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 Lagrangian are made.
Within the framework of the path-integral formalism we reinvestigate the different methods of removing the unphysical degrees of freedom from spontanously broken gauge theories. These are: construction of the unitary gauge by gauge fixing; \rx -limiting procedure; decoupling of the unphysical fields by point transformations. In the unitary gauge there exists an extra quartic divergent Higgs self-interaction term, which cannot be neglected if perturbative calculations are performed in this gauge. Using the Stückelberg formalism this procedure can be reversed, i.~e., a gauge theory can be recons…
Application of a Stueckelberg transformation allows one to connect various Lagrangians which have been independently proposed for non-standard couplings. We discuss the reduction of the number of independent parameters in the Lagrangian and compare symmetry arguments with dimensional arguments.
We study the renormalization of the nonlinear effective SU(2) Lagrangian up to $O(p^4)$ with spontaneous symmetry breaking. The Stueckelberg transformation, the background field gauge, the Schwinger proper time and heat kernel method, and the covariant short distance expansion technology, guarantee the gauge covariance and incooperate the Ward indentities in our calculations. The renormalization group equations of the effective couplings are derived and analyzed. We find that the difference between the results gotten from the direct method and the renormalization group equation method can be q…
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.
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 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.
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.
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 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…
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.
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 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 present the results of computing the $p^6$ order low energy constants in the anomalous part of chiral Lagrangian both for two and three flavor pseudoscalar mesons. This is a generalization of our previous work on calculating the $p^6$ order coefficients for the normal part chiral Lagrangian in terms of the quark self energy $Σ(p^2)$. We show that most of our results are consistent with those we can find in the literature.
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.
We review our recent work on Chiral Lagrangians out of thermal equilibrium, which are introduced to analyse the pion gas formed after a Relativistic Heavy Ion Collision. Chiral Perturbation Theory is extended by letting $\fpi$ be time dependent and allows to describe explosive production of pions in parametric resonance. This mechanism could be relevant if hadronization occurs at the chiral phase transition.
An overview of the field of Chiral Lagrangians is given. This includes Chiral Perturbation Theory and resummations to extend it to higher energies, applications to the muon anomalous magnetic moment, $ε^\prime/ε$ and others.
In this talk I summarize recently proposed mechanisms to understand pi pi scattering to 1 GeV in an effective chiral Lagrangian. The Lagrangian includes higher resonances in addition to pions consistently with the chiral symmetry. Iso-spin zero S-wave partial wave amplitude is reproduced up till about 1.2 GeV by including a pion self-interaction and resonant pole exchanges of rho, f0(980) and sigma derived from the effective chiral Lagrangian. The best fit shows that sigma has a mass of around 560 MeV and a width of about 370 MeV.
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.
We present a calculation of the coupling constants in the massive spin-1 field chiral Lagrangian to chiral ${\cal O}(p^3)$ in the context of an extended Nambu--Jona-Lasinio cut-off model. Phenomenological applications of this Lagrangian to anomalous and non-anomalous low-energy hadronic transitions involving spin-1 particles are also discussed.
In pure chiral perturbation theory (ChPT) the couplings of higher order Lagrangian terms are running parameters and hence can be determined only empirically from various low-energy hadronic processes. While this scenario works well for strong interactions, it is unsatisfactory for nonleptonic and radiative nonleptonic weak interactions: It is impossible, from the outset, to determine all unknown higher-order chiral couplings by experiment; theory is tested only by certain chiral constraints rather than by its quantitative predictions. Based on a QCD-motivated model for $p^4$ strong chiral Lagr…
A revised and complete list of the electroweak chiral lagrangian operators up to dimension-four is provided. The connection of these operators to the $S$, $T$ and $U$ parameters and the parameters describing the triple gauge boson vertices $WWγ$ and $WWZ$ is made, and the size of these parameters from new heavy physics is estimated using a one flavor-doublet model of heavy fermions. The coefficients of the chiral lagrangian operators are also computed in this model.
We present results of computing the p6 order low energy constants in the normal part of chiral Lagrangian both for two and three flavor pseudo-scalar mesons. This is a generalization of our previous work on calculating the p4 order coefficients of the chiral Lagrangian in terms of the quark self energy Sigma(p2) approximately from QCD. We show that most of our results are consistent with those we can find in the literature.
Equivalence of the hidden local symmetry formulation with non-minimal interactions and the anti-symmetric tensor field method of $ρ$ and $a_1$ mesons in the chiral lagrangian is shown by using the auxiliary field method. Violation of the KSRF I relation, which becomes important in the application of chiral lagrangian to {\em non QCD-like} technicolor models can be parametrized by non-minimal coupling in the hidden local symmetry formalism keeping low energy theorem of hidden local symmetry. We also obtain explicit correspondence of parameters in both formulations.
Effective Lagrangians containing arbitrary interactions of massive vector fields are quantized within the Hamiltonian path integral formalism. It is proven that correct Hamiltonian quantization of these models yields the same result as naive Lagrangian quantization (Matthews's theorem). This theorem holds for models without gauge freedom as well as for (linearly or nonlinearly realized) spontaneously broken gauge theories. The Stueckelberg formalism, a procedure to rewrite effective Lagrangians in a gauge invariant way, is reformulated within the Hamiltonian formalism as a transition from a se…
On the basis of an effective lagrangian incorporating approximate chiral symmetry and heavy-quark spin and flavor symmetries, and by use of information on leptonic decays, we estimate the effective $D^\star Dπ$ coupling.
We perform a systematic one-loop renormalization to the standard model with a nonlinearly realized Higgs boson field and the electroweak chiral Lagrangian up to $O(p^2)$ order. We find even in the nonlinear form, the Higgs model of the standard model is renormalizable in our procedure. We also examine $β$ functions of gauge couplings for the standard model and $β$ functions for anomalous couplings in the electroweak chiral Lagrangian up to $O(p^2)$ order, and find our results agree with all well-known results. Based on these observations, we conclude that our calculation procedure could be a c…
Chiral symmetry is used as the guiding principle to derive hard thermal loop effects in chiral perturbation theory. This is done by using a chiral invariant background field method for the non-linear sigma model and the Wess-Zumino-Witten lagrangian, with and without external vector and axial vector sources. It is then shown that the n-point hard thermal loop is the leading thermal correction for the Green function of n point vector soft quark currents.
The chiral effective meson-baryon Lagrangian for the description of interactions between the doubly charmed baryons and Goldstone bosons is constructed up to the order of $q^{4}$. The numbers of linearly independent invariant monomials of $\mathcal{O}(q^2)$, $\mathcal{O}(q^3)$ and $\mathcal{O}(q^4)$ are 8, 32 and 218, in order. The obtained Lagrangian can be used to study the chiral dynamics and relevant phenomenology of the doubly charmed baryons at complete one-loop level in future. For completeness, the non-relativistic reduction of the Lagrangian is also discussed.
Chiral perturbation theory is a powerful method to investigate the hadron properties. We apply the non-local chiral effective Lagrangian to study nucleon magnetic form factors. The octet and decuplet intermediate states are included in the one loop calculation. With the modified propagators and non-local interactions, the loop integral is convergent. The obtained proton and neutron magnetic form factors are both reasonable up to relatively large $Q^2$.
Electroweak chiral Lagrangian for a hypercharge-universal topcolor model is investigated. We find that the assignments of universal hypercharge improve the results obtained previously from K.Lane's prototype natural TC2 model by allowing a larger Z' mass resulting in a very small T parameter and the S parameter is still around the order of +1
It is shown that the implementation of the Large--$N_c$ approximation helps to get insight into the structure of, in principle, any QCD-like theory. As an example, we will compute the NLO corrections to $L_{10}$ in the chiral limit with a Lagrangian with Resonances.
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.
In this work we report on the results obtained in a detailed and systematical study of the possibility to measure the parameters appearing in the electroweak chiral lagrangian. The main novelty of our approach is that we do not use the Equivalence Theorem and therefore we work explicitly with all the gauge boson degrees of freedom.
We investigate the parity-violating pion-nucleon-nucleon coupling constant $h^1_{πNN}$, based on the chiral quark-soliton model. We employ an effective weak Hamiltonian that takes into account the next-to-leading order corrections from QCD to the weak interactions at the quark level. Using the gradient expansion, we derive the leading-order effective weak chiral Lagrangian with the low-energy constants determined. The effective weak chiral Lagrangian is incorporated in the chiral quark-soliton model to calculate the parity-violating $πNN$ constant $h^1_{πNN}$. We obtain a value of about $10^{-…
In this work we present a strong chiral meson Lagrangian up to and including $O(p^6)$ in the momentum expansion. It is derived from the Nambu--Jona-Lasinio (NJL) model using the heat-kernel method. Identities related to the properties of covariant derivatives of the chiral matrix $U$ as well as field transformations have been used to obtain a minimal set of linearly independent terms.
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.
Based on previous studies deriving the chiral Lagrangian for pseudo scalar mesons from the first principle of QCD in the path integral formalism, we derive the electroweak chiral Lagrangian and dynamically compute all its coefficients from the one family technicolor model. The numerical results of the $p^4$ order coefficients obtained in this paper are proportional to the technicolor number $N_{\rm TC}$ and the technifermion number $N_{\rm TF}$, which agrees with the arguments in previous works, and which confirms the reliability of this dynamical computation.
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…
The effective chiral Lagrangian in both nonlocal form $L_{ECCL}$ and standard local form $L_{ECL}$ are derived in QCD using the confining kernel, obtained in the vacuum correlator formalism. As a result all coefficients of $L_{ECL}$ can be computed via $q\bar q$ Green's functions. In the $p^2$ order of $L_{ECL}$ one obtains GOR relations and quark decay constants $f_a$ are calculated $a=1,...8$, while in the $p^4$ order the coefficients $L_1, L_2, L_3,L_4, L_5, L_6$ are obtained in good agreement with the values given by data. The chiral quark model is shown to be a simple consequence of $L_{E…
In the framework of the low energy Chiral Lagrangian, the renormalization group equations for the couplings are investigated up to order p^6, both for the SU(2) as for the SU(3) cases. Infrared attractive fixed points for ratios of couplings are found. These fixed points solutions turn out to agree with the values determined from experiment in a large number of cases.
We present a derivation of the low-energy effective meson Lagrangian of the extended Nambu -- Jona-Lasinio (ENJL) model. The case with linear realization of broken $SU(2)\times SU(2)$ chiral symmetry is considered. There are two crucial points why this revision is needed. Firstly it is the explicit chiral symmetry breaking effect. On the basis of symmetry arguments we show that relevant contributions related with the current quark mass terms are absent from the effective Lagrangians derived so far in the literature. Secondly we suggest a chiral covariant way to avoid non-diagonal terms respons…
Employing background-field method and super-heat-kernel expansion, we compute the complete one-loop renormalization of the electroweak chiral Lagrangian with a light Higgs boson. Earlier results from purely scalar fluctuations are confirmed as a special case. We also recover the one-loop renormalization of the conventional Standard Model in the appropriate limit.
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.
A $1/\N$ expansion of the chiral Lagrangian for baryons is formulated and used to study the low-energy dynamics of baryons interacting with the pion nonet $π$, $K$, $η$ and $η^\prime$ in a combined expansion in chiral symmetry breaking and $1/\N$. Strong $CP$-violation is included. The chiral Lagrangian correctly implements nonet symmetry and contracted spin-flavor symmetry for baryons in the large $\N$ limit. The implications of nonet symmetry for low-energy baryon-pion interactions are described in detail. The procedure for calculating non-analytic pion-loop corrections to baryon amplitudes …
We present in this talk the recent investigation of the effective weak chiral Lagrangian within the framework of the instanton-induced chiral quark model. The low energy constants in leading order $g_8$ and $g_{27}$, and their ratio are determined. The momentum-dependence of the constituent quark mass turns out to improve the low energy constants to the great extent, respecting the $ΔT=1/2$ enhancement.
We analyze the consequences of the inclusion of the gluonic Polyakov loop in chiral quark models at finite temperature. Specifically, the low-energy effective chiral Lagrangian from two such quark models is computed. The tree level vacuum energy density, quark condensate, pion decay constant and Gasser-Leutwyler coefficients are found to acquire a temperature dependence. This dependence is, however, exponentially small for temperatures below the mass gap in the full unquenched calculation. The introduction of the Polyakov loop and its quantum fluctuations is essential to achieve this result an…
A review of the recent results obtained in the Nambu -- Jona-Lasinio model is given. In particular, the effect of screening of meson fields at finite temperature or density is analyzed and the formulation of a chirally invariant transport theory for quark matter is presented.
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.
Using effective field theory methods, we integrate out the standard model Higgs boson to one loop and represent its non-decoupling effects by a set of gauge invariant effective operators of the electroweak chiral Lagrangian. We briefly discuss the relation between the renormalization of both the standard model and the effective theory, which is crucial for a correct understanding and use of the electroweak chiral Lagrangian. Some examples have been chosen to show the applicability of this effective Lagrangian approach in the calculation of low energy observables in electroweak theory.
We construct a chiral Lagrangian for doubly heavy baryons and heavy mesons that is invariant under heavy quark-diquark symmetry at leading order and includes the leading O(1/m_Q) symmetry violating operators. The theory is used to predict the electromagnetic decay width of the J=3/2 member of the ground state doubly heavy baryon doublet. Numerical estimates are provided for doubly charm baryons. We also calculate chiral corrections to doubly heavy baryon masses and strong decay widths of low lying excited doubly heavy baryons.
