Chiral perturbation theory in a nuclear background

We propose a novel way to formulate chiral perturbation theory (ChPT) in a nuclear background, characterized by a static, non-uniform distribution of the baryon number that describes the finite nucleus. In the limiting case of a uniform distribution, the theory reduces to the well-known zero-temperature in-medium ChPT. The proposed approach is used to calculate the self-energy of the charged pion in the background of the heavy nucleus at O(p⁵) in the chiral expansion, and to derive the leading terms of the pion-nucleus optical potential.     

On the perturbation theory in spatially closed background

Recent studies have shown that searches in the mono-photon and missing energy final state can be used to discover dark matter candidates at the ILC. While an excess in this final state over the Standard Model background would indicate the existence of a dark sector, no detailed information about the internal structure of this sector can be inferred. Here, we demonstrate how just a few observables can discriminate between various realisations of dark sectors, including e.g. the spin of mediators.     

The electromagnetic interaction in chiral perturbation theory

We investigate electromagnetic effects in the framework of chiral perturbation theory. Using a completely independent method, we confirm Urech’s results for the divergences of the one-loop functional in the electromagnetic sector. We perform a one-loop analysis of allP _t2 (P=π, K, η) and theK _t3 form factors $f_ + ^{K^ + \pi ^o } (0),f_ + ^{K^o \pi ^ - } (0)$ , including a systematic treatment of theO(e ² p ²) contributions in the mesonic part. We illustrate our results by several numerical estimates.     

The vierbein is irrelevant in perturbation theory

Proper gauge fixing permits the elimination of the vierbein in favor of the metric as the field variable of gravity even when fermions are present. The result is a much simpler computational formalism which is nonetheless background field invariant and possesses all the usual constraints of symmetry, locality, and canonical field dimension.     

The perturbation theory multi-cavity large-orbit gyro-klystron

The paper presents an application of perturbation theory to multi-cavity large-orbit gyro-klystron. By using this theory in every cavity, a recurrence formula about the azimuthal velocity of electron is obtained, which considers the prebunching function of every cavity. Furthermore, some analytical expressions are derived, such as the bunching formula of electrons, beam-wave interaction power and the gain, etc.     

Self-consistent perturbation theory

The density matrix form of Hartree-Fock perturbation theory is developed for the case in which the basis functions themselves are perturbation-dependent. Energy expressions are derived, through second order, for both single and double perturbations.

The theory is applied in the calculation of electric dipole polarizabilities and hyperpolarizabilities for atoms (He, Be) and molecules (H₂, LiH), with excellent results. The high computational efficiency of the method is discussed and possibilities of further development are outlined.     

The pionium lifetime in generalized chiral perturbation theory

Pionium lifetime corrections to the nonrelativistic formula are calculated in the framework of the quasipotential–constraint theory approach. The calculation extends an earlier evaluation, made in the scheme of standard chiral perturbation theory, to the scheme of generalized chiral perturbation theory, in which the quark condensate is left as a free parameter. The pionium lifetime is calculated as a function of the combination (a₀⁰−a₀²) of the ππ S-wave scattering lengths with isospin I=0, 2.     

Action-variable perturbation theory

A quantum mechanical perturbation theory based upon the recently introduced quantum action variable is developed and illustrated. Unlike Rayleigh-Schrödinger or other asymptotic theories, this theory can provide a natural solution for the bound states of any potential.     

The pionic beta decay in chiral perturbation theory

Within the framework of chiral perturbation theory with virtual photons and leptons, we present an updated analysis of the pionic beta decay including all electromagnetic contributions of order e ² p ² . We discuss the extraction of the Cabibbo-Kobayashi-Maskawa matrix element |V _ud | from the experimental data. The method employed here is consistent with the analogous treatment of the decays and the determination of |V _us |. Received: 19 September 2002 / Published online: 24 January 2003     

Wronskian perturbation theory

We develop a perturbation method that generalizes an approach proposed recently to treat velocity-dependent quantum-mechanical models. In order to test the present approach we apply it to some simple trivial and nontrivial examples.     

Topics in chiral perturbation theory

I consider some selected topics in chiral perturbation theory (CHPT). For the meson sector, emphasis is put on processes involving pions in the isospin zero S-wave which require multi-loop calculations. The advantages and shortcomings of heavy baryon CHPT are discussed. Some recent results on the structure of the baryons are also presented.     

Conformal invariance in perturbation theory

Asymptotic conformal invariance is proved to be true at all orders in perturbation theory. The correct Ward Identities for broken conformal invariance are derived: they are the extension of the Callan Symanzik equation from scale to conformal transformations.     

The region of validity of perturbation theory

We present a study of the region of validity of perturbation theory applied to rough surface scattering. We solve numerically the case of a periodic surface or grating varying in one dimension. For a statistical ensemble of gratings with a sufficiently long period one may obtain a good approximation of rough surface scattering. We use this to test the validity of perturbation theory.

Only the perfect conductor case was considered. We find that as the grazing angle becomes small the perturbation result for the TE (E horizontal) polarization remains valid, while for the TM (E vertical) polarization it breaks down. The results show that the perturbation results should be used carefully when being compared with experimental data at grazing angles.     

The region of validity of perturbation theory

Abstract

We present a study of the region of validity of perturbation theory applied to rough surface scattering. We solve numerically the case of a periodic surface or grating varying in one dimension. For a statistical ensemble of gratings with a sufficiently long period one may obtain a good approximation of rough surface scattering. We use this to test the validity of perturbation theory.

Only the perfect conductor case was considered. We find that as the grazing angle becomes small the perturbation result for the TE (E horizontal) polarization remains valid, while for the TM (E vertical) polarization it breaks down. The results show that the perturbation results should be used carefully when being compared with experimental data at grazing angles.     

Spin-adaptation in many-body perturbation theory

In this paper we present a method of incorporating spin-adapted configurations in a Many-Body Perturbation Theory (MBPT) framework. It has been demonstrated how the use of doubly excited Serber-type spinadapted configurations leads in a straightforward way to a well-defined MBPT series which in effect involves an infinite summation of orbital-diagonal ladders for all possible spin allocations. The formalism implicitly defines a partition of the hamiltonian in which the diagonal matrix elements of the hamiltonian in the Serber-type configurations figure as the unperturbed part. This may thus be called a spin-adapted Epstein-Nesbet (E-N) type of partition. The formalism has been tested on a selection of 6π-electron conjugated systems where we have calculated their orbital pair-correlation energies, and compared the performance against E-N perturbation results and a variational calculation of the same quantities. The comparison reveals that, with canonical Hartree-Fock orbitals, the E-N partition tends to overestimate the pair-correction energy which the spinadapted formalism tends to compensate, but without involving much additional effort. The results for the localized H-F orbitals are rather less sensitive and no definitive conclusions could be discerned for them. The advantages of using the spin-adapted MBPT formalism have also been delineated.     

Sum rules in perturbation theory

Sum rules derived from isospin current algebra are examined in perturbation theory for nucleons interacting with neutral pseudoscalar mesons and isovector pions. It is shown that the well-known sum rules for electromagnetic isovector form factors of nucleons and pions are correct in zero and second order of the meson-nucleon coupling constant.