89 research outputs found
Study of Stability of a Charged Topological Soliton in the System of Two Interacting Scalar Fields
An analytical-numerical analysis of the singular self-adjoint spectral
problem for a system of three linear ordinary second-order differential
equations defined on the entire real exis is presented. This problem comes to
existence in the nonlinear field theory. The dependence of the differential
equations on the spectral parameter is nonlinear, which results in a quadratic
operator Hermitian pencil.Comment: 22 pages, 2 figure
Comprehensive theory of the Lamb shift in light muonic atoms
We present a comprehensive theory of the Lamb shift in light muonic atoms,
such as H, D, He, and He, with all quantum
electrodynamic corrections included at the precision level constrained by the
uncertainty of nuclear structure effects. This analysis can be used in the
global adjustment of fundamental constants and in the determination of nuclear
charge radii. Further improvements in the understanding of electromagnetic
interactions of light nuclei will allow for a promising test of fundamental
interactions by comparison with "normal" atomic spectroscopy, in particular,
with H-D and He-He isotope shifts.Comment: 21 pages, 4 figures, expanded introductio
On U(1)-charged domain walls
A classical field system of two interacting fields -- a real Higgs field and
a complex scalar field -- is considered. It is shown that in such field system
a non-trivial solution exists, which is U(1) charged topological kink. Some
questions of stability of the obtained solution are discussed. An improved
variational procedure for searching of topological U(1) charged solutions is
given.Comment: 16 pages, LaTeX, 4 PostScript figure
Perturbative approach to the hydrogen atom in strong magnetic field
The states of hydrogen atom with principal quantum number n <= 3 and zero
magnetic quantum number in constant homogeneous magnetic field H are
considered. The perturbation theory series is summed with the help of Borel
transformation and conformal mapping of the Borel variable. Convergence of
approximate energy eigenvalues and their agreement with corresponding existing
results are observed for external fields up to n^3 H ~ 5. The possibility of
restoring the asymptotic behaviour of energy levels using perturbation theory
coefficients is also discussed.Comment: LaTeX, 8 pages with 5 eps figure
Towards a high precision calculation for the pion-nucleus scattering lengths
We calculate the leading isospin conserving few-nucleon contributions to pion
scattering on H, He, and He. We demonstrate that the strong
contributions to the pion-nucleus scattering lengths can be controlled
theoretically to an accuracy of a few percent for isoscalar nuclei and of 10%
for isovector nuclei. In particular, we find the -He scattering length
to be where the uncertainties are
due to ambiguities in the -N scattering lengths and few-nucleon effects,
respectively. To establish this accuracy we need to identify a suitable power
counting for pion-nucleus scattering. For this purpose we study the dependence
of the two-nucleon contributions to the scattering length on the binding energy
of H. Furthermore, we investigate the relative size of the leading two-,
three-, and four-nucleon contributions. For the numerical evaluation of the
pertinent integrals, aMonte Carlo method suitable for momentum space is
devised. Our results show that in general the power counting suggested by
Weinberg is capable to properly predict the relative importance of -nucleon
operators, however, it fails to capture the relative strength of - and
-nucleon operators, where we find a suppression by a factor of 5
compared to the predicted factor of 50. The relevance for the extraction of the
isoscalar -N scattering length from pionic H and He is discussed.
As a side result, we show that beyond the calculation of the -H
scattering length is already beyond the range of applicability of heavy pion
effective field theory.Comment: 24 pages, 14 figures, 10 table
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 (BPT) with pion, nucleon, and (1232)
degrees of freedom, up to and including the next-to-next-to-leading order
(NNLO). We include the effects of order , and , with
MeV the -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, ). Estimating the theoretical
uncertainty on the basis of natural size for 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 fm, in
significant disagreement with the current PDG value. Unlike the previous
PT 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 HBPT and BPT
results for polarizabilities is found to be appreciable. We discuss the chiral
behavior of proton polarizabilities in both HBPT and BPT 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.Comment: 24 pages, 9 figures, RevTeX4, revised version published in EPJ
Differential cross section and analysing power of the quasi-free pn -> {pp}_s pi- reaction at 353 MeV
In order to establish links between p-wave pion production in nucleon-nucleon
collisions and low energy three-nucleon scattering, an extensive programme of
experiments on pion production is currently underway at COSY-ANKE. The final
proton pair is measured at very low excitation energy, leading to an S-wave
diproton, denoted here as {pp}_s. By using a deuterium target we have obtained
data on the differential cross section and analysing power of the quasi-free
pol{p}n -> {pp}_s pi^- reaction at 353 MeV. The spectator proton p_sp was
either measured directly in silicon tracking telescopes or reconstructed using
the momentum of a detected pi^-. Both observables can be described in terms of
s-, p-, and d-wave pion production amplitudes. Taken together with the
analogous data on the pol{p}p -> {pp}_s pi^0 reaction, full partial wave
decompositions of both processes were carried out.Comment: The interested reader should also study the paper on pizero
production by D.Tsirkov et al., which has also been submitted to the arXi
Limitations of the heavy-baryon expansion as revealed by a pion-mass dispersion relation
The chiral expansion of nucleon properties such as mass, magnetic moment, and
magnetic polarizability are investigated in the framework of chiral
perturbation theory, with and without the heavy-baryon expansion. The analysis
makes use of a pion-mass dispersion relation, which is shown to hold in both
frameworks. The dispersion relation allows an ultraviolet cutoff to be
implemented without compromising the symmetries. After renormalization, the
leading-order heavy-baryon loops demonstrate a stronger dependence on the
cutoff scale, which results in weakened convergence of the expansion. This
conclusion is tested against the recent results of lattice quantum
chromodynamics simulations for nucleon mass and isovector magnetic moment. In
the case of the polarizability, the situation is even more dramatic as the
heavy-baryon expansion is unable to reproduce large soft contributions to this
quantity. Clearly, the heavy-baryon expansion is not suitable for every
quantity.Comment: Accepted for publication in EPJ C. Made changes based on referee
comments: clarifying sentences to conclusion 1. of Section IV, beginning of
Section V, and new footnote in Section VI, page 8. Added more detailed
explanation in paragraph 4 of Section III. Added citations of Phys.Rev. D60,
034014, and Phys.Lett. B716, 33
Causality in the relativistic bound-state problem
Although the exact Bethe-Salpeter equation is certainly the appropriate
field-theoretic framework to describe the non-perturbative problem of
scattering and bound states, the inevitable truncations introduce
inconsistencies such as loss of symmetries or incorrect one-body limit. I
conjecture that these problem can be overcome if the truncation preserves the
field-redefinition invariance of the exact equation. A sum rule for
light-by-light scattering can provide a testing ground of this conjecture.Comment: 4 pp, 2 figs; Contribution to the 5th Asia-Pacific Conference on
Few-Body Problems in Physics (APFB11
Chiral perturbation theory calculation for pn -> dpipi at threshold
We investigate the reaction pn -> dpipi in the framework of Chiral
Perturbation Theory. For the first time a complete calculation of the leading
order contributions is presented. We identify various diagrams that are of
equal importance as compared to those recognized in earlier works. The diagrams
at leading order behave as expected by the power counting. Also for the first
time the nucleon-nucleon interaction in the initial, intermediate and final
state is included consistently and found to be very important. This study
provides a theoretical basis for a controlled evaluation of the non-resonant
contributions in two-pion production reactions in nucleon-nucleon collisions.Comment: 24 pages, 3 figures, 3 table
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