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E. Epelbaum

Publications and source records attributed to E. Epelbaum.

At least 37 records · Page 2Linked to original sources
arXiv2023

Renormalization of nuclear chiral effective field theory with non-perturbative leading order interactions

We extend the renormalizability study of the formulation of chiral effective field theory with a finite cutoff, applied to nucleon-nucleon scattering, by taking into account non-perturbative effects. We consider the nucleon-nucleon interaction up to next-to-leading order in the chiral expansion. The leading-order interaction is treated non-perturbatively. In contrast to the previously considered case when the leading-order interaction was assumed to be perturbative, new features related to the renormalization of the effective field theory are revealed. In particular, more severe constraints on the leading-order potential are formulated, which can enforce the renormalizability and the correct power counting for the next-to-leading order amplitude. To illustrate our theoretical findings, several partial waves in the nucleon-nucleon scattering, $^3P_0$, $^3S_1-{^3D_1}$ and $^1S_0$ are analyzed numerically. The cutoff dependence and the convergence of the chiral expansion for those channels are discussed.

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arXiv2022

Is the "RG-invariant EFT'' for few-nucleon systems cutoff independent?

We consider nucleon-nucleon scattering using the formulation of chiral effective field theory which is claimed to be renormalization group invariant. The cornerstone of this framework is the existence of a well-defined infinite-cutoff limit for the scattering amplitude at each order of the expansion, which should not depend on a particular regulator form. Focusing on the $^3P_0$ partial wave as a representative example, we show that this requirement can in general not be fulfilled beyond the leading order, in spite of the perturbative treatment of subleading contributions to the amplitude. Several previous studies along these lines, including the next-to-leading order calculation by Long and Yang [Phys. Rev. C84, 057001 (2011)] and a toy model example with singular long-range potentials by Long and van Kolck [Annals Phys. 323, 1304-1323 (2008)], are critically reviewed and scrutinized in detail.

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arXiv2022

Gravitational form factors of the delta resonance in chiral EFT

The leading one-loop corrections to the gravitational form factors of the delta resonance are calculated in the framework of chiral effective field theory. Various contributions to the energy-momentum tensor and the renormalization of the low-energy constants are worked out. Using the small scale expansion, expressions for static quantities are obtained and the real and imaginary parts of the gravitational form factors are calculated numerically.

hep-ph↗
arXiv2022

Nucleon-nucleon scattering up to next-to-next-to-leading order in manifestly Lorentz-invariant chiral effective field theory: peripheral phases

We study the nucleon-nucleon interaction up to next-to-next-to-leading order using time-ordered perturbation theory in the framework of manifestly Lorentz-invariant chiral effective field theory. We present the two-pion exchange contribution at one-loop level, which is consistent with the corresponding non-relativistic expressions in the large-nucleon-mass limit. Using the Born series truncated at one-loop order, we calculate the phase shifts and mixing angles of the partial waves with the angular momentum $l\geq 2$. Comparing with the results of non-relativistic formulation, we find an improved description of the phase shifts for some $D$ waves such as the $^3D_3$ one. For the other partial waves, both approaches show the globally similar results.

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arXiv2022

Pion absorption from the lowest atomic orbital in 2H, 3H and 3He

The pi- + 2H -> n + n, pi- + 3H -> n + n + n, pi- + 3He -> n + d and pi- + 3He -> p + n + n capture reactions from the lowest atomic orbitals are studied under full inclusion of final state interactions. Our results are obtained with the single-nucleon and two-nucleon transition operators derived at leading order in chiral effective field theory. The initial and final three-nucleon states are calculated with the chiral nucleon-nucleon SMS potential up to N4LO+ augmented by the consistently regularized chiral N2LO three-nucleon potential. We found that absorption rates depend strongly on the nuclear pion absorption operator used, and its two-body parts change the rates by a few orders of magnitude. The final state interactions between nucleons generated by the two-nucleon forces are also important, while the three-nucleon interaction plays a visible role only in the pi- + 3He -> n + d reaction. Our absorption rate for the pi- + 2H -> n + n process is in good agreement with the experimental data from the hadronic ground-state broadening in pionic deuterium. The capture rates on 3He are also generally consistent with the spectroscopic data within error bars, though our central values are found to be systematically below the data. We show that for the three-body breakup processes the dominant contributions to the absorption rates arise from the quasi-free scattering and final-state interaction kinematical configurations.

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arXiv2022

Nuclear properties with semilocal momentum-space regularized chiral interactions beyond N2LO

We present a comprehensive investigation of few-nucleon systems as well as light and medium-mass nuclei up to $A=48$ using the current Low Energy Nuclear Physics International Collaboration two-nucleon interactions in combination with the third-order (N$^2$LO) three-nucleon forces. To address the systematic overbinding of nuclei starting from $A \sim 10$ found in our earlier study utilizing the N$^2$LO two- and three-nucleon forces, we take into account higher-order corrections to the two-nucleon potentials up through fifth order in chiral effective field theory. The resulting Hamiltonian can be completely determined using the $A=3$ binding energies and selected nucleon-deuteron cross sections as input. It is then shown to predict other nucleon-deuteron scattering observables and spectra of light $p$-shell nuclei, for which a detailed correlated truncation error analysis is performed, in agreement with experimental data. Moreover, the predicted ground state energies of nuclei in the oxygen isotopic chain from $^{14}$O to $^{26}$O as well as $^{40}$Ca and $^{48}$Ca show a remarkably good agreement with experimental values, given that the Hamiltonian is fixed completely from the $A \leq 3$ data, once the fourth-order (N$^3$LO) corrections to the two-nucleon interactions are taken into account. On the other hand, the charge radii are found to be underpredicted by $\sim 10\%$ for the oxygen isotopes and by almost $20\%$ for $^{40}$Ca and $^{48}$Ca.

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arXiv2022

Semi-local nuclear forces from chiral EFT: State-of-the-art & challenges

Recently, a new generation of nuclear forces has been developed in the framework of chiral EFT. An important feature of these potentials is a novel semi-local regularization approach that combines the advantages of a local regulator for long-range interactions with the convenience of an angle-independent nonlocal regulator for contact interactions. The authors discuss the key features of the semi-local two-nucleon potentials and demonstrate their outstanding performance in the two-nucleon sector by showing selected results up to fifth order in the EFT expansion. Also reviewed are applications to heavier systems, which are currently limited to third chiral order. This limitation reflects the conceptual difficulty in constructing a consistently regularized many-body forces and current operators and affects all currently available interactions. The authors outline possible ways to tackle this problem and discuss future directions in the field.

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arXiv2022

On the definition of local spatial densities in hadrons

We show that the matrix element of a local operator between hadronic states gives rise to an unambiguous definition of the associated spatial density. As an explicit example, we consider the charge density of a spinless particle in the rest and moving frames and clarify its relationship to the electric form factor. Our results suggest that the interpretation of the spatial densities of local operators and their moments such as the mean square charge radius needs to be revised.

hep-ph↗
arXiv2021

Is $Z_{cs}(3982)$ a molecular partner of $Z_c(3900)$ and $Z_c(4020)$ states?

We perform an effective-field-theory-based coupled-channel analysis of the recent BES III data on the $e^+e^-$ annihilation into the final state $K^+(D_s^-D^{*0}+D_s^{*-}D^0)$ in a wide energy range and extract the poles responsible for the formation of the $Z_{cs}(3982)$. We identify two scenarios which provide a similar description of the experimental mass distributions but result in utterly different predictions for the spin partners of the $Z_{cs}(3982)$: although both scenarios are consistent with the $Z_{cs}$ as a $SU(3)$ partner of the $Z_c(3900)$, the $Z_c(4020)$ appears naturally as a spin partner of these states only in one of them (fit 1) while in the other (fit 2) its nature has to be different. Also, the $Z_{cs}(3982)$ has a $J^{P}=1^+$ spin partner near the $\bar D_s^* D^*$ threshold in fit 1, while no such state exists in fit 2. We predict the $\bar{D}_s^*D^*$ invariant mass distribution in the $J^{P}=1^+$ channel for the reaction $e^+e^-\to K^+D_s^{*-}D^{*0}$ and argue that this line shape can be used to distinguish between the two scenarios once data in this channel are available.

hep-ph↗
arXiv2021

Nucleon-nucleon interaction in chiral EFT with a finite cutoff: explicit perturbative renormalization at next-to-leading order

We present a study of two-nucleon scattering in chiral effective field theory with a finite cutoff to next-to-leading order in the chiral expansion. In the proposed scheme, the contributions of the lowest-order interaction to the scattering amplitude are summed up to an arbitrary order, while the corrections beyond leading order are iterated only once. We consider a general form of the regulator for the leading-order potential including local and non-local structures. The main objective of the paper is to address formal aspects of renormalizability within the considered scheme. In particular, we provide a rigorous proof, valid to all orders in the iterations of the leading-order potential, that power-counting breaking terms originating from the integration regions with momenta of the order of the cutoff can be absorbed into the renormalization of the low energy constants of the leading contact interactions. We also demonstrate that the cutoff dependence of the scattering amplitude can be reduced by perturbatively subtracting the regulator artifacts at next-to-leading order. The obtained numerical results for phase shifts in $P$- and higher partial waves confirm the applicability of our scheme for nucleon-nucleon scattering.

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arXiv2021

Two-particle scattering from finite-volume quantization conditions using the plane wave basis

We propose an alternative approach to Lüscher's formula for extracting two-body scattering phase shifts from finite volume spectra with no reliance on the partial wave expansion. We use an effective-field-theory-based Hamiltonian method in the plane wave basis and decompose the corresponding matrix elements of operators into irreducible representations of the relevant point groups. The proposed approach allows one to benefit from the knowledge of the long-range interaction and avoids complications from partial wave mixing in a finite volume. We consider spin-singlet channels in the two-nucleon system and pion-pion scattering in the $ρ$-meson channel in the rest and moving frames to illustrate the method for non-relativistic and relativistic systems, respectively. For the two-nucleon system, the long-range interaction due to the one-pion exchange is found to make the single-channel Lüscher formula unreliable at the physical pion mass. For S-wave dominated states, the single-channel Lüscher method suffers from significant finite-volume artifacts for a $L=3$~fm box, but it works well for boxes with $L>5$~fm. However, for P-wave dominated states, significant partial wave mixing effects prevent the application of the single-channel Lüscher formula regardless of the box size (except for the near-threshold region). Using a toy model to generate synthetic data for finite-volume energies, we show that our effective-field-theory-based approach in the plane wave basis is capable of a reliable extraction of the phase shifts. For pion-pion scattering, we employ a phenomenological model to fit lattice QCD results at the physical pion mass. The extracted P-wave phase shifts are found to be in a good agreement with the experimental results.

hep-lat↗
arXiv2021

Chiral theory of $ρ$-meson gravitational form factors

The low-energy chiral effective field theory of vector mesons and Goldstone bosons in external gravitational field is considered. The energy-momentum tensor is obtained and the gravitational form factors of the $ρ$-meson are calculated up to next-to-leading order in the chiral expansion. This amounts to considering tree-level and one-loop order diagrams. The chiral expansion of the form factors at zero momentum transfer as well as of the slope parameters is worked out. Also, the long-range behaviour of the energy and internal force distributions is obtained and analysed.

hep-ph↗
arXiv2021

Pion photoproduction in chiral perturbation theory with explicit treatment of the $Δ(1232)$ resonance

We study the reaction of pion photoproduction on the nucleon in the framework of chiral perturbation theory with explicit $Δ(1232)$ degrees of freedom. In the covariant approach, we give results up to order $ε^3$ in the small scale expansion scheme. Furthermore, we provide $Δ$-less and $Δ$-full results obtained in the heavy-baryon scheme to analyze the differences to the covariant approach. Low energy constants are fitted to multipole amplitudes using theoretical truncation errors estimated by a Bayesian approach. We also compare our findings to data of neutral pion production cross sections and polarization asymmetries. The description of the reaction is clearly improved by the explicit treatment of the $Δ(1232)$ resonance.

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arXiv2021

Effective field theory for shallow P-wave states

We discuss the formulation of a non-relativistic effective field theory for two-body P-wave scattering in the presence of shallow states and critically address various approaches to renormalization proposed in the literature. It is demonstrated that the consistent renormalization involving only a finite number of parameters in the well-established formalism with auxiliary dimer fields corresponds to the inclusion of an infinite number of counterterms in the formulation with contact interactions only. We also discuss the implications from the Wilsonian renormalization group analysis of P-wave scattering.

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arXiv2021

Precision determination of pion-nucleon coupling constants using effective field theory

The pion-nucleon coupling constants determine the strength of the long-range nuclear forces and play a fundamental part in our understanding of nuclear physics. While the charged- and neutral-pion couplings to protons and neutrons are expected to be very similar, owing to the approximate isospin symmetry of the strong interaction, the different masses of the up- and down-quarks and electromagnetic effects may result in their slightly different values. Despite previous attempts to extract these coupling constants from different systems, our knowledge of their values is still deficient. In this Letter we present a precision determination of these fundamental observables with fully controlled uncertainties from neutron-proton and proton-proton scattering data using chiral effective field theory. To achieve this goal, we use a novel methodology based on the Bayesian approach and perform, for the first time, a full-fledged partial-wave analysis of nucleon-nucleon scattering up to the pion production threshold in the framework of chiral effective field theory, including a complete treatment of isospin-breaking effects and our own determination of mutually consistent data. The resulting values of the pion-nucleon coupling constants are accurate at the percent level and show no significant charge dependence. These results mark an important step towards developing a precision theory of nuclear forces and structure.

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arXiv2021

Comprehensive investigation of the symmetric space-star configuration in the nucleon-deuteron breakup

We examine a description of available cross section data for symmetric space star (SST) configurations in the neutron-deuteron (nd) and proton-deuteron (pd) breakup reaction using numerically exact solutions of the three-nucleon (3N) Faddeev equation based on two- and three-nucleon (semi)phenomenological and chiral forces. The predicted SST cross sections are very stable with respect to the underlying dynamics for incoming nucleon laboratory energies below $\approx 25$ MeV. We discuss possible origins of the surprising discrepancies between theory and data found in low-energy nd and pd SST breakup measurements.

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arXiv2021

Insights into $Z_b(10610)$ and $Z_b(10650)$ from dipion transitions from $Υ(10860)$

The dipion transitions $Υ(10860)\toπ^+π^-Υ(nS)$ ($n=1,2,3$) are studied in the framework of a unitary and analytic coupled-channel formalism previously developed for analysing experimental data on the bottomoniumlike states $Z_b(10610)$ and $Z_b(10650)$ [Phys. Rev. D 98, 074023 (2018)] and predicting the properties of their spin partners [Phys. Rev. D 99, 094013 (2019)]. In this work we use a relatively simple but realistic version of this approach, where the scattering and production amplitudes are constructed employing only short-ranged interactions between the open- and hidden-flavour channels consistent with the constraints from heavy quark spin symmetry, for an extended analysis of the experimental line shapes. In particular, the transitions from the $Υ(10860)$ to the final states $ππh_b(mP)$ ($m=1,2$) and $πB^{(*)}\bar B^* $ already studied before, are now augmented by the $Υ(10860)\toπ^+π^-Υ(nS)$ final states ($n=1,2,3$). This is achieved by employing dispersion theory to account for the final state interaction of the $ππ$ subsystem including its coupling to the $K\bar K$ channel. Fits to the two-dimensional Dalitz plots for the $π^+π^-Υ$ final states were performed. Two real subtraction constants are adjusted to achieve the best description of the Dalitz plot for each $Υ(nS)$ $(n=1,2,3)$ while all the parameters related to the properties of the $Z_b$'s are kept fixed from the previous study. A good overall description of the data for all $Υ(10860)\toπ^+π^-Υ(nS)$ channels achieved in this work provides additional strong support for the molecular interpretation of the $Z_b$ states.

hep-ph↗