Proceedings Series


Vol. 8 (2015), No. 1, pp. 1 – 278

EEF70 Workshop on Unquenched Hadron Spectroscopy: Non-Perturbative Models and Methods of QCD vs. Experiment --- At the occasion of Eef van Beveren's 70th birthday

Coimbra, Portugal; September 1–5, 2014

The Brief Life of a Hadron: QCD Unquenched

abstract

Once upon a time, the picture of hadrons was of mesons made of a quark and an antiquark, and baryons of three quarks. Though hadrons heavier than the ground states inevitably decay by the strong interaction, the successes of the quark model might suggest their decays are a mere perturbation. However, Eef van Beveren, whose career we celebrate here, recognised that decays are an integral part of the life of a hadron. The channels into which they decay are often essential to their very existence. These hold the secrets of strong coupling QCD and teach us the way quarks really build hadrons.


The Unquenched Quark Model

abstract

In this contribution, we briefly analyze the formalism of the unquenched quark model (UQM) and its application to the calculation of hadron spectra with self-energy corrections, due to the coupling to the meson–meson continuum. In the UQM, the effects of \(q \bar q\) sea pairs are introduced explicitly into the quark model through a QCD-inspired \(^{3}P_0\) pair-creation mechanism. The UQM formalism can be extended to include also the effects of hybrid mesons, i.e. hybrid loops. The main applications to spectroscopy and decays are analyzed.


Problems with Meson Spectroscopy Involving Perturbative Loop Corrections

abstract

In this paper, we review the limitations of including meson loops as perturbative corrections in a solvable quark model. We first discuss meson–meson scattering within a formalism which treats confined quark pairs and mesons on an equal footing. The interaction between the mesons proceeds through \(s\)-channel meson-exchange diagrams. Next, we develop a perturbative expansion of the model, and show that the resonance poles found in such a treatment, even by accounting for contributions up to fourth order, do not coincide with those obtained with the full model. We conclude that the resonance predictions based on perturbative approximations in quark models are not reliable, especially in those cases where the coupling to the scattering channels is large.


Meson Mass Splittings in Unquenched Quark Models

abstract

General results are obtained for meson mass splittings and mixings in unquenched (coupled-channel) quark models. Theorems derived previously in perturbation theory are generalised to the full coupled-channel system. A new formula is obtained for the mass splittings of physical states in terms of the splittings of the valence states. The \(S\)-wave hyperfine splitting decreases due to unquenching, but its relation to the vector \(e^+e^-\) width is unchanged; this yields a prediction for the missing \(\eta _b(3S)\). In the ordinary (quenched) quark model, the \(P\)-wave hyperfine splitting vanishes: this result also survives in the unquenched quark model, despite large mass shifts across the \(P\)-wave multiplet. A ratio of mass splittings used to discriminate quarkonium potential models is scarcely affected by unquenching.


An Unitarized Model for Tetraquarks with a Color Flip-flop Potential

abstract

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 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 crypto-exotic \(qQ\bar {q}\bar {Q}\) are also presented.


Summary of the Results on Spectroscopy from Belle

abstract

We present the recent results on the hadron spectroscopy measured by the Belle detector at the KEKB \(e^+ e^-\) collider. We picked up the bottomonium-like and charmonium-like mesons having the unanticipated properties from the \(q \bar q\) structures as well as the recently observed \(h_b(1,2P)\) mesons.


Recent Results from Charmonium Spectroscopy at BESIII

abstract

Recent BESIII results on studies related to the charmonium-like \(X\), \(Y\), and \(Z\) states are presented. This includes the observation of new charged and neutral \(Z_c\) and the production of \(X(3872)\) and \(\chi _{c1}\) in electron–positron annihilations at center-of-mass energies above 4 GeV.


Large-\(N_c\) Regge Spectroscopy

abstract

This paper, dedicated to Eef van Beveren on the occasion of his birthday, reviews some of our results concerning the hadron spectroscopy, Regge trajectories, and the large-\(N_c\) meson-dominance of hadronic form factors.


Tetraquarks, Why It Is so Difficult to Model Them

abstract

We review the difficulties in searching for exotic tetraquarks both in experiments, in numerical lattice QCD computations and in analytic quark models. We propose to address \(q q \bar Q\bar Q\) exotic tetraquark boundstates and resonances with a fully unitarized and microscopic quark model.


New Results on Charmonium Physics from BaBar

abstract

We study the processes \(\gamma \gamma \to K^+K^-\eta \) and \(\gamma \gamma \to K^+K^-\pi ^0\) using a data sample of 519 fb\(^{-1}\) recorded with the BaBar detector. We observe \(\eta _c \to K^+K^-\pi ^0\) and \(\eta _c \to K^+K^-\eta \) decays, measure their relative branching fraction, and perform a Dalitz plot analysis for each decay. We study the rare \(B\)-meson decays \(B^{\pm ,0} \rightarrow J/\psi K^+ K^- K^{\pm ,0}\), \(B^{\pm ,0} \rightarrow J/\psi \phi K^{\pm ,0}\), and search for \(B^0 \rightarrow J/\psi \phi \) finding no evidence of a signal. We present new measurements of branching fractions and a study of the \(J/\psi \phi \) mass distribution in search of new charmonium-like states.


Calculation of Regge Trajectories from Elastic Scattering Poles and the Non-ordinary \(f_0(500)\) Meson

abstract

We show how Regge trajectories of resonances appearing in elastic two-meson scattering can be obtained just from their pole position and coupling, using a dispersive formalism. In this way, the finite widths of resonances can be taken into account in Regge trajectories. For the \(\rho (770)\), \(f_2(1270)\) and \(f'_2(1525)\), this method leads to ordinary linear Regge trajectories with the universal slope, as expected for ordinary \(\bar qq\) resonances. In contrast, for the \(f_0(500)\) meson, the resulting Regge trajectory is non-linear and with much smaller slope, which is another strong indication of its non-ordinary nature.


Scalar Mesons in \(\tau \to K\pi \nu \) and \(\tau \to \eta \pi \nu \) Decays

abstract

The \(\tau \) decay modes \(\tau \to P_1 P_2\nu \) provide clean probes of the couplings of the flavoured scalar mesons to the \(\bar u{s}\) or \(\bar u{d}\) scalar currents. We review the theoretical constraints which relate the \(P_1P_2\) scalar form factors with \(P_1 P_2\) scattering for \(P_1P_2=K\pi , \eta \pi \) and their applications.


What Happened with the \(f_0(500)/\sigma \) Meson? Theory and Experiment

abstract

Presented are the most interesting and spectacular events in history of the \(\sigma \) meson and its almost rediscovery two years ago. Also proof of the uniqueness and correctness of the dispersion method used to precise determination of its parameters is shortly discussed. Example of a successful application of this method in modification of coupled channel \(\pi \pi \), \(K\bar K\) and \(\eta \eta \) amplitudes fitted in past only to experimental data and not fulfilling crossing symmetry condition is mentioned.


Hadron Scattering from a Lattice Perspective

abstract

Recent years have seen considerable progress in ab initio QCD calculations of hadron scattering threshold parameters and scattering phase shifts in the (elastic) resonance region. The lattice approach is becoming powerful enough to even predict states in the heavy quark sector. Methods and recent results for light quarks and heavy-light quark hadrons are discussed.


Aspects of Gluon Propagation in Landau Gauge: Spectral Densities, and Mass Scales at Finite Temperature

abstract

We discuss a method to extract the Källén–Lehmann spectral density of a particle (be it elementary or bound state) propagator and apply it to compute gluon spectral densities from lattice data. Furthermore, we also consider the interpretation of the Landau-gauge gluon propagator at finite temperature as a massive-type bosonic propagator.


Elements of a Non-Hermitian Quantum Theory Without Hermitian Conjugation — Scalar Product and Scattering

abstract

The description of — in a Hermitian setting — seemingly nonlocal and nonperturbative phenomena such as confinement or superconductivity is most conveniently performed by generalizing quantum theory to a non-Hermitian regime where these phenomena appear perturbative and local. The short presentation provides a clue how this can be done on the basis of Lorentz covariance while preserving the analyticity of the theory. After deriving with the help of Lorentz covariance a quantum scalar product without making any use of metric or complex conjugation, we sketch how the formalism of scattering theory can be extended analytically to a non-Hermitian regime.


A Covariant Constituent-quark Formalism for Mesons

abstract

Using the framework of the Covariant Spectator Theory (CST), we are developing a covariant model formulated in Minkowski space to study mesonic structure and spectra. Treating mesons as effective \(q\bar {q}\) states, we focused on the nonrelativistic bound-state problem in momentum space with a linear confining potential. Although integrable, this kernel has singularities which are difficult to handle numerically. We reformulate it into a form in which all singularities are explicitely removed. The resulting equations are then easier to solve, and yield accurate and stable solutions. In the present work, the same method is applied to the relativistic case, improving upon the results of the one-channel spectator equation (1CSE) presented in some previous works.


No Serious Meson Spectroscopy Without Scattering

abstract

The main goal of meson spectroscopy is to understand the confining force, assumed to be based on low-energy QCD. The usual quark models ignore the dynamical effects of \(q\bar {q}\) creation and decay. Very recent lattice calculations confirm much earlier model results showing that neglecting such effects, in the so-called quenched approximation, may give rise to large discrepancies, and so distort the meson spectra resulting from quark confinement only. Models that attempt to mimic unquenching by redefining the constituent quark mass or screening the confining potential at large \(r\) cannot account for the highly non-perturbative effects on mesonic bound-state and resonance poles, as demonstrated with some published examples.


Unquenching Weak Substructure

abstract

On assuming that weak substructure has a dynamics which is similar to quantum chromodynamics but much stronger, we conclude that unquenching is indispensable for predictions on the spectrum of weak-substructure resonances.


The Initial Single Chiral Particle Emission Mechanism and the Predictions of Charged Charmonium-like Structures

abstract

In this paper, we introduce our theoretical progress on the initial single chiral particle emission mechanism and the predictions of charged charmonium-like structures.


Recent LHCb Spectroscopy Results

abstract

Studies of \(B\) and \(B_s\) decays having a \(J/\psi \) in the final state have been performed which allow new measurements on the scalar and axial mesons mixing angles. Two new natural parity and two unnatural parity resonances are observed in the inclusive study of \(D^+\pi ^-\), \(D^0\pi ^+\) and \(D^{*+}\pi ^-\) final states. In a Dalitz plot analysis of \(B^0_s \to {\kern 0.18em\overline {\kern -0.18em D}}^0K^-\pi ^+\), an excess at \(m({\kern 0.18em\overline {\kern -0.18em D}}^0K^-) \approx 2.86\) GeV/\(c\) is found to be an admixture of spin-1 and spin-3 resonances. The analyses make use of data corresponding to 3 fb\(^{-1}\) of integrated luminosity collected with the LHCb detector using \(pp\) collisions.


Chiral Phase Transition in an Extended Linear Sigma Model: Initial Results

abstract

We investigate the scalar meson mass dependence on the chiral phase transition in the framework of an SU(3), (axial)vector meson extended linear sigma model with additional constituent quarks and Polyakov loops. We determine the parameters of the Lagrangian at zero temperature in a hybrid approach, where we treat the mesons at tree-level, while the constituent quarks at 1-loop level. We assume two nonzero scalar condensates and together with the Polyakov-loop variables we determine their temperature dependence according to the 1-loop level field equations.


\(\tau \) Vector Spectral Function from a Chirally Invariant Hadronic Model with Weak Interaction

abstract

The linear sigma model we present here describes the vacuum phenomenology of the \(N_F=2\) scalar, pseudoscalar, vector, and axial-vector mesons at energies \(\simeq 1\) GeV. Together with a local SU\((2)_L\times \mathrm {U}(1)_Y\) symmetry obtained from a local transformation of the fields, we obtain a gauge invariant effective description of electroweak interaction with hadrons in the vacuum. We show that the vector channel is described well and that the contributions from the direct decay of \(W^- \rightarrow \pi ^- \pi ^0\) are, although quantitatively small, necessary to reproduce the line shape of the vector spectral function.


The 3 Flavor Nambu–Jona-Lasinio with Explicit Symmetry Breaking Interactions: Scalar and Pseudoscalar Spectra and Decays

abstract

The effective quark interactions that break explicitly the chiral SU\((3)_{\mathrm {L}}\times {\mathrm {SU}}(3)_{\mathrm {R}}\) and U\(_{\mathrm {A}}(1)\) symmetries by current-quark mass source terms are considered in NLO in \(N_c\) counting. They are of the same order as the ’t Hooft flavor determinant and the eight quark interactions that extend the LO Nambu–Jona-Lasinio Lagrangian, and complete the set of non-derivative and spin 0 interactions relevant for the \(N_c\) scheme. The bosonized Lagrangian at meson tree level describes accurately the empirical ordering and magnitude of the splitting of states in the low-lying pseudoscalar and scalar meson nonets, for which the explicit symmetry breaking terms turn out to be essential. The strong interaction and radiative decays of the scalar mesons are understood in terms of the underlying microscopic multi-quark states, which are probed differently by the strong and the electromagnetic interactions. We also obtain that the anomalous two photon decays of the pseudoscalars are in very good agreement with data.


Non-uniform Phases in a Three-flavour ’t Hooft Extended Nambu–Jona-Lasinio Model

abstract

The possible existence of non-uniform phases in cold dense quark matter in the light quark sector (\(u,d,s\)) is addressed within the Nambu–Jona-Lasinio Model extended to include the flavour-mixing ’t Hooft determinant. The effect of changes in the coupling strengths of the model is discussed. It is seen that the inclusion of the strange sector catalyses the appearance of the non-uniform phases, extending the domain for their existence.


The \(T\)–\(\mu \) Phase Diagram of the Nambu–Jona-Lasinio Model in the Presence of Explicit Symmetry-breaking Interactions

abstract

It is shown that the strange-quark mass undergoes a first-order transition in a generalized 3 flavor Nambu–Jona-Lasinio (NJL) Lagrangian which includes a complete set of explicit chiral symmetry breaking interactions. This transition occurs in a moderate chemical potential region \(\mu \sim 400\) MeV, in addition to the usual chiral transition associated with the light-quark sector. This favors the formation of stable strange-quark matter at chemical potentials which are considerably lower than the ones discussed in the literature. The reason for this behavior is discussed.


Inverse Magnetic Catalysis in the Polyakov–Nambu–Jona-Lasinio and Entangled Polyakov–Nambu–Jona-Lasinio Models

abstract

We investigate the QCD phase diagram at zero chemical potential and finite temperature in the presence of an external magnetic field within the three flavor Polyakov–Nambu–Jona-Lasinio and entangled Polyakov–Nambu–Jona-Lasinio models looking for the inverse magnetic catalysis. Two scenarios for a scalar coupling parameter dependent on the magnetic field intensity are considered. These dependencies of the coupling allow to reproduce qualitatively lattice QCD results for the quark condensates and for the Polyakov loop: due to the magnetic field, the quark condensates are enhanced at low and high temperatures and suppressed for temperatures close to the transition temperatures, while the Polyakov loop increases with the increase of the magnetic field.


Meson Cloud Effects in Nucleon Resonances at Low and Intermediate Energies

abstract

We review some results obtained by the Coimbra–Ljubljana collaboration that reveal the important role of the pion cloud in the low- and intermediate-energy nucleon and delta resonances.


Scalar Glueball in a Top–Down Holographic Approach to QCD

abstract

Identification of glueballs — bound states of gauge bosons in Quantum Chromodynamics (QCD) — is a very important open question in dynamics of the strong interaction. The search for the glueball ground state, carrying scalar quantum numbers, poses a particular challenge due to the existence of (i) several candidates for its realisation in the physical spectrum and (ii) inevitable mixing of the pure glueball state with those comprised of quarks. In this article, I discuss implications of an approach in holographic QCD where, among others, the mass and the two-pion decay of the pure scalar glueball can be studied.


Neutrinos and the Average Thermal Evolution of the Universe

abstract

The cosmological effect of sterile neutrinos is estimated in a study of the average behavior of the \({\mit \Lambda }\)CDM universe. Dark matter is assumed to be composed of neutralinos and it is argued that dark energy may result from conformal variations of the metric. The eventual presence of sterile neutrinos does not noticeably change the evolution of the universe and we find that their density at primordial nucleosynthesis is consistent with predictions when the sterile neutrinos are in temperature equilibrium with the rest of the universe at the end of inflation.


Hamiltonian Approach to QCD in Coulomb Gauge: Deconfinement from Confinement

abstract

The deconfinement phase transition is studied within the Hamiltonian approach to QCD in Coulomb gauge. Assuming a quasiparticle picture for the grand canonical gluon ensemble, the thermal equilibrium state is found by minimizing the free energy with respect to the quasi-gluon energy. The deconfinement phase transition is accompanied by a drastic change of the infrared exponents of the ghost and gluon propagators. Above the phase transition, the ghost form factor remains infrared divergent but its infrared exponent is approximately halved. The gluon energy being infrared divergent in the confined phase becomes infrared finite in the deconfined phase. Furthermore, the effective potential of the order parameter for confinement is calculated for SU\((N)\) Yang–Mills theory in the Hamiltonian approach by compactifying one spatial dimension and using a background gauge fixing. In the simplest truncation, neglecting the ghost and using the ultraviolet form of the gluon energy, we recover the Weiss potential. From the full non-perturbative potential (with the ghost included), we extract a critical temperature of the deconfinement phase transition of \(269\) MeV for the gauge group SU\((2)\) and \(283\) MeV for SU\((3)\).


Reactions Involving Open Charm Mesons and Production of \(X(3872)\)

abstract

We show the results obtained for the cross sections of the processes \(\bar D D\), \(\bar D^* D\), \(\bar D^* D^*\to \pi X(3872)\), information on which is necessary to determine the \(X(3872)\) abundance in heavy ion collisions. Our formalism is based on the generation of \(X(3872)\) from the interaction of the hadrons \(\bar D^0 D^{*0} - {\mathrm {c.c.}}\), \(D^- D^{*+} - {\mathrm {c.c.}}\) and \(D^-_s D^{*+}_s - {\mathrm {c.c.}}\) and the calculation of the \(X\bar D^* D^*\) anomalous vertex considering \(X(3872)\) as a molecule of the above hadrons channels.


On the Origin of the Narrow Peak and the Isospin Symmetry Breaking of the \(X\)(3872)

abstract

The \(X(3872)\) formation and decay processes in \(B\) decay are investigated by a \(c\bar {c}\)–two-meson hybrid model. The two-meson state consists of the \(D^0\overline {{D}}{}^{*0}\), \(D^+D^{*-}\), \(J/\psi \rho \), and \(J/\psi \omega \) channels. The \(c\bar {c}(2P)\) state couples to the two \(D\overline {D}{}^*\) channels. The energy-dependent decay widths of the \(\rho \) and \(\omega \) mesons are introduced in the two-meson propagators. The isospin symmetry breaking in the present model comes from the mass difference of the charged and neutral \(D\) and \(D^*\) mesons. It is found that very narrow \(J/\psi \rho \) and \(J/\psi \omega \) peaks appear around the \(D^0\overline {{D}}{}^{*0}\) threshold. The size of the \(J/\psi \pi ^3\) peak that we calculated is 1.27–2.24 times as large as that of \(J/\psi \pi ^2\), which is comparable to the experimental results. It is also found that ratios of the transfer strengths provide information on the size of the \(c\bar {c}\)–\(D\overline {D}{}^*\) coupling as well as the \(X(3872)\) binding energy.


\(X(3872)\) Electromagnetic Decay in a Coupled-channel Model

abstract

A multichannel Schrödinger equation with both quark–antiquark and meson–meson components, using a harmonic-oscillator potential for \(q\bar {q}\) confinement and a delta-shell string-breaking potential for decay, is applied to the axial-vector \(X(3872)\) and lowest vector charmonia. The model parameters are fitted to the experimental values of the masses of the \(X(3872)\), \(J/\psi \) and \(\psi (2S)\). The wave functions of these states are computed and then used to calculate the electromagnetic decay widths of the \(X(3872)\) into \(J/\psi \gamma \) and \(\psi (2S)\gamma \).


Pseudospin and Spin Symmetries in the Dirac Equation for Confining Potentials with the Application to the Coulomb Potential in 1+1 Dimensions

abstract

In this paper, we revise the main features of pseudospin and spin symmetries of the Dirac equation with scalar and vector potentials and mention several of its applications to strong interacting physical systems. We present some recent results in which these symmetries are applied to Coulomb potentials in the Dirac equation in 1+1 dimensions, including also pseudoscalar potentials. These potentials are linear in \(|x|\) and may be applied in confining quark models. We explore all possible bound solutions, both for fermions and antifermions, and show the relation between spin and pseudospin symmetries by means of charge-conjugation and \(\gamma ^{5}\) chiral transformations.


Dynamical Generation of Hadronic Resonances

abstract

One type of dynamical generation consists in the formation of multiple hadronic resonances from single seed states by incorporating hadronic loop contributions on the level of \(s\)-wave propagators. Along this line, we study the propagator poles within two models of scalar resonances and report on the status of our work: (i) Using a simple quantum field theory describing the decay of \(f_{0}(500)\) into two pions, we may obtain a second, additional pole on the first Riemann sheet below the pion–pion threshold (i.e. , a stable state can emerge). (ii) We perform a numerical study of the pole(s) of \(a_{0}(1450)\) by using as an input the results obtained in the extended Linear Sigma Model (eLSM). Here, we do not find any additional pole besides the original one, thus we cannot obtain \(a_{0}(980)\) as an emerging state. (iii) We finally demonstrate that, although the coupling constants in typical effective models might be large, the next-to-leading-order contribution to the decay amplitude is usually small and can be neglected.


top

ver. 2024.03.17 • we use cookies and MathJax