Alfredo Vega, Francisca Rojas
We consider a Coulomb potential plus a confinement potential $ A r^ν $ and we study which of the two terms is dominant in the description of quarkonia. We find that in general the term of confinement is dominant, which allows us to understand why such potentials, like Martin's potential, are successful in describing of heavy mesons.
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We have calculated mass spectra of $D$, $D_s$ mesons using Dirac formalism with Martin-like potential in Potential model.
The mass spectrum and the pionic decay widths of the P-wave $D$ mesons are studied using the Dirac equation for the light quark. Our aim is to determine the Lorentz property of the confinement force. We find that the Lorentz scalar confinement is consistent with the mass spectrum, while a significant mixture of the Lorentz vector confinement is necessary to explain the decay widths.
Non-exotic scalar-meson resonances in S-wave meson-meson scattering are studied in the light of a unitarised Schroedinger model. The resulting poles in the scattering matrices, by analytical continuation into the complex-energy plane, are grouped into nonets of isoscalar, isodoublet, and isotriplet resonances. All singularities can be related to quark-antiquark confinement states, the light-quark nonet of which has ground states at 1.3 to 1.4 GeV and level spacings of some 300-400 MeV, except for a nonet of light scalar mesons below 1 GeV. All non-exotic S-wave resonances reported by experimen…
The form factors of the weak currents, which appear in the semileptonic decays of the heavy pseudoscalar mesons, are calculated within the quark confinement model by taking into account, for the first time, the structure of heavy meson vertex and the finite quark mass contribution in the heavy quark propagators. The results are in quite good agreement with the experimental data.
By using a new parametrization of the dilaton field and including a cubic term in the bulk scalar potential, we realize linear confinement in both meson and nucleon sectors within the framework of soft-wall AdS/QCD. At the same time this model also correctly incorporate chiral symmetry breaking. We compare our resulting mass spectra with experimental data and find good agreement between them.
Spectrum of masses of light pseudoscalar ($π, K, η, η'$) and vector ($ρ, K^*, ω, ϕ$) mesons can be explained on the base of the following assumptions: (1) analytical confinement (propagators of quarks and gluons are entire analytical functions of the Gaussian type), (2) mesons are bound states of quark and gluons (the Bethe-Salpeter equation in the one-gluon exchange approximation) and (3) QCD coupling constant $α_s(M)$ is a monotone decreasing function of mass of a bound state $M$. The decay constants $f_π$ and $f_K$ are calculated.
The reduced Bethe-Salpeter equation with scalar confinement and vector gluon exchange is applied to quark-antiquark bound states. The so called intrinsic flaw of Salpeter equation with static scalar confinement is investigated. The notorious problem of narrow level spacings is found to be remedied by taking into consideration the retardation effect of scalar confinement. Good fit for the mass spectrum of both heavy and light quarkomium states is then obtained.
In the framework of the dispersion relation N/D-method we restore the low-energy pi-pi (IJ^{PC}=00^{++})-wave amplitude sewing it with the previously obtained K-matrix solution for the region 450--1900 MeV [V.V. Anisovich, Yu.D. Prokoshkin and A.V. Sarantsev, Phys. Lett. B389, 388 (1996)]. The restored N/D-amplitude has a pole on the second sheet of the complex-s plane, near the pi-pi threshold. We discuss the hypothesis that this low-mass pole, or the low-mass sigma-meson, corresponds to the dynamical state related to the confinement forces, that is the eyewitness of confinement.
We present the results of a study of heavy-light-quark bound states in the context of the reduced Bethe-Salpeter equation with relativistic vector and scalar interactions. We find that satisfactory fits may also be obtained when the retarded effect of the quark-antiquark interaction is concerned.
I present a short review of the current understanding of the scalar meson sector, with special attention to the problem of the low-mass $σ$. The dispersion relation $N/D$-method used for the restoration of the low-energy $ππ$ $(IJ^{PC}=00^{++})$-wave amplitude is discussed. The low-energy $ππ$ amplitude was determined from the data in the energy region 280--500 MeV and it was sewn with the previously found $K$-matrix solution for the region 450--1950 MeV. The $N/D$-amplitude has a pole on the second sheet of the complex-$s$ plane, near the $ππ$ threshold at $\sqrt s \simeq 430-i325$ MeV, that …
Wavefunctions of a relativistic heavy quark-light quark $(Q,q)$ system described by a Dirac hamiltonian are analyzed. By assuming that the confinement potential is a Lorentz scalar (S), the slope of the Isgur-Wise function is calculated at zero recoil point. The result obtained is $ξ^\prime(1)=-0.93\pm 0.05.$ This means that the solutions are perfectly consistent. If relativistic corrections in the light quark wave functions are included the result is $ξ^\prime(1)=-1.01\pm 0.04.$ From heavy-light data this suggest that if relativistic effects are considered, scalar confinement is reliable in l…
In this paper, we study the chiral symmetry restoration in the hadronic spectrum in the framework of generalised Nambu-Jona-Lasinio quark models with instantaneous confining quark kernels. We investigate a heavy-light quarkonium and derive its bound-state equation in the form of a Schroedingerlike equation and, after the exact inverse Foldy-Wouthuysen transformation, in the form of a Diraclike quation. We discuss the Lorentz nature of confinement for such a system and demonstrate explicitly the effective chiral symmetry restoration for highly excited states in the mesonic spectrum. We give an …
An approach to QCD vacuum as a medium describable in terms of statistical ensemble of almost everywhere homogeneous Abelian (anti-)self-dual gluon fields is briefly reviewed. These fields play the role of the confining medium for color charged fields as well as underline the mechanism of realization of chiral $SU_{\rm L}(N_f)\times SU_{\rm R}(N_f)$ and $U_A(1)$ symmetries. Hadronization formalism based on this ensemble leads to manifestly defined quantum effective meson action. Strong, electromagnetic and weak interactions of mesons are represented in the action in terms of nonlocal $n$-point …
A simple relativistic quantum field model with the Yukawa-type interaction is considered to demonstrate that the analytic confinement of the constituent ("quarks") and carrier ("gluons") particles explains qualitatively the basic dynamical properties of the spectrum of mesons considered as two-particle stable bound states of quarks and gluons: the quarks and gluons are confined, the glueballs represent bound states of massless gluons, the masses of mesons are larger than the sum of the constituent quark masses and the Regge trajectories of mesonic orbital excitations are almost linear.
We discuss a mechanism by which a set of $q\bar q$-states mixes with an exotic one, so that the exotic state accumulates the widths of the overlapping $\bar qq$ resonances. The broad state created this way acts as a 'locking' state for the others. Using results of a previous analysis of the $(IJ^{PC}=00^{++})$-wave, we estimate the mean radius squared of the broad state $f_0 (1530^{+90}_{-250})$; it appears to be distinctly larger than the mean squared radii of the locked narrow states. This supports an idea about the constructive role of broad states in forming the confinement barrier.
A formalism for studying the confinement of heavy quarks by considering the renormalised quark Dyson-Schwinger equation in the limit m --> infinity is described. We are particularly interested in studying the analytic structure of heavy quark propagators in the region of the complex momentum plane close to the bare fermion mass pole.
In this paper the spectrum of quark-antiquark systems, including light mesons and tachyons, is studied in the true vacuum and in the chiral invariant vacuum. The mass gap equation for the vacua and the Salpeter-RPA equation for the mesons are solved for a simple chiral invariant and confining quark model. At T=0 and in the true vacuum, the scalar and pseudoscalar, or the vector and axial vector are not degenerate, and in the chiral limit, the pseudoscalar groundstates are Goldstone bosons. At T=0 the chiral invariant vacuum is an unstable vacuum, decaying through an infinite number of scalar a…
The light scalar mesons below 1 GeV as tetraquark states are studied in the framework of the flux-tube model, the multi-body confinement instead of the additive two-body confinement is used. From the calculated results, we find that the light scalar mesons, $σ$, $κ$ could be well accommodated in the diquark-antidiquark tetraquark picture in the flux-tube model and they could be color confinement resonances. The mass of the first radial excited state of $[ud][\bar{u}\bar{d}]$ is 1019 MeV, which is close to the mass of $f_0(980)$. Whereas $a_0(980)$ can not be fitted in this interpretation.
We describe the meson-meson data for the ($IJ^{PC}=00^{++}$) wave at $280\leq\sqrt s\leq 1900$ MeV in two approaches: (i) the K-matrix approach and (ii) the dispersion relation D-matrix method. With a good description of low energy data (at $280\leq\sqrt s\leq 900$ MeV) as well as the data of two-meson transition amplitudes and antiproton-proton annihilation into three pseudoscalar meson states (at $450\leq\sqrt s\leq 1950$ MeV) we have found the positions of the resonance poles: (i) for the $σ$ meson pole: $M_σ= (390\pm 35)-i(235\pm 50)$ MeV; (ii) two poles for the $f_0(980)$, on the second s…
The concept of Lorentz scalar quark confinement has a long history and is still widely used despite its well-known theoretical faults. We point out here that the predictions of scalar confinement also conflict directly with experiment. We investigate the dependence of heavy-light meson mass differences on the mass of the light quark. In particular, we examine the strange and non-strange D mesons. We find that the predictions of scalar confinement are in considerable conflict with measured values.
The most important advances achieved recently on the double heavy flavored mesons are reviewed. Some problems and outlooks on them are also outlined.
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.
For the first time, a solution to the $a_2/a_1$ sign problem in heavy meson decay based on PQCD factorization theorems. The point is to include QCD evolution effort characteristic scales involved in decay processes.
The effective quark Lagrangian is derived from the QCD action by means of averaging over the vacuum fields. In the limit of large N_c and keeping for simplicity the lowest order gluonic correlator one obtains nonlinear equations for the quark propagator, exhibiting scalar confinement. Connection to the quark zero mode density is discussed.
We consider the two-pion decay of the $ρ$-meson, the $^3S_1q\bar q$-state of the constituent quarks -- the decay being determined by the transition $q\bar q\to ππ$ contains information about confinement interactions. One can specify in this decay two types of transitions: ({\bf i}) the bremsstrahlung radiation of a pion $q\to q+π$ (or $\bar q\to\bar q+π$) with the subsequent fusion $q\bar q\to π$, and ({\bf ii}) the direct transition $q\bar q\to ππ$. We demonstrate how in the amplitudes of the corresponding transitions the quark singularities have to disappear, {\it i.e.} what is the way the q…
Propagation of the heavy quark in the field of a static antiquark source is studied in the framework of effective Dirac equation. The model of QCD vacuum is described by bilocal gluonic correlators. In the heavy quark limit the effective interaction is reduced to the potential one with 5/6 Lorentz scalar and 1/6 Lorentz vector linear confinement, while spin-orbit term is in agreement with Eichten-Feinberg-Gromes results. New spin-independent corrections to the leading confining regime are identified, which arise due to the nonlocality of the interaction in time direction and quark Zitterbewegu…
The formation and spectrum of two-particle bound states are investigated within a simple relativistic quantum field model with the Yukawa-type interaction. Within this approach, relatively weakly interacting quarks and gluons form stable bound states under the analytic confinement. By introducing a minimal set of free parameters (the quark masses, the coupling constant and the confinement 'radius') and by solving the Bethe-Salpeter equation with one-gluon exchange, we satisfactorily explain the experimental data for most known mesons and the glueball.
Electromagnetic interactions are introduced in the effective chiral Lagrangian for heavy mesons which includes light vector particles. A suitable notion of vector meson dominance is formulated. The constraints on the heavy meson -light vector and heavy meson-light pseudoscalar coupling constants are obtained using experimental $D^* \ra D \, γ$ branching ratios. These constraints are compared with values estimated from semi-leptonic transition amplitudes as well as from extension of the light meson coupling pattern. Application to the heavy baryon spectrum in the ``bound state " model is made.
We describe the effective heavy meson lagrangian for S- and P-wave heavy-light mesons in terms of a model based on meson-quark interactions, where mesonic transition amplitudes are represented by diagrams with heavy mesons attached to loops containing heavy and light constituent quarks. The model is relativistic and incorporates the heavy quark symmetries. The universal form factors of the heavy meson transition amplitudes are calculated together with their slopes and compared to existing data and limits. As further applications of the model, strong and radiative decays of D* and B* are consid…
The spin and flavor symmetries of the heavy quark effective theory are employed to discuss the exclusive cross sections for pair production of heavy mesons in photon-photon collision. The ratios of the exclusive cross sections for heavy mesons are obtained explicitly and the validity of results is discussed.
The amplitudes for one-pion mediated transitions between heavy meson excited states are obtained in the framework of the relativistic chiral quark model. The effective coupling constants to pions and the decay widths of excited heavy mesons with l<=2 for non-radially excited, and the l=0 radially excited mesons are presented for both charmed and beauty mesons. We also discuss the allowed decays of strange excited heavy mesons by emission of a K-meson.
In the framework of QCD sum rules one uses a scheme, allowing one to apply the conditions of both nonrelativistic heavy quark motion inside mesons and independence of nonsplitting nS-state density on the heavy quark flavours. In the leading order an analitic expression is derived for leptonic constants of both heavy quarkonia and heavy mesons with a single heavy quark. The expression allows one explicitly to determine scaling properties of the constants.
We examine the decays of excited heavy mesons, including the leading power corrections to the heavy quark limit. We find a new and natural explanation for the large deviation of the width of the $D_1(2420)$ from the heavy quark symmetry prediction. Our formalism leads to detailed predictions for the properties of the excited bottom mesons, some of which recently have been observed. Finally, we present a detailed analysis of the effect of power corrections and finite meson widths on the angular distributions which may be measured in heavy meson decays.
Spectra of heavy-light meson are studied using potential model and thermofield dynamics prescription. The mass spectra of different heavy-light mesons are calculated at different temperatures and compared with those at T=0. It is found that the binding mass of heavy-light meson decreases as temperature increases.
We calculate the coupling constants between the light vector mesons and heavy mesons within the framework of the light-cone QCD sum rule in the leading order of heavy quark effective theory. The sum rules are very stable with the variations of the Borel parameter and the continuum threshold. The extracted couplings will be useful in the study of the possible heavy meson molecular states. They may also helpful in the interpretation of the proximity of X(3872), Y(4260) and Z(4430) to the threshold of two charmed mesons through the couple-channel mechanism.
In this paper we obtain a heavy meson bound state equation from the heavy quark equation of motion in heavy quark effective theory (HQET) and the heavy meson effective field theory we developed very recently. The bound state equation is a covariant extention of the light-front bound state equation for heavy mesons derived from light-front QCD and HQET. We determine the covariant heavy meson wave function variationally by minimizing the binding energy $\barΛ$. Subsequently the other basic HQET parameters $λ_1$ and $λ_2$, and the heavy quark masses $m_b$ and $m_c$ can also be consistently determ…
The analytic behavior of the heavy-light meson form factor is investigated using several relativistic examples including unconfined, weakly confined, and strongly confined mesons. It is observed that confinement erases the anomalous threshold singularity and also induces an essential singularity at the normal annihilation threshold. In the weak confinement limit, the "would be" anomalous threshold contribution is identical to that of the real singularity on its space-like side.
Relations between the form factors that parametrize the hadronic matrix elements, in spectator decays of heavy mesons, have been derived by Stech within the constituent quark model. In here, we examine these relations using a slightly modified description of the meson states. We find new and very general relations for some of the form factors. For the other form factors, we obtain small modifications to the relations previously derived by Stech, in the case of heavy-to-light transitions.
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 argue that the ratio of $ϕ$ mesons multiplicity over cube of the mean $p_T$ is proportional to the degeneracy of the medium produced in ultra-relativistic heavy ion collisions. The ratio extracted from the existing $ϕ$ meson data in the energy range $\sqrt{s}$=6.3-200 GeV, indicate that beyond a threshold energy $\sqrt{s}_{th}=15.74\pm 8.10$ GeV, the medium crosses over from a confined phase to a deconfined phase.
We analyse the Lorentz structures of weak decay matrix elements bewteen meson states of arbitrary spin. Simplifications arise in the transition amplitudes for a heavy meson decaying into a light one via a Bethe-Salpeter approach which incorporates heavy quark symmetry. Phenomenological consequences on several semileptonic, nonleptonic and FCNC induced decays of heavy flavoured mesons are derived and discussed.
We show the 't Hooft Equation and the light-front holographic Schrödinger Equation are complementary to each other in governing the transverse and longitudinal dynamics of colour confinement in quark-antiquark mesons. Together, they predict remarkably well the light, heavy-light and heavy-heavy meson spectroscopic data. The universal emerging hadronic scale of light-front holography, $κ\approx 0.5$ GeV, controls the transverse dynamics of confinement in all mesons. In heavy-heavy mesons, it also coincides numerically with the 't Hooft coupling which governs longitudinal confinement, thus refle…
We consider an extended Nambu--Jona-Lasinio (NJL) model for the light meson sector of QCD where unphysical quark production thresholds are excluded by an infrared cut-off on the momentum integration within quark loop diagrams. This chiral quark model conserves the low energy theorems. The infrared cut-off is fixed selfconsistently by the dynamically generated quark mass (quark condensate). The masses and decay widths of the σ- and ρ-mesons are described in the model.
Heavy quark symmetry and its breaking in strong decays of P-wave heavy-light mesons are examined within the EHQ's method. The consistence of theory with experiments indicates that the breaking of heavy quark symmetry in the two-body strong decays of these mesons is not large. The relation between the EHQ's method and the $^3P_0$ model is investigated, and the phenomenological transition strengths $\mathcal {F}^{j_q,j'_q}_{j_h,l}(0)$ of the P-wave heavy-light mesons within the EHQ method are analytically derived within the $^3P_0$ model.
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 introduce a kinetical description of the hadronization of semi-deconfined quark matter produced in heavy ion collisions. A minimal microscopic model is considered in which the produced quarks and anti-quarks are redistributed into hadrons according to the additive quark model. Assuming thermalized quark matter and hadron matter we determine the appropriate parameters to describe the properties of both matter before and after hadronization. We find an adiabatic hadronization.
We propose an extended Nambu--Jona-Lasinio model to include the heavy mesons with the heavy quark symmetry. The quark current-current interaction is generalized to include the heavy quark currents. In order to comply with the heavy quark spin symmetry at the heavy quark limit, the quark mass dependence of the interaction strength is introduced. The light and heavy pseudo-scalar and vector meson, their masses and the weak decay constants, are calculated in the unified frame.
Introductory lectures (delivered at the VI Mexican School of Particles and Fields) on heavy quarks and heavy quark effective field theory. Applications to inclusive semileptonic decays and to interactions with light mesons are covered in detail.
We show how to obtain a ``heavy'' meson effective lagrangian for the case where the number of heavy particles is not conserved. We apply the method in a simple example at tree level and perform then the reduction for the case of vector mesons in Chiral Perturbation Theory in a manifestly chiral invariant fashion. Some examples showing that ``heavy'' meson effective theory also works at the one-loop level are included.
I review recent developments in the description of the interactions between light and heavy mesons by an effective chiral lagrangian having the symmetries of the Heavy Quark Effective Theory. In particular the problem of the determination of the strong coupling constants $g_{P^* P π}$ and $g_{P^* P ρ}$ ($P, P^*=$ heavy mesons) is addressed. Invited talk given at the 18th J. Hopkins Workshop (Florence, September 1994)
Using the calculated values of the strong coupling constants of the heavy sextet spin-3/2 baryons to sextet and antitriplet heavy spin-1/2 baryons with light mesons within the light cone QCD sum rules method, and vector meson dominance assumption, the radiative decay widths are calculated. These widths are compared with the "direct" radiative decay widths predicted in the framework of the light cone QCD sum rules.
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.
In this paper we present a detailed formulation for a recently proposed effective field theory to describe the nonperturbative QCD dynamics of heavy mesons. This effective theory incorporates with heavy quark symmetry (HQS) and the heavy quark effective theory (HQET). Heavy mesons in this theory are constructed as composite particles of a heavy quark bounded with the light degrees of freedom. The heavy meson properties in the heavy quark limit and the $1/m_Q$ corrections can then be explicitly evaluated from this effective theory. All the basic parameters of the HQET, namely, the heavy quark m…
We investigate decay constants of P and D-wave heavy-light mesons within the mock-meson approach. Numerical estimates are obtained using the relativistic quark model. We also comment on recent calculations of heavy-light pseudo-scalar and vector decay constants.
The effect of an extended Cornell potential on mass spectra of heavy and heavy-light mesons is studied. The Cornell potential is extended to include quadratic potential and inverse quadratic potential. The N-radial Schrodinger equation is solved by using series method. The results for charmonium and bottomonium, and light-heavy meson masses are obtained. A comparison with other recent works is discussed. The present results are improved in comparison with other recent works and are in good agreement with experimental data.
We have systematically studied the S-wave pseudoscalar meson and heavy vector meson scattering lengths to the third order with the chiral perturbation theory, which will be helpful to reveal their strong interaction. For comparison, we have presented the numerical results of the scattering lengths (1) in the framework of the heavy meson chiral perturbation theory and (2) in the framework of the infrared regularization. The chiral expansion converges well in some channels.
The spin-averaged binding energy and the hyperfine mass splitting of heavy-light mesons are investigated within the constituent quark model as a function of the inverse heavy-quark mass. It is shown that the so-called heavy-quark kinetic energy, -lambda1 / 2mQ, may differ remarkably from the non-relativistic expectation <p**2> / 2mQ, thanks to relativistic effects in the effective interquark potential for heavy-light mesons, which may yield substantial 1 / mQ corrections to the heavy-quark static limit. The determination of the difference of the hadronic parameter lambda1 in the B(u(d)) and B(…
We evaluate the radiative and hadronic decay rates of the $D^*$ mesons using the Heavy Quark Effective Theory and the Vector Meson Dominance hypothesis. We also estimate the width of the $B^*$ electromagnetic transitions and the radiative decays of positive parity $J^P=0^+, 1^+$ charmed mesons.
We use recent experimental data on charmed mesons to constrain three coupling constants in the effective lagrangian describing the interactions of excited heavy-light mesons with light pseudoscalar mesons at order $m_Q^{-1}$. Predictions in the beauty sector are also derived.
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.
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