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     

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.     

Predictive powers of chiral perturbation theory in Compton scattering off protons

We study low-energy nucleon Compton scattering in the framework of baryon chiral perturbation theory (BχPT) with pion, nucleon, and Δ(1232) degrees of freedom, up to and including the next-to-next-to-leading order (NNLO). We include the effects of order p ², p ³, and p ⁴/Δ, with Δ≈300 MeV the Δ-resonance excitation energy. These are all “predictive” powers in the sense that no unknown low-energy constants enter until at least one order higher (i.e., p ⁴). Estimating the theoretical uncertainty on the basis of natural size for p ⁴ effects, we find that uncertainty of such a NNLO result is comparable to the uncertainty of the present experimental data for low-energy Compton scattering. We find an excellent agreement with the experimental cross-section data up to at least the pion-production threshold. Nevertheless, for the proton’s magnetic polarizability we obtain a value of (4.0±0.7)×10^?4 fm³, in significant disagreement with the current PDG value. Unlike the previous χPT studies of Compton scattering, we perform the calculations in a manifestly Lorentz-covariant fashion, refraining from the heavy-baryon (HB) expansion. The difference between the lowest order HBχPT and BχPT results for polarizabilities is found to be appreciable. We discuss the chiral behavior of proton polarizabilities in both HBχPT and BχPT with the hope to confront it with lattice QCD calculations in a near future. In studying some of the polarized observables we identify the regime where their naive low-energy expansion begins to break down, thus addressing the forthcoming precision measurements at the HIGS facility.     

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.     

Chiral dynamics and the reactions pp↦dK+ and pp↦dπ+η

We perform a study of the final-state interactions of the K ⁺ and the d systems in the reactions pp↦dK ⁺ and pp↦dπ⁺η. Since the two-meson system couples strongly to the a ₀(980) resonance, these reactions are expected to be an additional source of information about the controversial scalar sector. We also show that these reactions present peculiar features which can shed additional light on the much debated meson-baryon scalar sector with strangeness -1. We deduce the general structure of the amplitudes close to the dK ⁺ threshold, allowing for primary K ⁺ as well as π⁺η production with the two mesons in relative S- or P-wave. The interactions of the mesons are accounted for by using chiral unitary techniques, which generate dynamically the a ₀(980) resonance, and the d interaction is also taken into account. General formulae are derived that allow to incorporate the final-state interactions in these systems for any model of the production mechanism. We illustrate this approach by considering two specific production mechanisms based on three flavor meson-baryon chiral perturbation theory. It is demonstrated that in this scenario the d interactions are very important and can change the cross-section by as much as one order of magnitude. The amount of π⁺ηversus K ⁺ production is shown to depend critically on the primary mixture of the two mechanisms, with large interference effects due to final-state interactions. These effects are also shown to occur in the event distributions of invariant masses which are drastically modified by the final-state interactions of the two-meson or the d system. Received: 28 September 2001 / Accepted: 26 November 2001     

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.     

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.     

Comparison of (π− d→nn withdσ(π+ d→pp) to test charge symmetry in the Δ-region

First results on ^– d are reported. The measurements were made using 8 specially designed neutron counters, which were carefully calibratedin situ. The differential cross sections atT =142, 180, 217, and 254 MeV were obtained at four angles between 0° and 90°, they are compared to ⁺ d pp data measured at the same energies and angles with the same setup. At every beam energy, the shape of the angular distributions of ^– d nn and ⁺ d pp is the same to ±2%. The absolute cross sections differ by 1 to 10%. The error in this comparison is ±4% implying a small violation of charge symmetry.Dedicated to Prof. I. laus on the occasion of his 60th birthdayDeceased     

Measurement of Tensor Analyzing Power Components of the γd→pnπ0 Reaction

Russian Physics Journal - The results of measurements of three tensor analyzing power components of the reaction of incoherent photoproduction of a π0-meson on a deuteron in the ranges of...     

Exclusive measurement of the pp → nnπ+π+ reaction at 1.1 GeV

First exclusive data for the $\ensuremath{pp \to nn\pi^+\pi^+}$ reaction have been obtained at CELSIUS with the WASA detector setup at a beam energy of T_p = 1.1 GeV. Total and differential cross-sections disagree with theoretical calculations, which predict the $ \Delta$ $ \Delta$ excitation to be the dominant process at this beam energy. Instead, the data require the excitation of one of the nucleons to a higher-lying $ \Delta$ state, preferably the $\ensuremath{\Delta(1600)P_{33}}$ , to be the leading process.     

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.     

High orders of perturbation theory. Are renormalons significant?

According to Lipatov [Sov. Phys. JETP 45, 216 (1977)], the high orders of perturbation theory are determined by saddle-point configurations, i.e., instantons, which correspond to functional integrals. According to another opinion, the contributions of individual large diagrams, i.e., renormalons, which, according to t’Hooft [The Whys of Subnuclear Physics: Proceedings of the 1977 International School of Subnuclear Physics (Erice, Trapani, Sicily, 1977), A. Zichichi (Ed.), Plenum Press, New York (1979)], are not contained in the Lipatov contribution, are also significant. The history of the conception of renormalons is presented, and the arguments in favor of and against their existence are discussed. The analytic properties of the Borel transforms of functional integrals, Green’s functions, vertex parts, and scaling functions are investigated in the case of ϕ ⁴ theory. Their analyticity in a complex plane with a cut from the first instanton singularity to infinity (the Le Guillou-Zinn-Justin hypothesis [Phys. Rev. Lett. 39, 95 (1977); Phys. Rev. B 21, 3976 (1980)] is proved. It rules out the existence of the renormalon singularities pointed out by t’Hooft and demonstrates the nonconstructiveness of the conception of renormalons as a whole. The results can be interpreted as an indication of the internal consistency of ϕ ⁴ theory. Zh. éksp. Teor. Fiz. 116, 369–389 (August 1999)     

QCD calculation of theB→π,K form factors

We calculate the form factors for the heavy-to-light transitionsB,K by means of QCD sum rules using andK light-cone wave functions. Higher twist contributions as well as gluonic corrections are taken into account. The sensitivity to the shape of the leading-twist wave functions and effects ofSU (3)-breaking are discussed. The results are compared with quark model predictions and with the results from QCD sum rules for three-point correlators.Work supported by the German Federal Ministry for Research and Technology under contract No. 05 6MU93P     

Numerically inspired new version of degenerate Rayleigh-Schrödinger perturbation theory

A new form of the degenerate perturbation series is proposed. Its construction is inspired by the standard numerical algorithm of inverse iterations: As input, we only assume knowledge of an approximate non-diagonal propagator matrix at some trial zero-order energy. The convergence and a few other technicalities are illustrated by the anharmonic oscillator.Dedicated to Ladislav Trlifaj on the occasion of his 65th birthday.     

Fully self-consistent calculation ofβ-decay half-lives within Skyrme energy density functional

β-decay half-lives of some magic and semi-magic nuclei have been studied in a fully self-consistent Skyrme Hartree-Fock(HF) plus charge-exchange random phase approximation(RPA).The self-consistency is addressed,in that the same Skyrme energy density functional is adopted in the calculation of ground states and Gamow-Teller excited states.First,the impact of J2 terms on the β-decay half-lives is investigated by using the SGII interaction,revealing a large influence.Subsequently,numerical calculations are performed for the selected nuclei with Skyrme energy density functionals SGII,LNS,SKX,and SAMi.Finally,comparisons to available experimental data and predictions of different theoretical models are discussed.     

On the application of Brillouin—Wigner perturbation theory to multireference configuration mixing

A posteriori corrections to state specific multireference configuration interaction are proposed which restore linear scaling with particle number. The corrections are based on an analysis of the Brillouin-Wigner perturbation theory, using a Lippmann-Schwinger-like equation.