Spectrum, radial wave functions at origin, decay constants, weak decay widths, life time and branching ratios for radially excited conventional and hybrid $B_c$ mesons are derived within non-relativistic quark model framework employing Schr$\ddot{\textrm{o}}$dinger equation by shooting method. Calculated results are compared with available theoretical results and experimental observations. This work may help in identifying the new discovered $B_c$ meson states at CDF ,LHCb and ATLAS.
We review lattice QCD results for glueballs (including a discussion of mixing with scalar mesons), hybrid mesons and exotic mesons (such as $B_s B_s$ molecules).
We expose arguments concerning the π_{1}(1400) observed decaying into ηπand claimed to be an exotic meson. We conclude that this object cannot be a qqbar-g hybrid meson.
We estimate the ground state masses of the heavy hybrid mesons using a phenomenological QCD-type potential. 0^{- -},1^{- -},0^{- +},1^{- +} and 0^{+ -} J^{PC} states are considered.
We calculate the $ρ$ meson couplings between the heavy hybrid doublets H^h/S^h/M^h/T^h and the ordinary q\bar{Q} doublets in the framework of the light-cone QCD sum rule. The sum rules obtained rely mildly on the Borel parameters in their working regions. The resulting coupling constants are rather small in most cases.
We calculate the strong decays of hybrid mesons to conventional mesons for all the lowest lying J^PC hybrids of flavour uu, dd, ss, cc and bb. A decay operator developed from the heavy quark expansion of quantum chromodynamics is employed. We show that the selection rule that hybrid mesons do not decay to identical S-wave mesons, found in other models, is preserved. We predict decays of charmonium hybrids, discuss decays of J^PC=1^-+ exotic isovector hybrids of various masses, and interpret the π(1800) as a hybrid meson.
We study mixing between conventional and hybrid mesons in vector and axial vector charmonium using QCD Laplace sum-rules. We compute meson-hybrid cross correlators within the operator product expansion, taking into account condensate contributions up to and including those of dimension-six as well as composite operator renormalization-induced diagrams. Using measured masses of charmonium-like states as input, we probe known resonances for nonzero coupling to both conventional and hybrid meson currents, a signal for meson-hybrid mixing.
A new formalism is developed for the two photon production of hybrid mesons via intermediate hadronic decays. In an adiabatic and non-relativistic context with spin 1 pair creation we obtain the first absolute estimates of unmixed hybrid production strengths to be small (0.03 - 3 eV) in relation to experimental meson widths (0.1 - 5 keV). Within this context, two photon experiments at Babar, Cleo II, LEP2 and LHC therefore strongly discriminate between hybrid and conventional meson wave function components, filtering out conventional meson components. Decay widths of unmixed hybrids vanish. Co…
We review lattice QCD results for glueballs (including a discussion of mixing with scalar mesons), hybrid mesons and exotic mesons (such as $B_s B_s$ molecules). We also discuss string breaking as a mixing between colour flux states and $B \bar{B}$ states.
We make the first calculation of the electroweak couplings of hybrid mesons to conventional mesons appropriate to photoproduction and to the decays of $B$ or $D$ mesons. $E1$ amplitudes are found to be large and may contribute in charge exchange $γp \to n H^+$ allowing production of (amongst others) the charged $1^{-+}$ exotic hybrid off $a_2$ exchange. Axial hybrid meson photoproduction is predicted to be large courtesy of $π$ exchange, and its strange hybrid counterpart is predicted in $B \to ψK_H(1^+)$ with $b.r. \sim 10^{-4}$. Higher multipoles, and some implications for hybrid charmonium …
We evaluate the leading order amplitude for the deep exclusive electroproduction of an exotic hybrid meson in the Bjorken regime. We show that, contrary to naive expectation, this amplitude factorizes at the twist 2 level and thus scales like usual meson electroproduction when the virtual photon and the hybrid meson are longitidinally polarized. Exotic hybrid mesons may thus be studied in electroproduction experiments at JLAB, HERA (HERMES) or CERN (COMPASS).
We revisited a model for charmonium hybrid meson with a magnetic gluon [Yu. S. Kalashnikova and A. V. Nefediev, Phys. Rev. D {\bf 77}, 054025 (2008)] and improved the numerical calculations. These improvements support the hybrid meson interpretation of X(4260). Within the same model, we computed the hybrid meson mass with an electric gluon which is resolved to be lighter. Relativistic effects and coupling channels decreased also the mass.
We show that hard electroproduction is a promising way to study exotic hybrid mesons, in particular through the hybrid decay channel $H \to πη$. We discuss the $πη$ generalized distribution amplitude, calculate the production amplitude and propose a forward-backward asymmetry as a signal for the hybrid meson production.
The existence of hadronic molecular-type hybrids consisting of a baryon and a meson is argued. Long-range interactions due to one-pion exchange is shown to be strong enough to produce a loosely bound state. Specific features of a molecular hybrid are discussed.
Recent lattice simulation studies of heavy-quark hybrid mesons in which the quark and antiquark are bound together by an excited gluon field are summarized.
The new recently experiments at the B-factories yield a renewed interest in the charm and charmonium spectroscopy. New intriguing states have been observed, which appear to be non-conventional mesons, such as X(3862) and Y(4260) and request more theoretical investigations. We will explore the possibility for the Y(4260) to be a c-cbar-g hybrid meson. Using the quark-gluon constituent model, we exclude its existence as QE-hybrid meson, and as mixing of c-cbar-g hybrid with conventional c-cbar meson. We find the only interpretation as GE-hybrid, decaying in D_(1)-Dbar channels. Then more experim…
Lattice QCD determinations appropriate to hadron spectroscopy are reviewed with emphasis on the glueball and hybrid meson states in the quenched approximation. Hybrids are discussed for heavy and for light quarks. The effects of sea quarks (unquenching) are explored.
Decay widths, branching ratios and production dynamics of some recently discovered $J^{PC} = 1^{-+}, 0^{-+}$,$1^{--}$ and $2^{-+}$ mesons are found to be in remarkable agreement with the predicted properties of hybrid mesons. We propose tests for this new dynamics, emphasise the critical role of $πb_1$ or $πh_1$ decay channels in discriminating hybrids from conventional states, and suggest that photoproduction may offer special opportunities for isolation and confirmation of hybrids.
We construct the B.S. equation for the hybrid mesons under instantaneous approximation. The kernel is chosen as the sum of an one-gluon exchange potential and a linear confining potential. The equations are solved by numerical method, and the spectrum of hybrid mesons $b\bar{b}g$ and $c\bar{c}g$ are obtained.
The phenomenology of a newly developed model of hybrid meson decay is developed. The decay mechanism is based on the heavy quark expansion of QCD and the strong coupling flux tube picture of nonperturbative glue. A comprehensive list of partial decay widths of a wide variety of light, $s\bar s$, $c\bar c$, and $b \bar b$ hybrid mesons is presented. Results which appear approximately universal are highlighted along with those which distinguish different hybrid decay models. Finally, we examine several interesting hybrid candidates in detail.
We present new results concerning the masses and the decay widths of the most interesting hybrid meson states taking as inputs the gluon mass mg and the non-perturbative QCD running coupling constant ?alpha_s(0) comming from both LQCD and SDE recent estimations.
The relativistic four-quark equations are found in the framework of the dispersion relation technique. The solutions of these equations using the method based on the extraction of leading singularities of the amplitudes are obtained. The mass spectrum values of lowest hybrid mesons are calculated.
The models for hybrid mesons are discussed, in which the gluonic excitations manifest themselves as the vibrations of the quark- antiquark QCD string. The predictions for the spectra, decays and mixing with hadronic channels are presented.
We estimate the sizeable cross section for deep exclusive electroproduction of an exotic $J^{PC}=1^{-+}$ hybrid meson in the Bjorken regime. The production amplitude scales like the one for usual meson electroproduction, i.e. as $1/Q^2$. This is due to the non-vanishing leading twist distribution amplitude for the hybrid meson, which may be normalized thanks to its relation to the energy momentum tensor and to the QCD sum rules technique. The hard amplitude is considered up to next-to-leading order in $α_{S}$ and we explore the consequences of fixing the renormalization scale ambiguity through…
The pionic coupling constants in the decays of the $1^{-+}$ hybrid meson are calculated. The double Borel transformation is invoked and continuum contribution is subtracted. The decay widths of the processes $1^{-+}\to ρπ, f_1 π, πγ$ are around $40, 100, 0.3$ MeV respectively.
A hybrid meson is a quark-antiquark pair in which, contrary to ordinary mesons, the gluon field is in an excited state. In the framework of constituent models, the interaction potential is assumed to be the energy of an excited string. An approximate, but accurate, analytical solution of the Schrödinger equation with such a potential is presented. When applied to hybrid charmonia and bottomonia, towers of states are predicted in which the masses are a linear function of a harmonic oscillator band number for the quark-antiquark pair. Such a formula could be a reliable guide for the experimental…
We study gluonic excitations inside a $B_{c} $ meson in the constituent gluon model, treating a bottom-charm hybrid meson $ c \bar{b} g $ as a three-body system. We obtain the mass spectra for the hybrid mesons with magnetic gluon and electric gluon and see that their lowest states appear above the $ D B $ threshold. Also, we consider the decays of the low-lying states of the hybrid meson into $ DB , \; D^{*} B, DB^{*} $, $ D^{*}B^{*} $, $ D_{s} B_{s} $, and $D_{s} B_{s}^{*} $ mesons, developing an existing model for the strong decays. We estimate their partial decay widths and find that the w…
In this paper, Schrodinger equation is numerically applied through non-relativistic potential model for deriving Spectrum, radial wave functions at origin, decay constants, lepton and photon decay widths for radial and orbital excited conventional as well as hybrid charmonium mesons. These calculated results are found in agreement with others theoretical results and with the experimental observations.
Using our analytical expressions that well model the lattice simulations of the gluonic excitations, we use the extended quark potential model to study the effects of orbital and radial excitations on the masses and sizes of conventional and hybrid $B_c$ mesons. A non relativistic formalism is used to numerically calculate the wave functions using the shooting method; this allows us also calculating the $E1$, $M1$ radiative partial widths for conventional meson to meson and hybrid to hybrid transitions. We incorporate spin mixing and compare our calculated spectrum and decay widths with the av…
In consistency with the b --> c type of (quasi) two body decays, recently observed two body decays of B mesons are studied in a hybrid perspective in which their amplitude is given by a sum of factorizable and non-factorizable ones, and a role of the latter in these decays are discussed.
We explore conventional meson-hybrid mixing in $J^{PC}=1^{++}$ heavy quarkonium using QCD Laplace sum-rules. We calculate the cross-correlator between a heavy conventional meson current and heavy hybrid current within the operator product expansion, including terms proportional to the four- and six-dimensional gluon condensates and the six-dimensional quark condensate. Using experimentally determined hadron masses, we construct models of the $1^{++}$ charmonium and bottomonium mass spectra. These models are used to investigate which resonances couple to both currents and thus exhibit conventio…
The observation of $π_1(1600) \to πρ$ is shown in the flux-tube model to be compatible with this state being a hybrid meson with branching ratio to this channel $\sim 30%$. The $πρ$ widths of other hybrids are related by rather general arguments. These results enable cross sections for photoproduction of hybrids to be predicted.
The quark potential model for mesons and its extension for hybrid mesons are used to study the effects of radial excitations on the masses, sizes and radial wave functions at the origin for conventional and hybrid charmonium mesons. These results can help in experimentally recognizing hybrid mesons. The properties of conventional and hybrid charmonium mesons are calculated for the ground and radially excited states using the shooting method to numerically solve the required Schrodinger equation for the radial wave functions. We compare our results with the experimentally observed masses and t…
The exotic J^{PC}= 1^{-+} resonance π_{1}(1600)is examined in the framework of the Quark Model with Constituent Gluon (QMCG). We report the possibility of interpreting that resonance as quark-antiquark-gluon hybrid meson, with a masse = 1.65+0.05-0.04 GeV and a rho-pi decay width = 0.28+0.14-0.09 GeV.
We use QCD Laplace sum-rules to explore mixing between conventional mesons and hybrids in the heavy quarkonium vector $J^{PC}\!=\!1^{--}$ channel. Our cross-correlator includes perturbation theory and contributions proportional to the four-dimensional and six-dimensional gluon condensates. We input experimentally determined charmonium and bottomonium hadron masses into both single and multi-resonance models in order to test them for conventional meson and hybrid components. In the charmonium sector we find evidence for meson-hybrid mixing in the $J/ψ$ and a $\approx4.3$ GeV resonance. In the b…
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.
We investigate the hybrid exotic meson with $J^{PC}=1^{-+}$ within the framework of an AdS/QCD model. Introducing a holographic field dual to the operator for hybrid exotic meson, we obtain the eigen-value equation for its mass. Fixing all free parameters by QCD observables such as the $ρ$-meson mass, we predict the masses of the hybrid exotic meson. The results turn out to be $1476 \mathrm{MeV}$ for the ground state, and $2611 \mathrm{MeV}$ for the first excited one. Being compared with the existing experimental data for the $π_1(1400)$, which is known to be $m_{π_1} = 1351\pm30 \mathrm{MeV}$…
We use QCD Laplace sum-rules to study meson-hybrid mixing in vector ($1^{--}$) heavy quarkonium. We compute the QCD cross-correlator between a heavy meson current and a heavy hybrid current within the operator product expansion. In addition to leading-order perturbation theory, we include four- and six-dimensional gluon condensate contributions as well as a six-dimensional quark condensate contribution. We construct several single and multi-resonance models that take known hadron masses as inputs. We investigate which resonances couple to both currents and so exhibit meson-hybrid mixing. Compa…
In this paper, lattice simulations are used to propose a potential model for gluonic excited $Σ^-_u$ states of bottomonium meson . This proposed model is used to calculate radial wave functions, masses and radii of $Σ_u^-$ bottomonium hybrid mesons. Here, gluonic field between a quark and an antiquark is treated as in the Born-Oppenheimer expansion, and Schr$\ddot{o}$dinger equation is numerically solved employing shooting method. Results of calculated masses for $Σ^-_{u}$ state are in quite good agreement with the lattice simulations.
We consider glueball- (hybrid) meson mixing for the low-lying four pseudovector states. The h_1'(1380) decays dominantly to K*K with some presence in rho pi and omega eta. The newly observed h_1(1600) has a D- to S-wave width ratio to omega eta which makes its interpretation as a conventional meson unlikely. We predict the decay pattern of the isopartner conventional or hybrid meson b_1(1650). A notably narrow s sbar partner h_1'(1810) is predicted.
We study the spectra of the hybrid mesons containing one heavy quark ($q\bar{Q}g$) within the framework of QCD sum rules in the heavy quark limit. The derived sum rules are stable with the variation of the Borel parameter within their corresponding working ranges. The extracted binding energy for the heavy hybrid doublets $H^h(S^h)$ and $M^h(T^h)$ is almost degenerate. We also calculate the pionic couplings between these heavy hybrid and the conventional heavy meson doublets using the light-cone QCD sum rule method. The extracted coupling constants are rather small as a whole. With these coupl…
Exotic hybrid mesons H, with quantum numbers J^{PC}= 1^{- +} may be copiously produced in the hard exclusive processes gamma^*(Q^2) gamma -> H and gamma^*(Q^2) P(p) -> H P(p') because they have a leading twist distribution amplitude with a sizable coupling constant f_H, which may be estimated through QCD sum rules. The reaction rates scale in the same way as the corresponding rates for usual mesons.
We propose that there coexist two scalar mesons of different structures (a conventional meson and a four-quark meson) in the recently observed broad bumps just below the large peak of the tensor meson in the D-pi mass distribution. We base this proposal on the interpretation of the charm-strange scalar meson of mass 2317 MeV as a four-quark meson. The strange counterparts of these scalar mesons are also studied.
In the framework of quark models, hybrid mesons are either seen as two-body $q\bar q$ systems with an excited flux tube connecting the quark to the antiquark or as three-body $q\bar q g$ systems including a constituent gluon. In this work we show that, starting from the three-body wave function of the $q\bar q g$ hybrid meson in which the gluonic degrees of freedom are averaged, the excited flux tube picture emerges as an equivalent $q\bar q$ potential. This equivalence between the excited flux tube and the constituent gluon approach is confirmed for heavy hybrid mesons but, for the first time…
We present a theoretical study of exotic hybrid meson (JPC=1-+) production in photon-photon collisions where one of the photons is deeply virtual, including twist 2 and twist 3 contributions. We calculate the cross section of this process which turns out to be large enough to imply sizeable counting rates in the present high luminosity electron-positron colliders. We emphasize theimportance of the pi eta decay channel for the detection of the hybrid meson candidate pi_1(1400) and calculate the cross section and the angular distribution for pi eta pair production in the unpolarized case. This a…
We propose some extensions of the quark potential model to hybrids, fit them to the lattice data and use them for the purpose of calculating the masses, root mean square radii and wave functions at the origin of the conventional and hybrid charmonium mesons. We treat the ground and excited gluonic field between a quark and an antiquark as in the Born-Oppenheimer expansion, and use the shooting method to numerically solve the required Schr$\ddot{\textrm{o}}$dinger equation for the radial wave functions; from these wave functions we calculate the mesonic properties. For masses we also check thro…
The existence of non-q\bar{q} hadrons such as glueballs and hybrids is one of the most important qualitative questions in QCD. The COMPASS experiment offers the possibility to unambiguously identify such states and map out the glueball and hybrid spectrum. In this review I discuss the expected properties of glueballs and hybrids and how they might be produced and studied by the COMPASS collaboration.
We calculate rates for hybrid meson production by electromagnetic and weak interactions in the flux-tube model. Applications include photo and electroproduction at Jefferson Laboratory and HERA, and the production of light strange and charmed hybrids in the weak decays of heavy flavours. Photoproduction of some light hybrids is predicted to be prominent in charge exchange reactions, $γp \to n \cal{H}$ and accessible in $γp \to p \cal{H}$. Production of light or charmed hybrids in $B$ and $D$ decays may be feasible with high statistics. Photoproduction of the axial hybrid meson is predicted to …
We estimate the sizeable cross section for deep exclusive electroproduction of an exotic $J^{PC}=1^{-+}$ hybrid meson in the Bjorken regime. The production amplitude scales like the one for usual meson electroproduction, {\it i.e.} as $1/Q^2$. This is due to the non-vanishing leading twist distribution amplitude for the hybrid meson, which may be normalized thanks to its relation to the energy momentum tensor and to the QCD sum rules technique. The hard amplitude is considered up to next--to--leading order in $α_{S}$ and we explore the consequences of fixing the renormalization scale ambiguity…
The associate productions of X(3872) and J/ψin hadron collisions and flavor independence of hadrons in ee^+\to X(3872)+hadrons and the decays X(3872)\to γ+hadrons are discussed. It is pointed out X(3872)\to J/ψ+σcould be a significant decay channel.
Hybrid mesons with exotic quantum numbers $J^{PC}=1^{-+}$ are examined in soft-wall AdS/QCD. The predicted mass spectrum is compared to the measured values of the candidates $π_1(1400)$, $π_1(1600)$ and $π_1(2015)$. Thermal effects are analysed through the spectral function in the AdS-Black Hole model, and the differences with the Hawking-Page description are discussed.
We calculate the next-to-leading order (NLO) $α_s$-corrections to the contributions of the condensates $<αG^2>$ and $<\bar qq>^2$ in the current-current correlator of the hybrid current $g\barq(x)γ_νiF_{μν}^aT^aq(x)$ using the external field method in Feynman gauge. After incorporating these NLO contributions into the Laplace sum-rules, the mass of the $J^{PC}$=$1^{-+}$ light hybrid meson is recalculated using the QCD sum rule approach. We find that the sum rules exhibit enhanced stability when the NLO $α_s$-corrections are included in the sum rule analysis, resulting in a $1^{-+}$ light hybri…
An effective Coulomb gauge Hamiltonian, H_eff, is used to calculate the light (u-ubar-g), strange (s-sbar-g) and charmed (c-cbar-g) hybrid meson spectra. For the same two parameter H_eff providing glueball masses consistent with lattice results and a good description of the observed u,d,s and c quark mesons, a large-scale variational treatment predicts the lightest hybrid has J^{PC}=0^{++} and mass 2100 MeV. The lightest exotic 1^{-+} state is just above 2200 MeV, near the upper limit of lattice and Flux Tube predictions. These theoretical formulations all indicate the observed 1^{-+} pi_1(160…
We estimate the energy of the lowest Charmonium and Upsilon states with hybrid admixtures using the method of QCD Sum Rules. Our results show that the $Ψ'(2S)$ and $Υ(3S)$ states both have about a 50% admixture of hybrid and meson components. From this we find explanations of both the famous $ρ-π$ puzzle for Charmonium, and the unusual pattern of $σ$ decays that have been found in $Υ$ decays. Moreover, this picture can be used for predictions of heavy quark production with the octet model for RHIC.
An analytic calculation of the breaking of excited chromoelectric flux-tubes is performed in an harmonic oscillator approximation and applied to predict the dynamics of all $J^{PC}$ low-lying gluonic excitations of mesons (hybrids). Widths, branching ratios and production dynamics of some recently discovered $J^{PC} = 1^{-+}, 0^{-+}$ and $1^{--}$ mesons are found to be in remarkable agreement with these results. We introduce the selection rules that can be used to understand the systematics of numerical decay calculations and we find possible significant breaking of these rules for specific ch…
We show how a field theory containing classical vortex solutions can be expressed as an effective string theory of long distance QCD describing the two transverse oscillations of the string. We use the semiclassical expansion of this effective string theory about a classical rotating string solution to obtain Regge trajectories for mesons with zero mass quarks. The first semiclassical correction adds the constant 1/12 to the classical Regge formula for the angular momentum of mesons on the leading Regge trajectory. In D spacetime dimensions, this additive constant is (D-2)/24. The excited stat…
Within QCD, colourless states may be constructed corresponding to exotic matter outside of the traditional quark model. Experiments have recently observed tetraquark and pentaquark states, but no definitive hybrid meson signals have been observed. With the construction of the PANDA experiment at FAIR, and with full commissioning of the GlueX experiment at JLab expected to be completed this year, the opportunity for the observation of hybrid mesons has greatly increased. However, theoretical calculations are necessary to ascertain the identity of any experimental resonances that may be observed…
