We construct the effective chiral Lagrangian involving hadronic and electromagnetic interactions originating from the QCD theta term. We impose vacuum alignment at both quark and hadronic levels, including field redefinitions to eliminate pion tadpoles. We show that leading time-reversal-violating (TV) hadronic interactions are related to isospin-violating interactions that can in principle be determined from charge-symmetry-breaking experiments. We discuss the complications that arise from TV electromagnetic interactions. Some implications of the expected sizes of various pion-nucleon TV interactions are presented, and the pion-nucleon form factor is used as an example.
Predictions for a light collective $Θ^+$ baryon state (with strangeness +1) based on the collective quantization of chiral soliton models are shown to be inconsistent with large $N_c$ QCD. The lightest strangeness +1 state to emerge from the analysis has an excitation energy which at large $N_c$ scales as $N_c^0$ while collective quantization is legitimate only for excitations which go to zero as $N_c \to \infty$. This inconsistency strongly suggests that predictions for $Θ^+$ properties based on collective quantization of chiral solitons are not valid.
In a conventional covark model we constructed the Theta pentaquark wave function using vector diquarks and calculating the mass spectrum of this exotic pentaquark.
We generalize the large N_c Di Vecchia-Veneziano-Witten (VVW) effective chiral Lagrangian to the case of finite N_c by constructing the anomalous effective Lagrangian for QCD. The latter is similar to its SUSY counterpart, and has a holomorphic structure. The VVW construction is then recovered, along with 1/N_c corrections, after integrating out the heavy "glueball" fields. A new mass formula for eta' meson in terms of QCD condensates is obtained. The picture of theta dependence in QCD for finite N_c is more complicated than the one predicted by the large N_c approach.
We calculate the electric dipole moments of the neutron and the Lambda within the framework of heavy baryon chiral perturbation theory. They are induced by strong CP-violating terms of the effective Lagrangian in the presence of the vacuum angle theta_0. The construction of such a Lagrangian is outlined and we are able to give an estimate for theta_0.
We investigate theta-vacuum effects on the QCD phase diagram for the realistic 2+1 flavor system, using the three-flavor Polyakov-extended Nambu-Jona-Lasinio (PNJL) model and the entanglement PNJL model as an extension of the PNJL model. The theta-vacuum effects make the chiral transition sharper. For large theta-vacuum angle the chiral transition becomes first order even if the quark number chemical potential is zero, when the entanglement coupling between the chiral condensate and the Polyakov loop is taken into account. We finally propose a way of circumventing the sign problem on lattice Q…
We consider chiral perturbation theory (ChPT) with a non-zero theta term. Due to the CP violating term, the vacuum of chiral fields is shifted to a non-trivial element on the SU(N_f) group manifold. The CP violation also provides mixing of different CP eigenstates, between scalar and pseudoscalar, or vector and axialvector operators. We investigate upto O(theta^2) effects on the mesonic two point correlators of ChPT to the one-loop order. We also address the effects of fixing topology, by using saddle point integration in the Fourier transform with respect to theta.
We propose a practical way of circumventing the sign problem in lattice QCD simulations with a theta-vacuum term. This method is the reweighting method for the QCD Lagrangian after the U_A(1) transformation. In the Lagrangian, the P-odd mass term as a cause of the sign problem is minimized. In order to find out a good reference system in the reweighting method, we estimate the average reweighting factor by using the two-flavor NJL model and eventually find a good reference system.
We construct a chiral lagrangian for pentaquark baryons assuming that the recently found Theta^+ (1540) state belongs to an antidecuplet of SU(3) flavor symmetry with J^P = (1/2)^(+-). We derive the Gell-Mann-Okubo formulae for the antidecuplet baryon masses, and a possible mixing between the antidecuplet and the pentaquark octet. Then we calculate the cross sections for pi^- p -> K^- Theta^+ and gamma n -> K^- Theta^+ using our chiral lagrangian. The resulting amplitudes respect the underlying chiral symmetry of QCD correctly. We also describe how to include the light vector mesons in the chi…
A new general parameterization with eight mixing parameters among Z, gamma and an extra neutral gauge boson Z' is proposed and subjected to phenomenological analysis. We show that in addition to the conventional Weinberg angle theta_W, there are seven other phenomenological parameters G', xi, eta, theta_l, theta_r, r, l for the most general Z-gamma-Z' mixings, in which parameter G' arises due to the presence of an extra Stueckelberg-type mass coupling. Combined with the conventional Z-Z' mass mixing angle theta', the remaining six parameters xi, eta, theta_l-theta', theta_r-theta', r, l are ca…
We suggest an anomalous effective Lagrangian which reproduces the anomalous conformal and chiral Ward identities and topological charge quantization in QCD. It is shown that the large N_c Di Vecchia-Veneziano-Witten effective chiral Lagrangian is locally recovered from our results, along with 1/N_c corrections, after integrating out the heavy "glueball" fields. All dimensionful parameters in our scheme are fixed in terms of the quark and gluon condensates and quark masses. We argue that for a certain range of parameters, metastable vacua appear which are separated from the true vacuum of lowes…
We elaborate how to construct interweaving chiral spirals in (2+1) dimensions, defined as a superposition of chiral spirals oriented in different directions. We divide a two-dimensional Fermi sea into distinct wedges, characterized by the opening angle 2Theta and depth Q ~ pF, where pF is the Fermi momentum. In each wedge, the energy is lowered by forming a single chiral spiral. The optimal values for Theta and Q are chosen by balancing this gain in energy versus the cost of deforming the Fermi surface (which dominates at large Theta) and patch-patch interactions (dominant at small Theta). Usi…
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.
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 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.
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…
In this work, extending a previous study at zero temperature ($T=0$), we perform a systematic study of the modifications to the QCD vacuum energy density $ε_{vac}$ in the finite-temperature case, above the chiral transition at $T_c$, caused by a nonzero value of the parameter $θ$, using two different effective Lagrangian models which implement the $U(1)$ axial anomaly of the fundamental theory and which are both well defined also above $T_c$. In particular, we derive (and critically compare) the expressions for the topological susceptibility $χ$ and for the second cumulant $c_4$ starting from …
The conventional view is that a solution of the strong CP problem lies beyond QCD. A strong argument supporting this view is that the chiral expansion shows that observables depend on theta (unless a quark mass is zero); this eliminates the possibility that theta is physically irrelevant and appears to necessitate an explanation beyond the standard model. However, scenarios that solve the strong CP problem exist that are consistent with known chiral behavior; in these, QCD becomes nonviable as a theory for nonzero theta. Such scenarios appear to be compatible with lattice studies of the topolo…
In a series of articles it was recently claimed that the quantum chromodynamic (QCD) condensates are not the properties of the vacuum but of the hadrons and are confined inside them. We point out that this claim is incompatible with the chiral Lagrangian and Bose-Einstein statistics of the Goldstone bosons (pions) in chiral limit and conclude that the quark condensate must be the property of the QCD vacuum.
I discuss in this lecture how to make a connection between effective chiral Lagrangians -- low-energy effective theory of QCD -- and Landau Fermi liquid theory extended by Migdal to nuclear matter. The practical purpose of such a connection is to provide a link between certain observables in relativistic heavy-ion processes and those in low-energy spectroscopy, giving a new insight into how chiral dynamics manifests itself in nuclear systems.
We perform a systematic study of the modifications to the QCD vacuum energy density $ε_{vac}$ in the zero-temperature case ($T=0$) caused by a small, but non-zero, value of the parameter $θ$, using different effective Lagrangian models which include the flavour-singlet meson field and implement the $U(1)$ axial anomaly of the fundamental theory. In particular, we derive the expressions for the topological susceptibility $χ$ and for the second cumulant $c_4$ starting from the $θ$ dependence of $ε_{vac}(θ)$ in the various models that we have considered. Moreover, we evaluate numerically our resu…
The cancellation between off-shell two body forces and three body forces implies a tremendous simplification in the study of three body resonances in two meson-one baryon systems. While this can be done by means of Faddeev equations we provide an alternative and simpler derivation using just the chiral Lagrangian and the field re-parametrization invariance.
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.
We show that effective chiral Lagrangians endowed with Brown-Rho scaling can be mapped to Landau Fermi-liquid fixed point theory in a way consistent with general constraints following from thermodynamics. This provides a unified scheme to treat, starting from normal nuclear matter, hadronic matter under extreme conditions that is encountered in relativistic heavy-ion collisions and in the interior of compact stars.
Effective chiral Lagrangians involving constituent quarks, Goldstone bosons and long-distance gluons are believed to describe the strong interactions in an intermediate energy region between the confinement scale and the chiral symmetry breaking scale. Baryons and mesons in such a description are bound states of constituent quarks. We discuss the combined use of the techniques of effective chiral field theory and of the field theoretic method known as Fock-Tani representation to derive effective hadron interactions. The Fock-Tani method is based on a change of representation by means of a unit…
We construct the minimal effective chiral pion-nucleon SU(2) Lagrangian at fourth order in the chiral expansion. The Lagrangian contains 118 in principle measurable terms. We develop both the relativistic as well as the heavy baryon formulation of the effective field theory. For the latter, we also work out explicitly all 1/m corrections at fourth order. We display all relevant relations needed to find the linearly independent terms.
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.
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 investigate a way of circumventing the sign problem in lattice QCD simulations with a theta-vacuum term, using the PNJL model. We consider the reweighting method for the QCD Lagrangian after the U_A(1) transformation. In the Lagrangian, the P-odd mass term as a cause of the sign problem is minimized. In order to find out a good reference system in the reweighting method, we estimate the average reweighting factor by using the two-flavor PNJL model and eventually find a good reference system.
We investigate the mass spectrum of the pentaquark baryon ($ udud \bar s $) in quenched lattice QCD with exact chiral symmetry. Using 3 different interpolating operators, we measure their $ 3 \times 3 $ correlation matrix and obtain the eigenvalues $ A^{\pm} (t) $ with $ \pm $ parity, for 100 gauge configurations generated with Wilson gauge action at $ β= 6.1 $ on the $ 20^3 \times 40 $ lattice. For the lowest-lying $ J^P = 1/2^- $ state, its effective mass is almost identical to that of the KN s-wave, while for the lowest-lying $ J^P = 1/2^+ $ state, its effective mass is smaller than that of…
We investigate the mass spectrum of the pentaquark baryon ($ udud \bar s $) in quenched lattice QCD with exact chiral symmetry. Using 3 different interpolating operators for $ Θ$, we measure the $ 3 \times 3 $ correlation matrix and obtain the eigenvalues $ A^{\pm} (t) $ with $ \pm $ parity, for 100 gauge configurations generated with Wilson gauge action at $ β= 6.1 $ on the $ 20^3 \times 40 $ lattice. For the lowest-lying $ J^P = 1/2^- $ state, its mass is almost identical to that of the KN S-wave, while for the lowest-lying $ J^P = 1/2^+ $ state, its mass is smaller than that of the KN P-wav…
The link between non-linear chiral effective Lagrangians and the Walecka model description of bulk nuclear matter [1] is questioned. This fact is by itself due to the Mean Field Approximation (MFA) which in nuclear mater makes the picture of a nucleon-nucleon interaction based on scalar(vector) meson exchange, equivalent to the description of a nuclear matter based on attractive and repulsive contact interactions. We present a linear chiral model where this link between the Walecka model and an underlying to chiral symmetry realization still holds, due to MFA.
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.
We calculate the cross-section for the thermal $n+p\rightarrow d+γ$ process in chiral perturbation theory to next-to-next-to-leading order using heavy-fermion formalism. The exchange current correction is found to be $(4.5\pm 0.3)~\%$ in amplitude and the chiral perturbation at one-loop order gives the cross section $σ_{th}^{np}=(334\pm 2)\ {\mbox mb}$ which is in agreement with the experimental value $(334.2\pm 0.5)\ {\mbox mb}$. Together with the axial charge transitions, this provides a strong support for the power of chiral Lagrangians for nuclear physics.
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 …
By means of a coupled channel non-perturbative unitary approach, it is possible to extend the strong constrains of Chiral Perturbation Theory to higher energies. In particular, it is possible to reproduce the lowest lying resonances in meson-meson scattering up to 1.2 GeV using the parameters of the O(p^2) and O(p^4) Chiral Lagrangian. We report on an update of these results examining their possible relevance for meson spectroscopy.
We discuss the Fermi-liquid properties of hadronic matter derived from a chiral Lagrangian field theory in which Brown-Rho (BR) scaling is incorporated. We identify the BR scaling as a contribution to Landau's Fermi liquid fixed-point quasiparticle parameter from "heavy" isoscalar meson degrees of freedom that are integrated out from a low-energy effective Lagrangian. We show that for the vector (convection) current, the result obtained in the chiral Lagrangian approach agrees precisely with that obtained in the semi-phenomenological Landau-Migdal approach. This precise agreement allows one to…
We investigate the $ΔS=0$ effective chiral Lagrangian from the instanton vacuum. Based on the $ΔS=0$ effective weak Hamiltonian from the operator product expansion and renormalization group equations, we derive the strangeness-conserving effective weak chiral Lagrangian from the instanton vacuum to order ${\cal O}(p^2)$ and the next-to-leading order in the $1/N_c$ expansion at the quark level. We find that the quark condensate and a dynamical term which arise from the QCD and electroweak penguin operators appear in the next-to-leading order in the $1/N_c$ expansion for the $ΔS =0$ effective we…
We study properties of the pentaquark particle Theta+ with emphasis on the role of chiral symmetry. It is shown that when chiral force is sufficiently strong, the positive parity Theta+ may be realized with a lower mass relative to the negative parity state. The decay width is then studied in the non-relativistic quark model. It is shown that the narrow width may be realized for the positive parity state, while the seemingly lowest negative parity state couples strongly to the continuum state resulting in a very broad width. Finally, Theta+ production is studied in photo-induced and proton-ind…
We briefly review the cases of forced and spontaneous chiral symmetry breaking. In particular the chiral condensate of q anti-q pairs is parametrized with two angles, phi which measures the chiral condensation, and theta which measures the chiral rotation. The strong CP problem arises when it is assumed that the current quark masses of the Standard Model, have a theta phase that differs from the phase induced by the instanton term wich is originated in the QCD sector of the Standard Model. We show how chiral symmetry breaking may solve the strong CP problem at the BCS level. We show variationa…
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.
The development of the early Universe is a remarkable laboratory for the study of most nontrivial properties of particle physics. What is more remarkable is the fact that these phenomena at the QCD scale can be, in principle, experimentally tested in heavy ion collisions. We expect that, in general, an arbitrary theta-state would be created in the heavy ion collisions, similar to the creation of the disoriented chiral condensate with an arbitrary isospin direction. It should be a large domain with a wrong $θ\neq 0$ orientation. We test this idea numerically in a simple model where we study the…
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.
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.
We adopt a covariant version of the naive dimensional analysis and construct the chiral two-nucleon contact Lagrangian constrained by Lorentz, parity, charge conjugation, hermitian conjugation, and chiral symmetries. We show that at $\mathcal{O}(q^0)$, $\mathcal{O}(q^2)$, $\mathcal{O}(q^4)$, where $q$ denotes a generic small quantity, there are 4, 13, and 23 terms, respectively. We find that by performing $1/m_N$ expansions, the covariant Lagrangian reduces to the conventional non-relativistic one, which includes 2, 7, and 15 terms at each corresponding order.
We trace the origin of theta-terms in non-linear sigma-models as a nonperturbative anomaly of current algebras. The non-linear sigma-models emerge as a low energy limit of fermionic sigma-models. The latter describe Dirac fermions coupled to chiral bosonic fields. We discuss the geometric phases in three hierarchies of fermionic sigma-models in spacetime dimension (d+1) with chiral bosonic fields taking values on d-, d+1-, and d+2-dimensional spheres. The geometric phases in the first two hierarchies are theta-terms. We emphasize a relation between theta-terms and quantum numbers of solitons.
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 have used the light-cone formulation of Chiral-Quark Soliton Model to estimate the width of the lightest pentaquark Theta+. We have found that the effect of nonzero momentum transfer is important and reduces drastically the width to about 0.43 MeV. This means that this effect is a piece of the small width puzzle of exotic baryons.
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.
The effective SU(2) chiral Lagrangian with external sources is given in the presence of non-vanishing nucleon densities by calculating the in-medium contributions of the chiral pion-nucleon Lagrangian. As a by product, a relativistic quantum field theory for Fermi many-particle systems at zero temperature is directly derived from relativistic quantum field theory with functional methods.
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.
