We derive the chiral effective Lagrangian for heavy-light mesons in the heavy quark limit from QCD under proper approximations. The low energy constants in the effective Lagrangian are expressed in terms of the light quark self-energy. With typical forms of the running coupling constant of QCD and the quark self-energy obtained from Dyson-Schwinger equations as well as lattice QCD, we estimate the low energy constants in the model and the strong decay widths. A comparison with data and some discussions of the numerical results are presented.
An investigation of the s-wave channels in meson-meson scattering is performed within a U(3) chiral unitary approach. Our calculations are based on a chiral effective Lagrangian which includes the eta' as an explicit degree of freedom and incorporates important features of the underlying QCD Lagrangian such as the axial U(1) anomaly. We employ a coupled channel Bethe-Salpeter equation to generate poles from composed states of two pseudoscalar mesons. Our results are compared with experimental phase shifts up to 1.5 GeV and effects of the eta' within this scheme are discussed.
Chiral effective lagrangians may differ in their prediction of meson-nucleon scattering amplitudes off-meson-mass-shell, but must yield identical S-matrix elements. We argue that the effective meson mass in nuclear matter obtained from chiral effective lagrangians is also unique. Off-mass-shell amplitudes obtained using the PCAC choice of pion field must therefore not be viewed as fundamental constraints on the dynamics, the determination of the effective meson mass in nuclear matter or the possible existence of meson condensates in the ground state of nuclear matter. This hypothesis is borne …
We construct the complete and minimal O(q^2) and O(q^3) three-flavour Lorentz invariant chiral meson-baryon Lagrangians for the first time in the literature. We compare with previous three-flavour studies reducing the number of independent monomials and adding new ones that were missing.
A qualitative account of the meson-meson and meson-baryon interactions using chiral Lagrangians and the inverse amplitude method in coupled channels is done. The method, imposing exact unitarity, proves to be very useful tool to extend the information contained in the chiral Lagrangians at energies beyond the realm of applicability of chiral perturbation theory.
We develop a coupled channel unitary approach describing the behavior at higher energies of systems whose low-energy dynamics is given by effective O(p^2) and O(p^4) chiral Lagrangians. Our free parameters are those of the O(p^4) Lagrangian. When applied to the meson-meson interaction, it yields a remarkable agreement with data up to sqrt{s}=1.2 GeV, dynamically generating the sigma, f_0, a_0,rho and K^* resonances. Further applications are also proposed.
We consider the chiral Lagrangian with a nonet of Goldstone bosons and a nonet of light vector mesons. The mixing between the pseudoscalar mesons eta and eta-prime is taken into account. A novel counting scheme is suggested that is based on hadrogenesis, which conjectures a mass gap in the meson spectrum of QCD in the limit of a large number of colors. Such a mass gap would justify to consider the vector mesons and the eta-prime meson as light degrees of freedom. The complete leading order Lagrangian is constructed and discussed. As a first application it is tested against electromagnetic tran…
A scaled SU(3) Nambu - Jona-Lasinio Lagrangian is used to compute the mass of the nine scalar mesons in the vacuum and the mass of the gluball. It is shown that a suitable choice of the vacuum gluon condensate allows to reproduce the experimental masses of the scalar mesons except for the {$K^*_{0}$}(1430). This choice corresponds to a weak coupling between the gluon and quark condensates, giving a {$f_{0}$}(1500) or a {$f_{J}$}(1710) which is nearly a pure glueball.
After our work was published, Frink and Meißner \cite{FM06} pointed out that our {\cal O}(q^3) three-flavour meson-baryon chiral Lagrangian was not minimal. Here, we discuss their findings and revise ours accordingly. We find that eight monomials in our ${\cal O}(q^3)$ Lagrangian are not independent, but in addition, two monomials were wrongly discarded, which, as a result, makes the agreement in the number of independent monomials with \cite{FM06} complete.
An effective potential in a meson-meson system is discussed based on the SU(3) chiral constituent quark model, and the analytic form of the potential is explicitly given. In addition, the effective potential is employed to study the bound state problem of ωϕwhich is related to the new resonance of f0(1810) observed in BESII very recently.
We report on recent nonperturbative techniques that combine the information of chiral Lagrangians (with and without resonances) with unitarity in coupled channels and other requirements of the S-matrix theory of the strong interactions. As a result, the region of applicability of such techniques is much larger than the one of Chiral Perturbation Theory allowing one to study also resonance physics. Applications to meson-meson and meson-baryon scattering, as well as to problems where pairs of mesons or a meson and a baryon appear in the initial or final state are shown. Implications in several n…
A new tool which combines chiral perturbation theory and unitarity in coupled channels is applied with success to the study of the meson-meson interaction, extending the theoretical predictions up to sqrt{s} = 1.2 GeV, hence improving considerably the convergence radius of conventional chiral perturbation theory. The method is applied to obtain the meson-meson phase shifts and inelasticities as well as the isoscalar pion-pion scattering amplitude inside a nuclear medium.
Using baryon chiral perturbation theory including vector mesons, we analyse various continuum contributions to the isoscalar electromagnetic spectral functions of the nucleon induced by the leading order couplings.
Chiral thermodynamics of charmed mesons is formulated at finite temperature within a $2+1+1$-flavored effective Lagrangian incorporating heavy quark symmetry. The charmed-meson mean fields act as an extra source which breaks the chiral symmetry explicitly. This leads to effective interactions between the light and heavy-light mesons, which intrinsically depend on temperature. Effective masses of the scalar and pseudoscalar charmed-mesons tend to approach each other as increasing temperature, so that the splitting between the chiral partners is reduced. These chiral splittings are shown to be l…
The approximate symmetries of Quantum ChromoDynamics in the infinite heavy quark ($Q=c,b$) mass limit ($m_Q \to \infty$) and in the chiral limit for the light quarks ($m_q \to 0,\;q=\,u,\,d,\,s$) can be used together to build up an effective chiral lagrangian for heavy and light mesons describing strong interactions among effective meson fields as well as their couplings to electromagnetic and weak currents, including the relevant symmetry breaking terms. The effective theory includes heavy ($Q \bar q$) mesons of both negative and positive parity, light pseudoscalars, as well as light vector m…
Here we point out that the four-nucleon terms incorporate into lowest order non-linear chiral effective Lagrangians the same description of bulk nuclear matter contained in the Walecka model, that is generally considered satisfactory. We find this point worth noticing because, while the Walecka model is an entirely phenomenological renormalizable model, non-linear chiral Lagrangians have a deep basis in elementary particle physics, and, in this sense, are more fundamental.
We study the spectrum of heavy-light mesons within a model with linear instantaneous confining potential. The single-quark Green function and spontaneous breaking of chiral symmetry are obtained from the Schwinger-Dyson (gap) equation. For the meson spectrum we derive a Bethe-Salpeter equation (BSE). We solve thiss equation numerically in the heavy-light limit and obtain effective restoration of chiral and $U(1)_A$ symmetries at large spins.
We study the nature of the scalar D_0 meson from the viewpoint of chiral symmetry. With the linear representation of chiral symmetry, we construct the D pi scattering amplitude satisfying the chiral low-energy theorem, in which the D_0 meson appears as an s-wave resonance. We show that the properties of the D_0 meson can be successfully reproduced as the chiral partner of the D meson coupled with the D pi scattering states. At the same time, we find that the spectral function and the pole position of D_0 are not very sensitive to the reduction of the chiral condensate, indicating the importanc…
We investigate the in-medium masses of a $\bar{D} (0^-)$ meson and a $\bar{D}_0^* (0^+)$ meson and spectral functions for $\bar{D}$ and $\bar{D}_0^*$ meson channels in nuclear matter. These mesons are introduced as chiral partner in the chiral symmetry broken vacuum, hence they are useful to explore the partial restoration of the broken chiral symmetry in nuclear matter. We consider the linear sigma model to describe the chiral symmetry breaking. Our study shows that the loop corrections to $\bar{D}$ and $\bar{D}_0^*$ meson masses provide a smaller mass splitting at finite density than that in…
We show the results for the scattering poles associated to the rho, f0, a0, K*, sigma and kappa resonances in meson-meson scattering. Our amplitudes are obtained from the complete one-loop meson-meson scattering amplitudes from Chiral Perturbation Theory. Once unitarized with the Inverse Amplitude Method, they describe remarkably well the data simultaneously in the low energy and resonance regions up to 1.2 GeV, using low energy parameters compatible with present determinations.
It is demonstrated that using a suitable renormalization condition one obtains a consistent power counting in manifestly Lorentz-invariant baryon chiral perturbation theory including vector mesons as explicit degrees of freedom.
Studies of the QCD phase diagram must properly include nucleonic degrees of freedom and their thermodynamics in the range of baryon chemical potentials characteristic of nuclear matter. A useful framework for incorporating relevant nuclear physics constraints in this context is a chiral nucleon-meson effective Lagrangian. In the present paper, such a chiral nucleon-meson model is extended with systematic inclusion of mesonic fluctuations using the functional renormalization group approach. The resulting description of the nuclear liquid-gas phase transition shows a remarkable agreement with th…
Expansion of model Nambu-Jona-Lasinio is considered and on its basis an effective lagrangian for mesons, baryons and baryon - meson interaction has been obtained.
Chiral symmetry is consistently implemented in the two-nucleon problem at low-energy through the general effective chiral lagrangian. The potential is obtained up to a certain order in chiral perturbation theory both in momentum and coordinate space. Results of a fit to scattering phase shifts and bound state data are presented, where satisfactory agreement is found for laboratory energies up to about 100 Mev.
We investigate the finite temperature behavior of the meson sector of an effective Lagrangian which describes nuclear matter. A method is developed for evaluating the logarithmic terms in the effective potential which involves expansion and resummation; the result is written in terms of the exponential integral. In the absence of explicit chiral symmetry breaking, a phase transition restores the symmetry at a temperature of 190 MeV; when the pion has a mass the transition is smooth. At a much higher temperature a first order phase transition restores scale symmetry.
We present the complete one-loop calculation of all the two meson scattering amplitudes within the framework of SU(3) Chiral Perturbation Theory, which includes pions, kaons and the eta. In addition, we have unitarized these amplitudes with the coupled channel Inverse Amplitude Method, which ensures simultaneously the good low energy properties of Chiral Perturbation Theory and unitarity. We show how this method provides a remarkable description of meson-meson scattering data up to 1.2 GeV including the scattering lengths and the generation of seven light resonances, which is consistent with p…
We compare the linear meson model and chiral perturbation theory in next to leading order in the quark mass expansion. In particular, we compute the couplings L_4--L_8 of chiral perturbation theory as functions of the parameters of the linear model. They are induced by the exchange of 0^{++} scalar mesons. We use a phenomenological analysis of the effective vertices of the linear model in terms of pseudoscalar meson masses and decay constants. Our results for the L_i agree with previous phenomenological estimates.
We construct the relativistic chiral Lagrangians with decuplet baryons up to the order $\mathcal{O}(p^4)$ (one loop). For the meson-decuplet-decuplet couplings, there are 1, 13, 55, and 548 terms in the $\mathcal{O}(p^1)$-$\mathcal{O}(p^4)$ order Lagrangians, respectively. For the meson-octet-decuplet Lagrangians, the number of independent terms from $\mathcal{O}(p^1)$ to $\mathcal{O}(p^4)$ are 1, 5, 67, and 611, respectively. For convenience of applications, the $πΔΔ$ and $πNΔ$ chiral Lagrangians are picked out. This new form of $Δ$ Lagrangians is equivalent to the original isovector-isospino…
A non-perturbative method which combines constraints from chiral symmetry breaking and coupled channel unitarity is used to describe the meson-meson interaction up to about 1.2 GeV. The approach uses the O(p^2) and O(p^4) chiral Lagrangians. The seven free parameters of the O(p^4) Lagrangian are fitted to the data. The results are in good agreement with a vast amount of experimental analyses. The amplitudes develop poles in the complex plane corresponding to the f0, a0, rho, K*, phi, sigma and kappa resonances; the latter two, very broad. The total and partial decay widths of the resonances ar…
We point out that the study of the density dependences of the masses of heavy-light mesons give some clues to the chiral symmetry structure in nuclear matter. We include the omega meson effect as well as the sigma meson effect at mean field level on the density dependence of the masses of heavy-light mesons with chiral partner structure. It is found that the omega meson affects the masses of the heavy-light mesons and their antiparticles in the opposite way, while it affects the masses of chiral partners in the same way. This is because the omega meson is sensitive to the baryon number of the …
Effective masses of $ρ$ and $ω$ mesons in nuclear medium are studied in a hadronic effective theory. Both the pole position and the screening mass decrease in nuclear matter due to the polarization of the nucleon Dirac sea. The physical origin of the decrease is a reduction of the wave function renormalization constant induced by the tensor (vector) interaction of the $ρ$ ($ω$) with the nucleon. Relation to the results of the QCD sum rules is also discussed.
The implication of chiral symmetry for the pion-induced dissociation of the J/psi is examined in detail. It is shown how the low-energy dynamics of pions, constrained by chiral symmetry, affect the dissociation cross-section. The derived soft-pion theorem is then integrated into a Lagrangian model which includes also abnormal parity content and chiral-symmetric form factors. Dissociation by the rho meson is also considered.
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.
We construct the three-flavor Lorentz-invariant meson-baryon chiral Lagrangians at the order $p^4$, with which a full one-loop investigation may be performed. One obtains 540 independent terms. The processes with the minimal number of mesons and photons that this order Lagrangians may contribute to are also presented.
We show that the recently constructed complete and ``minimal'' third order meson-baryon effective chiral Lagrangian can be further reduced from 84 to 78 independent operators.
We review two approaches to studying pseudoscalar meson-meson scattering amplitudes to beyond 1 GeV using non-linear and linear chiral Lagrangians. These approaches use two different unitarisation techniques - a generalised Breit Wigner prescription and K-matrix unitarization respectively. We also report some preliminary findings on K-matrix unitarisation of the I=J=0 pion-pion scattering amplitude in the non-linear chiral Lagrangian approach and make some remarks about the light scalar mesons.
The properties of $ρ$-mesons at finite temperature ($T$) are examined with an effective chiral lagrangian in which vector and axial-vector mesons are included as massive Yang-Mills fields of the chiral symmetry. It is shown that, at $T^2$ order, the effective mass is not changed but only the mixing effect in vector and axial-vector correlator appears.
The approach of path integral hadronization, applied to a quark-diquark toy model, is used to derive an effective chiral meson-baryon Lagrangian. In this approach the Goldberger-Treiman relation, found at the quark-meson level, is re-established at the composite hadron level. For illu- strations, electromagnetic low energy characteristics of composite nucleons are estimated.
Effective Chiral Lagrangian is derived from QCD in the framework of Field Correlator Method. It contains the effects of both confinement and chiral symmetry breaking due to a special structure of the resulting quark mass operator. It is shown that this Lagrangian describes light pseudoscalar mesons, and Gell-Mann-Oakes-Renner relations for pions, eta and K mesons are reproduced. Spectrum of radial excitations of pions and K mesons is found and compared to experimentally known masses.
We show that the number of operators in the presently known mesonic chiral Lagrangian of order p^6 in the two-flavour sector can be reduced by at least one from 57 to 56 by providing an explicit relation among the operators. We briefly discuss the relevance of this new relation.
The chiral SU(3) Lagrangian with pseudoscalar and vector $D$ mesons and with the octet and decuplet baryons is considered. The leading two-body counter terms involving two baryon fields and two $D$ meson fields are constructed in the open-charm sector. There are 26 terms. A combined expansion in the inverse of the charm quark mass and in the inverse of the number of colors provides sum rules that reduce the number of free parameter down to 5 only. Our result shows the feasibility of a systematic computation of the open-charm baryon spectrum based on coupled-channel dynamics.
The meson fields are simulated by quark operators and an effective chiral theory of mesons is presented. There are spontaneous chiral symmetry breaking and dynamical chiral symmetry breaking. Theoretical results agree with data well.
The chiral Lagrangians with vector mesons are constructed in different approaches, including the next-to-leading order Lagrangian in the vector-field approach, the next-to-next-to-leading order Lagrangians in the tensor-field and the hidden local symmetry approaches. Some redundant terms are found at the next-to-leading order in the tensor-field and the hidden local symmetry approaches. The corresponding relations between the next-to-next-to-leading order pseudoscalar mesonic low-energy constants and the ones in the hidden local symmetry approach are obtained at tree level. The equivalence bet…
We investigate the bulk properties of symmetric nuclear matter within the framework of an in-medium modified chiral solitonic model with $π$, $ρ$ and $ω$ mesons. We consider the modification of meson degrees of freedom in nuclear matter, based on phenomenology of pion-nucleus scattering and the empirical nuclear mass formula. We discuss the results of the density dependence of the volume term in the mass formula and the incompressibility of symmetric nuclear matter, comparing them with relativistic mean-field models. The mass dropping of the $ρ$ meson in nuclear matter is also obtained and dis…
Starting from a QCD inspired bilocal quark interaction we obtain a local effective meson lagrangian. In contrast to previous local (NJL-like) approaches, we include nonlocal corrections related to the finite meson size which we characterize by a small parameter. After bosonization using the heat-kernel method we predict the structure coefficients of the Gasser-Leutwyler $p^4$-lagrangian up to first order in this parameter. The modifications for the $L_i$ coefficients are typically of the order 10-20\%, except for $L_5$, where we find a stronger nonlocal influence.
We give the general framework for adding "light" vector particles to the heavy hadron effective chiral Lagrangian. This has strong motivations both from the phenomenological and aesthetic standpoints. An application to the already observed $D \rightarrow \overbar{K^*} $ weak transition amplitude is discussed.
We discuss a minimal holographic model for the description of heavy-light and light mesons with chiral symmetry, defined in a slab of AdS space. The model consists of a pair of chiral Yang-Mills and tachyon fields with specific boundary conditions that break spontaneously chiral symmetry in the infrared. The heavy-light spectrum and decay constants are evaluated explicitly. In the heavy mass limit the model exhibits both heavy-quark and chiral symmetry and allows for the explicit derivation of the one-pion axial couplings to the heavy-light mesons.
The status of lattice determinations of quark masses is reviewed (with the exception of m_b). Attempts to extract the low-energy constants in the effective chiral Lagrangian are discussed, with special emphasis on those couplings which are required to test the hypothesis of a massless up-quark. Furthermore, the issue of quenched chiral logarithms is addressed.
We calculate the mass of the vector meson in the chiral symmetry restored vacuum. This is accomplished by separating the four quark operators appearing in the vector and axial vector meson sum rules into chiral symmetric and symmetry breaking parts depending on the contribution of the fermion zero modes. We then identify each part from the fit to the vector and axial vector meson masses. By taking the chiral symmetry breaking part to be zero while keeping the symmetric operator to the vacuum value, we find that the chiral symmetric part of the vector and axial vector meson mass to be between 5…
Meson correlation functions are studied in the model with four-fermion interaction Lagrangian. We demonstrate that despite the singular character of system mean energy and corresponding quark condensate found out the meson observables are finite, quite well identified and compatible with experimental energy scale. It allows one to use the similar model Hamiltonians for describing the nonequilibrium features of quark/hadron systems which reveal themselves in studying ultrarelativistic heavy ion collisions. The analytical results for meson correlation functions in the Keldysh model are given.
Light meson ( $π,\ σ,\ a_0$) properties in the environment with chiral imbalance are analyzed with the help of meson effective Lagrangian associated with QCD. New spatial parity violating decays of scalar mesons arise as a result of mixing of $π$ and $a_0$ mesons under influence of chiral charge density. The pion electromagnetic form-factor gets an unusual parity-odd contribution. Pion effective masses depend on their velocities and may vanish in flight. The possible determination of chiral chemical potential in heavy ion collisions based on above mentioned phenomena is discussed.
As a successive work to [Phys.Rev.D 102 (2020), 034034], we derive the $1/m_Q$ corrections to chiral effective Lagrangian for heavy-light mesons from QCD under proper approximations. The low energy constants in the effective Lagrangian are expressed in terms of the light quark self-energy and heavy quark mass $m_Q$. Numerical results of the low energy constants with $1/m_Q$ corrections are given. We find that the results of pion decay constant and the masses of heavy-light mesons are improved coherently compared to that obtained in the heavy quark limit.
The chiral SU(3) Lagrangian with the baryon octet and decuplet fields is considered. The Q^2 counterterms involving the decuplet fields are constructed. We derive the correlation of the chiral parameters implied by the 1/N_c expansion at leading order in QCD.
The soliton breathing mode is investigated in the framework of linear response theory within a Skyrme model vector meson stabilized. The effective Lagrangian considered includes the $ρ$ (introduced following the standard prescription of nonlinear chiral symmetry) and the $ω$ mesons. The monopole response function is found to have a pronounced peak which is identified to the $P11$ (Roper) resonance. The results are compared to those obtained within the local approximation.
Some issues on the low-mass scalar mesons are discussed in relation to the chiral transition of QCD vacuum. The importance to explore the possible collective nature of the $σ$ meson is emphasized in association with the chiral properties of nuclear media.
Based on an effective chiral theory of pseudoscalar, vector, and axial-vector mesons, the coefficients of the chiral perturbation theory are predicted. There is no new parameter in these predictions.
We have derived the most general chirally invariant Lagrangian ${\cal L}_6$ for the meson sector at order $p^6$. The result provides an extension of the standard Gasser-Leutwyler Lagrangian ${\cal L}_4$ to one higher order, including as well all the odd intrinsic parity terms in the Lagrangian. The most difficult part of the derivation was developing a systematic strategy so as to get all of the independent terms and eliminate the redundant ones in an efficient way. The 'equation of motion' terms, which are redundant in the sense that they can be transformed away via field transformations, are…
We present the recent investigation of the $ΔS = 1$ effective weak chiral Lagrangian within the framework of the instanton-induced chiral quark model. Starting from the effective four-quark operators, we derive the effective weak chiral action by integrating out the constituent quark fields. Employing the derivative expansion, we obtain the effective weak chiral Lagrangian to ${\cal O} (p^4)$ order with low energy constants.
We construct the effective chiral Lagrangian for chiral perturbation theory in the mesonic even-intrinsic-parity sector at order $p^6$. The Lagrangian contains 112 in principle measurable + 3 contact terms for the general case of $n$ light flavours, 90+4 for three and 53+4 for two flavours. The equivalence between equations of motion and field redefinitions to remove spurious terms in the Lagrangians is shown to all orders in the chiral expansion. We also discuss and implement other methods for reducing the number of terms to a minimal set.
In the covariant level-classification scheme of hadrons proposed recently, the existence of "chiral particles", scalar and axial-vector mesons as the partners of the ground-state pseudo-scalar and vector mesons, respectively, were predicted in the D meson and B meson systems, realizing a linear representation of chiral symmetry. In this work we reanalyze the B0 pi mass spectra through Z0 decays to show a possibility for the scalar B_0chi.
