The present status of Chiral Perturbation Theory in the meson sector is discussed concentrating on recent developments. This write-up contains short discussions on a listing a few historical papers, the principles behind ChPT, two-flavour ChPT including some comments about the pion polarizability, three-flavour ChPT with a discussion of the recently found relations as tests of ChPT and preliminary results of a new fit of the NLO low-energy-constants (LECs). It discusses somewhat deeper $η\to3π$ and the arguments for the existence of a ``hard pion ChPT'' and its application to $K\to2π$.
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.
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.
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.
In terms of an effective chiral theory of mesons it is shown quantitatively that in the limit of $m_{q}=0$, the masses of $ρ$, $ω$, $K^{*}(892)$, $m_ϕ$, $a_{1}$, $f_{1}(1286)$, $K_{1}(1400)$, and $f_{1}(1510)$ mesons originate from dynamical chiral symmetry breaking.
We examine low energy limit of $U(3)_L\times U(3)_R$ chiral theory of mesons through integrating out fields of vector and axial-vector mesons. The effective lagrangian for pseudoscalar mesons at $O(p^4)$ has been obtained, and five low energy coupling constants $L_i(i=1,2,3,9,10)$ have been revealed. They are in good agreement with the results of CHPT's at $μ\sim m_ρ$.
We review our recent one-loop calculation of all the two meson scattering amplitudes within SU(3) Chiral Perturbation Theory, i.e. with pions, kaons and etas. By unitarizing these amplitudes we are able to generate dynamically the lightest resonances in meson-meson scattering. We thus obtain a remarkable description of the meson-meson scattering data right from threshold up to 1.2 GeV, in terms of chiral parameters in good agreement with previous determinations.
We determine chiral loop corrections to the B meson decay amplitudes to positive and negative parity charmed mesons within a framework which combines heavy quark and chiral symmetries. Then we investigate the impact of the lowest-lying positive parity heavy mesons on the determination of the Isgur-Wise functions. The corrections due to these states are competitive with the contributions arising from K and eta meson loops. Since lattice studies rely on the chiral behavior of the amplitudes we discuss the chiral limit of our results. We find that the determination of the slope at zero recoil of …
The chiral theory of mesons of two flavors have been extended to mesons containing strange flavor. Two new mass relations between vector and axial-vector mesons have been obtained. In chiral limit, the physical processes of normal parity and abnormal parity have been studied. Due to the universality of the coupling of this theory many interesting results have been obtained. In chiral limit theoretical results are in reasonable agreement with data.
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 $ωϕ$, which is related to the new resonance of $f_0(1810)$ observed in BESII very recently.
The interactions of $ρ$, $K^*$, $ϕ$ and $ω$ vector-mesons with low-momentum $π$, $K$ and $η$ pseudoscalar mesons are constrained by chiral symmetry. We derive a heavy vector-meson chiral Lagrangian in which the vector mesons are treated as heavy static matter fields. The unknown couplings of the chiral Lagrangian are further related using the $1/N_c$ expansion. Chiral perturbation theory is applied to the vector-meson mass matrix. At one-loop there are large corrections to the individual vector meson masses, but the singlet-octet mixing angle remains almost unchanged. The parity-violating $s$-…
The time evolution of quantum meson fields in the O(4) linear sigma model is investigated in a context of the dynamical chiral phase transition. It is shown that amplitudes of quantum pion modes are amplified due to both mechanisms of a parametric resonance and a resonance by the forced oscillation according to the small oscillation of the chiral condensate in the late time of chiral phase transition.
We study radial excitations of pseudoscalar and vector (q bar q) mesons within a chiral approach. We derive a general form for a chiral Lagrangian describing processes involving excited pseudoscalar and vector mesons. The parameters of the chiral Lagrangian are fitted using data and previous calculations in the framework of the 3P0 model. Finite-width effects are examined and predictions for mesons previously not discussed are given. Available experimental data is analyzed whenever possible. Possible hints for exotic mesons and open interpretation-issues are discussed.
We report on our one-loop calculation of all the two meson scattering amplitudes within SU(3) Chiral Perturbation Theory, i.e. with pions, kaons and etas. Once the amplitudes are unitarized with the coupled channel Inverse Amplitude Method, they satisfy simultaneously the correct low-energy chiral constraints and unitarity. We obtain a remarkable description of meson-meson scattering data up to 1.2 GeV including the scattering lengths and seven light resonances.
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.
We discuss scalar mesons properties on the light of chiral dynamics. Considering them as the chiral partners of pseudo-scalar mesons we propose an explanation to their unusual properties based on non-trivial vacuum effects coming from the interplay between spontaneous breaking of chiral symmetry and the violation of $U_A(1)$ symmetry by instantons. Including vector mesons as external sources we work out predictions for radiative decays of vector mesons and compare some of them with recent experimental results from high luminosity $Φ$ factories.
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.
The Wess-Zumino-Witten structure is supplemented by a simple vector-meson Lagrangian where the vector mesons are described by antisymmetric tensor fields. With the ρ-ω-π coupling as the only parameter in the sector of odd intrinsic parity, i.e. without additional contact terms, one can achieve a proper description of the decay of an ω-meson into three pions, the single- and double-virtual pion transition form factor and the three-pion production in electron-positron collisions.
We study the nuclear matter solution in the chiral quark soliton model coupled to $ρ$ and $ω$ vector mesons based on the Wigner-Seitz approximation. It is shown that the vector mesons stabilize the soliton at high-density region. As a result, the saturation property and incompressibility are significantly improved.
We examine the chiral corrections to exotic meson masses calculated in lattice QCD. In particular, we ask whether the non-linear chiral behavior at small quark masses, which has been found in other hadronic systems, could lead to large corrections to the predictions of exotic meson masses based on linear extrapolations to the chiral limit. We find that our present understanding of exotic meson decay dynamics suggests that open channels may not make a significant contribution to such non-linearities whereas the virtual, closed channels may be important.
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.
Chiral symmetry and heavy quark symmetry constrain the interactions of mesons containing a single heavy quark with low-momentum pions. Chiral corrections to the Isgur-Wise function for $\bar B_s \rightarrow D_s^{(*)}$ versus $\bar B \rightarrow D^{(*)}$ semileptonic decay, the ratio of heavy meson decay constants $f_{D_s}/ f_D$ or $f_{B_s}/ f_B$, the amplitudes for $B_s - \bar B_s$ versus $B^0 - \bar B{\,}^0$ mixing, and the heavy meson mass splittings are calculated in chiral perturbation theory. (Invited talk Rencontres de Moriond 1993)
Meson corrections on chiral condensate up to next-to-leading order in $1/N_c$ expansion at finite density are investigated in NJL model with chiral symmetry explicitly breaking. Compared with the mean-field results, the chiral phase transition is still of first order, while the properties at the critical density of chiral phase transition are found to change significantly.
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.
First radial excitations of the scalar meson nonet and pseudoscalar mesons η, η' are described in a nonlocal chiral quark model of the Nambu--Jona-Lasinio type with 't Hooft interaction. In this model simple form factors are used, which allows us to describe first radial excitations of the mesons and to conserve the gap equations describing spontaneous breaking of chiral symmetry in the standard form. The external parameters of form factors are fixed by masses of excited pseudoscalar mesons and the same form factors are used for predicting the masses of excited scalar mesons. Strong decays of …
We show that the non-strange scalar $σ$ meson, as now reported in the 1996 PDG tables, is a natural consequence of crossing symmetry as well as chiral dynamics for both strong interaction low energy $ππ$ scattering and also $K \to 2π$ weak decays.
We investigate the implications of large N_c and chiral symmetry for the mass spectra of meson resonances. Unlike for most other mesons, the mass matrix of the light scalars deviates strongly from its large-N_c limit. We discuss the possible assignments for the lightest scalar nonet that survives in the large-N_c limit.
We calculate the scattering lengths of Nambu-Goldstone bosons interacting with $D$ mesons in a covariant formulation of chiral perturbation theory, which satisfies heavy-quark spin symmetry and analytical properties of loop amplitudes. We compare our results with previous studies performed using heavy meson chiral perturbation theory and show that recoil corrections are sizable in most cases.
Using the Woods Saxon plus Coulomb type of interaction between two hadron molecules, we have calculated the binding energies and masses of the tetraquark states such as $D\bar{D}$, $D\bar{D}^*$, $D^*\bar{D}^*$, $D^+\bar{D}^*$ in the charm sector and $B\bar{B}$, $B^*\bar{B}^*$, $B\bar{B}^*$ in the bottom sector.
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)
We investigate the properties of new scalar X_B, X_D and axial-vector X_B*, X_D* mesons, which are recently predicted, in the covariant meson-classification scheme, to exist as the partners of ground-state pseudoscalar B, D and vector B*, D* mesons, respectively, realizing a linear representation of chiral symmetry for the light quark component in heavy-light-quark meson system. The mass splittings between the respective chiral partners are shown to be equal, and the decay widths of one pion emission of X_B, X_D, X_B* and X_D* become to have a common value, due to chiral and heavy quark symmet…
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 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 study SU(3)$_L\timesSU(3)_R$ chiral quark model of mesons up to the next to leading order of $1/N_c$ expansion. Composite vector and axial-vector mesons resonances are introduced via non-linear realization of chiral SU(3) and vector meson dominant. Effects of one-loop graphs of pseudoscalar, vector and axial-vector mesons is calculated systematically and the significant results are obtained. We also investigate correction of quark-gluon coupling and relationship between chiral quark model and QCD sum rules. Up to powers four of derivatives, chiral effective lagrangian of mesons is derived a…
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…
In the framework of an effective chiral theory of mesons, pi K scattering is stydied. The scattering lengths, phase shifts, and cross sections are calculated. Theoretical results agree well with data. There is no new parameter in this study.
Using the close relationship between the low--energy constants of chiral perturbation theory and the chiral invariant interactions of the vector meson resonances with the pseudoscalar mesons, we investigate the process $ρ^0 \ra π^+ π^- γ$. Compared with the contribution from the pure bremsstrahlung mechanism, we find an enhancement of the decay rate near the endpoint of the photon energy spectrum. Such a particular shape of the differential decay rate has indeed been observed experimentally and turns out to be an important confirmation of the theoretical concept of chiral vector meson dominanc…
Assuming the spin-independence for confining force, we give a covariant quark representation of general composite meson systems with definite Lorentz transformation properties. For benefit of this representation we are able to deduce automatically the transformation rules of composite mesons for general symmetry operations from those of constituent (exciton) quarks. Applying this we investigate especially physical implication of chiral symmetry for the meson systems, and point out a possibility of existence of new meson multiplets.
We study on-shell decays of light vector meson resonances $ρ$, $K^*$ and $ϕ$ in the framework of chiral constituent quark model using resummation calculations. Such studies are necessary for showing that chiral dynamics works well at this energy scale. The effective action is derived by proper vertex method, where resummation of all orders of momentum expansion is accomplished. The loop effects of pseudoscalar meson are also taken into account, which play an important role at this energy scale. The numerical results agree well with the experimental data. A new method to explore the Chiral Symm…
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 and B meson systems, realizing a linear representation of chiral symmetry. In this work we reanalyze the D* pi mass spectra obtained through the Upsilon (4S) and Z0 decays to show a possibility for the D_1chi.
We review our recent work on thermal meson properties within the Chiral Perturbation Theory framework. We will focus on the pion electromagnetic form factor, stressing its importance for Relativistic Heavy Ion Collisions. We obtain model-independent predictions (based only on chiral symmetry) such as the temperature dependence of the pion electromagnetic charge radius. Imposing unitarity allows to describe the thermal effects of resonances such as the $ρ$ meson.
In this talk we briefly review how the unitarization of Chiral Perturbation Theory with dispersion relations can successfully describe the meson-meson scattering data and generate light resonances, whose mass, width and nature can be related to QCD parameters like quark masses and the number of colors.
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.
Higher order effects of the two-dimensional non-Abelian gauge theories, in which the vector-meson mass is generated by chiral anomalies, will be studied. The $β$ function and the topological nature of the non-linear $σ$ model in the action and unitarity of the theory will be discussed.
We study the masses of the low-lying charmed mesons within the framework of heavy-hadron chiral perturbation theory. We work to third order in the chiral expansion, where meson loops contribute. In contrast to previous approaches, we use physical meson masses in evaluating these loops. This ensures that their imaginary parts are consistent with the observed widths of the D-mesons. The lowest odd- and even-parity, strange and nonstrange mesons provide enough constraints to determine only certain linear combinations of the low-energy constants in the effective Lagrangian. We comment on how latti…
A review of effective chiral theory of pseudoscalar, vector, and axial vector mesons is presented. 10 coefficients of the ChPT are predicted. A new symmetry breaking-axial-vector symmetry breaking is found and applied to EW theory. The masses of W and Z are dynamically generated and in agreement with data.
We base our chiral symmetry approach on the quark-level linear sigma model Lagrangian. Then we review the Nambu--Goldstone theorem with vanishing pi, K, eta_8 masses. Next we dynamically generate the pi, K, eta_8 masses away from the chiral limit. Then we study pion and kaon Goldberger-Treiman relations. Finally we extend this qbarq scheme to scalar and vector mesons. We also show the above qbarq meson scheme fits the higher mass octet baryon qqq pattern as well.
We calculate the leading quark mass corrections of order $m_q\log(m_q)$, $m_q$ and $m_q^{3/2}$ to the vector meson decay constants within Heavy Vector Meson Chiral Perturbation Theory. We discuss the issue of electromagnetic gauge invariance and the heavy mass expansion. Reasonably good fits to the observed decay constants are obtained.
Recent advances in the development of a chiral linear $σ$-model with (axial-)vector mesons are presented. The model is based on the basic requirements of global chiral symmetry and dilatation invariance. The role of (axial-)vector states turns out to be crucial both in the meson and the baryon sectors. First results at nonzero temperature and density are discussed.
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.
Assuming the spin-independence for confining force, we give a covariant quark representation of general composite meson systems with definite Lorentz transformation properties. For benefit of this representation we are able to deduce automatically the transformation rules of composite mesons for general symmetry operations from those of constituent (exciton) quarks. Applying this we investigate especially physical implication of chiral symmetry for the meson systems, and point out a possibility of existence of new meson multiplets.
We report on recent progress on the chiral unitary approach, which is shown to have a much larger convergence radius than ordinary chiral perturbation theory, allowing one to reproduce data for meson meson interaction up to 1.2 GeV and meson baryon interaction up to the first baryonic resonances. Applications to physical processes so far unsuited for a standard chiral perturbative approach are presented, concretely the K^- p\toΛ(1405)γreaction and the N^\ast (1535)N^\ast(1535)πand ηcouplings.
In a U(3)x U(3) quark chiral model of the Nambu-Jona-Lasinio type with the 't Hooft interaction, the ground scalar isoscalar mesons and a scalar glueball are described. The glueball (dilaton) is introduced into the effective meson Lagrangian written in a chirally symmetric form on the base of scale invariance. The singlet-octet mixing of scalar isoscalar mesons and their mixing with the glueball are taken into account. Mass spectra of the scalar mesons and glueball and their strong decays are described.
The contributions of the lightest tensor-meson resonances to the low-energy coupling constants of second order chiral perturbation theory with two flavours are evaluated and compared with the available phenomenological information as well as with similar results for other resonances.
If the phase transition of $QCD$ at nonzero temperature is dominated by the (approximate) restoration of chiral symmetry, then the transition might be characterized using a gauged linear sigma model. Assuming that vector meson dominance holds, such sigma models predict that at the temperature of chiral restoration, the pole mass of the thermal $ρ$ meson is greater than that at zero temperature; in the chiral limit and in weak coupling this mass is $\sim 962 \, MeV$. The width of the thermal $ρ-a_1$ peak is estimated to be about $200 - 250 \, MeV$.
We explore the mass splitting of the heavy-light mesons with chiral partner structure in nuclear matter. In our calculation, we employed the heavy hadron chiral perturbation theory with chiral partner structure and the nuclear matter is constructed by putting skyrmions from the standard Skyrme model onto the face-centered cubic crystal and regarding the skyrmion matter as nuclear matter. We find that, although the masses of the heavy-light mesons with chiral partner structure are splitted in the matter-free space and skyrmion phase, they are degenerated in the half-skyrmion phase in which the …
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.
