Heavy-particle formalism with Foldy-Wouthuysen representation

Utilizing the Foldy-Wouthuysen representation, we use a bottom-up approach to construct heavy-baryon Lagrangian terms, without employing a relativistic Lagrangian as the starting point. The couplings obtained this way feature a straightforward $1/m$ expansion, which ensures Lorentz invariance order by order in effective field theories. We illustrate possible applications with two examples in the context of chiral effective field theory: the pion-nucleon coupling, which reproduces the results in the literature, and the pion-nucleon-delta coupling, which does not employ the Rarita-Schwinger field for describing the delta isobar, and hence does not invoke any spurious degrees of freedom. In particular, we point out that one of the subleading $\pi N \Delta$ couplings used in the literature is, in fact, redundant, and discuss the implications of this. We also show that this redundant term should be dropped if one wants to use low-energy constants fitted from $\pi N$ scattering in calculations of $NN\to NN\pi$ reactions.Comment: 28 pages, 2 figures, RevTeX4, appendix added, version published in Phys. Rev.

Proton polarisabilities from Compton data using Covariant Chiral EFT

We present a fit of the spin-independent electromagnetic polarisabilities of the proton to low-energy Compton scattering data in the framework of covariant baryon chiral effective field theory. Using the Baldin sum rule to constrain their sum, we obtain $\alpha=[10.6\pm0.25$(stat)$\pm0.2$(Baldin)$\pm0.4$(theory)$]\times10^{-4}$fm$^3$ and $\beta =[3.2\mp0.25$(stat)$\pm0.2$(Baldin)$\mp0.4$(theory)$]\times10^{-4}$fm$^3$, in excellent agreement with other chiral extractions of the same quantities.Comment: 4 pages, 2 figure

Predictions of covariant chiral perturbation theory for nucleon polarisabilities and polarised Compton scattering

We update the predictions of the SU(2) baryon chiral perturbation theory for the dipole polarisabilities of the proton, $\{\alpha_{E1},\,\beta_{M1}\}_p=\{11.2(0.7),\,3.9(0.7)\}\times10^{-4}$fm$^3$, and obtain the corresponding predictions for the quadrupole, dispersive, and spin polarisabilities: $\{\alpha_{E2},\,\beta_{M2}\}_p=\{17.3(3.9),\,-15.5(3.5)\}\times10^{-4}$fm$^5$, $\{\alpha_{E1\nu},\,\beta_{M1\nu}\}_p=\{-1.3(1.0),\,7.1(2.5)\}\times10^{-4}$fm$^5$, and $\{\gamma_{E1E1},\,\gamma_{M1M1},\,\gamma_{E1M2},\,\gamma_{M1E2}\}_p=\{-3.3(0.8),\,2.9(1.5),\,0.2(0.2),\,1.1(0.3)\}\times10^{-4}$fm$^4$. The results for the scalar polarisabilities are in significant disagreement with semi-empirical analyses based on dispersion relations, however the results for the spin polarisabilities agree remarkably well. Results for proton Compton-scattering multipoles and polarised observables up to the Delta(1232) resonance region are presented too. The asymmetries $\Sigma_3$ and $\Sigma_{2x}$ reproduce the experimental data from LEGS and MAMI. Results for $\Sigma_{2z}$ agree with a recent sum rule evaluation in the forward kinematics. The asymmetry $\Sigma_{1z}$ near the pion production threshold shows a large sensitivity to chiral dynamics, but no data is available for this observable. We also provide the predictions for the polarisabilities of the neutron: $\{\alpha_{E1},\,\beta_{M1}\}_n=\{13.7(3.1),\,4.6(2.7)\}\times10^{-4}$fm$^3$, $\{\alpha_{E2},\,\beta_{M2}\}_n=\{16.2(3.7),\,-15.8(3.6)\}\times10^{-4}$fm$^5$, $\{\alpha_{E1\nu},\,\beta_{M1\nu}\}_n=\{0.1(1.0),\,7.2(2.5)\}\times10^{-4}$fm$^5$, and $\{\gamma_{E1E1},\,\gamma_{M1M1},\,\gamma_{E1M2},\,\gamma_{M1E2}\}_n=\{-4.7(1.1),\,2.9(1.5),\,0.2(0.2),\,1.6(0.4)\}\times10^{-4}$fm$^4$. The neutron dynamical polarisabilities and multipoles are examined too. We also discuss subtleties related to matching dynamical and static polarisabilities.Comment: 34 pages, 18 figures, minor updates and corrections, published versio

Chiral perturbation theory of muonic hydrogen Lamb shift: polarizability contribution

The proton polarizability effect in the muonic-hydrogen Lamb shift comes out as a prediction of baryon chiral perturbation theory at leading order and our calculation yields for it: $\Delta E^{(\mathrm{pol})} (2P-2S) = 8^{+3}_{-1}\, \mu$eV. This result is consistent with most of evaluations based on dispersive sum rules, but is about a factor of two smaller than the recent result obtained in {\em heavy-baryon} chiral perturbation theory. We also find that the effect of $\Delta(1232)$-resonance excitation on the Lamb-shift is suppressed, as is the entire contribution of the magnetic polarizability; the electric polarizability dominates. Our results reaffirm the point of view that the proton structure effects, beyond the charge radius, are too small to resolve the `proton radius puzzle'.Comment: 16 pages, 5 figure

The Dynamics of the Skin Temperature of the Dead Sea

We explored the dynamics of the temperature of the skin layer of the Dead Sea surface by means of in situ meteorological and hydrographic measurements from a buoy located near the center of the lake. The skin temperature is most highly correlated to air temperature (0.93–0.98) in all seasons. The skin temperature is much less correlated to the bulk surface water temperature in the summer (0.80), when the lake is thermally stratified, and uncorrelated in the winter, when the Dead Sea is vertically mixed. Low correlations were found between the skin temperature and the solar radiation and wind speed in all seasons. The skin, with its low thermal inertia, responds immediately to the atmospheric forcing. Heat fluxes across the sea surface are also presented. The high correlation of skin temperature to air temperature with minimal time lag is a result of the nearly immediate response of the thin skin layer to the surface heat fluxes, primarily the sensible heat flux

Kink excitation spectra in the (1+1)-dimensional φ8\varphi^8 model

We study excitation spectra of BPS-saturated topological solutions -- the kinks -- of the $\varphi^8$ scalar field model in $(1+1)$ dimensions, for three different choices of the model parameters. We demonstrate that some of these kinks have a vibrational mode, apart from the trivial zero (translational) excitation. One of the considered kinks is shown to have three vibrational modes. We perform a numerical calculation of the kink-kink scattering in one of the considered variants of the $\varphi^8$ model, and find the critical collision velocity v_{\scriptsize \mbox{cr}} that separates the different collision regimes: inelastic bounce of the kinks at v_{\scriptsize \mbox{in}}\ge v_{\scriptsize \mbox{cr}}, and capture at v_{\scriptsize \mbox{in}}. We also observe escape windows at some values of v_{\scriptsize \mbox{in}} where the kinks escape to infinity after bouncing off each other two or more times. We analyse the features of these windows and discuss their relation to the resonant energy exchange between the translational and the vibrational excitations of the colliding kinks.Comment: 20 pages, 14 figures; V2: minor changes to match version published in JHE