Two-pion Exchange Research Articles

Parity and time-reversal violating nuclear forces with explicit Δ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Delta $$\\end{document}-excitations

We emphasize the usefulness of treating delta resonances as explicit degrees of freedom in applications of chiral effective field theory (EFT) to parity-violating and time-reversal-violating (PVTV) nuclear interactions. Compared with the delta-less framework, the explicit inclusion of the delta isobar allows one to resum certain types of contributions to the PVTV two-pion exchange two- and three-nucleon potentials without at the same time introducing any unknown parameters up to next-to-next-to-leading order in the EFT expansion. We provide the corresponding expressions for the delta contributions in momentum and coordinate spaces and compare the convergence of the EFT expansion in both formulations.

The triton lifetime from nuclear lattice effective field theory

In this work, we present a calculation of the triton β-decay lifetime using Nuclear Lattice Effective Field Theory (NLEFT) at next-to-next-to-next-to-leading order in the chiral expansion. By incorporating a non-perturbative treatment of the higher-order corrections, we achieve consistent predictions for the Fermi and Gamow-Teller matrix elements, which are crucial for determining the triton lifetime. Our results are consistent with earlier theoretical calculations, confirming the robustness of our approach. This study marks a significant advancement in the systematic application of NLEFT to nuclear β-decay processes, paving the way for future high-precision calculations in more complex nuclear systems. Additionally, we discuss potential improvements to our approach, including the explicit inclusion of two-pion exchange mechanisms and the refinement of three-nucleon forces. These developments are essential for extending the applicability of NLEFT to a broader range of nuclear phenomena, including neutrinoless double-β decay.

Enhancement of deltaful two-pion exchange nuclear forces

The role of the delta isobar degrees of freedom in nucleon–nucleon scattering is revisited. We attempt to understand why the dimensionally regularized two-pion exchanges with the explicit delta isobar is much stronger than the ones with spectral function regularization. When the cut-off value of spectral function regularization is varied, the isoscalar central component exhibits a rather large cut-off variation. This reveals a surprisingly large numerical factor of the deltaful two-pion exchange potentials. The power counting is adjusted accordingly and we discuss the results and how to improve upon this finding.

Long-range S -wave DD* interaction in covariant chiral effective field theory

Motivated by the recent lattice QCD study of the DD* interaction at unphysical quark masses, we perform a theoretical study of the DD* interaction in covariant chiral effective field theory. In particular, we calculate the relevant leading-order two-pion exchange contributions. The results compare favorably with the lattice QCD results, supporting the conclusion that the intermediate-range DD* interaction is dominated by two-pion exchanges and the one-pion exchange contribution is absent. At a quantitative level, the covariant chiral perturbation theory results agree better with the lattice QCD results than their nonrelativistic counterparts, showing the relevance of relativistic corrections in the charm sector. Published by the American Physical Society 2024

Amplitudes of 3H, 3He Two-Particle Photo-Breakup in Non-Local QED Approach

Three-nucleon systems are essential for the investigation of many-body forces in nuclear physics. Well-grounded parametrization of their vertex functions with further application for the calculation of cross-sections in nonlocal QED approach provides the ground for investigation of the variety of multi-particle systems. In present paper we describe the process of parametrization of two-particle photo-breakup amplitudes of three-nucleon systems (3H, 3He). We provide the general description of the wave function construction for three-nucleon systems as well as the parametrization of their vertex functions accounting two- and three-nucleon interactions based on meson exchange current formalism. In our calculations we account first and second order one-pion exchange terms and the term related to the exchange of ω and ρ mesons. The three-nucleon interaction potential is given as a sum of attraction (two-pion exchange) term andappropriate repulsive part. Based on the variational ”Urbana + Model VII” amplitudes we provide the results for energy dependence of differential cross-section of 3He(γ, p)d reaction at proton angle θ = 90◦ from the threshold up to Eγ = 40 MeV and compare theoretical predictions with the available experimental data. The investigation is also provided for angular cross-section distributions at high photon energies (Eγ = 305 ± 5 MeV; 365 ± 5 MeV; 450 ± 10 MeV and 675 ± 50 MeV). Correct description of 3H, 3He photo-disintegration processes in a unified approach based on the gauge nature of the electromagnetic field implies application of this model for other multi-particle systems.

Revisiting the DD* chiral interactions with the local momentum-space regularization up to the third order and the nature of Tcc+

We revisit the $DD^\ast$ interactions in chiral effective field theory up to the third order for the first time. We deal with the pion-exchanged interactions via local momentum-space regularization, in which we focus on their long-range behaviors through demanding their contributions vanish at the origin in the coordinate space. The short-range contact interactions and subleading pion-charmed meson couplings are estimated with the phenomenological resonance saturation model. The subleading pion-charmed meson couplings are much weaker than those in the pion-nucleon system, thus the $DD^\ast$ binding mechanism is very different with that of the $NN$ system. We also obtain the analytic structure of the two-pion exchange interactions in the coordinate space, and we find that its asymptotic behavior at long distance is similar to but slightly different with the $NN$ interactions. We get the same asymptotic behavior of the two-pion exchange interaction with that from HAL QCD method but appearing in the longer distance rather than $1 <r<2\text{ fm}$. The binding solution only exists in the isoscalar channel. Our calculation supports the molecular interpretation of $T_{cc}^+$.

Attractive N−ϕ interaction and two-pion tail from lattice QCD near physical point

First results on the interaction between the $\ensuremath{\phi}$-meson and the nucleon ($N$) are presented based on the ($2+1$)-flavor lattice QCD simulations with nearly physical quark masses. Using the HAL QCD method, the spacetime correlation of the $N\text{\ensuremath{-}}\ensuremath{\phi}$ system in the spin $3/2$ channel is converted into the $N\text{\ensuremath{-}}\ensuremath{\phi}$ scattering phase shift through the interaction potential. The $N\text{\ensuremath{-}}\ensuremath{\phi}$ potential appears to be a combination of a short-range attractive core and a long-range attractive tail. The latter is found to be consistent with the two-pion exchange (TPE) obtained from the interaction between a color-dipole and the nucleon. The resultant scattering length and effective range for ${m}_{\ensuremath{\pi}}=146.4\text{ }\text{ }\mathrm{MeV}$ are ${a}_{0}^{(3/2)}=\ensuremath{-}1.43(23{)}_{\mathrm{stat}}({{\text{ }}_{\ensuremath{-}06}^{+36})}_{\mathrm{syst}}\text{ }\text{ }\mathrm{fm}$ and ${r}_{\mathrm{eff}}^{(3/2)}=2.36(10{)}_{\mathrm{stat}}{({\text{ }}_{\ensuremath{-}48}^{+02})}_{\mathrm{syst}}\text{ }\text{ }\mathrm{fm}$, respectively. The magnitude of the scattering length is shown to have nontrivial dependence of ${m}_{\ensuremath{\pi}}$ and is sensitive to the existence of the long-range tail from TPE.

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.

Two-pion exchange as a leading-order contribution in chiral effective field theory

Pion exchange is the central ingredient to nucleon-nucleon interactions used in nuclear structure calculations, and one pion exchange (OPE) enters at leading order in chiral effective field theory. In the $^{2S+1}L_J={^1S_0}$ partial wave, however, OPE and a contact term needed for proper renormalization fail to produce the qualitative, and quantitative, features of the scattering phase shifts. Cutoff variation also revealed a surprisingly low breakdown momentum of about 330 MeV in this partial wave. Here we show that potentials consisting of OPE, two pion exchange (TPE), and a single contact address these problems and yield accurate and renormalization group (RG) invariant phase shifts in the $^1S_0$ partial wave. We demonstrate that a leading-order potential with TPE can be systematically improved by adding a contact quadratic in momenta. For momentum cutoffs below about 500 MeV, the removal of relevant physics from TPE loops needs to be compensated by additional contacts to keep RG invariance. Inclusion of the $\Delta$ isobar degree of freedom in the potential does not change the strong contributions of TPE.

Study of the hidden charm DD¯* interactions in chiral effective field theory

We study the chiral interactions of the hidden charm $D\bar{D}^*$ system within chiral effective field theory. Chiral Lagrangians are constructed by incorporating the chiral symmetry, heavy quark symmetry as well as proper charge conjugation properties of the heavy mesons. The interacting potentials of the $S$-wave $D\bar{D}^*$ are calculated up to second chiral order at 1-loop level, where complete two-pion exchange interactions are included. We further investigate the behaviors of the potentials in coordinate space, as well as their bound state properties. Our studies indicate that there exists a interacting strength ordering among considered four channels: $\text{str.}[0^+(1^{++})]>\text{str.}[0^-(1^{+-})] > \text{str.}[1^+(1^{+-})] > \text{str.}[1^-(1^{++})]$ where str. stands for the strength of the $D\bar{D}^*$ interaction. Moreover, we find that $X(3872)$ can be treated as a good candidate of $0^+(1^{++})$ molecular state. There also tends to form $0^-(1^{+-})$ and $1^+(1^{+-})$ molecular states and we expect the experiments to search for the predicted multi-structures around the $D\bar{D}^*$ mass region.

Nonperturbative two-pion exchange contributions to the nucleon-nucleon interaction in covariant baryon chiral perturbation theory

We calculate the nonperturbative two-pion exchange (TPE) contributions to the $NN$ interaction in covariant baryon chiral perturbation theory. We study how the nonperturbative resummation affects the $NN$ phase shifts for partial waves with $J \geq 3$ and $L \leq 6$. No significant differences are observed between the nonperturbative phase shifts and perturbative ones for most partial waves except for $^3D_3$, for which the nonperturbative resummation greatly improves the description of the phase shifts. However, a significant cutoff dependence is found for this partial wave and a reasonable description of the phase shifts can only be obtained with a particular cutoff. Furthermore, we compare the so-obtained nonperturbative phase shifts with those obtained in the heavy baryon chiral perturbation theory. We show that the contributions from relativistic nonperturbative TPE are more moderate than those from the nonrelativistic TPE obtained in the dimensional regularization scheme. A proper convergence pattern is observed for most of the partial waves studied except for $^3F_3$, $^3F_4$, and $^3H_6$, for which the subleading TPE contributions are a bit strong. We find that for $H$ and $I$ partial waves, the OPE alone can already describe the phase shifts reasonably well.

The Relevance of Pion-Exchange Contributions Versus Contact Terms in the Chiral Effective Field Theory Description of Nucleon–Nucleon Scattering

The standard way to demonstrate the relevance of chiral symmetry for the NN interaction is to consider higher partial waves of NN scattering which are controlled entirely by chiral pion-exchanges (since contacts vanish). However, in applications of NN-potentials to nuclear structure and reactions, the lower partial waves are the important ones, making the largest contributions. Lower partial waves are sensitive to the short-range potential, and so, when the short-range contacts were to dominate over the chiral pion-contributions in lower partial waves, then the predictions from "chiral potentials" would have little to do with chiral symmetry. To address this issue, we investigate systematically the role of the (chiral) one- and two-pion exchanges, on the one hand, and the effect of the contacts, on the other hand, in the lower partial waves of NN scattering. We are able to clearly identify the signature of chiral symmetry in lower partial waves. Our study has also a pedagogical spin-off as it demonstrates in detail how the reproduction of the lower partial-wave phase shifts comes about from the various ingredients of the theory.

Two-pion exchange contributions to the nucleon-nucleon interaction in covariant baryon chiral perturbation theory

Employing the covariant baryon chiral perturbation theory, we calculate the leading and next-to-leading order two-pion exchange (TPE) contributions to $NN$ interaction up to order $O(p^3)$. We compare the so-obtained $NN$ phase shifts with $2\leq L\leq 6$ and mixing angles with $2\leq J\leq6$ with those obtained in the nonrelativistic baryon chiral perturbation theory, which allows us to check the relativistic corrections to the medium-range part of $NN$ interactions. We show that the contributions of relativistic TPE are more moderate than those of the nonrelativistic TPE. The relativistic corrections play an important role in F-waves especially the $^3\text{F}_2$ partial wave. Moreover, the relativistic results seem to converge faster than the nonrelativistic results in almost all the partial waves studied in the present work, consistent with the studies performed in the one-baryon sector.

Nucleon-nucleon scattering with coupled nucleon-delta channels in chiral effective field theory

In this work the elastic scattering of two nucleons is calculated in chiral effective field theory at next-to-leading order taking into account the coupled NΔ-, ΔN- and ΔΔ-channels. To solve the coupled channel scattering equation one needs as input the potentials for all combinations of these initial and final states. Up to next-to leading order these (transition) potentials arise from one-pion exchange, two-pion exchange and contact interactions. For the two-pion exchange we give analytic expressions for the spectral functions derived from all contributing one-loop diagrams. The forms of the contact potentials at leading and next-to-leading order are determined. We perform a fit of the low energy constants, that belong to the NN→NN contact potential and contribute up to next-to-leading order to S- and P-waves of NN scattering only. The influence of the Δ-isobar dynamics entering through the coupled channels is studied in detail.

Box diagram contribution to the axial two-nucleon current

Recently, we have worked out the axial two-nucleon current operator to leading one-loop order in chiral effective field theory using the method of unitary transformation. Our final expressions, however, differ from the ones derived by the JLab-Pisa group using time-ordered perturbation theory (Phys. Rev. C 93, no. 1, 015501 (2016) Erratum: [Phys. Rev. C 93, no. 4, 049902 (2016)] Erratum: [Phys. Rev. C 95, no. 5, 059901 (2017)]). In this paper we consider the box diagram contribution to the axial current and demonstrate that the results obtained using the two methods are unitary equivalent at the Fock-space level. We adjust the unitary phases by matching the corresponding two-pion exchange nucleon-nucleon potentials and rederive the box diagram contribution to the axial current operator following the approach of the JLab-Pisa group, thereby reproducing our original result. We provide a detailed information on the calculation including the relevant intermediate steps in order to facilitate a clarification of this disagreement.

Heavy hadron molecules in effective field theory: the emergence of exotic nuclear landscapes

Heavy hadron molecules were first theorized from a crude analogy with the deuteron and the nuclear forces binding it, a conjecture which was proven to be on the right track after the discovery of the $X(3872)$. However, this analogy with nuclear physics has not been seriously exploited beyond a few calculations in the two- and three-body sectors, leaving a great number of possible theoretical consequences unexplored. Here we show that nuclear and heavy hadron effective field theories are formally identical: using a suitable notation, there is no formal difference between these two effective field theories. For this, instead of using the standard heavy superfield notation, we have written the heavy hadron interactions directly in terms of the light quark degrees of freedom. We give a few examples of how to exploit this analogy, e.g. the calculation of the two-pion exchange diagrams. Yet the most relevant application of the present idea is the conjecture of exotic nuclear landscapes, i.e. the possibility of few heavy hadron bound states with characteristics similar to those of the standard nuclei.

Nuclear energy density functionals constrained by low-energy QCD

Relativistic nuclear energy density functionals are formulated and developed, guided by two important features that establish connections with chiral dynamics and the sym- metry breaking pattern of low-energy QCD: a) strong scalar and vector fields related to in-medium changes of QCD vacuum condensates; b) the long- and intermediate-range interactions generated by one-and two-pion exchange, derived from in-medium chiral per- turbation theory.

One pion exchange and the quantum numbers of the Pc(4440) and Pc(4457) pentaquarks

The LHCb collaboration has recently discovered three pentaquark-like states---the ${P}_{c}(4312)$, ${P}_{c}(4440)$ and ${P}_{c}(4457)$---close to the $\overline{D}{\mathrm{\ensuremath{\Sigma}}}_{c}$ and the ${\overline{D}}^{*}{\mathrm{\ensuremath{\Sigma}}}_{c}$ meson-baryon thresholds. The standard interpretation is that they are heavy antimeson-baryon molecules. Their quantum numbers have not been determined yet, which implies two possibilities for the ${P}_{c}(4440)$ and ${P}_{c}(4457)$: ${J}^{P}={\frac{1}{2}}^{\ensuremath{-}}$ and ${J}^{P}={\frac{3}{2}}^{\ensuremath{-}}$. The preferred interpretation within a contact-range effective field theory is that the ${P}_{c}(4440)$ is the ${J}^{P}={\frac{1}{2}}^{\ensuremath{-}}$ molecule, while the ${P}_{c}(4457)$ is the ${J}^{P}={\frac{3}{2}}^{\ensuremath{-}}$ one. Here we show that when the one pion exchange potential between the heavy antimeson and heavy baryon is taken into account, this conclusion changes, with the contrary identification being as likely as the original one. The identification is however cutoff dependent, which suggests that improvements of the present description (e.g., the inclusion of subleading order corrections, like two-pion exchanges) are necessary in order to disambiguate the spectroscopy of the molecular pentaquarks.

Vector mesons as dynamical resonances in the Bethe–Salpeter framework

We present the first dynamical calculation of the ρ-meson as a resonance in the Dyson–Schwinger/Bethe–Salpeter framework by including explicit two-pion exchange in addition to the t-channel one-gluon exchange of rainbow-ladder in the interaction kernel. The width is determined from the imaginary part of the resonance pole and is generated by the singularity structure of the integrand, treated by means of suitable path deformations. We find the resonant mass and width to be 640 MeV and 100 MeV respectively, corresponding to a coupling constant gρππ=5.7; repulsive corrections beyond rainbow-ladder are expected to bring these in line with experiment. Furthermore we present the dependence of these parameters on the pion mass and compare with results from lattice QCD.

Hidden charm pentaquark states and ΣcD¯(*) interaction in chiral perturbation theory

In this work, we employ the heavy hadron chiral perturbation theory (HHChPT) to calculate the $\Sigma_c\bar{D}^{(*)}$ potentials to the next-to-leading order. The contact, the one-pion exchange and the two-pion exchange interactions are included. Besides, the mass splittings between the heavy quark spin symmetry (HQSS) multiplets are kept in calculations. Our result shows that neglecting the heavy quark symmetry (HQS) violation effect may be misleading to predict the potentials between the charmed hadrons. We perform numerical analysis with three scenarios. In the first scenario, we relate the low-energy constants (LECs) in the contact terms of $\Sigma_c\bar{D}^{(*)}$ to those of nucleon systems, and reproduce the $P_c(4312)$ and $P_c(4440)$ as loosely bound states. In the second scenario, we vary the unknown LECs and find a small parameter region in which $P_c(4312)$, $P_c(4440)$ and $P_c(4457)$ can coexist as molecular states. In the third scenario, we include the coupled-channel effect on the basis of scenario II, and notice that the three $P_c$ states can be reproduced as molecular states simultaneously in a large region of parameters. Our analytical results can be used for the chiral extrapolations in lattice QCD. With the lattice QCD results in the future as inputs, the identification of the $P_c$ states and predictions for other systems would be more reliable.