Current Algebra Approach Research Articles

Current algebra approach to two-dimensional interacting chiral metals

We reinterpret the chiral $U(N)$ Wess-Zumino-Witten (WZW) model at level $k>1$ in $(1+1)$ dimensions as an interacting chiral metal in two space dimensions. In this reinterpretation, spatial translations along one of the spatial dimensions in the two-dimensional chiral metal arise from a generator of the $U(N)$ symmetry of the WZW model. The WZW model at $k=1$ is equivalent to Balents and Fisher's free chiral metal [L. Balents and M. P. A. Fisher, Phys. Rev. Lett. 76, 2782 (1996)]. Here, the $U(N)$ symmetry corresponds to the IR symmetry of a chiral Fermi gas with (half of a) Fermi surface, with $N$ equal to the number of points on the Fermi surface. We argue that exactly solvable interacting generalizations occur for levels $k>1$. Importantly, these interacting chiral metals maintain the $U(N)$ symmetry of the free system. We calculate two-point correlation functions of the single-particle fermion operator, the $U(1)$ number density, and current operators in these theories for general $k$. We find that interactions ($k>1$) produce $1/N$ corrections to scaling of the single-particle fermion operator as $N\ensuremath{\rightarrow}\ensuremath{\infty}$ and renormalize the amplitudes of the density and current two-point functions. This construction illustrates the ersatz Fermi liquid proposal of Else et al. [Phys. Rev. X 11, 021005 (2021)].

Analysis of the nonleptonic two-body decays of the Λ hyperon

We systematically study two-body nonleptonic decays of light lambda hyperon $\Lambda \to p \pi^- (n\pi^0)$ with account for both short- and long-distance effects. The short-distance effects are induced by five topologies of external and internal weak $W^\pm$ exchange, while long-distance effects are saturated by an inclusion of the so-called pole diagrams with intermediate $\frac{1}{2}^+$ and $\frac{1}{2}^-$ baryon resonances. The contributions from $\frac12^+$ resonances are calculated straightforwardly by account for nucleon and $\Sigma$ baryons whereas the contributions from $\frac{1}{2}^-$ resonances are calculated by using the well-known soft-pion theorem in the current-algebra approach. It allows one to express the parity-violating $S$-wave amplitude in terms of parity-conserving matrix elements. From our previous analysis of heavy baryons we know that short-distance effects induced by internal topologies are not suppressed in comparison with external $W$-exchange diagram and must be included for description of data. Here, in the case of $\Lambda$ decays we found that the contribution of external and internal $W$-exchange diagrams is sizably suppressed, e.g., by one order of magnitude in comparison with data, which are known with quite good accuracy. Pole diagrams play the major role to get consistency with experiment.

A new theory framework for the electroweak radiative corrections in Kl3 decays

We propose a new theory framework to study the electroweak radiative corrections in Kl3 decays by combining the classic current algebra approach with the modern effective field theory. Under this framework, the most important mathcal{O} (GFα) radiative corrections are described by a single tensor Tμν involving the time-ordered product between the charged weak current and the electromagnetic current, and all remaining pieces are calculable order-by-order in Chiral Perturbation Theory. We further point out a special advantage in the {K}_{l3}^0 channel that it suffers the least impact from the poorly-constrained low-energy constants. This finding may serve as a basis for a more precise extraction of the matrix element Vus in the future.

Singly Cabibbo-suppressed hadronic decays of Λc+

We study singly Cabibbo-suppressed two-body hadronic decays of the charmed baryon $\Lambda_c^+$, namely, $\Lambda_c^+\to \Lambda K^+, p\pi^0, p\eta, n\pi^+,\Sigma^0K^+,\Sigma^+ K^0$. We use the measured rate of $\Lambda_c^+\to p\phi$ to fix the effective Wilson coefficient $a_2$ for naive color-suppressed modes and the effective number of color $N_c^{\rm eff}$. We rely on the current-algebra approach to evaluate $W$-exchange and nonfactorizable internal $W$-emission amplitudes, that is, the commutator terms for the $S$-wave and the pole terms for the $P$-wave. Our prediction for $\Lambda_c^+\to p\eta$ is in excellent agreement with the BESIII measurement. The $p\eta$ ($p\pi^0$) mode has a large (small) rate because of a large constructive (destructive) interference between the factorizable and nonfactorizable amplitudes for both $S$- and $P$-waves. Some of the SU(3) relations such as $M(\Lambda_c^+\to n\pi^+)=\sqrt{2}M(\Lambda_c^+\to p\pi^0)$ derived under the assumption of sextet dominance are not valid for decays with factorizable terms. Our calculation indicates that the branching fraction of $\Lambda_c^+\to n\pi^+$ is about 3.5 times larger than that of $\Lambda_c^+\to p\pi^0$. Decay asymmetries are found to be negative for all singly Cabibbo-suppressed modes and range from $-0.56$ to $-0.96$.

Formalization in PVS of Balancing Properties Necessary for Proving Security of the Dolev-Yao Cascade Protocol Model

In this work, we present an algebraic approach for modeling the two-party cascade protocol of Dolev-Yao and for fully formalizing its security in the specification language of the Prototype Verification System PVS. Although cascade protocols could be argued to be a very limited model, it should be stressed here that they are the basis of more sophisticated protocols of great applicability, such as those which allow treatment of multiparty, tuples, nonces, name-stamps, signatures, etc. In the current algebraic approach, steps of the protocol are modeled in a monoid freely generated by the cryptographic operators. Words in this monoid are specified as finite sequences and the whole protocol as a finite sequence of protocol steps, that are functions from pairs of users to sequences of cryptographic operators. In a previous work, assuming that for balanced protocols admissible words produced by a potential intruder should be balanced, a formalization of the characterization of security of this kind of protocols was given in PVS. In this work, the previously assumed property is also formalized, obtaining in this way a complete formalization which mathematically guarantees the security of these protocols. Despite such property being relatively easy to specify, obtaining a complete formalization requires a great amount of effort, because several algebraic properties, that are related to the preservation of the balancing property of the admissible language of the intruder, should be formalized in the granularity of the underlying data structure (of finite sequences used in the specification). Among these properties, the most complex are related to the notion of linkage property, which allows for a systematic analysis of words of the admissible language of a potential saboteur, showing how he/she is unable to isolate private keys of other users under the assumption of balanced protocols. The difficulties that arose in conducting this formalization are also presented in this work.

A current algebra approach to the equilibrium classical statistical mechanics and its applications

The non-relativistic current algebra approach is analyzed subject to its application to studying the distribution functions of many-particle systems at the temperature equilibrium and their stability properties. We show that the classical Bogolubov generating functional method is a very effective tool for constructing the irreducible current algebra representations and the corresponding different generalized measure expansions including collective variables transform. The effective Hamiltonian operator construction and its spectrum peculiarities subject to the stability of equilibrium many-particle systems are discussed.

Quantum theory of optical temporal phase and instantaneous frequency

We propose a general quantum theory of optical phase and instantaneous frequency in the time domain for slowly varying optical signals. Guided by classical estimation theory, we design homodyne phase-locked loops that enable quantum-limited measurements of temporal phase and instantaneous frequency. Standard and Heisenberg quantum limits to such measurements are then derived. For optical sensing applications, we propose multipass and Fabry-P\'erot position and velocity sensors that take advantage of the signal-to-noise-ratio enhancement effect of wide-band angle modulation without requiring nonclassical light. We also generalize our theory to three spatial dimensions for nonrelativistic bosons and define a Hermitian fluid velocity operator, which provides a theoretical underpinning to the current-algebra approach of quantum hydrodynamics.

Nonlinear bi-Hamiltonian dynamical systems: Current lie algebraic approach

Using the current Lie algebraic approach, bi-Hamiltonian formulation and the so-called dual hierarchies of nonlinear integrable dynamical systems in (1 + 1) dimensions are constructed. This formalism is illustrated for the Camassa-Holm equation.

BEAUTY-CONSERVING STRANGENESS-CHANGING TWO-BODY HADRONIC DECAYS OF BEAUTY BARYONS

The beauty-conserving strangeness-changing two-body hadronic decays of beauty baryons are examined. Unlike in charm sector where the heavy flavor conserving but strangeness-changing decays are Cabibbo suppressed, in the b-sector they are CKM allowed. The numerical estimates for decay widths of some of the modes are presented in current algebra approach, factorization and quark diagram approach.

The Gerasimov-Drell-Hearn sum rule and the infinite-momentum limit

We study the current-algebra approach to the Gerasimov-Drell-Hearn sum rule, paying particular attention to the infinite-momentum limit. Employing the order-alpha^2 Weinberg-Salam model of weak interactions as a testing ground, we find that the legitimacy of the infinite-momentum limit is intimately connected with the validity of the naive equal-times algebra of electric charge densities. Our results considerably reduce the reliability of a recently proposed modification of the Gerasimov-Drell-Hearn sum rule, originating from an anomalous charge-density algebra.

THE PROTON SPIN AND GLUEBALL EFFECTS

We consider the smallness of the proton spin measured in polarized lepton–proton scattering experiments. The proton spin is expressed by the matrix element of the flavor singlet axial vector current. Under the PCAC assumption, in which the divergence of the flavor singlet axial vector current is replaced by the pseudoscalar meson η, η′ and glueball ι fields, we get a Goldberger–Treiman type relation. We estimate the coupling constants f0η, f0η′ and f0ι using the U (3)× U (3) current-algebraic approach. Because the estimated f0ι is of the same order as f0η′, the smallness of the proton spin results in gNNι being comparable to gNNπ in magnitude.

Confining flux tubes in a current algebra approach.

We describe flux tubes and their interactions in a low energy \ensuremath{\sigma} model induced by SU(${\mathit{N}}_{\mathit{f}}$)\ensuremath{\rightarrow}SO(${\mathit{N}}_{\mathit{f}}$) flavor symmetry breaking in SO(${\mathit{N}}_{\mathit{c}}$) QCD. Unlike standard QCD, this model allows gauge confinement to manifest itself in the low energy theory, which has unscreened spinor color sources and global ${\mathit{Z}}_{2}$ flux tubes. We construct the flux tubes and show how they mediate the confinement of spinor sources. We further examine the flux tubes' quantum stability, spectrum, and interactions. We find that flux tubes are Alice strings, despite ambiguities in defining parallel transport. Furthermore, twisted loops of flux tube support Skyrmion number, just as gauged Alice strings form loops that support monopole charge. This model, while phenomenologically unviable, thus affords a perspective on both the dynamics of confinement and on subtleties which arise for global Alice strings.

Current algebra approach to heavy top effects in [formula omitted

The O( αm t 2/ m W 2) and O( αm t 2/ m W 2) corrections to the partial decay width Γ(Z → b+ b) are computed using the current algebra formulation of radiative corrections. This framework allows one to easily enforce the relevant Ward identity that greatly simplifies the calculations. As a result, the one-loop O( αm t 2/ m W 2) contribution is comoputed through the investigation of only two convergent diagrams. The computation of the QCD corrections to the one-loop O( αm t 2/ m W 2) term,s involved fewer diagrams than in the standard approach. In particular, the number of infrared divergent contributions is reduced. The calculation is performed in the dimensional regularization scheme and no term more divergent than 1/( n − 4) is found. Our result confirms the screening of the one-loop top mass effect recently found by Fleischer et al.

Low-energy hadronic interactions beyond the current algebra approach

Within chiral perturbation theory at the quark level (CHPT) q with linear realization of chiral U(3) × U(3) symmetry the new low-energy AP 3-interaction, produced by convergent box-constituent-quark-loop diagrams, is obtained, and its contributions to processes of low-energy interactions of low-lying mesons are investigated. The new interaction goes beyond the framework of the low-energy current algebra approach and effective chiral Lagrangians with linear realization of chiral symmetry, constructed at the hadronic level.

Nucleon electric dipole moment and gluonic content of light hadrons.

We discuss the contributions to the nucleon electric dipole moment {ital d}{sub {ital N}} associated with the flavor-diagonal purely gluonic and mixed quark-gluon {ital P}- and {ital CP}-violating {ital J}{sup {ital P}{ital C}}=0{sup {minus}+} operators. These include the dimension-5 and -6 operators, corresponding to the color-electric dipole moment of quarks and gluons, and the set of dimension-8 purely gluonic operators. The large-{ital N}{sub {ital c}} current-algebra ({eta}{sub 0}-meson dominance) approach relates the hadronic matrix elements of these higher-dimension operators to the amplitudes involving the dimension-4 topological field operator {ital Q}({ital x}){similar to}{ital G{tilde G}}. The basic parameters which appear in these relations correspond to the {eta}{sub 0}-meson decay coupling constants induced by the higher-dimension operators. These parameters determine the long-distance behavior of the mixed vacuum correlation function between {ital Q}({ital x}) and the higher-dimension operators. We evaluate these parameters by an application of the QCD sum-rule method. The treatment of dimension-8 operators is incomplete, due to a restriction to a subset of contributions to coefficient functions and to use of vacuum factorization. Estimates for {ital d}{sub {ital N}} are presented for the case where the {ital CP} violation is induced by the neutral Higgs sector of the two-Higgs-doublet extension ofmore » the standard model.« less

Current and density algebra approach to low-energy heavy-ion collisions

A method is proposed to derive the hamiltonian in terms of the collective and intrinsic variables on the basis of the general fermion hamiltonian. The method admits the formulation in a completely self-consistent way or in partly self-consistent way when the average density and the single-particle potential are introduced phenomenologically but other aspects of the hamiltonian are determined microscopically. A method is proposed for the description of the low-energy heavy-ion collisions.

A current algebra approach to the Kondo effect

The Kondo effect is studied using current algebra techniques which allow a separation of charge and spin degrees of freedom. An algebraic interpretation of the low-temperature fixed point is obtained. The Wilson ratio is shown to be the ratio of the specific heat for the total system to that of the spin sector which is expressed in terms of the conformal anomaly parameter of a Kac-Moody theory.

Neutral pion production at threshold and low-energy theorems

Recent experiments of neutral pion photoproduction show a strong discrepancy between experimental data and the predictions of low-energy theorems (LET). The basic ingredients of these theorems are the conservation of the electromagnetic current and the hypothesis of a partially conserved axial current (PCAC). Both, anomalies in the t-channel, and rescattering in a simple R-matrix formalism, lead to small corrections of the order of 10 – 20 %. However, the investigation of the effects of chiral symmetry breaking and isospin symmetry breaking at the quark level in a current algebraic approach leads to substantial contributions of the right order of magnitude.

Self-dual fields and the Thirring model.

A recently proposed Lagrangian for self-dual fields is used to analyze the Thirring model as a superposition of right- and left-moving fields. We show that the systematic construction of the Thirring field, based on the current-algebra approach, follows from this Lagrangian and Dirac's theory for constrained systems.

Remarks on degenerate theories of the conformal invariant quantum field theory

It is remarked that conformally invariant degenerate theories can be found along the current algebra approach to quantum field theory. The only input is the definition of the product of single-valued fields with other fields.