The hidden-charm pentaquark and tetraquark states

A large number of experimental discoveries especially in the heavy quarkonium sector that did not at all fit to the expectations of the until then very successful quark model led to a renaissance of hadron spectroscopy Among various explanations of the internal structure of these excitations, hadronic molecules, being analogues of light nuclei, play a unique role since for those predictions can be made with controlled uncertainty We review experimental evidences of various candidates of hadronic molecules, and methods of identifying such structures Nonrelativistic effective field theories are the suitable framework for studying hadronic molecules, and are discussed in both the continuum and finite volumes Also pertinent lattice QCD results are presented Further, we discuss the production mechanisms and decays of hadronic molecules, and comment on the reliability of certain assertions often made in the literature

Hadronic molecules

Quantum chromodynamics (QCD), the generally accepted theory for strong interactions, describes the interactions between quarks and gluons. The strongly interacting particles that are seen in nature are hadrons, which are composites of quarks and gluons. Since QCD is a strongly coupled theory at distance scales that are characteristic of observable hadrons, there are no rigorous, first-principle methods to derive the spectrum and properties of the hadrons from the QCD Lagrangian, except for lattice QCD simulations that are not yet able to cope with all aspects of complex and short-lived states. Instead, a variety of “QCD inspired” phenomenological models have been proposed. Common features of these models are predictions for the existence of hadrons with substructures that are more complex than the standard quark-antiquark mesons and the three-quark baryons of the original quark model that provides a concise description of most of the low-mass hadrons. Recently, an assortment of candidates for nonstandard multiquark mesons, meson-gluon hybrids, and pentaquark baryons that contain heavy (charm or bottom) quarks has been discovered. Here the experimental evidence for these states is reviewed and some general comparisons of their measured properties with standard quark model expectations and predictions of various models for nonstandard hadrons are made. The conclusion is that the spectroscopy of all but the simplest hadrons is not yet understood.

https://link.aps.org/accepted/10.1103/RevModPhys.90.015003

Nonstandard heavy mesons and baryons: Experimental evidence

We review lattice results related to pion, kaon, D-meson, B-meson, and nucleon physics with the aim of making them easily accessible to the nuclear and particle physics communities. More specifically, we report on the determination of the light-quark masses, the form factor $f_+(0)$ arising in the semileptonic $K \rightarrow \pi $ transition at zero momentum transfer, as well as the decay constant ratio $f_K/f_\pi $ and its consequences for the CKM matrix elements $V_{us}$ and $V_{ud}$. Furthermore, we describe the results obtained on the lattice for some of the low-energy constants of $SU(2)_L\times SU(2)_R$ and $SU(3)_L\times SU(3)_R$ Chiral Perturbation Theory. We review the determination of the $B_K$ parameter of neutral kaon mixing as well as the additional four B parameters that arise in theories of physics beyond the Standard Model. For the heavy-quark sector, we provide results for $m_c$ and $m_b$ as well as those for D- and B-meson decay constants, form factors, and mixing parameters. These are the heavy-quark quantities most relevant for the determination of CKM matrix elements and the global CKM unitarity-triangle fit. We review the status of lattice determinations of the strong coupling constant $\alpha _s$. Finally, in this review we have added a new section reviewing results for nucleon matrix elements of the axial, scalar and tensor bilinears, both isovector and flavor diagonal.

FLAG Review 2019

Multiquark resonances are undoubtedly experimentally observed The number of states and the amount of details on their properties has been growing over the years It is very recent the discovery of two pentaquarks and the confirmation of four tetraquarks, two of which had not been observed before We mainly review the theoretical understanding of this sector of particle physics phenomenology and present some considerations attempting a coherent description of the so called X and Z resonances The prominent problems plaguing theoretical models, like the absence of selection rules limiting the number of states predicted, motivate new directions in model building Data are reviewed going through all of the observed resonances with particular attention to their common features and the purpose of providing a starting point to further research

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Multiquark Resonances

The scalar meson D*(s0)(2317) is found 37(17) MeV below the DK threshold in a lattice simulation of the J(P)=0(+) channel using, for the first time, both DK as well as s¯c interpolating fields. The simulation is done on N(f)=2+1 gauge configurations with m(π) is approximately equal to 156 MeV, and the resulting M(D*(s0))-1/4(M(D(s))+3M(D*(s)))=266(16) MeV is close to the experimental value 241.5(0.8) MeV. The energy level related to the scalar meson is accompanied by additional discrete levels due to DK scattering states. The levels near threshold lead to the negative DK scattering length a(0)=-1.33(20) fm that indicates the presence of a state below threshold.

/pdf/d-s0-2317-meson-and-d-meson-kaon-scattering-from-lattice-qcd-22na0p401r.pdf

$D_{s0}^*(2317)$ Meson and $D$-Meson-Kaon Scattering from Lattice QCD

${D}_{s}$ mesons are studied in three quantum channels (${J}^{P}={0}^{+}$, ${1}^{+}$ and ${2}^{+}$), where experiments have identified the very narrow ${D}_{s0}^{*}(2317)$, ${D}_{s1}(2460)$ and narrow ${D}_{s1}(2536)$, ${D}_{s2}^{*}(2573)$. We explore the effect of nearby $DK$ and ${D}^{*}K$ thresholds on the subthreshold states using lattice QCD. Our simulation is done on two very different ensembles of gauge configurations (2 or $2+1$ dynamical quarks, Pion mass of 266 or 156 MeV, lattice size $1{6}^{3}\ifmmode\times\else\texttimes\fi{}32$ or $3{2}^{3}\ifmmode\times\else\texttimes\fi{}64$). In addition to $\overline{q}q$ operators we also include meson-meson interpolators in the correlation functions. This clarifies the identification of the states above and below the scattering thresholds. The ensemble with ${m}_{\ensuremath{\pi}}\ensuremath{\simeq}156\text{ }\text{ }\mathrm{MeV}$ renders the ${D}_{s1}(2460)$ as a strong interaction bound state 44(10) MeV below ${D}^{*}K$ threshold, which is in agreement with the experiment. The ${D}_{s0}^{*}(2317)$ is found 37(17) MeV below $DK$ threshold, close to the experiment value of 45 MeV. The narrow resonances ${D}_{s1}(2536)$ and ${D}_{s2}^{*}(2573)$ are also found close to the experimental masses.

Dsmesons withDKandD*Kscattering near threshold

A candidate for the charmonium(like) state X(3872) is found 11±7 MeV below the DD* threshold using dynamical N(f)=2 lattice simulation with J(PC)=1(++) and I=0. This is the first lattice simulation that establishes a candidate for X(3872) in addition to the nearby scattering states DD* and J/ψω, which inevitably have to be present in dynamical QCD. We extract large and negative DD* scattering length a(0)(DD*)=-1.7±0.4 fm and the effective range r(0)(DD*)=0.5±0.1 fm, but their reliable determination will have to wait for a simulation on a larger volume. In I=1 channel, only the DD* and J/ψρ scattering states are found and no candidate for X(3872). This is in agreement with the interpretation that X(3872) is dominantly I=0, while its small I=1 component arises solely from the isospin breaking and is therefore absent in our simulation with m(u)=m(d).

Evidence for X(3872) from DD* scattering on the lattice.

We derive the relation between the scattering phase shift and the two-particle energy in the finite box, which is relevant for extracting the strong phase shifts in lattice QCD. We consider elastic scattering of two particles with different mass and with nonzero total momentum in the lattice frame. This is a generalization of the L\"uscher formula, which considers zero total momentum, and a generalization of Rummukainen-Gottlieb's formula, which considers degenerate particles with nonzero total momentum. We focus on the most relevant total momenta in practice, i.e. $\mathbf{P}=(2\ensuremath{\pi}/L){e}_{z}$ and $\mathbf{P}=(2\ensuremath{\pi}/L)({e}_{x}+{e}_{y})$, including their multiples and permutations. We find that the $P$-wave phase shift can be reliably extracted from the two-particle energy if the phase shifts for $l\ensuremath{\ge}2$ can be neglected, and we present the corresponding relations. The reliable extraction of the $S$-wave phase shift is much more challenging since ${\ensuremath{\delta}}_{l=0}$ is always accompanied by ${\ensuremath{\delta}}_{l=1}$ in the phase shift relations, and we propose strategies for estimating ${\ensuremath{\delta}}_{l=0}$. We also propose the quark-antiquark and meson-meson interpolators that transform according the considered irreducible representations.

Scattering phase shifts for two particles of different mass and nonzero total momentum in lattice QCD

Recently experimentalists have discovered several charged charmoniumlike hadrons ${Z}_{c}^{+}$ with unconventional quark content $\overline{c}c\overline{d}u$. We perform a search for ${Z}_{c}^{+}$ with mass below 4.2 GeV in the channel ${I}^{G}({J}^{PC})={1}^{+}({1}^{+\ensuremath{-}})$ using lattice QCD. The major challenge is presented by the two-meson states $J/\ensuremath{\psi}\ensuremath{\pi}$, ${\ensuremath{\psi}}_{2S}\ensuremath{\pi}$, ${\ensuremath{\psi}}_{1D}\ensuremath{\pi}$, $D{\overline{D}}^{*}$, ${D}^{*}{\overline{D}}^{*}$, ${\ensuremath{\eta}}_{c}\ensuremath{\rho}$ that are inevitably present in this channel. The spectrum of eigenstates is extracted using a number of meson-meson and diquark-antidiquark interpolating fields. For our pion mass of 266 MeV we find all the expected two-meson states but no additional candidate for ${Z}_{c}^{+}$ below 4.2 GeV. Possible reasons for not seeing an additional eigenstate related to ${Z}_{c}^{+}$ are discussed. We also illustrate how a simulation incorporating interpolators with a structure resembling low-lying two-meson states seems to render a ${Z}_{c}^{+}$ candidate, which is however not robust after further two-meson states around 4.2 GeV are implemented.

Luka Leskovec

Papers

$D_{s0}^*(2317)$ Meson and $D$-Meson-Kaon Scattering from Lattice QCD

Dsmesons withDKandD*Kscattering near threshold

Evidence for X(3872) from DD* scattering on the lattice.

Scattering phase shifts for two particles of different mass and nonzero total momentum in lattice QCD

Study of the $Z_c^+$ channel using lattice QCD