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The present work reviews the various aspects of the extension of the large-$N_c$ approach, as had been proposed and developed by 't Hooft, to the case of tetraquark states, which are a category of the general class of exotic states, also called multiquark states, whose internal valence-quark structure does not match with that of ordinary hadrons, and which have received, in recent years, many experimental confirmations. The primary question of describing, or probing, on theoretical grounds, multiquark states is first examined. The signature of such states inside Feynman diagrams in relation with their singularities is highlighted. The main mechanisms of formation of tetraquark states, provided by the diquark model and the molecular scheme, are considered together with their specific implications. The properties of tetraquark states at large $N_c$ are analyzed through the Feynman diagrams that describe two-meson scattering amplitudes. It turns out that, in that limit, the possible formation of tetraquark states is mainly due to the mutual interactions of their internal mesonic clusters. These essentially arise from the quark-rearrangement, or quark-interchange, mechanism. In coupled-channel meson-meson scattering amplitudes, one may expect the occurrence of two independent tetraquark states, each having priviledged couplings with the two mesons of their dominant channel. The question of the energy balance of various schemes in the static limit is also analyzed. The clarification of the mechanisms that are at work in the formation of tetraquarks is the main outcome from the large-$N_c$ approach to this problem., Comment: 132 pages, 53 figures. Review article. v2: Sections 2.7 and 5.4 have been slightly extended; a few clarifying comments have been added in other sections; figure 43 has been completed; references have been added

International audience; Considering quantum chromodynamics in the consistent limit of simultaneous correlated increase of the number of colours, $N_c$, 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-$N_c$ behaviour of the total decay widths but differing in, and hence discriminable by, their predominant decay modes into two conventional mesons. This pairwise appearance is in conflict with the unique variant of such a four-quark bound state arising from the binding of diquark and antidiquark to a tetraquark by the strong interactions.

Despite recent developments, there are a number of conceptual issues on the hadronic light-by-light (HLbL) contribution to the muon (g−2) which remain unresolved. One of the most controversial ones is the precise way in which short-distance constraints get saturated by resonance exchange, particularly in the so-called Melnikov-Vainshtein limit. In this paper we address this and related issues from a novel perspective, employing a warped five-dimensional model as a tool to generate a consistent realization of QCD in the large-Nc limit. This approach differs from previous ones in that we can work at the level of an effective action, which guarantees that unitarity is preserved and the chiral anomaly is consistently implemented at the hadronic level. We use the model to evaluate the inclusive contribution of Goldstone modes and axial-vector mesons to the HLbL. We find that both anomaly matching and the Melnikov-Vainshtein constraint cannot be fulfilled with a finite number of resonances (including the pion) and instead require an infinite number of axial-vector states. Our numbers for the HLbL point at a non-negligible role of axial-vector mesons, which is closely linked to a correct implementation of QCD short-distance constraints.

Parton showers are among the most widely used tools in collider physics. Despite their key importance, none so far has been able to demonstrate accuracy beyond a basic level known as leading logarithmic (LL) order, with ensuing limitations across a broad spectrum of physics applications. In this letter, we propose criteria for showers to be considered next-to-leading logarithmic (NLL) accurate. We then introduce new classes of shower, for final-state radiation, that satisfy the main elements of these criteria in the widely used large-$N_C$ limit. As a proof of concept, we demonstrate these showers' agreement with all-order analytical NLL calculations for a range of observables, something never so far achieved for any parton shower., 6 pages, 2 figures, plus supplemental material; v2 brings extra references and clarifications, as accepted by Physical Review Letters

Despite recent developments, there are a number of conceptual issues on the hadronic light-by-light (HLbL) contribution to the muon $(g-2)$ which remain unresolved. One of the most controversial ones is the precise way in which short-distance constraints get saturated by resonance exchange, particularly in the so-called Melnikov-Vainshtein (MV) limit. In this paper we address this and related issues from a novel perspective, employing a warped five-dimensional model as a tool to generate a consistent realization of QCD in the large-$N_c$ limit. This approach differs from previous ones in that we can work at the level of an effective action, which guarantees that unitarity is preserved and the chiral anomaly is consistently implemented at the hadronic level. We use the model to evaluate the inclusive contribution of Goldstone modes and axial-vector mesons to the HLbL. We find that both anomaly matching and the MV constraint cannot be fulfilled with a finite number of resonances (including the pion) and instead require an infinite number of axial-vector states. Our numbers for the HLbL point at a non-negligible role of axial-vector mesons, which is closely linked to a correct implementation of QCD short-distance constraints., 22 pages, 10 figures. One added figure (Fig. 10) and improvements in Figs. 7,8 and 9. This version matches the published one

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., 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)

International audience; 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.

Physics letters / B B 802, 135217 - (2020). doi:10.1016/j.physletb.2020.135217, Recently, the Belle Collaboration has updated the analysis of the cross sections for the processes e+e−→ϒ(nS)π+π− ( n=1,2,3 ) in the e+e− center-of-mass energy range from 10.52 to 11.02 GeV. A new structure, called here Yb(10750) , with the mass M(Yb)=(10752.7±5.9−1.1+0.7) MeV and the Breit-Wigner width Γ(Yb)=(35.5−11.3−3.3+17.6+3.9) MeV was observed [1] . We interpret Yb(10750) as a compact JPC=1−− state with a dominant tetraquark component. The mass eigenstate Yb(10750) is treated as a linear combination of the diquark-antidiquark and bb¯ components due to the mixing via gluonic exchanges shown recently to arise in the limit of large number of quark colors. The mixing angle between Yb and ϒ(5S) can be estimated from the electronic width, recently determined to be Γee(Yb)=(13.7±1.8) eV. The mixing provides a plausible mechanism for Yb(10750) production in high energy collisions from its bb¯ component and we work out the Drell-Yan and prompt production cross sections for pp→Yb(10750)→ϒ(nS)π+π− at the LHC. The resonant part of the dipion invariant mass spectrum in Yb(10750)→ϒ(1S)π+π− and the corresponding angular distribution of π+ -meson in the dipion rest frame are presented as an example., Published by North-Holland Publ., Amsterdam

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 $T_A\to M_{\bar a d}M_{\bar c b}$ and $T_B\to M_{\bar a b}M_{\bar c d}$. On the other hand, we have at hand only one diquark-antidiquark flavor structure $(\bar a \bar c)(b d)$ that might produce a compact tetraquark bound state. Taking into account that the diquark-antidiquark structure is the only viable candidate for a compact tetraquark state, one concludes that it is impossible to have two different narrow tetraquarks decaying dominantly into different two-meson channels. This contradiction suggests that large-$N_c$ QCD does not support the existence of narrow flavor-exotic tetraquarks. This argument does not rule out the possible existence of broad molecular-type flavor-exotic states, or of molecular-type bound states lying very close to the two-meson thresholds., 8 pages

International audience; 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 tetraquarks, already at lowest possible order in an expansion in inverse powers of the number of colours implies the existence of two types of flavour-exotic tetraquarks, distinguishable by their dominant transitions to two ordinary mesons. On the other hand, we are aware of merely a single, unique colour-singlet arrangement of two quarks and two antiquarks capable of tolerating a compact flavour-exotic tetraquark, a bound state of colour-antisymmetric diquark and antidiquark. In view of these two clearly contradictory observations, we are led to the plausible conclusion that, within the considered limiting case of quantum chromodynamics, a conceivable explanation of the riddle might consist in the non-existence of any flavour-exotic tetraquarks in formof narrowstates.

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., Comment: 5 pages, 4 figures, contributed to "QCD@Work 2018 - International Workshop on Quantum Chromodynamics: Theory and Experiment" (25 - 28 June 2018, Matera, Italy)

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, emerge in the contributions compatible with our criteria at largest admissible order of $N_c$, we deduce, for the categories of tetraquarks that exhibit either four or only two different open quark flavours, that the decay rates of these tetraquark types are, at least, of order $1/N_c^2$ and that internal consistency requires all the members of the first species to exist pairwise, distinguishable by their favoured two-ordinary-meson decay channels., 8 pages, 5 figures, talk presented at "QUARKS-2018 - XXth International Seminar on High Energy Physics" (27 May - 2 June 2018, Valday, Russia)

Following Golterman and Shamir, we develop scale-chiral perturbation theory in the large $N_c$ and large $N_f$ Veneziano limit that incorporates both light-quark baryons and hidden local symmetric bosons and derive a leading-order scale symmetry Lagrangian applicable in nuclear physics. Some applications in the medium-free space and baryonic matter are discussed., 8 pages

Physical review letters 121(23), 231602 (2018). doi:10.1103/PhysRevLett.121.231602, We propose an integrability setup for the computation of correlation functions of gauge-invariant operators in $\mathcal{N}=4$ supersymmetric Yang-Mills theory at higher orders in the large $N_c$ genus expansion and at any order in the ’t Hooft coupling $g_{YM}^{2}N_c$. In this multistep proposal, one polygonizes the string world sheet in all possible ways, hexagonalizes all resulting polygons, and sprinkles mirror particles over all hexagon junctions to obtain the full correlator. We test our integrability-based conjecture against a nonplanar four-point correlator of large 1/2 Bogomol’nyi-Prasad-Sommerfield operators at one and two loops., Published by APS, College Park, Md.

We propose an integrability setup for the computation of correlation functions of gauge-invariant operators in $\mathcal{N}=4$ supersymmetric Yang-Mills theory at higher orders in the large $N_{\text{c}}$ genus expansion and at any order in the 't Hooft coupling $g_{\text{YM}}^2N_{\text{c}}$. In this multi-step proposal, one polygonizes the string worldsheet in all possible ways, hexagonalizes all resulting polygons, and sprinkles mirror particles over all hexagon junctions to obtain the full correlator. We test our integrability-based conjecture against a non-planar four-point correlator of large half-BPS operators at one and two loops., 6 pages, 4 figures; v2: updated references, typos, minor improvements (published version)

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 two narrow flavor-exotic states, each coupling dominantly to one specific meson-meson channel., 5 pages, version to appear in PRD, minor text modifications, conclusions remain unchanged

Considering four-point correlation functions of color-singlet quark bilinears, we investigate, in the large-$N_{\mathrm{c}}$ limit of QCD, the subleading diagrams that involve, in the $s$-channel of meson-meson scattering amplitudes, two-quark--two-antiquark intermediate states. The latter contribute, together with gluon exchanges, to the formation, at the hadronic level, of two-meson and tetraquark intermediate states. It is shown that the two-meson contributions, which are predictable, in general, from leading-order $N_{\mathrm{c}}$-behaviors, consistently satisfy the constraints resulting from the $1/N_{\mathrm{c}}$ expansion procedure and thus provide a firm basis for the extraction of tetraquark properties from $N_{\mathrm{c}}$-subleading diagrams. We find that, in general, tetraquarks, if they exist in compact form, should have narrow decay widths, of the order of $N_{\mathrm{c}}^{-2}$. For the particular case of exotic tetraquarks, involving four different quark flavors, two different types of tetraquark are needed, each having a preferred decay channel, to satisfy the consistency constraints., 23 pages, 24 figures. A few clarifying paragraphs, two figures and one reference have been added

Universität Hamburg, Diss., 2006; 91 pp., (2006). doi:10.3204/DESY-THESIS-2006-034, Published by Deutsches Elektronen-Synchrotron, DESY, Hamburg

Physical review / D 60(1), 014010 (1999). doi:10.1103/PhysRevD.60.014010, The amplitude for hard exclusive pseudoscalar meson electroproduction off nucleon (nuclear) targets is computed in QCD within the leading $\alpha_s \ln {Q^2/\lambda_{QCD}^{2}}$ approximation. We show that the distribution of recoil nucleons depends strongly on the angle between the momentum of the recoil nucleon and the polarization vector of the target (or outgoing nucleon). This dependence is especially sensitive to the spin flip skewed parton distribution (SPD) $\widetilde E$. We argue also that the scaling for this spin asymmetry sets in at lower Q^2 than that for the absolute cross section. Basing on the chiral quark-soliton model of the nucleon we estimate quantitatively the spin asymmetry. In the case of pi+ production this asymmetry is dominated at small t by the contribution of the pion pole in the isovector SPD $\widetilde E$ as required by PCAC. In the case of K0 production off a proton we find a large enhancement of the cross section as compared to the case of pi0 production. For the forward production of neutral pseudoscalar mesons off a deuteron target we find the cross section should be zero for the zero deuteron helicity (along the $\gamma^*D$ direction). We consider also cross sections of quasielastic processes off nuclei including the feasibility to implant K+,rho-mesons into nuclear volume., Published by Inst., Woodbury, NY

We employ the recently improved description of dense baryonic matter within the Witten-Sakai-Sugimoto model to construct neutron stars. In contrast to previous holographic approaches, the presence of an isospin asymmetry allows us to implement beta equilibrium and electric charge neutrality. As a consequence, we are able to model the crust of the star within the same formalism and compute the location of the crust-core transition dynamically. After showing that a simple pointlike approximation for the baryons fails to satisfy astrophysical constraints, we demonstrate that our improved description does account for neutron stars that meet the current experimental constraints for mass, radius, and tidal deformability. However, we also point out tensions in the parameter fit and large-$N_c$ artifacts and discuss how to potentially resolve them in the future., 19 pages, 12 figures; v2: small correction in Table I, reference added, accepted for publication in PRD; v3: typos in last line of p7 and equation (34b) corrected