K → πππγ in chiral perturbation theory

We present a complete analysis K → 3ππγ decays to (p ⁴) in the low-energy expansion of the Standard Model. We employ the notion of “generalized bremsstrahlung” to take full advantage of experimental information on the corresponding non-radiative K → 3π decays     

Tensor polarized γ-deuteron Compton scattering in effective field theory

The differential cross section for γ-deuteron Compton scattering from a tensor polarized deuteron is computed in an effective field theory. The first non-vanishing contributions to this differential cross section are the interference terms between the leading electric coupling diagrams and the subleading single potential pion exchange diagrams or the subleading magnetic moment coupling diagrams. At 90° photon scattering angle, only the pion term contributes at this order to the tensor polarized differential cross section. This provides a clean way to study the photon pion dynamics in the two nucleon sector. The effect is measurable for photon energies between 40 and 80 MeV provided the uncertainty in the measured cross sections are ≲ 7%.     

K→ππγ and chiral perturbation theory

Weak radiative decaysK _L,S →π⁺π^?γ andK ⁺→π⁺π⁰γ are reexamined. The electromagnetic form factors and long-distance contributions to the direct photon emission are evaluated using the higher order effective chiral Lagrangian. We find that (1) the naive soft-pion theorem cannot be applied to the magnetic-type transition amplitude, (2) the shortdistance contribution toK _L →π⁺π^?γ is comparable to or even bigger than the long-distance one, (3) the ΔI=1/2 enhancement persists in the decayK ⁺→π⁺π⁰γ, (4) to the order of 1/Λ _χ ² (Λ _χ being the chiral-symmetry breaking scale) the direct photon emission amplitude does not receive a contribution from penguin operators, and (5) the 1/N _c expansion improves the discrepancy between theory and experiment.     

“Phonon” scattering beyond perturbation theory

Searching and designing materials with intrinsically low lattice thermal conductivity(LTC) have attracted extensive consideration in thermoelectrics and thermal management community. The concept of part-crystalline part-liquid state, or even part-crystalline part-amorphous state, has recently been proposed to describe the exotic structure of materials with chemical-bond hierarchy, in which a set of atoms is weakly bonded to the rest species while the other sublattices retain relatively strong rigidity. The whole system inherently manifests the coexistence of rigid crystalline sublattices and fluctuating noncrystalline substructures. Representative materials in the unusual state can be classified into two categories, i.e., caged and non-caged ones. LTCs in both systems deviate from the traditional T~(-1) relationship(T, the absolute temperature), which can hardly be described by small-parameter-based perturbation approaches. Beyond the classical perturbation theory, an extra rattling-like scattering should be considered to interpret the liquid-like and sublattice-amorphization-induced heat transport. Such a kind of compounds could be promising high-performance thermoelectric materials, due to the extremely low LTCs. Other physical properties for these part-crystalline substances should also exhibit certain novelty and deserve further exploration.     

Resonance chiral theory for low-energy ππ scattering

The scattering of a pion on a pion in the energy region $\sqrt s $ ≤1 GeV is successfully described on the basis of pole diagrams featuring spinless, spin-1, and spin-2 intermediate particles, provided that the properties of these particles and of their interactions are deduced from the basic principles of QCD and from the requirements of chiral theory.     

K0 → π0γγ decays in chiral perturbation theory

The decays K_L,S → π⁰γγ are calculated within the framework of chiral perturbation theory. The amplitude for K_L → π⁰γγ is found to be finite at the one-loop level yielding a branching ratio of 6.8 × 10⁻⁷. The decay spectra of both decays are very characteristic and provide good tests of the effective chiral symmetry realization of the standard model.     

Precision calculation of γd↦πnn within chiral perturbation theory

The reaction γd↦π⁺nn is calculated up to order χ^5/2 in chiral perturbation theory, where χ denotes the ratio of the pion to the nucleon mass. Special emphasis is put on the role of nucleon recoil corrections that are the source of contributions with fractional power in χ. Using the known near-threshold production amplitude for γp↦π⁺n as the only input, the total cross-section for γd↦π⁺nn is described very well. A conservative estimate suggests that the theoretical uncertainty for the transition operator amounts to 3% for the computed amplitude near threshold.     

Observation of the Higgs Boson of strong interaction via Compton scattering by the nucleon

It is shown that the Quark-Level Linear σ Model (QLLσM) leads to a prediction for the diamagnetic term of the polarizabilities of the nucleon which is in excellent agreement with experimental data. The bare mass of the σ meson is predicted to be m _σ =666 MeV and the two-photon width Γ(σ→γ γ)=(2.6±0.3) keV. It is argued that the mass predicted by the QLLσM corresponds to the $\gamma\gamma\to\sigma\to N\bar{N}$ reaction, i.e. to a t-channel pole of the γ N→N γ reaction. Large-angle Compton scattering experiments revealing effects of the σ meson in the differential cross section are discussed. Arguments are presented that these findings may be understood as an observation of the Higgs boson of the strong interaction while being a part of the constituent quark.     

Accurate nucleon–nucleon potential based upon chiral perturbation theory

We present an accurate nucleon–nucleon (NN) potential based upon chiral effective Lagrangians. The model includes one- and two-pion exchange contributions up to chiral order three. We show that a quantitative fit of the NN D-wave phase shifts requires contact terms (which represent the short range force) of order four. Within this framework, the NN phase shifts below 300 MeV lab. energy and the properties of the deuteron are reproduced with high-precision. This chiral NN potential represents a reliable starting point for testing the chiral effective field theory approach in exact few-nucleon and microscopic nuclear many-body calculations. An important implication of the present work is that the chiral 2π exchange at order four is of crucial interest for future chiral NN potential development.     

Compton scattering in the Buchholz–Roberts framework of relativistic QED

We consider a Haag–Kastler net in a positive energy representation, admitting massive Wigner particles and asymptotic fields of massless bosons. We show that massive single-particle states are always vacua of the massless asymptotic fields. Our argument is based on the Mean Ergodic Theorem in a certain extended Hilbert space. As an application of this result, we construct the outgoing isometric wave operator for Compton scattering in QED in a class of representations recently proposed by Buchholz and Roberts. In the course of this analysis, we use our new technique to further simplify scattering theory of massless bosons in the vacuum sector. A general discussion of the status of the infrared problem in the setting of Buchholz and Roberts is given.     

Convergence of rayleigh-schrödinger perturbation theory in calculations of multiphoton processes

Abstract

We have calculated the high-order ac Stark Shift, multiphoton ionization rates, and nonlinear susceptibilities for high harmonic generation for the hydrogen atom in a radiation field. The calculations are done in the framework of Rayleigh-Schrödinger perturbation theory applied to a complex-rotated Hamiltonian. Our intention is to investigate the limitations of perturbation theory in calculations of multiphoton processes. Comparisons are made with results from nonperturbative calculations. For some frequencies the results of lowest-order perturbation theory are found to disagree with nonperturbative calculations even at moderate to low intensities (I ～ 10¹¹ W cm^?2) and in the absence of resonances. We find that the high-order perturbation expansion theory is not a reliable predictor of the behavior of hydrogen atoms in radiation fields with intensities greater than ～ 10¹² W cm^?2.     

Compton mechanism of γ-quanta emission in the extremely inelastic scattering of electrons by hadrons

The Compton mechanism at the emission of -quanta, in the extremely inelastic scattering of charged leptons by hadrons is investigated using the quark-parton model. The cross section of the e^– + qe^– + q + (q-quark) process, in which two particles are recorded in the final state corresponding to the Compton mechanism, is calculated. The structural functions of the extremely inelastic scattering of electrons by nucleons are obtained for this mechanism. A violation of the gauge invariance of extremely inelastic scattering due to consideration of the radiational corrections is pointed out.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 9–13, January, 1982.     

Commutators of Schrödinger Hamiltonians and applications in scattering theory

We give results on the behaviour at infinity of commutators of the form [(H), f(Q)], where H is a Schrödinger operator and Q denotes the position operator in [(H),f(Q)]. These results are applied to obtain propagation properties and asymptotic completeness below the three-body threshold for N-body systems.     

Soliton perturbation theory of Biswas–Milovic equation

This paper studies the perturbed Biswas–Milovic equation by the aid of soliton perturbation theory. The adiabatic variation of the soliton parameters is derived from the modified integrals of motion. The velocity of the soliton is also obtained when these perturbation terms are turned on. There are four types of nonlinear media that are taken into consideration.     

The Aharonov–Bohm effect in scattering theory

The Aharonov–Bohm effect is considered as a scattering event with nonrelativistic charged particles of the wavelength which is less than the transverse size of an impenetrable magnetic vortex. The quasiclassical WKB method is shown to be efficient in solving this scattering problem. We find that the scattering cross section consists of two terms, one describing the classical phenomenon of elastic reflection and another one describing the quantum phenomenon of diffraction; the Aharonov–Bohm effect is manifested as a fringe shift in the diffraction pattern. Both the classical and the quantum phenomena are independent of the choice of a boundary condition at the vortex edge, providing that probability is conserved. We show that a propagation of charged particles can be controlled by altering the flux of a magnetic vortex placed on their way.