Our calculation uses clover u, d valence quarks and NRQCD b valence quarks on gauge-link ensembles with HISQ sea quarks that were generated by the MILC collaboration.
b̄b̄ud tetraquark resonances in the Born-Oppenheimer approximation using lattice QCD potentials
(2018)
We study tetraquark resonances using lattice QCD potentials for a pair of static antiquarks b¯b¯ in the presence of two light quarks ud. The system is treated in the Born-Oppenheimer approximation and we use the emergent wave method. We focus on the isospin I=0 channel, but consider different orbital angular momenta l of the heavy antiquarks b¯b¯. We extract the phase shifts and search for S and T matrix poles on the second Riemann sheet. For orbital angular momentum l=1 we find a tetraquark resonance with quantum numbers I(JP)=0(1−), resonance mass m=10576+4−4MeV and decay width Γ=112+90−103MeV, which can decay into two B mesons.
Study of I = 0 bottomonium bound states and resonances based on lattice QCD static potentials
(2022)
We investigate I=0 bottomonium bound states and resonances in S, P, D and F waves using lattice QCD static-static-light-light potentials. We consider five coupled channels, one confined quarkonium and four open B(∗)B¯(∗) and B(∗)sB¯(∗)s meson-meson channels and use the Born-Oppenheimer approximation and the emergent wave method to compute poles of the T matrix. We discuss results for masses and decay widths and compare them to existing experimental results. Moreover, we determine the quarkonium and meson-meson composition of these states to clarify, whether they are ordinary quarkonium or should rather be interpreted as tetraquarks.
We use lattice QCD to investigate the existence of strong-interaction-stable antiheavy-antiheavy-light-light tetraquarks. We study the ¯𝑏¯𝑏𝑢𝑠 system with quantum numbers 𝐽𝑃=1+ as well as the ¯𝑏¯𝑐𝑢𝑑 systems with quantum numbers 𝐼(𝐽𝑃)=0(0+) and 𝐼(𝐽𝑃)=0(1+). We carry out computations on five gauge-link ensembles with 2+1 flavors of domain-wall fermions, including one at the physical pion mass. The bottom quarks are implemented using lattice nonrelativistic QCD, and the charm quarks using an anisotropic clover action. In addition to local diquark-antidiquark and local meson-meson interpolating operators, we include nonlocal meson-meson operators at the sink, which facilitates the reliable determination of the low-lying energy levels. We find clear evidence for the existence of a strong-interaction-stable ¯𝑏¯𝑏𝑢𝑠 tetraquark with binding energy (−86±22±10) MeV and mass (10609±22±10) MeV. For the ¯𝑏¯𝑐𝑢𝑑 systems we do not find any indication for the existence of bound states, but cannot rule out their existence either.
Pflaumer, Martin ; Alexandrou, Constantia ; Finkenrath, Jacob ; Leontiou, Theodoros ; Meinel, Stefan ; Wagner, Marc
We present our recent results on antiheavy-antiheavy-light-light tetraquark systems using lattice QCD. Our study of the b¯b¯us four-quark system with quantum numbers JP=1+ and the b¯c¯ud four-quark systems with I(JP)=0(0+) and I(JP)=0(1+) utilizes scattering operators at the sink to improve the extraction of the low-lying energy levels. We found a bound state for b¯b¯us with Ebind,b¯b¯us=(−86±22±10)MeV, but no indication for a bound state in both b¯c¯ud channels. Moreover, we show preliminary results for b¯b¯ud with I(JP)=0(1+), where we used scattering operators both at the sink and the source. We found a bound state and determined its infinite-volume binding energy with a scattering analysis, resulting in Ebind,b¯b¯ud=(−103±8)MeV.