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Hagop Sazdjian

Publications and source records attributed to Hagop Sazdjian.

36 records · Page 2Linked to original sources
arXiv2019

Tetraquark-Adequate QCD Sum Rules

With the experimental observation of several credible candidates for multiquark hadrons, the latter states re-entered the focus of interest of theoretical strong-interaction physics. Proper treatment of hadronic bound states by quantum chromodynamics, QCD, the quantum field theory governing all strong interactions, necessitates a nonperturbative approach. A well-established framework of this kind is provided by QCD sum rules relating hadron features to the parameters of QCD. Conceptual reconsideration, however, reveals that, in order to really match the peculiarities of multiquarks, the long-standing conventional QCD sum-rule techniques evidently must be subjected to considerable modification. The so far overlooked necessity for such adaptations is most easily demonstrated for the case of least complexity, that is, for tetraquarks, bound states of two quarks and two antiquarks.

hep-ph↗
arXiv2019

Tetraquark-adequate formulation of QCD sum rules

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 specific non-factorizable parts of the exotic Green functions; the relevant non-factorizable diagrams start at order $O(α_s^2)$.

hep-ph↗
arXiv2018

Large-$N_c$ QCD and tetraquarks

Tetraquark properties are examined in the limit of large $N_c$ of color in QCD. The qualitative differences between molecular and compact tetraquarks are outlined. Consequences of the possible existence of compact tetraquarks are analyzed and shown to lead to upper bounds in the $N_c$-behavior of their decay widths. Open questions on theoretical grounds, related to the dynamics of systems composed of two quarks and two antiquarks, are addressed.

hep-ph↗
arXiv2018

Compact Flavour-Exotic Tetraquarks in Large-${N_{\rm c}}$ QCD - To Be or Not to Be?

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 form of narrow states.

hep-ph↗
arXiv2018

Are there narrow flavor-exotic tetraquarks in large-$N_c$ QCD?

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.

hep-ph↗
arXiv2018

Compact Exotic Tetraquark Mesons in Large-$N_c$ QCD

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.

hep-ph↗
arXiv2017

Tetraquark and two-meson states at large $N_{\mathrm{c}}$

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.

hep-ph↗
arXiv2017

Narrow-width tetraquarks in large-$N_{\mathrm{c}}^{}$ QCD

The properties of possibly existing tetraquarks are studied in the large-$N_{\mathrm{c}}^{}$ limit of QCD by means of four-point correlation functions of meson currents.The necessity of a detailed analysis of the singularities of Feynman diagrams, by means of the Landau equations, to recognize those diagrams that might contribute to the formation of tetraquark states, is emphasized. It is found, in general, that tetraquarks, if they exist, should have narrow widths of the order of $N_{\mathrm{c}}^{-2}$.

hep-ph↗
arXiv2017

Constraints from the $1/N_{\rm c}$ Expansion on Properties of Exotic Tetraquark Mesons

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 in (and thus readily identifiable by) the large-$N_{\rm c}$ behaviour of their couplings to two ordinary mesons. Quite generally, irrespective of their flavour composition, all tetraquarks prove to be narrow. Their decay rates behave, for large $N_{\rm c},$ like $1/N_{\rm c}^2$ and thus decrease faster than those of ordinary mesons.

hep-ph↗
arXiv2017

Exotic states and their properties from large-$N_{\rm c}$ QCD

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 their preferred couplings to two ordinary mesons, whereas, for cryptoexotic tetraquarks, our constraints may be satisfied by a single tetraquark state, which then, however, may mix with ordinary mesons. For elucidation of the tetraquark features, the consideration of the subleading contributions proves to be mandatory: for both variants of tetraquarks, their decay widths fall off like $1/N_{\rm c}^2$ for large $N_{\rm c}.$

hep-ph↗
arXiv2017

Narrow exotic tetraquark mesons in large-$N_c$ QCD

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.

hep-ph↗
arXiv2016

Strong Couplings of Three Mesons with Charm(ing) Involvement

We determine the strong couplings of three mesons that involve, at least, one $η_c$ or $J/ψ$ meson, within the framework of a constituent-quark model by means of relativistic dispersion formulations. For strong couplings of $J/ψ$ mesons to two charmed mesons, our approach leads to predictions roughly twice as large as those arising from QCD sum rules.

hep-ph↗
arXiv2015

Strong three-meson couplings of $J/ψ$ and $η_c$

We discuss the strong couplings $g_{PPV}$ and $g_{VVP}$ for vector ($V$) and pseudoscalar ($P$) mesons, at least one of which is a charmonium state $J/ψ$ or $η_c$. The strong couplings are obtained as residues at the poles of suitable form factors, calculated in a broad range of momentum transfers using a dispersion formulation of the relativistic constituent quark model. The form factors obtained in this approach satisfy all constraints known for these quantities in the heavy-quark limit. Our results suggest sizably higher values for the strong meson couplings than those reported in the literature from QCD sum rules.

hep-ph↗
arXiv2015

Strong Couplings of Charmed Mesons and Quarkonia

We extract the strong coupling constants of three mesons, each of which is composed of either two charm quarks or one charm quark and one light (i.e., $u$, $d$, or $s$) quark, from the matrix elements for the transitions of two of these mesons induced by appropriate quark currents within the framework of a relativistic dispersion approach to the constituent-quark picture of mesons. Among others, we also analyse the impact of the violation of the SU(3) flavour symmetry by the quark masses. In the case of mesons containing one light quark, we observe, in two respects, discrepancies between our findings and the predictions of QCD sum rules: our strong couplings exceed considerably the ones emerging from QCD sum rules, and, in our approach, the replacement of a light quark by a strange quark entails, in contrast to QCD sum rules, a reduction of the magnitudes of the strong couplings.

hep-ph↗
arXiv2009

Effective continuum threshold for vacuum-to-bound-state correlators

We formulate a new algorithm for obtaining the effective continuum threshold in vacuum-to-bound-state correlators - the basic objects for the calculation of hadron form factors in the method of light-cone sum rules in QCD. The effective continuum threshold is one of the key ingredients of the method which to a large extent determines the value of the form factor extracted from the relevant correlator. In a quantum-mechanical potential model, where the exact form factor is known, the application of our algorithm is shown to lead to a dramatic increase of the accuracy of the extracted form factor compared to the standard procedures adopted in the method of sum rules in QCD. Moreover, the application of our algorithm considerably enlarges the range of the momentum transfer where the form factor may be extracted from the correlator.

hep-ph↗
arXiv1995

There are no abnormal solutions of the Bethe$-$Salpeter equation in the static model

The four-point Green's function of static QED, where a fermion and an antifermion are located at fixed space positions, is calculated in covariant gauges. The bound state spectrum does not display any abnormal state corresponding to excitations of the relative time. The equation that was established by Mugibayashi in this model and which has abnormal solutions does not coincide with the Bethe$-$Salpeter equation. Gauge transformation from the Coulomb gauge also confirms the absence of abnormal solutions in the Bethe$-$Salpeter equation.

hep-th↗