Dispersive evaluation of the Lamb shift in muonic deuterium from chiral effective field theory
We merge the dispersive relation approach and the ab initio method to compute nuclear structure corrections to the Lamb shift in muonic deuterium. We calculate the deuteron response functions and corresponding uncertainties up to next-to-next-to-next-to-leading order in chiral effective field theory and compare our results to selected electromagnetic data to test the validity of the theory. We then feed response functions calculated over a wide range of kinematics to the dispersion-theory formalism and show that an improved accuracy is obtained compared to that with the use of available experimental data in the dispersive analysis. This opens up the possibility of applying this hybrid metho…
Forward doubly-virtual Compton scattering off the nucleon in chiral perturbation theory: II. Spin polarizabilities and moments of polarized structure functions
We examine the polarized doubly-virtual Compton scattering (VVCS) off the nucleon using chiral perturbation theory ($\chi$PT). The polarized VVCS contains a wealth of information on the spin structure of the nucleon which is relevant to the calculation of the two-photon-exchange effects in atomic spectroscopy and electron scattering. We report on a complete next-to-leading-order (NLO) calculation of the polarized VVCS amplitudes $S_1(\nu, Q^2)$ and $S_2(\nu, Q^2)$, and the corresponding polarized spin structure functions $g_1(x, Q^2)$ and $g_2(x,Q^2)$. Our results for the moments of polarized structure functions, partially related to different spin polarizabilities, are compared to other th…
Description of light nuclei in pionless effective field theory using the stochastic variational method
We construct a coordinate-space potential based on pionless effective field theory with a Gaussian regulator. Charge-symmetry breaking is included through the Coulomb potential and through two- and three-body contact interactions. Starting with the effective field theory potential, we apply the stochastic variational method to determine the ground states of nuclei with mass number $A\leq 4$. At next-to-next-to-leading order, two out of three independent three-body parameters can be fitted to the three-body binding energies. To fix the remaining one, we look for a simultaneous description of the binding energy of $^4$He and the charge radii of $^3$He and $^4$He. We show that at the order con…
Partial-wave analysis of proton Compton scattering data below the pion-production threshold
Low-energy Compton scattering off the proton is used for determination of the proton polarizabilities. However, the present empirical determinations rely heavily on the theoretical description(s) of the experimental cross sections in terms of polarizabilities. The most recent determinations are based on either the fixed-$t$ dispersion relations (DR) or chiral perturbation theory in the single-baryon sector ($\chi$PT). The two approaches obtain rather different results for proton polarizabilities, most notably for $\beta_{M1}$ (magnetic dipole polarizability). We attempt to resolve this discrepancy by performing a partial-wave analysis of the world data on proton Compton scattering below thr…
Forward doubly-virtual Compton scattering off the nucleon in chiral perturbation theory: The subtraction function and moments of unpolarized structure functions
The forward doubly-virtual Compton scattering (VVCS) off the nucleon contains a wealth of information on nucleon structure, relevant to the calculation of the two-photon-exchange effects in atomic spectroscopy and electron scattering. We report on a complete next-to-leading-order (NLO) calculation of low-energy VVCS in chiral perturbation theory ($\chi$PT). Here we focus on the unpolarized VVCS amplitudes $T_1(\nu, Q^2)$ and $T_2(\nu, Q^2)$, and the corresponding structure functions $F_1(x, Q^2)$ and $F_2(x,Q^2)$. Our results are confronted, where possible, with "data-driven" dispersive evaluations of low-energy structure quantities, such as nucleon polarizabilities. We find significant dis…
Sum rules across the unpolarized Compton processes involving generalized polarizabilities and moments of nucleon structure functions
We derive two new sum rules for the unpolarized doubly virtual Compton scattering process on a nucleon, which establish novel low-$Q^2$ relations involving the nucleon's generalized polarizabilities and moments of the nucleon's unpolarized structure functions $F_1(x,Q^2)$ and $F_2(x,Q^2)$. These relations facilitate the determination of some structure constants which can only be accessed in off-forward doubly virtual Compton scattering, not experimentally accessible at present. We perform an empirical determination for the proton and compare our results with a next-to-leading-order chiral perturbation theory prediction. We also show how these relations may be useful for a model-independent …
Spin-dependent sum rules connecting real and virtual Compton scattering verified
We present a detailed derivation of the two sum rules relating the spin polarizabilities measured in real, virtual, and doubly-virtual Compton scattering. For example, the polarizability $\delta_{LT}$, accessed in inclusive electron scattering, is related to the spin polarizability $\gamma_{E1E1}$ and the slope of generalized polarizabilities $P^{(M1,M1)1}-P^{(L1,L1)1}$, measured in, respectively, the real and the virtual Compton scattering. We verify these sum rules in different variants of chiral perturbation theory, discuss their empirical verification for the proton, and prospect their use in studies of the nucleon spin structure.
Polarisabilities of the nucleon in baryon chiral perturbation theory and beyond
We review the recent baryon chiral perturbation theory results for the nucleon polarisabilities that describe the different regimes of nucleon Compton scattering --- real, virtual, and doubly virtual. We stress the importance of the empirical verification of the theory in the context of the calculation of the inelastic nucleon structure corrections, such as the two-photon exchange contributions. We also discuss the recently obtained constraints that relate the different regimes of nucleon Compton scattering and can provide additional information on the nucleon structure.
Moments of nucleon structure functions at next-to-leading order in baryon chiral perturbation theory
We obtain leading- and next-to-leading-order predictions of chiral perturbation theory for several prominent moments of nucleon structure functions. These parameter-free results turn out to be in overall agreement with the available empirical information on nearly all of the considered moments, in the region of low momentum transfer $({Q}^{2}l0.3\phantom{\rule{4pt}{0ex}}{\mathrm{GeV}}^{2})$. Especially surprising is the situation for the spin polarizability ${\ensuremath{\delta}}_{LT}$, which thus far was not reproducible in chiral perturbation theory for proton and neutron simultaneously. This problem, known as the ``${\ensuremath{\delta}}_{LT}$ puzzle,'' is not seen in the present calcula…
Generalized polarizabilities of the nucleon in baryon chiral perturbation theory
The nucleon generalized polarizabilities (GPs), probed in virtual Compton scattering (VCS), describe the spatial distribution of the polarization density in a nucleon. They are accessed experimentally via the process of electron-proton bremsstrahlung ($ep\to ep\gamma$) at electron-beam facilities, such as MIT-Bates, CEBAF (Jefferson Lab), and MAMI (Mainz). We present the calculation of the nucleon GPs and VCS observables at next-to-leading order in baryon chiral perturbation theory (B$\chi$PT), and confront the results with the empirical information. At this order our results are predictions, in the sense that all the parameters are well-known from elsewhere. Within the relatively large unc…
Gold-plated moments of nucleon structure functions in baryon chiral perturbation theory
We obtain leading- and next-to-leading order predictions of chiral perturbation theory for several prominent moments of nucleon structure functions. These free-parameter free results turn out to be in overall agreement with the available empirical information on nearly all of the considered moments, in the region of low-momentum transfer ($Q^2 < 0.3$ GeV$^2$). Especially surprising is the situation for the spin polarizability $\delta_{LT}$, which thus far was not reproducible in chiral perturbation theory for proton and neutron simultaneously. This problem, known as the "$\delta_{LT}$ puzzle," is not seen in the present calculation.
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 …
Near-threshold $\pi^-$ photoproduction on the deuteron
The first experimental investigation of the near-threshold cross section for incoherent $\pi^-$ photoproduction on the deuteron $\gamma$ d -> $\pi^-$ pp is presented. The experimental technique involved detection of the ~131 MeV gamma ray resulting from the radiative capture of photoproduced $\pi^-$ in the target. The total cross section has been measured using an unpolarized tagged-photon beam, a liquid-deuterium target, and three very large NaI(Tl) spectrometers. The data are compared to theoretical models that give insight into the elementary reaction $\gamma$ n -> $\pi^-$ p and pion-nucleon and nucleon-nucleon final-state interactions.
Excitation spectra of solitary waves in scalar field models with polynomial self-interaction
We study excitations of solitary waves -- the kinks -- in scalar models with degree eight polynomial self-interaction in (1+1) dimensions. We perform numerical studies of scattering of two kinks with an exponential asymptotic off each other and analyse the occurring resonance phenomena. We connect these phenomena to the energy exchange between the translational and the vibrational modes of the colliding kinks. We also point out that the interaction of two kinks with power-law asymptotic can lead to a long-range interaction between the two kinks.