Colour flux-tubes in static Pentaquark and Tetraquark systems
Pedro Bicudo, Nuno Cardoso, Marco Cardoso
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7 pages, 6 figures, contribution to the International School of Nuclear Physics, 33rd Course From Quarks and Gluons to Hadrons and Nuclei, Erice-Sicily: 16 - 24 September 2011
The colour fields created by the static tetraquark and pentaquark systems are computed in quenched SU(3) lattice QCD, with gauge invariant lattice operators, in a 24^3 x 48 lattice at beta=6.2. We generate our quenched configurations with GPUs, and detail the respective benchmanrks in different SU(N) groups. While at smaller distances the coulomb potential is expected to dominate, at larger distances it is expected that fundamental flux tubes, similar to the flux-tube between a quark and an antiquark, emerge and confine the quarks. In order to minimize the potential the fundamental flux tubes should connect at 120o angles. We compute the square of the colour fields utilizing plaquettes, and locate the static sources with generalized Wilson loops and with APE smearing. The tetraquark system is well described by a double-Y-shaped flux-tube, with two Steiner points, but when quark-antiquark pairs are close enough the two junctions collapse and we have an X-shaped flux-tube, with one Steiner point. The pentaquark system is well described by a three-Y-shaped flux-tube where the three flux the junctions are Steiner points.
We evaluate the static $qq\bar{q}\bar{q}$ and $qqqq\bar{q}$ potentials in the quenched theory at $β=5.8$ and $β=6.0$ on a lattice of size $16^3\times 32$. We compare the static potentials to the sum of two meson potentials for the tetraquark system and to the sum of the baryonic and mesonic potentials for the pentaquark state, as well as, with the confining potential obtained in the strong coupling expansion.
We compute the colour fields of SU(3) lattice QCD created by static pentaquark systems, in a $24^3\times 48$ lattice at $β=6.2$ corresponding to a lattice spacing $a=0.07261(85)$ fm. We find that the pentaquark colour fields are well described by a multi-Y-type shaped flux tube. The flux tube junction points are compatible with Fermat-Steiner points minimizing the total flux tube length. We also compare the pentaquark flux tube profile with diquark-diantiquark central flux tube profile in the tetraquark and the quark-antiquark fundamental flux tube profile in the meson, and they match, thus sh…
We review how lattice QCD can contribute to the prediction and the comprehension of tetraquarks, pentaquarks and related exotic hadrons, with at least one heavy quark. We include all families of exotic hadrons, except for the quarkless glueballs and the hexaquarks which are related to nuclear physics. Since the discovery of quarks and the development of the QCD theory, there has been a large interest in exotic hadrons, initiated by the tetraquark models developed by Jaffe in 1977. Lattice QCD, being a first principle approach to solve non-perturbative QCD, has been crucial not only to compute …
The colour fields created by the static tetraquark and pentaquark systems are computed in quenched SU(3) lattice QCD, with gauge invariant lattice operators, in a 24^3 x 48 lattice at beta=6.2 . We generate our quenched configurations with GPUs, and detail the respective benchmanrks in different SU(N) groups. While at smaller distances the coulomb potential is expected to dominate, at larger distances it is expected that fundamental flux tubes, similar to the flux-tube between a quark and an antiquark, emerge and confine the quarks. In order to minimize the potential the fundamental flux tubes…
In the past decade many charmonium-like states were observed experimentally. Especially those charged charmonium-like $Z_c$ states and bottomonium-like $Z_b$ states can not be accommodated within the naive quark model. These charged $Z_c$ states are good candidates of either the hidden-charm tetraquark states or molecules composed of a pair of charmed mesons. Recently, the LHCb Collaboration discovered two hidden-charm pentaquark states, which are also beyond the quark model. In this work, we review the current experimental progress and investigate various theoretical interpretations of these …
Here we study the static potential for the two quarks and two antiquarks system. First this is done using the tetraquark operator, which has been previously used to calculate the static potential. This is found to give good results in the region where the tetraquark is expected to be the ground state, however failing outside it. To repair this, we resort to a variational method. This let us study the first excited state besides the ground state of the system in two different particle dispositions, one where the quarks are on the same side of a rectangle and the other where they are at opposite…
The colour fields created by the static tetraquark system are computed in quenched SU(3) lattice QCD, in a 24^3 x 48 lattice at beta=6.2 corresponding to a lattice spacing a=0.07261(85) fm. We find that the tetraquark colour fields are well described by a double-Y, or butterfly, shaped flux tube. The two flux tube junction points are compatible with Fermat points minimizing the total flux tube length. We also compare the diquark-diantiquark central flux tube profile in the tetraquark with the quark-antiquark fundamental flux tube profile in the meson, and they match, thus showing that the tetr…
The past seventeen years have witnessed tremendous progress on the experimental and theoretical explorations of the multiquark states. The hidden-charm and hidden-bottom multiquark systems were reviewed extensively in [Phys. Rept. 639 (2016) 1-121]. In this article, we shall update the experimental and theoretical efforts on the hidden heavy flavor multiquark systems in the past three years. Especially the LHCb collaboration not only confirmed the existence of the hidden-charm pentaquarks but also provided strong evidence of the molecular picture. Besides the well-known $XYZ$ and $P_c$ states,…
Quantum chromodynamics - the theory of quarks and gluons - has been known for decades, but it is yet to be fully understood. A recent example is the prediction and experimental discovery of tetraquarks, that opened a new research field. Crucially, numerous unsolved questions of the standard model can exclusively be addressed by nonperturbative calculations. Quantum computers can solve problems for which well established QCD methods are inapplicable, such as real-time evolution. We take a key step in exploring this possibility by performing a real-time evolution of tetraquark and pentaquark phy…
The fully-charm and -bottom pentaquarks, \emph{i.e.} $cccc\bar{c}$ and $bbbb\bar{b}$, with spin-parity quantum numbers $J^P=\frac{1}{2}^-$, $\frac{3}{2}^-$ and $\frac{5}{2}^-$, are investigated within a Lattice-QCD inspired quark model, which has already successfully described the recently announced fully-charm tetraquark candidate $X(6900)$, and has also predicted several other fully-heavy tetraquarks. A powerful computational technique, based on the Gaussian expansion method combined with a complex-scaling range approach, is employed to predict, and distinguish, bound, resonance and scatteri…
We perform the detailed study of the tetraquark (4Q) potential $V_{\rm 4Q}$ for various QQ-$\rm \bar{Q}\bar{Q}$ systems in SU(3) lattice QCD with $β=6.0$ and $16^3 \times 32$ at the quenched level. For about 200 different patterns of 4Q systems, $V_{\rm 4Q}$ is extracted from the 4Q Wilson loop in 300 gauge configurations, with the smearing method to enhance the ground-state component. We calculate $V_{\rm 4Q}$ for planar, twisted, asymmetric, and large-size 4Q configurations, respectively. Here, the calculation for large-size 4Q configurations is done by identifying $16^2 \times 32$ as the sp…
The static penta-quark (5Q) potential $V_{\rm 5Q}$ is studied in SU(3) lattice QCD with $16^3\times 32$ and $β$=6.0 at the quenched level. From the 5Q Wilson loop, $V_{\rm 5Q}$ is calculated in a gauge-invariant manner, with the smearing method to enhance the ground-state component. $V_{\rm 5Q}$ is well described by the OGE plus multi-Y Ansatz: a sum of the OGE Coulomb term and the multi-Y-type linear term proportional to the minimal total length of the flux-tube linking the five quarks. Comparing with ${\rm Q \bar Q}$ and 3Q potentials, we find a universality of the string tension, $σ_{\rm Q …
Using the picture of the flux tube model, we propose that the $Θ_5$ pentaquark as the first candidate of the three-dimensional non-planar hadron with the extremely stable diamond structure. The up and down quarks lie at the corners of the diamond while the anti-strange quark sits in the center. Various un-excited color flux tubes between the five quarks bind them into a stable and narrow color-singlet. Such a configuration allows the lowest state having the negative parity naturally. The decay of the $Θ_5$ pentaquark into the nucleon and kaon requires the breakup of the non-planar diamond conf…
The hidden-charm tetraquarks with strangeness, $c\bar{c}s\bar{q}$ $(q=u,\,d)$, in $J^P=0^+$, $1^+$ and $2^+$ are systematically investigated in the framework of real- and complex-scaling range of a chiral quark model, whose parameters have been fixed in advance describing hadron, hadron-hadron and multiquark phenomenology. Each tetraquark configuration, compatible with the quantum numbers studied, is taken into account; this includes meson-meson, diquark-antidiquark and K-type arrangements of quarks with all possible color wave functions in four-body sector. Among the different numerical techn…
DeepQuark: A Deep-Neural-Network Approach to Multiquark Bound States
School of Physics, Peking University, Beijing 100871, China（北京大学物理系）；School of Physics, Southeast University, Nanjing 211189, China（东南大学物理系）；School of Physics（物理系）；Center of High Energy Physics, Peking University, Beijing 100871, China（北京大学高能物理中心）
The color fields in a system composed by two static quarks and two static antiquarks are studied. In particular, we consider the four particles in the corners of a rectangle, and two possible alignment of the particles, one in which the quarks are at the same side of the rectangle, and the other where they are at opposite sides. We use a variational method, to probe not only the ground state but also the first excited state. This results permit us to observe and interpret the flux-tube recombination in the mesons to mesons and the tetraquark to mesons transitions, for both states. The results …
The multiquark confining potential is proportional to the total distance of the fundamental strings linking the quarks and antiquarks. We address the computation of the total string distance an of the Fermat points where the different strings meet. For a meson (quark-antiquark system) the distance is trivially the quark-antiquark distance. For a baryon (three quark system) the problem was solved geometrically from the onset, by Fermat and by Torricelli. The geometrical solution can be determined just with a rule and a compass, but translation of the geometrical solution to an analytical expres…
