The Breathing Mode in Extended Skyrme Model

We study an extended Skyrme model which includes fourth and sixth-order terms. We explore some static properties like the $\Delta$-nucleon mass splitting and investigate the Skyrmion breathing mode in the framework of the linear response theory. We find that the monopole response function has a pronounced peak located at $\sim$ 400 MeV, which we identify to the Roper resonance $N(1440)$. As compared to the standard one, the extended Skyrme model provides a more accurate description of baryon properties.Comment: 12 pages of plain Latex and 3 figures (available from the authors), preprint IPNO/TH 93-0

Bethe-Salpeter Approach for Unitarized Chiral Perturbation Theory

The Bethe-Salpeter equation restores exact elastic unitarity in the $s-$ channel by summing up an infinite set of chiral loops. We use this equation to show how a chiral expansion can be undertaken in the two particle irreducible amplitude and the propagators accomplishing exact elastic unitarity at any step. Renormalizability of the amplitudes can be achieved by allowing for an infinite set of counter-terms as it is the case in ordinary Chiral Perturbation Theory. Crossing constraints can be imposed on the parameters to a given order. Within this framework, we calculate the leading and next-to-leading contributions to the elastic $\pi \pi$ scattering amplitudes, for all isospin channels, and to the vector and scalar pion form factors in several renormalization schemes. A satisfactory description of amplitudes and form factors is obtained. In this latter case, Watson's theorem is automatically satisfied. From such studies we obtain a quite accurate determination of some of the ChPT $SU(2)-$low energy parameters ({\bar l}_1 - {\bar l}_2 = -6.1\er{0.1}{0.3} and ${\bar l}_6= 19.14 \pm 0.19$). We also compare the two loop piece of our amplitudes to recent two--loop calculations.Comment: 63 pages, 9 figures. Some discussions on off-shell ambiguities and convergence of the expansion adde

pi-pi scattering in a QCD based model field theory

A model field theory, in which the interaction between quarks is mediated by dressed vector boson exchange, is used to analyse the pionic sector of QCD. It is shown that this model, which incorporates dynamical chiral symmetry breaking, asymptotic freedom and quark confinement, allows one to calculate $f_\pi$, $m_\pi$, $r_\pi$ and the partial wave amplitudes in $\pi$-$\pi$ scattering and obtain good agreement with the experimental data, with the latter being well described up to energies \mbox{$E\simeq 700$ MeV}.Comment: 23 Pages, 4 figures in PostScript format, PHY-7512-TH-93, REVTEX Available via anonymous ftp in /pub: login anonymou get pipi93.tex Fig1.ps Fig2.ps Fig3.ps Fig4.p

Isospin breaking corrections to low-energy pi-K scattering

We evaluate the matrix elements for the processes pi^0 K^0 -> pi^0 K^0 and pi^- K^+ -> pi^0 K^0 in the presence of isospin breaking terms at leading and next-to-leading order. As a direct application the releveant combination of the S-wave scattering lengths involved in the pion-kaon atom lifetime is determined. We discuss the sensitivity of the results with respect to the input parameters.Comment: 33 pages, plain latex, 2 figure

Chiral symmetry and the pion gas virial expansion

In this work we study the thermodynamic properties of the pion gas starting from the realistic elastic scattering phase-shifts obtained from Chiral Perturbation Theory and using the virial expansion. In particular we study the state equation and the behavior of the quark condensate as a function of the temperature and the density.Comment: 16 Pages, 12 figure

Isospin breaking in Kl4 decays

Data on Ke4 decays allow one to extract experimental information on the elastic pi pi scattering amplitude near threshold, and to confront the outcome of the analysis with predictions made in the framework of QCD. These predictions concern an isospin symmetric world, while experiments are carried out in the real world, where isospin breaking effects - generated by electromagnetic interactions and by the mass difference of the up and down quarks - are always present. We discuss the corrections required to account for these, so that a meaningful comparison with the predictions becomes possible. In particular, we note that there is a spectacular isospin breaking effect in Ke4 decays. Once it is taken into account, the previous discrepancy between NA48/2 data on Ke4 decays and the prediction of pi pi scattering lengths disappears.Comment: 33 pages, 12 figure

CP-violation in K_{S,L}->\pi^{+}\pi^{-}\gamma and K_{S,L}->\pi^{+}\pi^{-}e^{+}e^{-} decays

The dependence of K_{S,L}->\pi^{+}\pi^{-}\gamma decay probabilities on photon polarization is calculated. The phases of terms of amplitude that arise from the pion-pion interaction are obtained by using a simple realistic model of pion-pion interaction via virtual \rho-meson, instead of the ChPT. The results are compared with those of other authors and the origin of slight discrepancies is explained. It is shown that the standard ChPT approach for K_{S,L}-> \pi^{+}\pi^{-}\gamma decays cannot reproduce the contribution of the \rho-meson to the P-wave \pi\pi interaction. The departure of the photon spectrum from pure bremsstrahlung due to the pion loop contribution to the direct emission amplitude is calculated. It is shown that the interference between the terms of amplitude with different CP-parity appears only when the photon is polarized (linearly or circularly). Instead of measuring the linear polarization, the angular correlation between the \pi^{+}\pi^{-} and e^{+}e^{-} planes in K_{S,L}->\pi^{+}\pi^{-}e^{+}e^{-} decay can be studied.Comment: 32 pages, 10 figures, 1 table, LaTex ; added figure, the comparison with ChPT revise

Using Robson's Ten‐Group Classification System for comparing caesarean section rates in Europe: an analysis of routine data from the Euro‐Peristat study

Objective Robson's Ten Group Classification System (TGCS) creates clinically relevant sub‐groups for monitoring caesarean birth rates. This study assesses whether this classification can be derived from routine data in Europe and uses it to analyse national caesarean rates. Design Observational study using routine data. Setting Twenty‐seven EU member states plus Iceland, Norway, Switzerland and the UK. Population All births at ≥22 weeks of gestational age in 2015. Methods National statistical offices and medical birth registers derived numbers of caesarean births in TGCS groups. Main outcome measures Overall caesarean rate, prevalence and caesarean rates in each of the TGCS groups. Results Of 31 countries, 18 were able to provide data on the TGCS groups, with UK data available only from Northern Ireland. Caesarean birth rates ranged from 16.1 to 56.9%. Countries providing TGCS data had lower caesarean rates than countries without data (25.8% versus 32.9%, P = 0.04). Countries with higher caesarean rates tended to have higher rates in all TGCS groups. Substantial heterogeneity was observed, however, especially for groups 5 (previous caesarean section), 6, 7 (nulliparous/multiparous breech) and 10 (singleton cephalic preterm). The differences in percentages of abnormal lies, group 9, illustrate potential misclassification arising from unstandardised definitions. Conclusions Although further validation of data quality is needed, using TGCS in Europe provides valuable comparator and baseline data for benchmarking and surveillance. Higher caesarean rates in countries unable to construct the TGCS suggest that effective routine information systems may be an indicator of a country's investment in implementing evidence‐based caesarean policies. Tweetable abstract Many European countries can provide Robson's Ten‐Group Classification to improve caesarean rate comparisons