Mesonic Currents Research Articles

QCD sum rule study on the fully strange tetraquark states of JPC = 2++

We apply the QCD sum rule method to systematically study the fully strange tetraquark states with the quantum number JPC = 2++. We construct both the diquark–antidiquark and mesonic–mesonic currents and calculate both their diagonal and off-diagonal correlation functions. Based on the obtained results, we further construct three mixing currents that are nearly non-correlated. We use one mixing current to extract the mass of the lowest-lying state to be 2.03−0.15+0.16 GeV, which can be used to explain f2(2010) as a fully strange tetraquark state of JPC = 2++. This state was observed by BESIII in the ϕϕ channel, and we propose to confirm it in the η(′)η(′) channel.

Highly excited and exotic fully-strange tetraquark states

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 that are nearly non-correlated, and we use one of them to extract the mass of the lowest-lying state to be 2.85^{+0.19}_{-0.22} GeV. We apply the Fierz rearrangement to transform this mixing current to be the combination of three meson–meson currents, and the obtained Fierz identity suggests that this state dominantly decays into the P-wave phi (1020) f_2^prime (1525) channel. This fully-strange tetraquark state of J^{PC}=4^{+-} is a purely exotic hadron to be potentially observed in future particle experiments.

Narrow-width tetraquarks in large-Nc QCD

The properties of possibly existing tetraquarks are studied in the large-Nc 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-2c.

$\rho $-Meson Form Factors in the Point Form

We present a calculation of the electromagnetic form factors of the $\rho^+$ meson. Our formalism is based on the point-form of relativistic quantum mechanics. Electron-$\rho$-meson scattering is formulated as a coupled-channel problem for a Bakamjian-Thomas mass operator, such that the dynamics of the exchanged photon is taken explicitly into account. The $\rho$-meson current is extracted from on-shell matrix elements of the optical potential of the scattering process. As a consequence of the violation of cluster separability in the Bakamjian-Thomas framework, our current includes additional, unphysical contributions, which can be separated from the physical ones uniquely. Our results for the form factors are in good agreement with other approaches.

On vector dominance

We argue that a Regge-pole modification of the VDM puts on equal footing the asymptotic behavior of electromagnetic and neutral vector meson currents.

Electroweak form factors of heavy-light mesons: A relativistic point-form approach

We present a general relativistic framework for the calculation of the electroweak structure of heavy-light mesons within constituent-quark models. To this aim the physical processes in which the structure is measured, i.e., electron-meson scattering and semileptonic weak decays, are treated in a Poincar\'e-invariant way by making use of the point form of relativistic quantum mechanics. The electromagnetic and weak meson currents are extracted from the $1\mathrm{\text{\ensuremath{-}}}\ensuremath{\gamma}$- and $1\mathrm{\text{\ensuremath{-}}}W$-exchange amplitudes that result from a Bakamjian-Thomas type mass operator for the respective systems. The covariant decomposition of these currents provides the electromagnetic and weak (transition) form factors. Problems with cluster separability, which are inherent in the Bakamjian-Thomas construction, are discussed and it is shown how to keep them under control. It is proved that the heavy-quark limit of the electroweak form factors leads to one universal function, the Isgur-Wise function, confirming that the requirements of heavy-quark symmetry are satisfied. A simple analytical expression is given for the Isgur-Wise function and its agreement with a corresponding front-form calculation is verified numerically. Electromagnetic form factors for ${B}^{\ensuremath{-}}$ and ${D}^{+}$ and weak $B\ensuremath{\rightarrow}{D}^{(*)}$ decay form factors are calculated with a simple harmonic-oscillator wave function and heavy-quark symmetry breaking due to finite masses of the heavy quarks is discussed.

Combined Analysis of ?? Meson Hadro- and Photo-production off Nucleons

The $\eta$-meson production in photon- and hadron-induced reactions, namely, $\gamma p \to p \eta$, $\pi^- p \to n \eta$, $pp \to pp\eta$, and $pn \to pn\eta$, are investigated in a combined analysis in order to learn about the relevant production mechanisms and the possible role of nucleon resonances in these reactions. We consider the nucleonic, mesonic, and nucleon resonance currents constructed within an effective Lagrangian approach and compare the results with the available data for cross sections and spin asymmetries for these reactions. We found that the reaction $\gamma p \to p \eta$ could be described well with the inclusion of the well-established $S_{11}(1535)$, $S_{11}(1650)$, $D_{13}(1520)$, and $D_{13}(1700)$ resonances, in addition to the mesonic current. Consideration of other well-established resonances in the same mass region, including the spin-5/2 resonances, $D_{15}(1675)$ and $F_{15}(1680)$, does not further improve the results qualitatively. For the reaction $\pi^- p \to n \eta$, the $P_{13}(1720)$ resonance is found to be important for reproducing the structure observed in the differential cross section data. Our model also improves the description of the reaction $NN \to NN\eta$ to a large extent compared to the earlier results by Nakayama \textit{et al.} [Phys.\ Rev.\ C \textbf{68}, 045201 (2003)]. For this reaction, we address two cases where either the $S_{11}(1535)$ or the $D_{13}$ dominates. Further improvement in the description of these reactions and the difficulty to uniquely determine the nucleon resonance parameters in the present type of analysis are discussed.

ω AND η (η') MESONS FROM NN AND ND COLLISIONS AT INTERMEDIATE ENERGIES

The production of pseudo scalar, η, η′, and vector, ω, ρ, ϕ, mesons in NN collisions at threshold-near energies is analyzed within a covariant effective meson-nucleon theory. It is shown that a good description of cross sections and angular distributions, for vector meson production, can be accomplished by considering meson and nucleon currents only, while for pseudo scalar production an inclusion of nucleon resonances is needed. The di-electron production from subsequent Dalitz decay of the produced mesons, η′ → γγ* → γe+e- and ω → πγ* → πe+e- is also considered and numerical results are presented for intermediate energies and kinematics of possible experiments with HADES, CLAS and KEK-PS. We argue that the transition form factor ω → γ*π as well as η′ → γ*γ can be defined in a fairly model independent way and the feasibility of an experimental access to transition form factors is discussed.

He6 β-decay rate and the suppression of the axial constant in nuclear matter

We present a microscopic calculation of the $^{6}\mathrm{He} \ensuremath{\beta}$-decay into the ground state of $^{6}\mathrm{Li}$. To this end, we use chiral perturbation theory at next-to-next-to-next-to-leading order to describe the nuclear weak-currents. The nuclear wave functions are derived from the $J$-matrix inverse scattering nucleon-nucleon potential (JISP), and the Schr\"odinger equation is solved using the hyperspherical-harmonics expansion. Our calculation brings the theoretical decay-rate within $3%$ of the measured one. This success is attributed to the use of chiral perturbation theory based mesonic currents, whose contribution is qualitatively different compared to the standard nuclear physics approach, where the use of meson exchange currents worsens the comparison to experiment. The inherent inconsistency in the use of the JISP potential together with chiral perturbation theory based is argued not to affect this conclusion, though a more detailed investigation is called for. We conclude that any suppression of the axial constant in nuclear matter is included in this description of the weak interaction in the nucleus.

η′ meson production in nucleon-nucleon collisions near the threshold

The production of η′ mesons in the reactions pp → ppη′ and pn → pnη′ at threshold-near energies is analyzed within a covariant effective meson-nucleon theory. The description of cross-section and angular distributions of the available data in this kinematical region in the pp channel is accomplished by including meson currents and nucleon currents with the resonances S 11(1650), P 11(1710) and P 13(1720). Predictions for the pn channel are given. The di-electron production from subsequent η′ Dalitz decay η′ → γγ * → γe + e − is also calculated and numerical results are presented for intermediate energy and kinematics of possible experiments with HADES, CLAS and KEK-PS.

Chromomagnetic stability of the CFL phase with a meson current

We show that the color-flavor locked (CFL) phase of dense quark matter is unstable with respect to the formation of a Goldstone boson current in the vicinity of the point m s 2 = 2 μ Δ . In this Goldstone boson current phase all components of the magnetic screening mass are real.

Meson current in the color-flavor-locked phase

We study the stability of the color-flavor-locked (CFL) phase of dense quark matter with regard to the formation of a nonzero Goldstone boson current. We show that an instability appears in the vicinity of the point ${\ensuremath{\mu}}_{s}=\ensuremath{\Delta}$ which marks the appearance of gapless fermion modes in the CFL phase. Here, ${\ensuremath{\mu}}_{s}={m}_{s}^{2}/(2\ensuremath{\mu})$ is the shift in chemical potential due to the strange quark mass and $\ensuremath{\Delta}$ is the gap in the chiral limit. We show that in the Goldstone boson current phase all components of the magnetic screening mass are real. In this work we do not take into account homogeneous kaon condensation. We study the effects of an instanton induced interaction of the magnitude required to suppress kaon condensation.

Meson Supercurrent State in High-Density QCD

The ground state of three flavor quark matter at asymptotically large density is believed to be the color-flavor-locked (CFL) phase. At nonasymptotic density the effect of the nonzero strange quark mass cannot be neglected. If the strange quark mass exceeds m(s) approximately m(u)(1/3)delta(2/3), the CFL state becomes unstable toward the formation of a neutral kaon condensate. Recently, several authors discovered that for m(s) approximately (2deltap(F))(1/2) the CFL state contains gapless fermions, and that the gapless modes lead to an instability in current-current correlation functions. Using an effective theory of the CFL state, we demonstrate that this instability can be resolved by the formation of a meson supercurrent, analogous to Migdal's p-wave pion condensate. This state has a nonzero meson current that is canceled by a backflow of gapless fermions.

Selection rules forJPCexotic hybrid meson decay in largeNc

The coupling of a neutral hybrid {1,3,5...}^-+ exotic particle (or current) to two neutral (hybrid) meson particles with the same J^PC and J=0 is proved to be sub-leading to the usual large-N_c QCD counting. The coupling of the same exotic particle to certain two - (hybrid) meson currents with the same J^PC and J=0 is also sub-leading. The decay of a {1,3,5...}^-+ hybrid to eta pi^0, eta' pi^0, eta' eta, eta(1295) pi^0, pi(1300)^0 pi0, eta(1440) pi^0, a_0(980)^0 sigma or f_0(980) sigma is sub-leading, assuming that these final state particles are (hybrid) mesons in the limit of large N_c.

Consistent analysis of the reactionsγp→pη′andpp→ppη′

The production of ${\ensuremath{\eta}}^{\ensuremath{'}}$ mesons in the reactions $\ensuremath{\gamma}p\ensuremath{\rightarrow}p{\ensuremath{\eta}}^{\ensuremath{'}}$ and $pp\ensuremath{\rightarrow}pp{\ensuremath{\eta}}^{\ensuremath{'}}$ is described consistently within a relativistic meson exchange model of hadronic interactions. The photoproduction can be described quite well over the entire energy range of available data by considering an ${S}_{11}$ and a ${P}_{11}$ resonance, in addition to the $t$-channel mesonic current. The observed angular distribution is due to the interference between the $t$-channel and the nucleon resonance $s$- and $u$-channel contributions. Our analysis yields positions close to $1650\phantom{\rule{0.3em}{0ex}}\text{MeV}$ and $1870\phantom{\rule{0.3em}{0ex}}\text{MeV}$ for the ${S}_{11}$ and ${P}_{11}$ resonances, respectively. We argue that, at present, identifying these states with the known ${S}_{11}(1650)$ resonance and the missing ${P}_{11}$ resonance predicted at $1880\phantom{\rule{0.3em}{0ex}}\text{MeV}$, respectively, would be premature. It is found that the nucleonic current is relatively small and that the $NN{\ensuremath{\eta}}^{\ensuremath{'}}$ coupling constant cannot be much larger than ${g}_{NN{\ensuremath{\eta}}^{\ensuremath{'}}}=3$. As for the $pp\ensuremath{\rightarrow}pp{\ensuremath{\eta}}^{\ensuremath{'}}$ reaction, different current contributions are constrained by a combined analysis of this and the photoproduction reaction. Difficulties to simultaneously account for the $47\phantom{\rule{0.3em}{0ex}}\text{MeV}$ and $144\phantom{\rule{0.3em}{0ex}}\text{MeV}$ angular distributions measured by the COSY-11 and DISTO collaborations, respectively, are addressed.

Form factors in the [formula omitted] vertex

The J/ψDD form factor is evaluated in a QCD sum rule calculation for both D and J ψ off-shell mesons. We study the double Borel sum rule for the three point function of two pseudoscalar and one vector meson current. We find that the momentum dependence of the form factors is different if the D or the J ψ meson is off-shell, but they lead to the same coupling constant in the J ψDD vertex.

Quark condensate effects on charmonium-pion scattering

TheJ/ψπ → -DD*,-DD,-D*D* and -DD* cross-sections as a function of √s are evaluated in a QCD sum rule calculation. We study the Borel sum rule for the four point function involving pseudoscalar and vector meson currents, up to dimension four in the operator product expansion. We find that our results are close to those obtained with quark exchange models. We also find that the quark condensate gives the main nonperturbative contribution to the cross-section.

The J/ ψDD vertex in QCD sum rules

The J/ ψDD form factor is evaluated in a QCD sum rule calculation for both D and J/ ψ off-shell mesons. We study the double Borel sum rule for the three point function of two pseudoscalar and one vector meson current. We find that the momentum dependence of the form factors is different if the D or the J/ ψ meson is off-shell, but they lead to the same coupling constant in the J/ ψDD vertex.

Charmonium–pion cross section from QCD sum rules

The $J/\psi \pi\to \bar{D} D^*, \bar{D} D$, ${\bar D}^* D^*$ and ${\bar D} D^*$ cross sections as a function of $\sqrt{s}$ are evaluated in a QCD sum rule calculation. We study the Borel sum rule for the four point function involving pseudoscalar and vector meson currents, up to dimension four in the operator product expansion. We find that our results are smaller than the $J/\psi \pi\to {charmed mesons}$ cross sections obtained with models based on meson exchange, but are close to those obtained with quark exchange models.

D*Dπform factor reexamined

The $D^*D\pi$ form factor is evaluated in a QCD sum rule calculation for both $D$ and $\pi$ off-shell mesons. We study the Borel sum rule for the three-point function of one pseudoscalar, one axial and one vector meson currents. We find that the momentum dependence of the form factors is very different if the $D$ or the $\pi$ meson is off-shell, but they lead to the same coupling constant in the $D^*D\pi$ vertex.