Quantum chromodynamics (QCD), the quantum field theory of strong interactions, is highly nonpertubative in the low-energy sector, where confinement dominates and resonance phenomena are observed. Therefore, phenomenological unquenched models based on the old ideas of the $\mathcal{S}$-matrix theory give a fundamental contribution to understand the complex pattern of masses, widths and shapes of experimentally observed meson resonances. In the present thesis we employ the Resonance-Spectrum-Expansion coupled-channel model to study two enigmatic meson states, the isoscalar vector $ϕ(2170)$ and the charmonium-like axial-vector $X(3872)$. The same model is applied to describe the peculiar pattern of masses and widths of the open-charm axial-vectors - pseudovectors $D_1(2420)$ and $D_1(2430)$, and $D_{s1}(2460)$ and $D_{s1}(2536)$. Furthermore, a simplified Schrödinger model is used to study the dominant wave-function components of $X(3872)$ near its resonance mass. Both models successfully describe the whole variety of special features observed in experiment, which are not so easily explained in QCD-inspired quenched models.
In this paper, we calculate mass and probability fractions of meson-meson components of $X(3872)$ in an unquenched quark model. Different from most of other unquenched quark models, the quark pairs creation operator from $^3P_0$ is modified by considering effects of the created quark pair energy and separation between the created quark pair and the valence quark-pair. In the calculation, all the wavefunctions of mesons and the relative motion between two mesons are obtained by solving the corresponding Schrödinger equation with the help of gaussian expansion method. The multi-channel coupling …
In this contribution, we briefly discuss the results for charmonium and bottomonium spectra with self-energy corrections in the unquenched quark model, due to the coupling to the meson-meson continuum. The UQM formalism can be extended to include also the effects of hybrid mesons, i.e. hybrid loops. Finally, we discuss the results of a calculation of hybrid mesons spectrum in Coulomb Gauge QCD.
Most models for the strong decay of mesons, as well as unquenched quark models which incorporate the effect of coupling to meson-meson channels, assume that the coupling is driven by the creation of a quark-antiquark pair in spin triplet. Their matrix elements can be factorised into a sum over (model-dependent) spatial matrix elements multiplied by (model-independent) coefficients. A general expression for these coefficients is obtained, and their properties are studied. Numerical tables of the coefficients can be used as a starting point for future calculations. The coefficients lead to model…
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 $η_b(3S)$. The ordinary (quenched) quark model result that the P-wave hyperfine splitting vanishes also…
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.
In most meson strong decay and unquenched (coupled-channel) quark models, the pair-creation operator is a scalar product of vectors in the spin and spatial degrees of freedom. While differing in the spatial part, most models have the same spin part, which creates a qq* pair coupled to spin triplet, with the spins of the initial quarks as spectators. This is a basic assumption of the 3P0 model, and is well-known to arise also in the flux tube model, starting from the strong coupling expansion of lattice QCD. In this article the same structure is shown to emerge in the Cornell model, in the domi…
We present recent results for the prediction of the Bs lifetime difference from lattice Heavy Quark Effective Theory simulations. In order to get a next-to-leading order result we have calculated the matching between QCD and HQET and the two-loop anomalous dimensions in the HQET for all the ΔB=2 operators, in particular for the operators which enter the width difference. We present results from quenched and, for the first time, from unquenched simulations. We obtain for the Bs lifetime difference, (ΔΓ_Bs/Γ_Bs)^{(que.)}=(5.1+/- 1.9+/- 1.7)10^(-2) and (ΔΓ_Bs/Γ_Bs)^{(unq.)}=(4.3+/- 2.0+/- 1.9)10^…
We discuss some applications of the unquenched quark model which is an extension of the CQM that includes the effects of sea quarks via a 3P0 quark-antiquark pair-creation mechanism. Particular attention is paid to the electromagnetic couplings and beta decays of baryons. It is shown that the observed discrepancies between the experimental data and the predictions of the CQM can be accounted for in large part by the effects of sea quarks in the unquenched quark model.
Unquenching of the Polyakov-loop potential showed to be an important improvement for the description of the phase structure and thermodynamics of strongly-interacting matter at zero quark chemical potentials with Polyakov-loop extended chiral models. This work constitutes the first application of the quark backreaction on the Polyakov-loop potential at nonzero density. The observation is that it links the chiral and deconfinement phase transition also at small temperatures and large quark chemical potentials. The build up of the surface tension in the Polyakov-loop extended Quark-Meson model i…
We present determinations of the B meson decay constant f_B and of the ratio f_{B_s}/f_B using the MILC collaboration unquenched gauge configurations which include three flavors of light sea quarks. The mass of one of the sea quarks is kept around the strange quark mass, and we explore a range in masses for the two lighter sea quarks down to m_s/8. The heavy b quark is simulated using Nonrelativistic QCD, and both the valence and sea light quarks are represented by the highly improved (AsqTad) staggered quark action. The good chiral properties of the latter action allow for a much smoother chi…
We present non-perturbative first-principle results for quark-, gluon- and meson $1$PI correlation functions of two-flavour Landau-gauge QCD in the vacuum. These correlation functions carry the full information about the theory. They are obtained by solving their Functional Renormalisation Group equations in a systematic vertex expansion, aiming at apparent convergence. This work represents a crucial prerequisite for quantitative first-principle studies of the QCD phase diagram and the hadron spectrum within this framework. In particular, we have computed the gluon, ghost, quark and scalar-pse…
Calculations in unquenched QCD for the scalar glueball spectrum have confirmed previous results of Gluodynamics finding a glueball at ~ 1750 MeV. I analyze the implications of this discovery from the point of view of glueball-meson mixing at the light of the experimental scalar sprectrum.
In this contribution, we will discuss our unquenched quark model re- sults for the spectra of cc and bb states. The spectra are calculated in the unquenched quark model formalism, where the physical mass of a meson is the sum of a bare mass contribution plus a self-energy correc- tion, due to the coupling to the meson-meson continuum. We will also discuss the quark structure of the X(3872). Its open-flavor and radiative decays are calculated in the quark model formalism. In our interpreta- tion, the wave function of the X(3872) is the sum of two contributions, a cc core plus higher Fock compon…
In this contribution, we discuss our recent unquenched quark model results for the spectrum of $b \bar b$ mesons with self energy corrections, due to the coupling to the meson-meson continuum. Our unquenched quark model predictions for the masses of the recently discovered $χ_b(3P)$ states are compared to those of a re-fit of Godfrey and Isgur's relativized quark model to the most recent experimental data. The possible importance of continuum effects in the $χ_b(3P)$ states is discussed. Finally, we show our quark model results for the radiative decays of the $χ_b(3P)$ system and the open-bott…
Higher excited charmed and charmed-strange mesons in an unquenched quark model
University of Chinese Academy of Sciences（中国科学院大学）；Institute of Modern Physics, Chinese Academy of Sciences（中国科学院近代物理研究所）；Hunan Normal University（湖南师范大学）
We perform a coupled-channels calculation of the masses of light mesons with the quantum numbers $IJ^{P=-}$, $(I,J)=0,1$, by including $q\bar{q}$ and $(q\bar{q})^2$ components in a nonrelativistic chiral quark model. The coupling between two- and four-quark configurations is realized through a $^3P_0$ quark-pair creation model. With the usual form of this operator, the mass shifts are large and negative, an outcome which raises serious issues of validity for the quenched quark model. Herein, therefore, we introduce some improvements of the $^3P_0$ operator in order to reduce the size of the ma…
We discuss the recent progress in computing the D-meson decay constant and D->pi l nu form factors from the lattice QCD simulations with Nf=2 dynamical using Wilson quarks. We report fD=201(20)MeV and F+(1GeV^2)/fD=4.04(78)GeV^-1 at a=0.08fm.
A recent quark-model description of X(3872) as an unquenched $2\,{}^{3\!}P_1$ $c\bar{c}$ state is generalised by now including all relevant meson-meson configurations, in order to calculate the widths of the experimentally observed electromagnetic decays $X(3872) \to γJ/ψ$ and $X(3872) \to γψ(2S)$. Interestingly, the inclusion of additional two-meson channels, most importantly $D^\pm D^{\star\mp}$, leads to a sizeable increase of the $c\bar{c}$ probability in the total wave function, although the $D^0\bar{D}^{\star0}$ component remains the dominant one. As for the electromagnetic decays, unque…
We study $B_d$ and $B_s$ mixing in unquenched lattice QCD employing the MILC collaboration gauge configurations that include u, d, and s sea quarks based on the improved staggered quark (AsqTad) action and a highly improved gluon action. We implement the valence light quarks also with the AsqTad action and use the nonrelativistic NRQCD action for the valence b quark. We calculate hadronic matrix elements necessary for extracting CKM matrix elements from experimental measurements of mass differences $ΔM_d$ and $ΔM_s$. We find $ξ= f_{B_s} \sqrt{\hat{B}_{B_s}} / f_{B_d} \sqrt{\hat{B}_{B_d}} = 1.2…
We extend our previous studies to calculate the B meson B parameters B_B and B_S on the lattice, and present an update of the results for the B_s meson width difference. We perform an extensive study of systematic errors in the quenched calculation of the B-parameters, and find that the systematic errors are in good control using the NRQCD action for heavy quark. We also report our preliminary results from unquenched simulations.
We present a precise lattice computation of pseudoscalar and vector heavy-light meson masses for heavy-quark masses ranging from the physical charm mass up to $\simeq 4$ times the physical b-quark mass. We employ the gauge configurations generated by the European Twisted Mass Collaboration (ETMC) with $N_f = 2+1+1$ dynamical quarks at three values of the lattice spacing ($a \simeq 0.062, 0.082, 0.089$ fm) with pion masses in the range $M_π\simeq 210 - 450$ MeV. The heavy-quark mass is simulated directly on the lattice up to $\simeq 3$ times the physical charm mass. The interpolation to the phy…
We present an unquenched lattice calculation for the $B^0-\bar{B}^0$ transition amplitude. The calculation, carried out at an inverse lattice spacing $1/a$ = 2.22(4) GeV, incorporates two flavors of dynamical quarks described by the fully $O(a)$-improved Wilson fermion action and heavy quarks described by NRQCD. A particular attention is paid to the uncertainty that arises from the chiral extrapolation, especially the effect of pion loops, for light quarks, which we find could be sizable for the leptonic decay of the $B_d$ meson, whereas it is small for the $B_s$ meson and the $B$ parameters. …
We calculate the $\bar{s}s$ condensate in the D - and B - mesons using the unquenched hopping parameter expansion at infinite coupling for the Wilson lattice action. We discuss the phenomenological relevance of our result.
While many properties of the vector charmonium first excitations are yet to be measured, enhancements at unexpected energies are intriguing, alias the $Y$ states. In order to understand the naturally unquenched mesonic line-shapes, the influence of the most relevant hadronic decay channels must be taken into account. Within an unitary effective approach we present results where mesonic loops are included in an equivalent manner to coupled-channels. We show results for the $ψ(3770)$ and $ψ(4160)$ systems, where we find the nonperturbative effects of dynamical generation of poles and line-shape …
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 for their very existence. These hold the secrets of strong coupling QCD and teach us the way quarks really build hadrons.
We determine hadronic matrix elements relevant for the mass and width differences, $ΔM_s$ & $ΔΓ_s$ in the $B^0_s - \bar{B^0_s}$ meson system using fully unquenched lattice QCD. We employ the MILC collaboration gauge configurations that include $u$, $d$ and $s$ sea quarks using the improved staggered quark (AsqTad) action and a highly improved gluon action. We implement the valence $s$ quark also with the AsqTad action and use Nonrelativistic QCD for the valence $b$ quark. For the nonperturbative QCD input into the Standard Model expression for $ΔM_s$ we find $f_{B_s} \sqrt{\hat{B}_{B_s}} = 0.2…
We calculate the light meson spectrum and the light quark masses by lattice QCD simulation, treating all light quarks dynamically and employing the Iwasaki gluon action and the nonperturbatively O(a)-improved Wilson quark action. The calculations are made at the squared lattice spacings at an equal distance a^2~0.005, 0.01 and 0.015 fm^2, and the continuum limit is taken assuming an O(a^2) discretization error. The light meson spectrum is consistent with experiment. The up, down and strange quark masses in the \bar{MS} scheme at 2 GeV are \bar{m}=(m_{u}+m_{d})/2=3.55^{+0.65}_{-0.28} MeV and m_…
The semileptonic process, B --> πl ν, is studied via full QCD Lattice simulations. We use unquenched gauge configurations generated by the MILC collaboration. These include the effect of vacuum polarization from three quark flavors: the $s$ quark and two very light flavors ($u/d$) of variable mass allowing extrapolations to the physical chiral limit. We employ Nonrelativistic QCD to simulate the $b$ quark and a highly improved staggered quark action for the light sea and valence quarks. We calculate the form factors $f_+(q^2)$ and $f_0(q^2)$ in the chiral limit for the range 16 GeV$^2 \leq q^2…
Mesons with masses below their lowest OZI-allowed strong-decay thresholds have very small widths. Thus, it is usually believed that they can be safely treated as pure quark-antiquark bound states in spectroscopy models. However, unitarised and coupled-channel models from decades ago already indicated that this may not be the case, owing to significant virtual meson-loop contributions. Recent unquenched lattice calculations that include two-meson interpolators besides the usual $q\bar{q}$ ones confirm the latter conclusion, in particular for the enigmatic narrow $D_{s0}^\star(2317)$, $D_{s1}(24…
The interquark static potential for heavy mesons described by a massive One Gluon Exchange interaction obtained from the propagator of the truncated Dyson-Schwinger equations does not reproduced the expected Cornell potential. I show that no formulation based on a finite propagator will lead to confinement of quenched QCD. I propose a mechanism based on a singular nonperturbative coupling constant which has the virtue of giving rise to a finite gluon propagator and (almost) linear confinement. The mechanism can be slightly modified to produce the screened potentials of unquenched QCD.
The light hadron spectrum as computed in nonperturbative QCD is reviewed and compared to lattice data and experiment. The mixing of mesons, hybrids and glueballs is calculated in the Field Correlator Method. The strong decay mechanisms are found out in the method and compared to the known phenomenological models. The role of sea quarks (unquenched approximation) is studied analytically using radially excited mesons as an example, and compared to experiment.
The current situation for vector meson spectroscopy is outlined, and it is shown that the data are inconsistent with the generally-accepted model for meson decay. A possible resolution in terms of exotic mesons is given. Although this resolves some of the issues, fresh theoretical questions are raised.
In this mini-review I discuss three topics in meson spectroscopy. The production of heavy quarkonium states, S-wave scattering below 1 GeV, and exotic hybrid meson production. This is not intended to be a comprehensive review, just an overview of several topics of current interest.
Interactions in coupled channels pipi, KKbar and an effective 2pi2pi in scalar-isoscalar wave have been analysed. Influence of interchannel couplings on analytical structure of multichannel interaction amplitudes has been studied. Interplay of S-matrix zeroes and poles and their relation with parameters of scalar resonances has been investigated.
In this talk I comment on some theoretical expectations for exotic light meson spectroscopy below 2 GeV and their potential interest for a future energy upgrade of DAFNE.
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.
The current situation for vector meson spectroscopy is outlined, and it is shown that the data are inconsistent with the generally-accepted model for meson decay. A possible resolution in terms of exotic (hybrid) mesons is given. Although this hypothesis resolves some of the issues, fresh theoretical questions are raised. It is argued that high-precision $e^+e^-$ annihilation data provide an excellent laboratory for studying many aspects of nonperturbative QCD.
The experimental status of light vector meson spectroscopy is discussed. The last results of $e^+e^-$ experiments obtained at the VEPP-2M collider in Novosibirsk are described and the comparison with the old data in the mass region from 1 GeV to 2.5 GeV is performed.
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.
The theory of heavy meson masses, in which the symmetries of heavy and light quarks are exploited, can be used to describe the low energy interaction among heavy mesons to a better extent. The spin-flavor symmetry leads to many interesting relations between the properties of hadrons containing a heavy quark. The most direct consequences concern the spectroscopy of such states. We use such symmetries to explore some of the states of B-meson and predictions are found to be in agreement with the experimental data.
The meson spectroscopy is studied in the framework of the QCD string model. The mesons are composed of spinless quarks which move relativistically. We show that the QCD string model reproduces the straight line Regge trajectories and exibit the correct string slopes for both light-light and heavy-light mesons. We also present the exact numerical solution and the analytic approximation solution of the QCD string equations for the light-light mesons under the deep radial limit. We demonstrate that the QCD string model describes the universal relations for the light-light and heavy-light meson sp…
Dispersive approaches provide model independent description of meson-meson scattering. We first review here the use of dispersion relations to obtain a model independent unitarization of Chiral Perturbation Theory amplitudes, that establish the existence of light scalar mesons and whose leading 1/N_c behavior suggest they ahve a non q-qbar dominant component. We also review the forward dispersion relation checks on conflicting experimental data and the resulting very precise pion-pion scattering scattering amplitudes.
We study meson-meson scattering in a soluble model which describes asymptotically free mesons and confined quark-antiquark pairs via coupled channels. Concretely, the two scattered mesons are assumed to interact through s-channel meson-exchange diagrams. Furthermore, we develop a perturbative expansion of the model, and show that the thus found resonance pole positions, including contributions up to fourth order in perturbation theory, completely fail to reproduce the exact results. This shows that the resonance predictions based on perturbative approximations in quark models may be highly unr…
Using a quite accurate flavour-independence of $nS$-level mass differences in heavy quarkonia and a corresponding quasiclassical expression for the heavy quark binding energy, one shows that experimental data on masses of mesons with heavy quarks allow one to make the estimate $\bar Λ= 0.63\pm 0.03$ GeV.
New solutions on the scalar -- isoscalar $ππ$ phase shifts are analysed together with previous $K\bar{K}$ results using a separable potential model of three coupled channels ($ππ$, $K\bar{K}$ and an effective $2π2π$ system). Model parameters are fitted to two sets of solutions obtained in a recent analysis of the CERN-Cracow-Munich measurements of the $π^- p_{\uparrow} \to π^+ π^- n$ reaction on a polarized target. A relatively narrow (90 -- 180 MeV) scalar resonance $f_0(1400-1460)$ is found, in contrast to a much broader ($Γ\approx 500$ MeV) state emerging from the analysis of previous unpol…
Masses of the lowest multiplets of c,b-mesons in S- and P-wave states with quantum numbers JPC: 0-+, 1--, 0++, 1+-, 1++, 2++ are obtained with the help of dispersion N/D method of heavy quark effective theory. The results are in a good agreement with experimental data. Radiative decay widths for some states mentioned above were calculated.
The four-quark equations are found in the framework of the dispersion relation technique. The approximate solutions of these equations using the method based on the extraction of leading singularities of the amplitudes are obtained. The four-quark amplitudes of cryptoexotic mesons including the quarks of three flavours (u, d, s) are calculated. The mass values of low-lying cryptoexotic mesons are calculated.
I discuss the most recently discovered open charm mesons, both with and without strangeness. By exploiting the heavy quark limit, strong decay widths of such mesons are computed. Comparison between theoretical predictions and experimental measurements are useful to assign the right quantum numbers to such states. As for hidden charm mesons, I consider the case of X(3872). Analysis of its radiative decays to $J/ψγ$ and $ψ(2S) γ$ shows the plausibility of the identification with $χ_{c1}(2P)$.
Quenched and partially quenched chiral perturbation theory for vector mesons is developed and is used to extract chiral loop correction to the $ρ$ meson mass. Connections to fully quenched and totally unquenched chiral perturbation theory results are discussed. It is also shown that (partially) quenched perturbation theory for tensor mesons can be formulated analogously, and the chiral corrections for tensor meson masses are directly proportional to their counterparts in the vector meson sector. Utilizing this observation and non-relativistic quark model, we point out that mass difference $(m_…
Selected recent results from the H1 and ZEUS experiments are reviewed, illustrating some of the many facets of ``meson physics'' at the HERA ep collider. The results cover exclusive elastic and proton-dissociative diffractive vector meson production and comparisons with recent theoretical calculations show that perturbative QCD models are successful in describing these processes when at least one of the involved scales have large values. Furthermore a search for odderon induced exclusive photoproduction of pseudoscalar and tensor mesons is described; upper limits for the cross sections are bel…
We do meson spectroscopy by studying the behavior of S-matrix poles in the complex-energy plane, as a function of the coupling strength for triplet-P-zero quark-pair creation. Thereto, a general formula for non-exotic hadron-hadron scattering involving arbitrary quark confinement is used, which can be applied to all flavors. We find two distinct types of poles, which we call "confinement" and "continuum" poles, respectively. Together, they suffice to understand the experimental meson spectrum.
We present a calculation of the finite volume corrections to meson masses and decay constants in three flavour Partially Quenched Chiral Perturbation Theory (PQChPT) through two-loop order in the chiral expansion for the flavour-charged (or off-diagonal) pseudoscalar mesons. The analytical results are obtained for three sea quark flavours with one, two or three different masses. We reproduce the known infinite volume results and the finite volume results in the unquenched case. The calculation has been performed using the supersymmetric formulation of PQChPT as well as with a quark-flow techni…
Using the concept of collision time (time delay) introduced by Eisenbud and Wigner and its connection to on-shell intermediate unstable states, we study mesonic resonances in pi-pi and pi-K scattering. The time-delay method proves its usefulness by revealing the spectrum of the well-known rho- and K*-mesons and by supporting some speculations on rho-mesons in the 1200 MeV region. We use this method further to shed some light on more speculative meson resonances, among others the enigmatic scalars. We confirm the existence of chiralons below 1 GeV in the unflavoured and strange meson sector.
