Flavour-Exotic Tetraquarks in Large-$N_{\rm c}$ QCD: Do They Exist?
Wolfgang Lucha, Dmitri Melikhov, Hagop Sazdjian
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7 pages, 4 figures, talk presented at the "European Physical Society Conference on High Energy Physics - EPS-HEP 2019" (10 - 17 July 2019, Ghent, Belgium)
Flavour-exotic tetraquark mesons, by definition bound states of two quarks and two antiquarks of four mutually different quark flavours, are, for given Lorentz features, subject to two incompatible constraints: On the one hand, within quantum chromodynamics a formation of compact tetraquark states is most easily envisaged by merging two colour-antisymmetric two-quark clusters, a diquark and an antidiquark. This path, however, leads to merely a single tetraquark state of chosen Lorentz characteristics. On the other hand, in the limit of the number of colour degrees of freedom growing beyond bounds, internal consistency at leading order calls for the presence of (at least) two of such tetraquark states of identical quark-flavour composition. The failure of attempts to reconcile these two contradictory insights suggests the nonexistence of compact flavour-exotic tetraquark mesons.
The chromomagnetic interaction, with full account for flavour-symmetry breaking, is applied to S-wave configurations containing two quarks and two antiquarks. Phenomenological implications are discussed for light, charmed, charmed and strange, hidden-charm and double-charm mesons, and extended to their analogues with beauty.
We analyse exotic tetraquark mesons - bound states formed by two quarks and two antiquarks - for the specific case of four different quark flavours within the framework of a well-defined limit of quantum chromodynamics characterized by the correlated growth without bound of the number of colour degrees of freedom and approach to zero of the coupling constant of the strong interactions. On the one hand, the assumption that the tetraquarks of the kind defined above show up, as poles in the amplitudes for the scattering of two ordinary mesons with flavour quantum numbers that match those of these…
Two-ordinary-meson scattering in large-$N_c$ QCD implies consistency criteria for intermediate-tetraquark contributions. Their fulfilment at $N_c$-leading order constrains the nature of the spectrum of genuinely exotic tetraquark states.
Frequently, theoretical discussions of multiquark hadron states prove to be contaminated or even dominated by contributions of conventional hadrons. For the approach to QCD bound states in terms of QCD sum rules, we show how to get rid of all unwanted ordinary-hadron ballast by boiling down the traditional QCD sum-rule formalism to the nonconventional aspects in the focus of interest.
Discussing four-point Green functions of bilinear quark currents in large-$N_c$ QCD, we formulate rigorous criteria for selecting diagrams appropriate for the analysis of potential tetraquark poles. We find that both flavor-exotic and cryptoexotic (i.e., flavor-nonexotic) tetraquarks, if such poles exist, have a width of order $O(1/N_c^2)$, so they are parametrically narrower compared to the ordinary $\bar qq$ mesons, which have a width of order $O(1/N_c)$. Moreover, for flavor-exotic states, the consistency of the large-$N_c$ behavior of "direct" and "recombination" Green functions requires t…
A salient feature shared by all tetraquark candidates observed in experiment is the absence of flavor-exotic states of the type $\bar a b\bar c d$, with four different quark flavors. This phenomenon may be understood from the properties of large-$N_c$ QCD: On the one hand, consistency conditions for flavor-exotic Green functions, potentially containing these tetraquark poles, require the existence of two tetraquarks $T_A$ and $T_B$: each of them should decay dominantly via a single two-meson channel, $T_A\to M_{\bar a b}M_{\bar c d}$ and $T_B\to M_{\bar a d}M_{\bar c b}$, with suppressed rates…
A general classification of tetraquark states in terms of the spin-flavour, colour and spatial degrees of freedom has been constructed. The permutational symmetry properties of both the spin-flavour and orbital parts of the quark-quark and antiquark-antiquark subsystems are discussed in short. This classification is model indipendent and useful both for model-builders and experimentalists. An evaluation of the tetraquark spectrum is obtained from a generalization of a Iachello mass formula, originally developed for the $q\bar q$ mesons. The ground state tetraquark nonet is identified with $f_{…
A classification of tetraquark states in terms of the spin-flavour, colour and spatial degrees of freedom has been constructed. The permutational symmetry properties of both the spin-flavour and orbital parts of the quark-quark and antiquark-antiquark subsystems are briefly discussed. This classification is useful both for model-builders and experimentalists. An evaluation of the tetraquark spectrum is obtained from a Iachello mass formula for tetraquark systems. The ground state tetraquark nonet is identified with $f_{0}(600)$, $κ(800)$, $f_{0}(980)$, $a_{0}(980)$. The mass splittings predict…
Scrutinizing the scattering of ordinary mesons in the limiting case of the number of colour degrees of freedom $N_{\rm c}$ of quantum chromodynamics approaching infinity, we formulate Feynman-diagram selection criteria and from these deduce rigorous self-consistency conditions for the manifestation of a tetraquark, a two-quark-two-antiquark bound state, as a pole in the corresponding amplitudes. Our constraints bear rather far-reaching consequences: In particular, all flavour-exotic tetraquarks, composed of four (anti)quarks of disparate flavour, must come in, at least, two variants differing …
A systematic study of multiquark exotics with one or $N_c-1$ heavy quarks in the large $N_c$ limit is presented. By binding a chiral soliton to a heavy meson, either a normal $N_c$-quark baryon or an exotic $(N_c+2)$-quark baryon is obtained. By replacing the heavy quark with $N_c-1$ heavy antiquarks, exotic $(2N_c-2)$-quark and $2N_c$-quark mesons are obtained. When $N_c = 3$, they are just the normal triquark baryon $Qqq$, the exotic pentaquark baryon $Q\bar q\bar q\bar q\bar q$, tetraquark di-meson $\bar Q \bar Q qq$ and the hexaquark di-baryon $\bar Q \bar Q \bar q \bar q\ bar q \bar q$ re…
We study details of QCD sum rules à la Shifman-Vainshtein-Zakharov for exotic tetraquark states. We point out that duality relations for correlators involving exotic currents have fundamental differences compared with the duality relations for the correlators of bilinear quark currents: namely, the $O(1)$ and $O(α_s)$ [$α_s$ the strong coupling constant] terms in the operator product expansion for the exotic correlators exactly cancel against the contributions of the two-meson states on the hadron side of QCD sum rules. As a result, the tetraquark properties turn out to be related to the speci…
We study a QCD sum rule analysis for an exotic tetraquark ud bar[s] bar[s] of J^P=0^+ and I = 1. We construct q q bar[q] bar[q] currents in a local product form and find that there are five independent currents for this channel. Due to high dimensional nature of the current, it is not easy to form a good sum rule when using a single current. This means that we do not find any sum rule window to extract reliable results, due to the insufficient convergence of the OPE and to the exceptional important role of QCD continuum. Then we examine sum rules by using currents of linear combinations of two…
We embark on systematic explorations of the behaviour of tetraquark mesons (colour-singlet bound states of two quarks and two antiquarks) in the (idealized) limit of a large number $N_c$ of colour degrees of freedom of quantum chromodynamics. Considering the scattering of two ordinary mesons into two ordinary mesons, we start off with formulating a set of selection criteria that should enable us to unambiguously single out precisely those contributions to all encountered scattering amplitudes that potentially will develop tetraquark poles. Assuming that tetraquark mesons do exist and, if so, e…
The analysis of two-ordinary-meson scattering amplitudes in the limit of a large number $N_{\rm c}$ of the colour degrees of freedom of quantum chromodynamics, with suitably decreasing strong coupling and all quarks transforming according to the gauge group's fundamental representation, enables us to establish a set of rigorous consistency conditions for the emergence of a tetraquark (i.e., a bound state of two quarks and two antiquarks) as a pole in these amplitudes. For genuinely flavour-exotic tetraquarks, these constraints require the existence of two tetraquark states distinguishable by t…
Considering quantum chromodynamics in the consistent limit of simultaneous correlated increase of the number of colours, $N_{\rm c}$, beyond bounds and decrease of the strong coupling to zero allows for solid statements about qualitative features of the class of "truly exotic" tetraquark mesons carrying four mutually distinct quark flavours. Consistency criteria extracted from correlation functions for two-ordinary-meson scattering suggest the existence of more than one such tetraquarks, at least, of two tetraquarks of identical quark-flavour content and large-$N_{\rm c}$ behaviour of the tota…
We discuss the specific features of extracting properties of the exotic polyquark hadrons (tetraquarks, pentaquarks) compared to the usual hadrons by the QCD sum-rule approach. In the case of the ordinary hadrons, already the one-loop leading-order correlation functions provide the bulk of the hadron observables, e.g., of the form factor; inclusion of radiative corrections modifies already nonzero one-loop contributions. In the case of an exotic hadron, the situation is qualitatively different: discussing strong decays of an exotic tetraquark meson, which provide the main contribution to its w…
In the framework of the color-magnetic interaction, we systematically investigate the mass splittings of the $QQ\bar{Q}\bar{q}$ tetraquark states and estimated their rough masses in this work. These systems include the explicitly exotic states $cc\bar{b}\bar{q}$ and $bb\bar{c}\bar{q}$ and the hidden exotic states $cc\bar{c}\bar{q}$, $cb\bar{b}\bar{q}$, $bc\bar{c}\bar{q}$, and $bb\bar{b}\bar{q}$. If a state around the estimated mass region could be observed, its nature as a genuine tetraquark is favored. The strong decay patterns shown here will be helpful to the experimental search for these e…
We investigate the widths of the recently observed charmonium like resonances X(3872), Z(4430) and Z_2(4250) using QCD sum rules. Extending previous analyses regarding these states as diquark-antiquark states or molecules of D mesons, we introduce the Breit-Wigner function in the pole term. We find that introducing the width increases the mass at small Borel window region. Using the OPE up to dimension eight, we find that the sum rules based on interpolating current with molecular components give a stable Borel curve from which both the masses and widths of these resonances can be well obtaine…
We use the twist dimensions of the operators underlying the dynamical behavior of exclusive production processes as a tool for determining the structure of exotic heavy-quark states such as the $Z_c^+(4430)$ tetraquark. The resulting counting rules predict distinctive fall-offs of the cross sections in center-of-mass energy, thus distinguishing whether the tetraquarks are segregated into di-meson molecules, diquark-antidiquark pairs, or more democratically arranged four-quark states. In addition, we propose straightforward methods of experimentally producing additional exotic multiquark states…
Spectrum of the low-lying hidden- and double-charm tetraquark states are investigated in a nonrelativistic quark potential model, where the Instanton-induced interaction is taken as the residual spin-dependent hyperfine interaction between quarks. The model parameters are fixed by fitting the spectrum of the ground hadron states. Our numerical results show that masses of several presently studied tetraquark states are close to those of the experimentally observed candidates of exotic meson, which indicates that the corresponding compact tetraquark components may take considerable probabilities…
It is shown that the large $N_c$ limit of QCD with quarks in the two-index antisymmetric color representation [QCD(AS)] has narrow tetraquark states with exotic flavor quantum numbers. They decay into mesons with a width that is parametrically $O(1/N_c^2)$. Tetraquarks with non-exotic quantum numbers mix at leading order with mesons of the same overall quantum numbers. QCD(AS) at $N_c=3$ corresponds to ordinary QCD; its large $N_c$ limit represents an alternative starting point for a $1/N_c$ expansion to the standard one with quarks in the fundamental color representation.
We investigate the production of exotic tetraquarks, $QQ\bar{q}\bar{q} \equiv T_{QQ}$ ($Q=c$ or $b$ and $q=u$ or $d$), in relativistic heavy-ion collisions using the quark coalescence model. The $T_{QQ}$ yield is given by the overlap of the density matrix of the constituents in the emission source with the Wigner function of the produced tetraquark. The tetraquark wave function is obtained from exact solutions of the four-body problem using realistic constituent models. The production yields are typically one order of magnitude smaller than previous estimations based on simplified wave functio…
A complete classification of $qq \bar q \bar q$ tetraquark states in terms of the spin-flavour, colour and spatial degrees of freedom has been constructed. The permutational symmetry properties of both the spin-flavour and orbital parts of the $qq$ and $\bar{q}\bar{q}$ subsystems are discussed. This complete classification is general and model independent and it is useful both for model builders and experimentalists. The total wave functions are also explicitly constructed in the hypothesis of ideal mixing; this basis for tetraquark states will enable the eigenvalue problem to be solved for a …
We formulate rigorous criteria for selecting diagrams to be taken into account in the analysis of potential polyquark (tetra or penta) poles in QCD. The central point of these criteria is the requirement that the Feynman diagrams for the relevant Green functions contain four-quark (or, respectively, five-quark in the pentaquark case) intermediate states and the corresponding cuts. It is shown that some diagrams which "visually" seem to contain the four-quark cuts, turn out to be free of these singularities and therefore should not be taken into account when calculating the tetraquark propertie…
We present a general class of operators resembling compact tetraquarks which have a range of colour-flavour-spin structures, transform irreducibly under the symmetries of the lattice and respect other relevant symmetries. These constructions are demonstrated in lattice QCD calculations with light quarks corresponding to $m_π=$ 391 MeV. Using the distillation framework, correlation functions involving large bases of meson-meson and tetraquark operators are computed in the isospin-1 hidden-charm and doubly-charmed sectors, and finite-volume spectra are extracted with the variational method. We f…
We propose a new interpretation of the neutral and charged X, Z exotic hadron resonances. Hybridized-tetraquarks are neither purely compact tetraquark states nor bound or loosely bound molecules. The latter would require a negative or zero binding energy whose counterpart in h-tetraquarks is a positive quantity. The formation mechanism of this new class of hadrons is inspired by that of Feshbach metastable states in atomic physics. The recent claim of an exotic resonance in the Bs pi+- channel by the D0 collaboration and the negative result presented subsequently by the LHCb collaboration are …
We study the possible exotic states with $J^{PC} = 0^{+-}$ using the tetraquark interpolating currents with the QCD sum rule approach. The extracted masses are around 4.85 GeV for the charmonium-like states and 11.25 GeV for the bottomomium-like states. There is no working region for the light tetraquark currents, which implies the light $0^{+-}$ state may not exist below 2 GeV.
Highlights in the search for nonconventional (non qqbar) meson states are the pi_1(1400) and pi_1(1600) exotic candidates. Should they exist, mounting theoretical arguments suggest that they are tetraquark molecular resonances excitable by meson rescattering. We report a new tetraquark calculation within a model field theory approximation to Quantum Chromodynamics in the Coulomb gauge supporting this conjecture. We also strengthen this claim by consistently contrasting results with exotic state predictions for hybrid (q qbar g) mesons within the same theoretical framework. Our findings confirm…
During recent years, the study of exotic hadrons including tetraquarks and pentaquarks has attracted a lot of interests and more studies are in progress experimentally and theoretically. It is well-known that at sufficiently large transverse momentum the dominant production mechanism for standard heavy hadrons (mesons/baryons) is actually the fragmentation so that the same mechanism is also proposed for the production of heavy exotic hadrons. This work is the first attempt to study the direct fragmentation of a heavy quark into ground state heavy tetraquarks in leading order of perturbative QC…
The molecular picture and the constituent-quark model of exotic hadrons are reviewed, with application to the states recently discovered in the hidden-charm and hidden beauty sectors, and to other configurations.
We apply the method of QCD sum rules to study the $s q \bar s \bar q$ tetraquark states with the exotic quantum number $J^{PC} = 3^{-+}$, and extract mass of the lowest-lying state to be $2.33^{+0.19}_{-0.16}$ GeV. To construct the relevant tetraquark currents we need to explicitly add the covariant derivative operator. Our systematical analysis on their relevant interpolating currents indicates that: a) this state well decays into the $P$-wave $ρϕ/ωϕ$ channel but not into the $ρf_2(1525)/ωf_2(1525)/ϕf_2(1270)$ channels, and b) it well decays into the $K^*(892) \bar K_2^*(1430)$ channel but no…
The LHCb Collaboration has reported resonant activity in the channel $D^+ K^-$, identifying two components: $X_0(2900)$ with $J^P = 0^+$ at $2866 {\pm} 7$ MeV, $Γ_0=57{\pm} 13$ MeV and $X_1(2900)$ with $J^P = 1^-$ at $2904 {\pm} 7$ MeV, $Γ_1=110{\pm} 12$ MeV. We interpret the $X_0(2900)$ component as a $cs \bar u\bar d$ isosinglet compact tetraquark, calculating its mass to be $2863 {\pm} 12$ MeV. This is the first exotic hadron with open heavy flavor. The analogous $bs\bar u\bar d$ tetraquark is predicted at $6213 {\pm} 12$ MeV. We discuss possible interpretations of the heavier and wider $X_…
We investigate the chiral (flavor) structure of tetraquarks, and study chiral transformation properties of the "non-exotic" [(3_bar,3)+(3,3_bar)] and [(8,1)+(1,8)] tetraquark chiral multiplets. We find that as long as this kind of tetraquark states contains one quark and one antiquark having the same chirality, such as (q_L q_L \bar q_L \bar q_R + q_R q_R \bar q_R \bar q_L), they transform in the same way as the lowest level (\bar q q) chiral multiplets under chiral transformations. There is only one [(3_bar,3)+(3,3_bar)] chiral multiplet whose quark-antiquark pairs all have the opposite chira…
The relativistic four-quark equations are found in the framework of coupled-channel formalism. The dynamical mixing of the meson-meson states with the four-quark states is considered. The approximate solutions of these equations using the method based on the extraction of leading singularities of the amplitudes are obtained. The four-quark amplitudes of cryptoexotic mesons including the quarks of three flavours (u, d, s) and the charmed quark are constructed. The poles of these amplitudes determine the masses of tetraquarks. The mass values of low-lying tetraquarks are calculated.
The Coulomb gauge Hamiltonian model is used to calculate masses for selected J^{PC} states consisting of exotic combinations of quarks and gluons: ggg glueballs (oddballs), q bar{q} g hybrid mesons and q bar{q} q bar{q} tetraquark systems. An odderon Regge trajectory is computed for the J^{--} glueballs with intercept much smaller than the pomeron, explaining its nonobservation. The lowest 1^{-+} hybrid meson mass is found to be just above 2.2 GeV while the lightest tetraquark state mass with these exotic quantum numbers is predicted around 1.4 GeV consistent with the observed pi(1400).
We discuss the production of the exotic doubly-charmed tetraquark mesons ${\rm T}_{{\rm c}{\rm c}}({\rm c}{\rm c}\bar{\rm u}\bar{\rm d})$ from electron-positron collisions. ${\rm T}_{{\rm c}{\rm c}}({\rm c}{\rm c}\bar{\rm u}\bar{\rm d})$ is a compact exotic hadron whose binding energy is provided by the diquark correlations. We evaluate the production cross section in the electron-positron collisions using the nonrelativistic QCD framework, and investigate the difference of the production cross section for different color configurations in two charm quarks (antitriplet and sextet), where the m…
Recently, a QCD sum-rule analysis of tetraquark molecular states has been published, having the objective of demonstrating that our previously formulated tetraquark-adequate QCD sum rules are not correct. This comment brings to the attention of the reader inconsistencies in that article and explains some subtle details of QCD sum rules for exotic states.
In order to explore the possible existence of the exotic $0^{--}$ state, we have constructed the tetraquark interpolating operators systematically. As a byproduct, we notice the $0^{+-}$ tetraquark operators without derivatives do not exist. The special Lorentz structure of the $0^{--}$ currents forbids the four-quark correction to the spectral density. Now the gluon condensate is the dominant power correction. Within the framework of the finite energy sum rule, none of the seven interpolating currents supports a resonant signal. Therefore we conclude that the exotic $0^{--}$ state does not ex…
We provide comprehensive investigations for the mass spectrum of exotic open-flavor charmed/bottom $sq\bar q\bar c$, $qq\bar q\bar c$, $sq\bar q\bar b$, $qq\bar q\bar b$ tetraquark states with various spin-parity assignments $J^P=0^+, 1^+, 2^+$ and $0^-, 1^-$ in the framework of QCD sum rules. In the diquark configuration, we construct the diquark-antidiquark interpolating tetraquark currents using the color-antisymmetric scalar and axial-vector diquark fields. The stable mass sum rules are established in reasonable parameter working ranges, which are used to give reliable mass predictions for…
We perform an $n_f=2+1$ lattice study of a number of channels where past claims exist in the literature for the existence of strong-interaction-stable light-heavy tetraquarks. We find no evidence for any such deeply-bound states, beyond the $J^P=1^+$, $I=0$ $ud\bar{b}\bar{b}$ and $I=1/2$ $ls\bar{b}\bar{b}$ states already identified in earlier lattice studies. We also describe a number of systematic improvements to our previous lattice studies, including working with larger $m_πL$ to better suppress possible finite volume effects, employing extended sinks to better control excited-state contami…
We provide a holographic description of non-strange multiquark exotics as compact topological molecules by binding heavy-light mesons to a tunneling configuration in D8-D$\bar 8$ that is homotopic to the vacuum state with fixed Chern-Simons number. In the tunneling process, the heavy-light mesons transmute to fermions. Their binding is generic and arises from a trade-off between the dipole attraction induced by the Chern-Simons term and the U(1) fermionic repulsion. In the heavy quark limit, the open-flavor tetraquark exotics $QQ\bar q\bar q$ and $\bar Q\bar Q qq$, emerge as bound Efimov state…
In this work, a color structure dependent flip-flop potential is developed for the two quarks and two antiquarks system. Then, this potential is applied to a microscopic quark model which, by integrating the internal degrees of freedom, is transformed into a model of mesons with non-local interactions. With this, the T matrix for the system is constructed and meson-meson scattering is studied. Tetraquarks states, interpreted as poles of of the T matrix, both bound states and resonances, are found. Special emphasis is given to the truly exotic $qq\bar{Q}\bar{Q}$ system, but some results for the…
Weinberg recently pointed out a flaw in the standard argument that large $N_c$ QCD with color-fundamental quarks [QCD(F)] cannot yield narrow tetraquark states. In particular, he observed that the argument does not rule out narrow tetraquarks associated with the leading-order connected diagrams; such tetraquarks would have a width scaling as $N_c^{-1}$. It is shown here, however, that while the standard analysis of tetraquarks does not rule them out, a more thorough analysis rules out quantum-number exotic tetraquarks associated with the leading-order connected diagrams. This analysis is based…
Structure and production of doubly charmed tetraquarks T_cc (cc ubar dbar) are studied from the viewpoint of color configurations. Based on the diquark correlation, the tetraquark T_cc with I(JP)=0(1+) is considered to be stable against strong decay. We discuss that the mixing probability of color antitriplet and sextet cc components in T_cc is suppressed by 1/m_c^2, so the two configurations are separately realized in the heavy quark limit. Utilizing the nonrelativistic QCD framework, we evaluate the production cross sections of T_cc in electron-positron collisions. The momentum dependence of…
A menage a trois is very different from an ordinary family. Similarly, exotic hadrons with both qq and qbar q pairs have important color-space correlations that are completely absent in ordinary mesons and baryons. The presence of both types of pairs requires attention to the basic QCD physics that the q qbar interaction is much stronger than the qq interaction. This new physics in multiquark systems produces color structures totally different from those of normal hadrons, for example the ud system is utterly unlike the ud diquark in the uds Lambda baryon. The color-space correlations produce …
We study the exotic $bc\bar{q}\bar{q}$, $bc\bar{s}\bar{s}$ and $qc\bar{q}\bar{b}$, $sc\bar{s}\bar{b}$ systems by constructing the corresponding tetraquark currents with $J^P=0^+$ and $1^+$. After investigating the two-point correlation functions and the spectral densities, we perform QCD sum rule analysis and extract the masses of these open-flavor tetraquark states. Our results indicate that the masses of both the scalar and axial vector tetraquark states are about $7.1-7.2$ GeV for the $bc\bar{q}\bar{q}$ system and $7.2-7.3$ GeV for the $bc\bar{s}\bar{s}$ system. For the $qc\bar{q}\bar{b}$ t…
We consider the interplay of the pentaquark states and strange tetraquark states in the decay $Λ^0_b\to K^-J/ψp$. Possible existence of ($cs\bar c\bar u$)-states is taken up and their manifestation in the $K^-J/ψ$-channel is discussed. It is emphasised that these exotic mesons can imitate broad bumps in the in the $pJ/ψ$-channel.
This paper focuses on tetraquarks containing two heavy quarks in the formal limit where the heavy quark masses are taken to be arbitrarily large. There are well-established model-independent arguments for the existence of deeply bound exotic $\bar{q}\bar{q}'QQ$ tetraquark in the formal limit of arbitrarily large heavy quark masses. However, these previous arguments did not address the question whether tetraquark states exist close to the threshold for breaking up into two heavy mesons. Such states are not stable under strong interactions---they can emit pions and decay to lower-lying tetraquar…
Inclusive production cross sections of the possible exotic state X(3872) in proton-proton, pionp-roton and proton-antiproton collisions are calculated using a statistical based model, which is previously used to describe inclusive charmed and bottomed hadron production cross sections in the low energy region. With the extensions made here, the model is capable to include tetraquarks as well, using the diquark picture of tetraquarks. The evaluated cross section ratio of $Ψ(2S)$ and $X(3872)$ at $\sqrt{s}=7$ TeV agrees well with the measured value.
A flavour gauge theory is observable only if the symmetry is broken at relatively low energies. The intrinsic parity-violation of the fermion representations in a flavour theory describing quark, lepton and higgsino masses and mixings generically requires anomaly cancellation by new fermions. Benchmark supersymmetric flavour models are built and studied to argue that: i) the flavour symmetry breaking should be about three orders of magnitude above the higgsino mass, enough also to efficiently suppress FCNC and CP violations coming from higher-dimensional operators; ii) new fermions with exotic…
Some hadrons have the exotic quantum numbers that the traditional $\bar q q$ mesons and $qqq$ baryons can not reach, such as $J^{PC} = 0^{--}/0^{+-}/1^{-+}/2^{+-}/3^{-+}/4^{+-}$, etc. We investigate for the first time the exotic quantum number $J^{PC}=4^{+-}$, and study the fully-strange tetraquark states with such an exotic quantum number. We systematically construct all the diquark-antidiquark interpolating currents, and apply the method of QCD sum rules to calculate both the diagonal and off-diagonal correlation functions. The obtained results are used to construct three mixing currents tha…
