Effective lagrangians with U(1) axial anomaly (II)

Properties of the effective lagrangian obeying anomalous U(3) × U(3) current algebra constraints are discussed. Analytic formulae are deduced for the current interpolating constants F_ab, the topological constant C (governing the strength of coupling of the topological charge to the physical meson spectrum) and the wave-function renormalization matrix (√Z)_ab. Numerical evaluations of F_ab, C and the gluon content of the η and η′ are obtained.     

Duality in the U(1) Higgs model with an external field

An external electromagnetic field is coupled to the lattice U(1) Higgs model in a Villain form. Duality transformations are then used to express the partition function in terms of an effective lagrangian of topological excitations and their couplings to the external field. Consequences for the phase diagram are derived.     

THE U(3) ANOMALY

The U(3) anomaly will be given based upon the geometrical and topological method which was used in deterurinating the anomalies for SU(N) and SO(N) gauge fields. It is shown that both the non-Abelian and the Abelian anomaly can be derived in unified treatment from the third Chern class and corresponding Chern-Simons secondary class of the U(3) group.     

Vector dominance and radiative meson decays

The vector dominance model is reexamined in a semi-empirical approach. Vector-meson-photon couplings are determined from leptonic decays, and the vector-meson mixing angle and a single vector-vector-pseudoscalar coupling constant for an effective VVP lagrangian, which is constrained by Zweig's rule, is calculated from the V→πλ decay widths. The lagrangian is observed to be the same as that obtained by gauging the U(3)_L × U(3)_R hidden symmetry of the nonlinear pseudoscalar chiral lagrangian. The results are in reasonably good agreement with the data. Discrepancies are isolated and found to be substantially cured by a small symmetry breaking mass factor in the coupling constant.     

The supersymmetric Wess-Zumino action and U(1) gauge fields

The supersymmetric effective action is constructed which when varied under gauge groups containing explicit U(1) factors reproduces the mixed gauge field contribution to the SU(N) anomaly while being U(1) invariant. It constitutes generalization of the supersymmetric Wess-Zumino action. The form of supersymmetric mixed anomaly is also discussed.     

2d SUGRA: Supersymmetric form of the effective action leading to the conformal anomaly

For the two-dimensional (1,1) and (1,0) supergravity we construct the locally supersymmetric effective lagrangian whose superconformal variation leads to the conformal anomaly.     

Effective chiral meson lagrangian with Weinberg and KSFR relations from microscopic four-quark interactions

An effective chiral meson lagrangian is derived from a microscopic quark lagrangian. It contains a partial Higgs mechanism for ϱ-A₁ mass splitting reproducing Weinberg and KSFR relations, and includes quartic derivative “Skyrme” terms and the gauges Wess-Zumino term. The connection to previous approaches deriving the effective lagrangian exclusively from the chiral anomaly including “normal-parity” terms is established.     

Effective chiral hadron lagrangian with anomalies and skyrme terms from quark flavour dynamics

By bosonization of an extended Nambu-Jona-Lasinio type of quark model with explicit breaking of chiral U(n) × U(n) symmetry we derive a effective low-energy lagrangian of composite scalar, pseudoscalar, vector and axial-vector mesons. This lagrangian contains the gauged Wess-Zumino term as well as higher order derivative terms of the Skyrme type, the coefficients of which agree with recent phenomenological estimates. In particular, the value predicted for the strength of the standard fourth-order Skyrme term is in satisfactory agreement with the results obtained by fitting the nucleon and delta masses. Our effective chiral lagrangian reproduces the wealth of the results of successful phenomenological lagrangians as, e.g. soft-pion theorems, Goldberger-Treiman relations, PCAC, the KSFR relation, the (approximate) Weinberg relation, etc. Moreover, the predicted mass spectra and decay constants of composite mesons are in qualitative agreement with the experimental findings. Furthermore, when electroweak interactions are included the lagrangian contains vector (axial-vector) dominance based on field-current identities.     

Kähler-Dirac ghosts for self-dual fields

We present the generalization to spacetime dimension D=4n+2 of the Lorentz covariant quadratic lagrangian for pairs of (anti)self-dual fields previously obtained by the authors in D=2. In the process BRST quantizing this lagrangian a first-order quadratic lagrangian for ghost (anti)self-dual fields is found which, after gauge fixing, can be written in terms of bispinors and it turns out to be a Kähler-Dirac lagrangian. The coupling to gravity is straightforward and the gravitational anomaly due to (anti)self-dual fields is obtained directly from an action principle.     

An effective lagrangian with no U(1) problem in CPn−1 models and QCD

We write an effective lagrangian which gives two-point Green's functions satisfying the anomalous Ward identities for the U(1) axial vector current with a singlet particle that has a non-vanishing mass in the chiral limit. We show that the mechanism that has been postulated by Witten and Veneziano for solving the U(1) problem in the framework of the 1/n expansion in QCD is fully active in the two-dimensional CP^n? model where the 1/n expansion can be explicitly performed.     

Chiral anomalies, effective lagrangians and differential geometry

Using the differential geometric approach developed by Zumino and others, we study the relation between chiral anomalies and the effective lagrangian. We present a simple formula for the non-abelian (Bardeen) anomaly in any even dimensions. This is used to introduce gauge couplings to the Wess-Zumino effective action, as suggested by Witten.     

t夸克圈对TC理论的中性PG玻色子反常耦合的影响

推出了TC理论的中性PG玻色子与规范玻色子(Z、γ、g)的总耦合拉氏量,计算了t夸克圈对中性PG玻色子衰变宽度的影响.结果表明t夸克圈能有效地增加反常耦合强度,为在实验上寻找PG玻包子提供了理论依据.     

Hamiltonian formulation of anomaly free chiral bosons

Starting out with an anomaly free lagrangian formulation for chiral scalars, which includes a Wess-Zumino term (to cancel the anomaly), we formulate the corresponding hamiltonian problem. Then we use the (quantum) Siegel invariance to choose a particular solution, which turns out to coincide with the one obtained by Floreanini and Jackiw.     

How instantons solve the U(1) problem

The gauge theory for strong interactions, QCD, has an apparent U(1) symmetry that is not realized in the real world. The violation of the U(1) symmetry can be attributed to a well-known anomaly in the regularization of the theory, which in field configurations called “instantons” can be seen to give rise to interactions that explicitly break the symmetry. A simple polynomial effective Lagrangian describes these effects qualitatively very well. In particular it is seen that no unwanted Goldstone bosons appear and the eta particle owes a large fraction of its mass to instantons. There is no need for field configurations with fractional winding numbers and it is explained how a spurious U(1) symmetry that remains in QCD even after introducing instantons, does not affect these results.     

Finite-temperature effect on broken UA(1) symmetry and the η′ mass

The U_A(1) symmetry-breaking effective lagrangian mediated by the instanton is calculated in the semiclassical approximation at finite temperature. It is found that the strength of the effective vertex decreases with increasing temperature up to the QCD scale. Also, we discuss the possible variation of the η′ and other pseudoscalar meson masses.     

Decays of kaons in a weak-gauged U(4)L U(4)R chiral lagrangian model

We present a U(4)_L(4)_R chiral lagrangian model for mesons where the electroweak interactions are introduced as a gauge theory over the mesons degrees of freedom. Therefore we have good control over the weak symmetries of the standard model. We study the process K→πℓ⁺ℓ⁻ to one loop in our model. Inclusion of charmed mesons makes the γπK vertex finite as a particular realization of the GIM mechanism. The results are in good agreement with the experimental ones and the predictions coming from chiral perturbation theory.     

Massless QCD and chiral symmetry breaking

It is well known that chiral symmetry is spontaneously broken in QCD. To relate this fact to non-perturbative features of the theory, like instantons, we start with a massless lagrangian and perform a non-linear chiral colored singlet transformation on the quark fields which yields (by means of Fujikawa's method) essentially two terms in the lagrangian. First a quark mass term induced by instantons and secondly a coupling between pseudoscalar mesons and the axial anomaly. Ward-Takahashi identities can be derived. To clarify the presence of this induced mass term we calculate its first perturbative part up to the two-loop level.     

Analytic approximations to Hamiltonian lattice field theories (II). The weak-coupling behavior of U(1) theories

It is shown that at weak coupling physical quantities in hamiltonian U(1) lattive gauge (or global symmetric) theories of arbitrary dimension are provided as expectation values in a d ? 1 dimensional lagrangian Z(2) gauge (or spin) theory with calculable long-range interactions.Confinement and the existence of a magnetic mass gap are equivalent to the existence of infinite-range plaquette-plaquette (or link-link) correlations in the spin field. The existence of infinite range correlations is simply related to the dimension of the lattice and the transformation property of the order parameter. As expected, only the d = 2+1 U(1) gauge theory confines electric charges at all non-vanishing coupling.     

The soliton of the effective chiral action in a heat-kernel expansion

It is shown that the heat-kernel expansion (rather than the gradient expansion) of the effective chiral action of the quark loop yields in next-to-leading (i.e., fourth) order an effective low-energy lagrangian which possesses stable soliton solutions. The baryon number-one soliton solution of this effective chiral lagrangian is found numerically.     

Effective lagrangian and dynamical symmetry breaking in strongly coupled lattice QCD

A method is proposed for computing effective lagrangians in QCD with N colors using lattice regularization. The meson field lagrangian is worked out in detail in the strong coupling limit with various lattice fermion formulations. For generalized Susskind fermions the spontaneous breakdown U(n) ? U(n) → U(n) (diagonal) is found at large N and a generalized version of the non-linear σ model emerges in a natural way. The Nambu-Goldstone spectrum is investigated and a continuous transition is made to Wilson fermions, for which the effective potential and the ππ scattering amplitude are tested on chiral symmetry. Large d (=dimension) approximations are compared with the large N limit and applied to N = 3.