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A. M. Gasparyan

Publications and source records attributed to A. M. Gasparyan.

At least 19 recordsLinked to original sources
arXiv2026

Scrutiny of the new class of three-nucleon forces

In a recent publication, Cirigliano {\it et al.} [Phys. Rev. Lett. 135, 022501 (2025)] argue that three-nucleon forces (3NFs) involving short-range operators that couple two pions with two nucleons are enhanced beyond what is expected in chiral effective field theory based on naive dimensional analysis. Here, we scrutinize the arguments and conclusions of that paper by taking into account renormalization scheme dependence of the corresponding low-energy constants. We gain further insights into the expected impact of these 3NFs by comparing them with contributions of similar type, induced by pion-exchange diagrams at lower orders in the chiral expansion. We also estimate the impact of these 3NFs on properties of nuclear matter. After removal of scheme-dependent short-distance components in pion loops, the 3NFs considered by Cirigliano {\it et al.} are shown to yield reasonably small contributions to the equation of state of neutron and symmetric nuclear matter in agreement with expectations based on Weinberg's power counting.

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arXiv2025

Renormalizability and nonrenormalizability of nonlocal potentials

We consider separable toy models of the nucleon-nucleon interaction inspired by chiral effective field theory. We show that nonlocality of the long-range forces causes the need for nonlocal counter terms, or even makes the whole approach nonrenormalizable.

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arXiv2025

Criteria of Renormalizability in Effective Field Theories

Any effective field theory relies on power counting rules that allow one to perform a systematic expansion of calculated quantities in terms of some soft scales. However, a naive power counting can be violated due to the presence of various hard scales in a given scheme. A typical example of such a scale is an ultraviolet regulator. This issue is particularly challenging when the interaction is nonperturbative. The power counting is expected to be restored in the course of renormalization, that is by redefining bare low-energy constants in the effective Lagrangian. Whether this procedure eventually leads to a self-consistent framework is not a priory obvious. We discuss various criteria of renormalizability in application to nuclear chiral effective field theory and provide several instructive counterexamples.

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arXiv2024

Gravitational form factors of the deuteron

The gravitational form factors of the deuteron are calculated in the framework of non-relativistic chiral effective field theory. Non-relativistic reduction of the matrix element of the energy-momentum tensor operator for spin-one systems is worked out, and the gravitational form factors of the deuteron are extracted from the three-point function of the energy-momentum tensor using the LSZ reduction formula. The obtained form factors are compared to results of model calculations available in the literature.

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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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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

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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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

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

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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arXiv2018

How (not) to renormalize integral equations with singular potentials in effective field theory

We discuss the connection between the perturbative and non-perturbative renormalization and related conceptual issues in the few-nucleon sector of the low-energy effective field theory of the strong interactions. General arguments are supported by examples from effective theories with and without pions as dynamical degrees of freedom. A quantum mechanical potential with explicitly specified short- and long-range parts is considered as an "underlying fundamental theory" and the corresponding effective field theory potential is constructed. Further, the problem of the effective field theoretical renormalization of the Skornyakov-Ter-Martyrosian equation is revisited.

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arXiv2018

Three-nucleon force in chiral EFT with explicit $Δ(1232)$ degrees of freedom: Longest-range contributions at fourth order

We analyze the longest-range two-pion exchange contributions to the three-nucleon force at leading-loop order in the framework of heavy-baryon chiral effective field theory with explicit $Δ(1232)$ degrees of freedom. All relevant low-energy constants which appear in the calculation are determined from pion-nucleon scattering. Comparing our results with the ones obtained in the $Δ$-less theory at N4LO, we find effects of the $Δ$ isobar for this particular topology to be rather well represented in terms of resonance saturation of various low-energy constants in the $Δ$-less approach.

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arXiv2016

Pion-nucleon scattering in covariant baryon chiral perturbation theory with explicit Delta resonances

We present the results of a third order calculation of the pion-nucleon scattering amplitude in a chiral effective field theory with pions, nucleons and delta resonances as explicit degrees of freedom. We work in a manifestly Lorentz invariant formulation of baryon chiral perturbation theory using dimensional regularization and the extended on-mass-shell renormalization scheme. In the delta resonance sector, the on mass-shell renormalization is realized as a complex-mass scheme. By fitting the low-energy constants of the effective Lagrangian to the $S$- and $P$-partial waves a satisfactory description of the phase shifts from the analysis of the Roy-Steiner equations is obtained. We predict the phase shifts for the $D$ and $F$ waves and compare them with the results of the analysis of the George Washington University group. The threshold parameters are calculated both in the delta-less and delta-full cases. Based on the determined low-energy constants, we discuss the pion-nucleon sigma term. Additionally, in order to determine the strangeness content of the nucleon, we calculate the octet baryon masses in the presence of decuplet resonances up to next-to-next-to-leading order in SU(3) baryon chiral perturbation theory. The octet baryon sigma terms are predicted as a byproduct of this calculation.

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arXiv2015

$^1S_0$ nucleon-nucleon scattering in the modified Weinberg approach

Nucleon-nucleon scattering in the $^1S_0$ partial wave is considered in chiral effective field theory within the renormalizable formulation of Ref. [1] beyond the leading-order approximation. By applying subtractive renormalization, the subleading contact interaction in this channel is taken into account non-perturbatively. For a proper choice of renormalization conditions, the predicted energy dependence of the phase shift and the coefficients in the effective range expansion are found to be in a good agreement with the results of the Nijmegen partial wave analysis.

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arXiv2014

Three-nucleon force at large distances: Insights from chiral effective field theory and the large-N_c expansion

We confirm the claim of Ref. [D.R. Phillips, C. Schat, Phys. Rev. C88 (2013) 3, 034002] that 20 operators are sufficient to represent the most general local isospin-invariant three-nucleon force and derive explicit relations between the two sets of operators suggested in Refs. [D.R. Phillips, C. Schat, Phys. Rev. C88 (2013) 3, 034002] and [H. Krebs, A.M. Gasparyan, E. Epelbaum, Phys.Rev. C87 (2013) 5, 054007]. We use the set of 20 operators to discuss the chiral expansion of the long- and intermediate-range parts of the three-nucleon force up to next-to-next-to-next-to-next-to-leading order in the standard formulation without explicit Delta(1232) degrees of freedom. We also address implications of the large-N_c expansion in QCD for the size of the various three-nucleon force contributions.

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