Cusps in K --> 3 pi decays

The pion mass difference generates a pronounced cusp in K --> 3 pi decays. As has recently been pointed out by Cabibbo and Isidori, an accurate measurement of the cusp may allow one to pin down the S-wave pi pi scattering lengths to high precision. Here, we present and illustrate an effective field theory framework that allows one to determine the structure of this cusp in a straightforward manner. The strictures imposed by analyticity and unitarity are respected automatically.Comment: 14 pages, 3 figures, uses Elsevier styl

Complete phase diagram for the integrable chain with alternating spins in the sectors with competing interactions

We investigate the anisotropic integrable spin chain consisting of spins $s={1/2}$ and $s=1$ by means of thermodynamic Bethe ansatz for the anisotropy $\gamma>\pi/3$, where the analysis of the Takahashi conditions leads to a more complicated string picture. We give the phase diagram with respect to the two real coupling constants $\bar{c}$ and $\tilde{c}$, which contains a new region where the ground state is formed by strings with infinite Fermi zones. In this region the velocities of sound for the two physical excitations have been calculated from the dressed energies. This leads to an additional line of conformal invariance not known before.Comment: 13 pages, LaTeX, uses ioplppt.sty and epsfig.sty, figure 3 correcte

Chiral Lagrangians for Baryons coupled to massive Spin-1 Fields

We analyze the effective low--energy field theory of Goldstone bosons and baryons chirally coupled to massive spin--1 fields. We use the electromagnetic baryon form factors to demonstrate the formal equivalence between the vector and the tensor field formulation for the spin--1 fields. We also discuss the origin of the so--called Weinberg term in pion--nucleon scattering and the role of $\rho$--meson exchange. Chirally coupled vector mesons do not give rise to this two--pion nucleon seagull interaction but rather to higher order corrections. Some problems of the formal equivalence arising in higher orders and related to loops are touched upon.Comment: 26 pp, LaTeX, uses epsf and elsart12.sty, 3 figures in separate self-unpacking fil

Behavior of the collective rotor in wobbling motion

The behavior of the collective rotor in wobbling motion is investigated within the particle-rotor model for the nucleus $^{135}$Pr by transforming the wave functions from the $K$-representation to the $R$-representation. After reproducing the experimental energy spectra and wobbling frequencies, the evolution of the wobbling mode in $^{135}$Pr, from transverse at low spins to longitudinal at high spins, is illustrated by the distributions of the total angular momentum in the intrinsic reference frame (azimuthal plot). Finally, the coupling schemes of the angular momenta of the rotor and the high-$j$ particle for transverse and longitudinal wobbling are obtained from the analysis of the probability distributions of the rotor angular momentum ($R$-plots) and their projections onto the three principal axes ($K_R$-plots).Comment: 21 pages, 9 page

Behavior of the collective rotor in nuclear chiral motion

The behavior of the collective rotor in the chiral motion of triaxially deformed nuclei is investigated using the particle rotor model by transforming the wave functions from the $K$-representation to the $R$-representation. After examining the energy spectra of the doublet bands and their energy differences as functions of the triaxial deformation, the angular momentum components of the rotor, proton, neutron, and the total system are investigated. Moreover, the probability distributions of the rotor angular momentum ($R$-plots) and their projections onto the three principal axes ($K_R$-plots) are analyzed. The evolution of the chiral mode from a chiral vibration at the low spins to a chiral rotation at high spins is illustrated at triaxial deformations $\gamma=20^\circ$ and $30^\circ$.Comment: 21 pages, 6 figure

Effective field theory for triaxially deformed nuclei

Effective field theory (EFT) is generalized to investigate the rotational motion of triaxially deformed even-even nuclei. A Hamiltonian, called the triaxial rotor model (TRM), is obtained up to next-to-leading order (NLO) within the EFT formalism. Its applicability is examined by comparing with a five-dimensional collective Hamiltonian (5DCH) for the description of the energy spectra of the ground state and $\gamma$ band in Ru isotopes. It is found that by taking into account the NLO corrections, the ground state band in the whole spin region and the $\gamma$ band in the low spin region are well described. The results presented here indicate that it should be possible to further generalize the EFT to triaxial nuclei with odd mass number.Comment: 21 pages, 9 figure

Gauge invariance in two-particle scattering

It is shown how gauge invariance is obtained for the coupling of a photon to a two-body state described by the solution of the Bethe-Salpeter equation. This is illustrated both for a complex scalar field theory and for interaction kernels derived from chiral effective Lagrangians.Comment: 16 pages, 2 figures, references added and commented o

Dispersion relations and speeds of sound in special sectors for the integrable chain with alternating spins

Based on our previous analysis \cite{doerfel3} of the anisotropic integrable chain consisting of spins $s=1/2$ and $s=1$ we compare the dispersion relations for the sectors with infinite Fermi zones. Further we calculate the speeds of sound for regions close to sector borders, where the Fermi radii either vanish or diverge, and compare the results.Comment: 11 pages, LaTeX2e, uses iopart.cls,graphicx.sty and psfrag.sty, 2 figure