Chiral Effective Field Theory Approach Research Articles

Magnetic structure of few-nucleon systems at high momentum transfers in a chiral effective field theory approach

The five low-energy constants (LECs) in the electromagnetic current derived in chiral effective field theory ($\chi$EFT) up to one loop are determined by a simultaneous fit to the $A\,$=$\,2$--3 nuclei magnetic moments and to the deuteron magnetic form factor and threshold electrodisintegration at backward angles over a wide range of momentum transfers. The resulting parametrization then yields predictions for the $^3$He/$^3$H magnetic form factors in excellent accord with the experimental values for momentum transfers ranging up to $\approx 0.8$ GeV/c, beyond the expected regime of validity of the $\chi$EFT approach. The calculations are based on last-generation two-nucleon interactions including high orders in the chiral expansion and derived by Entem, Macheleidt, and Nosyk [Phys.\ Rev.\ C {\bf 96}, 024004 (2017)] and by Piarulli {\it et al.} [Phys.\ Rev.\ C {\bf 94}, 054007 (2016)], using different $\chi$EFT formulations. In the $A\,$=$\,3$ calculations, (chiral) three-nucleon interactions are also accounted for. The model dependence resulting from these different formulations of the interactions is found to be mild for momentum transfer below $\approx0.8$ GeV/c. An analysis of the convergence of the chiral expansion is also provided.

First experimental constraints on WIMP couplings in the effective field theory framework from CDEX

We present weakly interacting massive particles (WIMPs) search results performed using two approaches of effective field theory from the China Dark Matter Experiment (CDEX), based on the data from both CDEX-1B and CDEX-10 stages. In the nonrelativistic effective field theory approach, both time-integrated and annual modulation analyses were used to set new limits for the coupling of WIMP-nucleon effective operators at 90% confidence level (C.L.) and improve over the current bounds in the low $m_{\chi}$ region. In the chiral effective field theory approach, data from CDEX-10 were used to set an upper limit on WIMP-pion coupling at 90% C.L. We for the first time extended the limit to the $m_{\chi}<$ 6 GeV/$c^2$ region.

Magnetic structure and radiative captures of few-nucleon systems: status and prospects

We review the main ingredients for an ab-initio study of few-nucleon reactions of astrophysical interest within the chiral effective field theory approach, with particular attention to radiative captures relevant for Big Bang Nucleosynthesis and stellar evolution. We conclude with an outlook for ongoing and future work.

Revisiting the hypertriton lifetime puzzle

Conflicting values of the hypertriton (Λ3H) lifetime were extracted in recent relativistic heavy-ion collision experiments. The ALICE Collaboration's reported Λ3H lifetime τ(Λ3H) is compatible within measurement uncertainties with the free Λ lifetime τΛ, as naively expected for a loosely bound Λ hyperon in Λ3H, whereas STAR's reported range of τ(Λ3H) values is considerably shorter: τSTAR(Λ3H)∼(0.4-0.7)τΛ. This Λ3H lifetime puzzle is revisited theoretically, using Λ3H three-body wavefunctions generated in a chiral effective field theory approach to calculate the decay rate Γ(Λ3H→3He+π−). Significant but opposing contributions arise from ΣNN admixtures in Λ3H and from π−-3He final-state interaction. Evaluating the inclusive π− decay rate Γπ−(Λ3H) via a branching ratio Γ(Λ3H→3He+π−)/Γπ−(Λ3H) determined in helium bubble-chamber experiments, and adding Γπ0(Λ3H) through the ΔI=12 rule, we derive τ(Λ3H) assuming several different values of the Λ separation energy BΛ(Λ3H). It is concluded that each of ALICE and STAR reported τ(Λ3H) intervals implies its own constraint on BΛ(Λ3H): BΛ≲0.1 MeV for ALICE, BΛ≳0.2 MeV for STAR.

Recent Progresses in Ab-Initio Studies of Low-Energy Few-Nucleon Reactions of Astrophysical Interest

We review the most recent theoretical studies of nuclear reactions of astrophysical interest involving few-nucleon systems. In particular, we focus on the radiative capture of protons by deuterons in the energy range of interest for Big Bang Nucleosynthesis. Related to this, we will discuss also the most recent calculation of tritium $$\beta $$ -decay. Two frameworks will be considered, the conventional and the chiral effective field theory approach.

Foundations of strangeness nuclear physics derived from chiral effective field theory

Dense compact objects like neutron stars or black holes have always been one of Gerry Brown’s favorite research topics. This is closely related to the effects of strangeness in nuclear physics. Here, we review the chiral Effective Field Theory approach to interactions involving nucleons and hyperons, the possible existence of strange dibaryons, the fate of hyperons in nuclear matter and the present status of three-body forces involving hyperons and nucleons.

Molecular partners of the X(3872) from heavy-quark spin symmetry: a fresh look

The heavy-quark spin symmetry (HQSS) partners of the X(3872) molecule are investigated in a chiral effective field theory (EFT) approach which incorporates contact and one-pion exchange interactions. The integral equations of the Lippmann-Schwinger type are formulated and solved for the coupled-channel problem for the DD , DD *, and D*D * systems with the quantum numbers J PC = 1 ++ , 1+− , 0 ++ , and 2 ++ . We confirm that, if the X (3872) is a 1 ++ DD * molecular state then, in the strict heavy-quark limit, there exist three partner states, with the quantum numbers 1 +− , 0 ++ , and 2 ++ , which are degenerate in mass. At first glance, this result looks natural only for the purely contact pionless theory since pions contribute differently to different transition potentials and, therefore, may lift the above degeneracy. Nevertheless, it is shown that, by an appropriate unitary transformation, the Lippmann-Schwinger equation in each channel still can be brought to a block-diagonal form, with the same blocks for all quantum numbers, so that the degeneracy of the bound states in different channels is preserved. We stress that neglecting some of the coupled-channel transitions in an inconsistent manner leads to a severe violation of HQSS and yields regulator-dependent results for the partner states. The effect of HQSS violation in combination with nonperturbative pion dynamics on the pole positions of the partner states is discussed.

Mass and width of the Delta resonance using complex-mass renormalization

The pole mass and width of the Delta resonance are calculated in the relativistic chiral effective field theory approach. We choose a systematic power-counting procedure by applying the complex-mass scheme (CMS).

New insights into theDs0*(2317)and other charm scalar mesons

Through the scattering of light-pseudoscalar mesons ($\pi,K,\eta,\eta'$) off charmed mesons ($D, D_s$), we study the $D^{*}_{s0}(2317)$ state and other relevant charm scalar mesons in a unitarized chiral effective field theory approach. We investigate the charm scalar meson poles with different strangeness ($S$) and isospin ($I$) quantum numbers as well as their corresponding residues, which provide the coupling strengths of the charm scalar mesons. Both the light-quark mass and $N_C$ dependences of the pole positions of the $D^{*}_{s0}(2317)$ and the poles with $(S,I)=(0,1/2)$ are analyzed in detail in this work. Interestingly we observe quite similar pion mass trajectories for the resonance pole at around 2.1 GeV with $(S,I)=(0,1/2)$ to those of the $f_0(500)$ given in the literature. When increasing the values of $N_C$ we find that a bound state and a virtual state in the $(S,I)=(1,0)$ channel asymmetrically approach the $D K$ threshold for $N_C<6$, and they meet at this threshold at $N_C=6$. When $N_C>6$, the bound and virtual states move into the complex plane on the second Riemann sheet and become a symmetric pair of resonance poles. For large enough values of $N_C$, neither the $D^{*}_{s0}(2317)$ pole nor the poles with $(S,I)=(0,1/2)$ tend to fall down to the real axis, indicating that they do not behave like a standard quark-antiquark meson at large $N_C$.

Dense baryonic matter: Constraints from recent neutron star observations

Updated constraints from neutron star masses and radii impose stronger restrictions on the equation of state for baryonic matter at high densities and low temperatures. The existence of two-solar-mass neutron stars rules out many soft equations of state with prominent "exotic" compositions. The present work reviews the conditions required for the pressure as a function of baryon density in order to satisfy these new constraints. Several scenarios for sufficiently stiff equations of state are evaluated. The common starting point is a realistic description of both nuclear and neutron matter based on a chiral effective field theory approach to the nuclear many-body problem. Possible forms of hybrid matter featuring a quark core in the center of the star are discussed using a three-flavor Polyakov--Nambu--Jona-Lasinio (PNJL) model. It is found that a conventional equation of state based on nuclear chiral dynamics meets the astrophysical constraints. Hybrid matter generally turns out to be too soft unless additional strongly repulsive correlations, e.g. through vector current interactions between quarks, are introduced. The extent to which strangeness can accumulate in the equation of state is also discussed.

The proton-proton weak capture reaction within chiral effective field theory

We review the results of the most recent calculation for the astrophysical S-factor of the weak proton-proton capture reaction, over a range for the center-of-mass relative energy of 0-100 keV. The so-called chiral effective field theory approach is used, where the chiral two- nucleon potential is derived up to next-to-next-to-next-to leading order and is augmented by the full electromagnetic interaction. The low-energy constants (LEC's) entering the weak current operators are fixed so as to reproduce the A = 3 binding energies and magnetic moments, and the Gamow-Teller matrix element in tritium β-decay. Contributions from S and P partial waves in the incoming two-proton channel are retained. The S-factor at zero energy is found to be ~1% larger than the value reported in the literature, mostly due to the P-waves contributions.

Deuteron electromagnetic form factors in a renormalizable formulation of chiral effective field theory

We calculate the deuteron electromagnetic form factors in a modified version of Weinberg's chiral effective field theory approach to the two-nucleon system. We derive renormalizable integral equations for the deuteron without partial wave decomposition. Deuteron form factors are extracted by applying the Lehmann-Symanzik-Zimmermann reduction formalism to the three-point correlation function of deuteron interpolating fields and the electromagnetic current operator. Numerical results of a leading-order calculation with removed cutoff regularization agree well with experimental data.

How neutron stars constrain the nuclear equation of state

Recent neutron star observations set new constraints for the equation of state of baryonic matter. A chiral effective field theory approach is used for the description of neutron-dominated nuclear matter present in the outer core of neutron stars. Possible hybrid stars with quark matter in the inner core are discussed using a three-flavor Nambu–Jona-Lasinio model.

THE ROLE OF THE Δ(1232)-RESONANCE IN COVARIANT BARYON CHIRAL PERTURBATION THEORY

We stress, on theoretical and phenomenological grounds, the importance of the Δ(1232)-resonance in a chiral effective field theory approach to the study of πN scattering. We show how its inclusion as a dynamical degree of freedom allow us to obtain reliably valuable information from πN scattering data.

Low energy electromagnetic processes based on the chiral effective field theory approach

Chiral effective field theory describes the interaction of nucleons and pions in the low-energy regime of QCD. This theory offers a consistent picture of nuclear forces and nuclear current operators. We study the electromagnetic processes based on ChEFT dynamical picture and compare our predictions to results obtained in the conventional framework. In particular, we consider low energy photo-disintegration of the deuteron at different orders of the chiral expansion. We investigate a role of different ingredients in the two-nucleon current operator. For the first time calculations involve consistent contributions from long-range two-pion exchange currents which appear at next-to-leading order of the chiral expansion. We present novel results for cross sections and various polarization observables.

RECENT ADVANCES IN THE THEORY OF NUCLEAR FORCES AND ITS RELEVANCE FOR THE MICROSCOPIC APPROACH TO DENSE MATTER

The theory of nuclear forces has made great progress since the turn of the millenium using the framework of chiral effective field theory (ChEFT). The advantage of this approach, which was originally proposed by Weinberg, is that it has a firm basis in quantum-chromodynamics and allows for quantitative calculations. Moreover, this theory generates two-nucleon forces (2NF) and many-body forces on an equal footing and provides an explanation for the empirically known fact that 2NF ≫ 3NF ≫ 4NF. I will present the recent advances in more detail and put them into historical context. In addition, I will also provide a critical evaluation of the progress made including a discussion of the limitations of the ChEFT approach.

Strange two-baryon interactions using chiral effective field theory

We have constructed the leading-order strangeness S = −1, −2 baryon-baryon potential in a chiral effective field theory approach. The chiral potential consists of one-pseudoscalar-meson exchanges and non-derivative four-baryon contact terms. The potential, derived using SU(3) f symmetry constraints, contains six independent low-energy coefficients. We have solved a regularized Lippmann-Schwinger equation and achieved a good description of the available scattering data. Furthermore a correctly bound hypertriton has been obtained.

Hyperon–nucleon interactions—a chiral effective field theory approach

We construct the leading order hyperon–nucleon potential in chiral effective field theory. We show that a good description of the available data is possible and discuss briefly further improvements of this scheme.

Resonance saturation for four-nucleon operators

In the modern description of nuclear forces based on chiral effective field theory, four-nucleon operators with unknown coupling constants appear. These couplings can be fixed by a fit to the low partial waves of neutron-proton scattering. We show that the so determined numerical values can be understood on the basis of phenomenological one-boson-exchange models. We also extract these values from various modern high accuracy nucleon-nucleon potentials and demonstrate their consistency and remarkable agreement with the values in the chiral effective field theory approach. This paves the way for estimating the low-energy constants of operators with more nucleon fields and/or external probes.

Accurate nucleon–nucleon potential based upon chiral perturbation theory

We present an accurate nucleon-nucleon ($NN$) potential based upon chiral effective Lagrangians. The model includes one- and two-pion exchange contributions up to chiral order three. We show that a quantitative fit of the $NN$ $D$-wave phase shifts requires contact terms (which represent the short range force) of order four. Within this framework, the $NN$ phase shifts below 300 MeV lab. energy and the properties of the deuteron are reproduced with high-precision. This chiral $NN$ potential represents a reliable starting point for testing the chiral effective field theory approach in exact few-nucleon and microscopic nuclear many-body calculations. An important implication of the present work is that the chiral $2\pi$ exchange at order four is of crucial interest for future chiral $NN$ potential development.