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E. Epelbaum

Publications and source records attributed to E. Epelbaum.

At least 55 records · Page 3Linked to original sources
arXiv2021

The $Λ(1405)$ in resummed chiral effective field theory

We study the unitarized meson-baryon scattering amplitude at leading order in the strangeness $S=-1$ sector using time-ordered perturbation theory for a manifestly Lorentz-invariant formulation of chiral effective field theory. By solving the coupled-channel integral equations with the full off-shell dependence of the effective potential and applying subtractive renormalization, we analyze the renormalized scattering amplitudes and obtain the two-pole structure of the $Λ(1405)$ resonance. We also point out the necessity of including higher-order terms.

hep-ph↗
arXiv2020

Light nuclei with semilocal momentum-space regularized chiral interactions up to third order

We present a systematic investigation of few-nucleon systems and light nuclei using the current LENPIC interactions comprising semilocal momentum-space regularized two- and three-nucleon forces up to third chiral order (N$^2$LO). Following our earlier study utilizing the coordinate-space regularized interactions, the two low-energy constants entering the three-body force are determined from the triton binding energy and the differential cross section minimum in elastic nucleon-deuteron scattering. Predictions are made for selected observables in elastic nucleon-deuteron scattering and in the deuteron breakup reactions, for properties of the $A=3$ and $A=4$ nuclei, and for spectra of $p$-shell nuclei up to $A = 16$. A comprehensive error analysis is performed including an estimation of correlated truncation uncertainties for nuclear spectra. The obtained predictions are generally found to agree with experimental data within errors. Similar to the coordinate-space regularized chiral interactions at the same order, a systematic overbinding of heavier nuclei is observed, which sets in for $A \sim 10$ and increases with $A$.

nucl-th↗
arXiv2020

High-accuracy calculation of the deuteron charge and quadrupole form factors in chiral effective field theory

We present a comprehensive analysis of the deuteron charge and quadrupole form factors based on the latest two-nucleon potentials and charge density operators derived in chiral effective field theory. The single- and two-nucleon contributions to the charge density are expressed in terms of the proton and neutron form factors, for which the most up-to-date empirical parametrizations are employed. By adjusting the fifth-order short-range terms in the two-nucleon charge density operator to reproduce the world data on the momentum-transfer dependence of the deuteron charge and quadrupole form factors, we predict the values of the structure radius and the quadrupole moment of the deuteron: $r_{\rm str}=1.9729\substack{+0.0015\\ -0.0012}\ \text{fm},\ Q_d=0.2854\substack{+0.0038\\ -0.0017}\ \text{fm}^2. $ A comprehensive and systematic analysis of various sources of uncertainty in our predictions is performed. Following the strategy advocated in our recent publication Phys. Rev. Lett. 124, 082501 (2020), we employ the extracted structure radius together with the accurate atomic data for the deuteron-proton mean-square charge radii difference to update the determination of the neutron charge radius, for which we find: $r_n^2=-0.105\substack{+0.005\\ -0.006} \, \text{fm}^2$. Given the observed rapid convergence of the deuteron form factors in the momentum-transfer range of $Q \simeq 1-2.5$ fm$^{-1}$, we argue that this intermediate-energy domain is particularly sensitive to the details of the nucleon form factors and can be used to test different parametrizations.

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arXiv2020

Radiative pion photoproduction in covariant chiral perturbation theory

We present a calculation of radiative pion photoproduction in the framework of covariant chiral perturbation theory with explicit $Δ(1232)$ degrees of freedom. The analysis is performed employing the small scale expansion scheme adjusted for the $Δ$ region. Depending on the channel, we include contributions up to next-to-next-to-leading order. We fit the available experimental data for the reaction $ γp\toγpπ^0 $ and extract the value of the $Δ^+$ magnetic moment. Errors from the truncation of the small scale expansion are estimated using the Bayesian approach. We compare our results both with the previous studies within the $δ$-expansion scheme and with the $Δ$-less theory. We also give predictions for radiative charged-pion photoproduction.

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arXiv2020

Applications of the chiral potential with the semi-local regularization in momentum space to the disintegration processes

We apply the chiral potential with the momentum space semi-local regularization to the $^2$H and $^3$He photodisintegration processes and to the (anti)neutrino induced deuteron breakup reactions. Specifically, the differential cross section, the photon analyzing power and the final proton polarization have been calculated for the deuteron photodisintegration at the photon energies 30 MeV and 100 MeV. For the $^3$He photodisintegration predictions for the semi-inclusive and exclusive differential cross sections are presented for the photon energies up to 120 MeV. The total cross section is calculated for the (anti)neutrino disintegrations of the deuteron for the (anti)neutrino energies below 200 MeV. The predictions based on the Argonne V18 potential or on the older chiral force with regularization applied in coordinate space are used for comparison. Using the fifth order chiral nucleon-nucleon potential supplemented with dominant contributions from the sixth order allows us to obtain converged predictions for the regarded reactions and observables. Our results based on the newest semi-local chiral potentials show even smaller cutoff dependence for the considered electroweak observables than the previously reported ones with a coordinate-space regulator. However, some of the studied polarization observables in the deuteron photodisintegration process reveal more sensitivity to the regulator value than the unpolarized cross section. The chiral potential regularized semi-locally in momentum space yields also fast convergence of results with the chiral order. These features make the used potential a high quality tool to study electroweak processes.

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arXiv2020

Nucleon polarizabilities in covariant baryon chiral perturbation theory with explicit $Δ$ degrees of freedom

We compute various nucleon polarizabilities in chiral perturbation theory implementing the $Δ$-full ($Δ$-less) approach up to order $ε^3 + q^4$ ($q^4$) in the small-scale (chiral) expansion. The calculation is carried out using the covariant formulation of $χ$PT by utilizing the extended on-mass shell renormalization scheme. Except for the spin-independent dipole polarizabilities used to fix the values of certain low-energy constants, our results for the nucleon polarizabilities are pure predictions. We compare our calculations with available experimental data and other theoretical results. The importance of the explicit treatment of the $Δ$ degree of freedom in the effective field theory description of the nucleon polarizabilities is analyzed. We also study the convergence of the $1/m$ expansion and analyze the efficiency of the heavy-baryon approach for the nucleon polarizabilities.

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arXiv2020

How to renormalize integral equations with singular potentials in effective field theory

We briefly review general concepts of renormalization in quantum field theory and discuss their application to solutions of integral equations with singular potentials in the few-nucleon sector of the low-energy effective field theory of QCD. We also describe a particular subtractive renormalization scheme and consider a specific application to a toy-model with a singular potential serving as its effective field theoretical leading-order approximation.

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arXiv2020

Meson-baryon scattering in resummed baryon chiral perturbation theory using time-ordered perturbation theory

Integral equations for meson-baryon scattering amplitudes are obtained by utilizing time-ordered perturbation theory for a manifestly Lorentz-invariant formulation of baryon chiral perturbation theory. Effective potentials are defined as sums of two-particle irreducible contributions of time-ordered diagrams and the scattering amplitudes are obtained as solutions of integral equations. Ultraviolet renormalizability is achieved by solving integral equations for the leading order amplitude and including higher order corrections perturbatively. As an application of the developed formalism, pion-nucleon scattering is considered.

hep-ph↗
arXiv2020

Uncertainty of three-nucleon continuum observables arising from uncertainties of two-nucleon potential parameters

Propagation of uncertainties from two-nucleon potential parameters to three-nucleon observables, that is statistical errors for the neutron-deuteron elastic scattering and the deuteron breakup reaction at neutron laboratory energies up to 200 MeV is investigated. To that end we use the chiral nucleon-nucleon interaction with the semi-local momentum-space regularization at various orders of the chiral expansion, exploiting knowledge of the covariance matrix of its parameters. For both reactions we compare statistical uncertainties for chiral predictions with the uncertainties obtained in the same way but for the semi-phenomenological One-Pion-Exchange two-nucleon force. In addition for the elastic scattering we show also the truncation errors arising from restriction to a given order of chiral predictions, estimated among others within the Bayesian method, and the cutoff dependence of chiral predictions. We find that the resulting statistical uncertainty is smaller than the truncation errors for the chiral force at lower orders of the chiral expansion. At the higher orders of the chiral expansion and at low energies the statistical errors exceed the truncation ones but at intermediate and higher energies truncation errors are more important. Overall, magnitudes of the theoretical uncertainties are small and amount up to 0.5\%-4\%, depending on the observable and energy. We also find that the magnitudes of statistical uncertainties for the chiral and semi-phenomenological potentials are similar and that the dependence of predictions on the regularization parameter values is important at all investigated energies.

nucl-th↗
arXiv2020

Lambda-nucleon scattering in baryon chiral perturbation theory

We calculate the lambda-nucleon scattering phase shifts and mixing angles by applying time-ordered perturbation theory to the manifestly Lorentz-invariant formulation of SU(3) baryon chiral perturbation theory. Scattering amplitudes are obtained by solving the corresponding coupled-channel integral equations that have a milder ultraviolet behavior compared to their non-relativistic analogs. This allows us to consider the removed cutoff limit in our leading-order calculations also in the $^3P_0$ and $^3P_1$ partial waves. We find that, in the framework we are using, at least some part of the higher-order contributions to the baryon-baryon potential in these channels needs to be treated nonperturbatively and demonstrate how this can be achieved in a way consistent with quantum field theoretical renormalization for the leading contact interactions. We compare our results with the ones of the non-relativistic approach and lattice QCD phase shifts obtained for non-physical pion masses.

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arXiv2020

Extraction of the neutron charge radius from a precision calculation of the deuteron structure radius

We present a high-accuracy calculation of the deuteron structure radius in chiral effective field theory. Our analysis employs the state-of-the-art semilocal two-nucleon potentials and takes into account two-body contributions to the charge density operators up to fifth order in the chiral expansion. The strength of the fifth-order short-range two-body contribution to the charge density operator is adjusted to the experimental data on the deuteron charge form factor. A detailed error analysis is performed by propagating the statistical uncertainties of the low-energy constants entering the two-nucleon potentials and by estimating errors from the truncation of the chiral expansion as well as from uncertainties in the nucleon form factors. Using the predicted value for the deuteron structure radius together with the very accurate atomic data for the difference of the deuteron and proton charge radii we, for the first time, extract the charge radius of the neutron from light nuclei. The extracted value reads $r_n^2 = - 0.106 \substack{ +0.007\\ -0.005\\} \, \text{fm}^2$ and its magnitude is about $1.7σ$ smaller than the current value given by the Particle Data Group. In addition, given the high accuracy of the calculated deuteron charge form factor and its careful and systematic error analysis, our results open the way for an accurate determination of the nucleon form factors from elastic electron-deuteron scattering data measured at the Mainz Microtron and other experimental facilities.

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arXiv2020

Elastic and inelastic pion-nucleon scattering to fourth order in chiral perturbation theory

We extend our previous study of elastic pion-nucleon scattering in the framework of chiral perturbation theory by performing a combined analysis of the reactions $πN \to πN$ and $πN \to ππN$. The calculation is carried out to fourth order in the chiral expansion using the heavy baryon approach and the covariant formulation supplemented with a modified version of the extended on-mass-shell renormalization scheme. We demonstrate that a combined fit to experimental data in both channels leads to a reduced amount of correlations between the low-energy constants. A satisfactory description of the experimental data in both channels is obtained, which is further improved upon including tree-level contributions of the $Δ$(1232) resonance. We also explore a possibility of using the empirical information about $πN$ subthreshold parameters obtained recently by means of the Roy-Steiner equations to stabilize the fits.

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arXiv2020

Parity- and time-reversal-violating nuclear forces

Parity-violating and time-reversal conserving (PVTC) and parity-violating and time-reversal-violating (PVTV) forces in nuclei form only a tiny component of the total interaction between nucleons. The study of these tiny forces can nevertheless be of extreme interest because they allow to obtain information on fundamental symmetries using nuclear systems. The PVTC interaction derives from the weak interaction between the quarks inside nucleons and nuclei and the study of PVTC effects opens a window on the quark-quark weak interaction. The PVTV interaction is sensitive to more exotic interactions at the fundamental level, in particular to strong CP violation in the Standard Model Lagrangian, or even to exotic phenomena predicted in various beyond-the-Standard-Model scenarios. The presence of these interactions can be revealed either by studying various asymmetries in polarized scattering of nuclear systems, or by measuring the presence of non-vanishing permanent electric dipole moments of nucleons, nuclei and diamagnetic atoms and molecules. In this contribution, we review the derivation of the nuclear PVTC and PVTV interactions within various frameworks. We focus in particular on the application of chiral effective field theory, which allows for a more strict connection with the fundamental interactions at the quark level. We investigate PVTC and PVTV effects induced by these potential on several few-nucleon observables, such as the longitudinal asymmetry in proton-proton scattering and radiative neutron-proton capture, and the electric dipole momentsof the deuteron and the trinucleon system.

nucl-th↗
arXiv2019

Implications of spin symmetry for XYZ states

Numerous exotic candidates containing a heavy quark and anti-quark (the so-called $XYZ$ states) have been reported since the observation of the $X(3872)$ in 2003. For these systems a study of the implications of the heavy quark spin symmetry and its breaking is expected to provide useful guidance towards a better understanding of their nature. For instance, since the formation of the complete spin multiplets is described with the same parameter sets, in some cases the currently available experimental data on the $XYZ$ states allows us to predict properties of spin partner states. To illustrate this point we extract the parameters of the two $Z_b$ states by analyzing the most recent experimental data within an effective-field theory approach which treats both short-ranged contact interactions and the long-ranged one-pion/one-eta Goldstone boson exchanges (OPE/OEE) dynamically. The line shapes and pole positions of their spin partners are then predicted in a parameter-free way and await to be tested by future experimental data.

hep-ph↗
arXiv2019

High-precision nuclear forces from chiral EFT: State-of-the-art, challenges and outlook

We review a new generation of nuclear forces derived in chiral effective field theory using the recently proposed semilocal regularization method. We outline the conceptual foundations of nuclear chiral effective field theory, discuss all steps needed to compute nuclear observables starting from the effective chiral Lagrangian and consider selected applications in the two- and few-nucleon sectors. We highlight key challenges in developing high-precision tree-body forces, such as the need to maintain consistency between two- and many-body interactions and constraints placed by the chiral and gauge symmetries after regularization.

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arXiv2019

Towards baryon-baryon scattering in manifestly Lorentz-invariant formulation of SU(3) baryon chiral perturbation theory

We study baryon-baryon scattering by applying time-ordered perturbation theory to the manifestly Lorentz-invariant formulation of SU(3) baryon chiral perturbation theory. We derive the corresponding diagrammatic rules paying special attention to complications caused by momentum-dependent interactions and propagators of particles with non-zero spin. We define the effective potential as a sum of two-baryon irreducible contributions of time-ordered diagrams and derive a system of integral equations for the scattering amplitude, which provides a coupled-channel generalization of the Kadyshevsky equation. The obtained leading-order baryon-baryon potentials are perturbatively renormalizable, and the corresponding integral equations have unique solutions in all partial waves. We discuss the issue of additional finite subtractions required to improve the ultraviolet convergence of (finite) loop integrals on the example of nucleon-nucleon scattering in the $^3P_0$ partial wave. Assuming that corrections beyond leading order can be treated perturbatively, we obtain a fully renormalizable formalism which can be employed to study baryon-baryon scattering.

nucl-th↗
arXiv2019

Towards high-order calculations of three-nucleon scattering in chiral effective field theory

We discuss the current status of chiral effective field theory in the three-nucleon sector and present selected results for nucleon-deuteron scattering observables based on semilocal momentum-space-regularized chiral two-nucleon potentials together with consistently regularized three-nucleon forces up to third chiral order. Using a Bayesian model for estimating truncation errors, the obtained results are found to provide a good description of the experimental data. We confirm our earlier findings that a high-precision description of nucleon-deuteron scattering data below pion production threshold will require the theory to be pushed to fifth chiral order. This conclusion is substantiated by an exploratory study of selected short-range contributions to the three-nucleon force at that order, which, as expected, are found to have significant effects on polarization observables at intermediate and high energies. We also outline the challenges that will need to be addressed in order to push the chiral expansion of three-nucleon scattering observables to higher orders.

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