Christoph Haefeli, Mikhail A. Ivanov, Martin Schmid, Gerhard Ecker
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.
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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.
We study the effect of a thermal quark mass, m_T, on the chiral phase transition and mesonic excitations in the light quark sector at finite temperature in a simple chirally-symmetric model. We show that while nonzero m_T lowers the chiral condensate, the chiral transition remains of second order. It is argued that the mesonic excitations have large decay rate at energies below 2m_T, owing to the Landau damping of the quarks and the van Hove singularities of the collective modes.
Using constituent quarks coupled to a linear sigma model at nonzero temperature, I show that many anomalous mesonic amplitudes, such as $π^0 \rightarrow γγ$, vanish in a chirally symmetric phase. Processes which are allowed, such as $π^0 σ\rightarrow γγ$, are computed to leading order in a loop expansion.
The mesonic quantum fluctuations and their corrections on the chiral condensate and pion polarization function are investigated in the self-consistent scheme of SU(2) Nambu-Jona-Lasinio model by exactly calculating the next-to-leading order (NLO) Feynman diagrams in $1/N_c$ expansion. While the fluctuations and corrections depend strongly on the meson's three-momentum cut-off $Λ_M$, no chiral symmetry restoration is found since the cancellation between the NLO and the one-quark-loop diagram with quark mass deviated from the mean-field value.
We construct the full p6 order chiral Lagrangians for the unitary group and special unitary groups, including nf-, three- and two-flavor cases, all bilinear currents (scalar, pseudoscalar, vector, axial-vector and tensor currents) and theta parameter. The number of independent operators are 1391, 1326 and 969 for each of the flavor unitary groups. From these results, we find one extra linear relation among the traditional p4 order low-energy constants under the U(3) group, and some more linear relations with tensor sources for the p6 order low-energy constants in the special unitary groups. We…
In the present work, higher-order mesonic interactions are included in the linear sigma model at a finite temperature. The effective potential is minimized in the calculations of the sigma and pion effective masses. The field equations have been solved in the mean-field approximation, by using the extended iteration method at a finite temperature. The order of chiral phase transition, the effective sigma and pion masses, and the effective mesonic potential are investigated as functions of the temperature. We find that the chiral phase transition satisfies the Goldstone theorem below the critic…
The chiral symmetry breaking in the presence of external magnetic field is studied in the framework of logarithmic quark-sigma model. The effective logarithmic mesonic potential is employed and is numerically solved in the mean-field approximation. We find that the chiral symmetry breaking enhances in comparison with the original sigma model. Two sets of parameterization are investigated in the present model. We find that increasing coupling constant enhances the breaking symmetry while increasing sigma mass inhibits enhancing chiral broken vacuum state. A comparison with the Numbu-Jona-Lasini…
Scale factor matrices relating mesonic fields in chiral Lagrangians and quark-level operators of QCD sum-rules are shown to be constrained by chiral symmetry, resulting in universal scale factors for each chiral nonet. Built upon this interplay between chiral Lagrangians and QCD sum-rules, the scale factors relating the $a_0$ isotriplet scalar mesons to their underlying quark composite field were recently determined. It is shown that the same technique when applied to $K_0^*$ isodoublet scalars reproduces the same scale factors, confirming the universality property and further validating this …
We derive the chiral Lagrangian at next-to-next-to-next-to-leading order (NNNLO) for a general number $N_f$ of light quark flavours as well as for $N_f=2,3$. We enumerate the contact terms separately. We also discuss the cases where some of the external fields are not included. An example of a choice of Lagrangian is given in the supplementary material.
It is shown how a chiral Lagrangian framework can be used to derive relationships connecting quark-level QCD correlation functions to mesonic-level two-point functions. Crucial ingredients of this connection are scale factor matrices relating each distinct quark-level substructure (e.g., quark-antiquark, four-quark) to its mesonic counterpart. The scale factors and mixing angles are combined into a projection matrix to obtain the physical (hadronic) projection of the QCD correlation function matrix. Such relationships provide a powerful bridge between chiral Lagrangians and QCD sum-rules that …
A general expression of the axial-vector current is presented, in which both the effects of the chiral symmetry breaking and the spontaneous chiral symmetry breaking are included. A new resonance formula of the axial-vector meson is derived and in the limit of $q^{2}\rightarrow 0$ this formula doesn't go back to the ``chiral limit``. The studies show that the dominance of the axial-vector meson is associated with the satisfaction of PCAC. The dominance of pion exchange is companied by the strong anomaly of PCAC.
Chiral Lagrangian mesonic fields can be connected to QCD quark operators via matrix operators containing scale factors. These scale factor matrices are shown to be constrained by chiral symmetry, resulting in a universal scale factor for each Chiral Lagrangian nonet. QCD sum-rules, combined with mixing angles from Chiral Lagrangian analyses, are used to determine the scale factors for the $a_0$ isotriplet and $K_0^*$ isodoublet scalar mesons. The resulting scale factors verify the universality property, providing a validation of the scale factor matrices connecting Chiral Lagrangian mesonic fi…
We investigate the properties of scalar and pseudo-scalar mesons at finite temperature and quark chemical potential in the framework of the Nambu-Jona-Lasinio (NJL) model coupled to the Polyakov loop (PNJL model) with the aim of taking into account features of both chiral symmetry breaking and deconfinement. The mesonic correlators are obtained by solving the Schwinger-Dyson equation in the RPA approximation with the Hartree (mean field) quark propagator at finite temperature and density. In the phase of broken chiral symmetry a narrower width for the sigma meson is obtained with respect to th…
We study the effects of pion and sigma meson backcoupling on the chiral order parameters and the QCD phase diagram and determine their effect on the location of the chiral critical endpoint. To this end, we solve a coupled set of truncated Dyson--Schwinger equations for Landau gauge quark and gluon propagators with $N_f=2+1$ dynamical quark flavors and explicitly backcoupled mesons. The corresponding meson bound-state properties and the quark-meson Bethe--Salpeter vertices are obtained from their homogeneous Bethe--Salpeter equation. We find chiral-restoration effects of the pion and/or sigma …
Temperature dependence of the $U_A(1)$ anomaly is investigated by taking into account mesonic fluctuations in the $U(3)\times U(3)$ linear sigma model. A field dependent anomaly coefficient function of the effective potential is calculated within the finite temperature functional renormalization group approach. The applied approximation scheme is a generalization of the chiral invariant expansion technique developed in [G. Fejos, Phys. Rev. D 90, 096011 (2014)]. We provide an analytic expression and also numerical evidence that depending on the relationship between the two quartic couplings, m…
Complete $CP$ Eigen-bases of Mesonic Chiral Lagrangian up to $p^8$-order
本文使用Young张量技术构建了手征微扰理论中直至$p^8$阶的纯介子有效算符基，并按$CP$本征态分类给出了$SU(2)$和$SU(3)$情形下的算符数量，结果与Hilbert级数一致。
Strong anomaly of the PCAC is found in $τ\rightarrowωππν$ and $ωρν$ in the chiral limit. It originates in WZW anomaly. Theoretical result of $τ\rightarrowωππν$ agrees with data well and the measurement of $τ\rightarrowωρν$ will confirm the strong anomaly of PCAC. The strong anomaly of PCAC is studied.
The form factor $g_{ρπ}^{(S)}(Q^{2})$ of the strange vector current transition matrix element $<ρ| \bar{s}γ_\mus|π>$ is calculated within the chiral quark model. A strange vector current of the constituent $U$- and D-quarks is induced by kaon radiative corrections and this mechanism yields the nonvanishing values of $g_{ρπ}^{(S)}(0)$. The numerical result at the photon point is consistent with the one given by the $ϕ$-meson dominance model, but the fall-off in the $Q^{2}$-dependence is faster than the monopole form factor. Mesonic radiative corrections are also examined for the electromagnetic…
Properties of the scale-factor matrices forming a bridge between the mesonic fields of chiral Lagrangians and quark-level structures of QCD sum-rules are reviewed. The scale-factor matrices combined with mixing angles provide a physical projection of a QCD correlation function matrix that disentangles the mesonic states. This methodology is illustrated for the isotriplet $a_0(980)$-$a_0(1450)$ system, and the scale factors are determined from the combined inputs of QCD sum-rules and chiral Lagrangians. The resulting scale factors are shown to be in good agreement with the vacuum expectation va…
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…
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…
The recently discovered Z(4430) mesonic resonance is believed to be a strong tetraquark candidate. The photoproduction in the channel $γp\rightarrow Z^{+}(4430)n\rightarrow ψ' π^{+} n$ has been proposed as the most effective way to confirm the Z(4430) presence and to measure its quantum numbers. In this work we present a model for high energy and forward angle Z(4430) photoproduction in a effective Lagrangian approach. This model is based on the use of Regge trajectories exchange, thus a Regge propagator replaces the usual Feynman propagator. The differential and total cross sections and the a…
We extend earlier work on leading logarithms in the massive nonlinear O(n) sigma model to the case of SU(N)xSU(N)/SU(N) which coincides with mesonic chiral perturbation theory for N flavours of light quarks. We discuss the leading logarithms for the mass and decay constant to six loops and for the vacuum expectation value <\bar{q}q> to seven loops. For dynamical quantities the expressions grow extremely large much faster such that we only quote the leading logarithms to five loops for the vector and scalar form factor and for meson-meson scattering. The last quantity we consider is the vector-…
The effect of the higher-order mesonic interactions is investigated on the chiral symmetry breaking in the presence of an external magnetic field. The effective of higher-order mesonic potential is employed and is numerically solved in the mean-field approximation. The chiral symmetry breaking increases with increasing magnetic field. Two sets of free parameterization are investigated on the magnetic catalysis. A comparison is discussed with the original sigma model and other studies. The obtained results are included that the higher-order mesonic interactions play an important role in the mag…
The Polyakov loop extended Nambu and Jona-Lasinio model (PNJL model) in a mean field framework shows astonishingly good agreement with lattice QCD calculations which needs to be better understood. The present work reports on further developments concerning both Polyakov loop and mesonic fluctuations beyond mean field approximation. Corrections beyond mean field are of special interest for the thermal expectation values of the Polyakov loop $Φ$ and its conjugate $Φ^*$, which differ once the quark chemical potential is non-zero. Mesonic fluctuations are also considered with emphasis on the role …
The progress in determining the coupling constants of mesonic chiral Lagrangians is reviewed, with emphasis on the work performed in three successive European Networks (Eurodaphne I and II, Euridice). Reliable estimates of those constants are essential for making full use of next-to-next-to-leading-order calculations in chiral perturbation theory. The precision in the values of the strong coupling constants of O(p^4) has been increasing steadily over the years. The situation is less satisfactory in the nonleptonic weak sector where further phenomenological input and more theoretical work are n…
The derivative of the grand potential in mean field approximation, non-strange and strange condensates and deconfinement phase-transition in thermal and dense hadronic medium are verified in extended SU(3) linear sigma-model (eLSM). In determining the chiral phase-transition, the chiral condensates sigma_x and sigma_y are analysed. The chiral mesonic phase-structures in temperature- and density-dependence are taken as free parameters to be fitted. These parameters are classified corresponding to scalar meson nonets; (pseudo)-scalar and (axial)-vector. For deconfinement phase-transition, effect…
A method to find relations between the operators in the mesonic Lagrangian of Chiral Perturbation Theory at order p^6 is presented. The procedure can be used to establish if the basis of operators in the Lagrangian is minimal. As an example, we apply the method to the two-flavour case in the absence of scalar and pseudo-scalar sources (s=p=0), and conclude that the minimal Lagrangian contains 27 independent operators.
We study the impact of higher order quark-meson scattering processes on the chiral phase structure of two-flavour QCD at finite temperature and quark density. Thermal, density and quantum fluctuations are included within a functional renormalisation group approach to the quark-meson model. We present results on the chiral phase boundary, the critical endpoint, and the curvature of the phase transition line at vanishing density.
We review the status of the coupling constants of chiral Lagrangians in the meson sector, the so-called low-energy constants (LECs). Special emphasis is put on the chiral $SU(2)$ and $SU(3)$ Lagrangians for the strong interactions of light mesons. The theoretical and experimental input for determining the corresponding LECs is discussed. In the two-flavour sector, we review the knowledge of the $O(p^4)$ LECs from both continuum fits and lattice QCD analyses. For chiral $SU(3)$, NNLO effects play a much bigger role. Our main new results are fits of the LECs $L_i$ both at NLO and NNLO, making ex…
Various thermodynamic quantities and the phase diagram of strongly interacting hot and dense magnetized quark matter are obtained with the $ 2 $-flavour Nambu-Jona-Lasinio model with Polyakov loop considering finite values of the anomalous magnetic moment (AMM) of the quarks. Susceptibilities associated with constituent quark mass and traced Polyakov loop are used to evaluate chiral and deconfinement transition temperatures. It is found that, inclusion of the AMM of the quarks in presence of the background magnetic field results in a substantial decrease in the chiral as well as deconfinement …
We explore the phase diagram and the modification of mesonic observables in a hot and dense medium using the (2+1) Polyakov-Nambu-Jona-Lasinio model. We present the phase diagram in the ($T,\,μ_B$)-plane, with its isentropic trajectories, paying special attention to the chiral critical end point (CEP). Chiral and deconfinement transitions are examined. The modifications of mesonic observables in the medium are explored as a tool to analyze the effective restoration of chiral symmetry for different regions of the phase diagram. It is shown that the meson masses, namely that of the kaons, change…
We have combined a new systematic calculation of mesonic matrix elements at O(p^6) from an effective chiral lagrangian approach using Wilson coefficients taken from [G.Buchalla, A.J.Buras, M.E.Lautenbacher, Rev.Mod.Phys. 68 (1996) 1125], derived in the framework of perturbative QCD, and restricted partly by experimental data. We derive complete expressions for K --> 2pi amplitudes and give new estimates for epsilon'/epsilon.
In this paper, we study generic non-local NJL models for four-dimensional QCD in the limit of a large number of colours. We diagonalise, through a Bogoliubov-type transformation, the Hamiltonian of the model completely in terms of the compound operators creating/annihilating mesons - bound states of dressed quarks and antiquarks - and demonstrate a one-to-one correspondence between the Bogoliubov diagonalisation condition and the Bethe-Salpeter equation for bound states. We conclude that, in the leading order in N_C, the nontrivial contents of the theory is entirely encoded in the chiral angle…
We determine the leading order mesonic~($B_0$ and $F_0$) and baryonic~($m_0$, $D$ and $F$) SU(3) chiral perturbation theory low energy constants from lattice QCD. We employ gauge ensembles with $N_f=3$ (i.e., $m_u=m_d=m_s$) non-perturbatively improved Wilson fermions at six distinct values of the lattice spacing in the range $a\approx (0.039 - 0.098)$ fm, which constitute a subset of the Coordinated Lattice Simulations (CLS) gauge ensembles. The pseudoscalar meson mass $M_π$ ranges from around $430$ MeV down to $240$ MeV and the linear spatial lattice extent $L$ from $6.4\,M_π^{-1}$ to $3.3\,M…
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 construct the effective chiral Lagrangian for chiral perturbation theory in the mesonic odd-intrinsic-parity sector at order $p^6$. The Lagrangian contains 24 in principle measurable terms and no contact terms for the general case of $N_f$ light flavours, 23 terms for three and 5 for two flavours. In the two flavour case we need a total of 13 terms if an external singlet vector field is included. We discuss and implement the methods used to reduce to a minimal set. The infinite parts needed for renormalization are calculated and presented as well.
In order to study the fate of mesons in thermal QCD at finite baryon chemical potential, we consider light mesonic correlation functions using the Taylor expansion to ${\cal O}((μ/T)^2)$, in both the hadronic and quark-gluon plasma phases. We use the FASTSUM anisotropic fixed-scale lattices with $N_f = 2+1$ flavours of Wilson fermion. We find that mesonic correlators are sensitive to finite-density corrections and that the second-order terms indicate the chiral crossover in the vector and axial-vector channels.
We have combined a new systematic calculation of mesonic matrix elements at O(p^6) from an effective chiral lagrangian approach with Wilson coefficients taken from paper by G.Buchalla et al. Rev.Mod.Phys. 68 (1996) 1125, derived in the framework of perturbative QCD, and restricted partly by experimental data. We derive complete expressions for K-->2pi amplitudes and compare the results for epsilon'/epsilon with experiment.
We find possible candidates for the new type of q bar q meson, mesonic chiralons, whose existence is predicted in the covariant level-classification scheme of hadrons with U(12)_SF * O(3,1)_L symmetry, by assigning all the known light-unflavored and strange mesons, with masses below about 1.8 GeV, to U(12)_SF * O(3,1)_L multiplets.
We apply Hilbert series techniques to the enumeration of operators in the mesonic QCD chiral Lagrangian. Existing Hilbert series technologies for non-linear realizations are extended to incorporate the external fields. The action of charge conjugation is addressed by folding the $\frak{su}(n)$ Dynkin diagrams, which we detail in an appendix that can be read separately as it has potential broader applications. New results include the enumeration of anomalous operators appearing in the chiral Lagrangian at order $p^8$, as well as enumeration of $CP$-even, $CP$-odd, $C$-odd, and $P$-odd terms beg…
We investigate the modifications of mesonic properties in a hot medium having in mind to use the mesonic modes as a tool to analyze the restoration of chiral and axial symmetries in the context of the SU(3) Polyakov--Nambu--Jona-Lasinio (PNJL) model. The results lead to the conclusion that the effects of the Polyakov loop are fundamental for reproducing lattice findings. It is found that the restoration of chiral symmetry in the PNJL model occurs in a small range of temperature (smaller that in the Nambu--Jona-Lasinio (NJL)), and the topological susceptibility reproduces well the lattice resul…
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.
Effective tree Chiral Lagrangian is interpreted as a power series expansion of the kinematical variables. In the presence of the strong interaction this expansion is valid below the unitarity cut, hence in the unphysical region. Consequences of this reinterpretation of the Chiral Lagrangian are analysed for the relation between K-pi and K-pipi transitions.
We study the effective chiral Lagrangian in the chiral limit from the instanton vacuum. Starting from the nonlocal effective chiral action, we derive the effective chiral Lagrangian, using the derivative expansion to order $O(p^4)$ in the chiral limit. The low energy constants, $L_1$, $L_2$, and $L_3$ are determined and compared with various models and the corresponding empirical data. The results are in a good agreement with the data. We also discuss about the upper limit of the sigma meson, based on the present results.
We present a revised and extended construction of the mesonic Lagrangian density in chiral perturbation theory (ChPT) at order $p^6$ in the anomalous (or epsilon) sector, ${\cal{L}}_{6,ε}$. After improving several aspects of the strategy we used originally, i.e., a more efficient application of partial integration, the implementation of so-called Bianchi identities, and additional trace relations, we find the new monomial sets to include 24 $SU(N_f)$, 23 SU(3), and 5 SU(2) elements. Furthermore, we introduce 8 supplementary terms due to the extension of the chiral group to $SU(N_f)_L \times SU…
Parameters of Gasser Leutwyler chiral Lagrangian are proved saturated by dynamical quark self energy Sigma(k^2) in a gauge invariant, nonlocal, dynamical quark model.
Traditional Stueckelberg Mechanism is shown equivalent to set up a gauged U(1) chiral Lagrangian and fix special gauge. With this mechanism, the original electro-weak chiral Lagrangian is inlarged by including an extra U(1) symmetry to represent physics for $Z'$ boson. We build up complete list of electro-weak chiral Lagrangian up to order of $p^4$ including $Z'$ and higgs bosons. The most general mixing among neutral gauge bosons is diagonalized completely and the connections among these operators to triple, quartic couplings involving $Z'$ boson and to that in traditional electro-weak chiral…
We construct in a manifestly supersymmetric form the leading and subleading terms in momentum for an effective supersymmetric chiral Lagrangian in terms of complex pions and their superpartners. A soft supersymmetry breaking term is included and below the supersymmetry breaking scale the Lagrangian reduces to the usual bosonic chiral Lagrangian in terms of real pions.
The interplay of mesonic fluctuations with an axial $U(1)_A$-symmetry breaking and resulting effects on the location of a possibly existing critical endpoint in the QCD phase diagram are investigated in a framework of the functional renormalization group within a $N_f = 2 + 1$ flavor quark-meson model truncation. The axial $U(1)_A$-symmetry breaking is imposed by a mesonic Kobayashi-Maskawa-'t Hooft determinant. The quark mass sensitivity of the chiral phase transition with and without the $U(1)_A$-symmetry breaking is studied.
The compact form of the electroweak chiral Lagrangian is a reformulation of its original form and is expressed in terms of chiral rotated electroweak gauge fields, which is crucial for relating the information of underlying theories to the coefficients of the low-energy effective Lagrangian. However the compact form obtained in previous works is not complete. In this letter we add several new chiral invariant terms to it and discuss the contributions of these terms to the original electroweak chiral Lagrangian.
We update the uncertainty analysis on $S$ parameter of the electroweak chiral Lagrangian (EWCL) by including the LEP-II W pair production data. We find that experimental data still allow a positive $S^{EXP}(1\textrm{TeV})$.
The complete list of electroweak chiral Lagrangian up to order of p4 for left-right symmetric models with a neutral light higgs is provided. The connection of these operators to left and right gauge boson mixings and masses is made and their contribution to conventional generalized electroweak chiral Lagrangian with a neutral light higgs included in is estimated.
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 present a systematic way to combine the global color model and the instanton liquid model to calculate the chiral Lagrangian coefficients. Our numerical results are in agreement well with the experimental values.
We match the electroweak chiral Lagrangian with two singlet scalars to the next-to-minimal composite Higgs model with $ SO(6)/SO(5) $ coset structure and extract the scalar divergences to one loop. Assuming the additional scalar to be heavy, we integrate it out and perform a matching to the well-established electroweak chiral Lagrangian with one light Higgs.
An effective Lagrangian for the light quark in the field of a static source is derived systematically using the exact field correlator expansion. The lowest Gaussian term is bosonized using nonlocal colorless bosonic fields and a general structure of effective chiral Lagrangian is obtained containing all set of fields. The new and crucial result is that the condensation of scalar isoscalar field which is a usual onset of chiral symmetry breaking and is constant in space-time, assumes here the form of the confining string and contributes to the confining potential, while the rest bosonic fields…
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.
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 investigate the $ΔS = 1,2$ effective weak chiral Lagrangian within the framework of the 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 order ${\cal O} (p^4)$. We examine the contributions of the order ${\cal O} (N_c)$ to the ratio $g_{\underline{8}}/g_{\underline{27}}$, considering e.g. the quark axial-vector constant $g_{\rm A}$ different from unity. The low energy constants of the counterter…
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