Baryon-baryon Interaction Research Articles

Prospects to study hyperon-nucleon interactions at BESIII* *Supported by the National Natural Science Foundation of China (NSFC) (11935018, 11875054, 12165022), the Chinese Academy of Sciences (CAS) Key Research Program of Frontier Sciences (QYZDJ-SSW-SLH003), and the Fundamental Research Project of Yunnan Province, China (202301AT070162)

The prospects to study hyperon-nucleus/nucleon interactions at BESIII and similar colliders are analyzed in this paper. Utilizing the large quantity of hyperons produced by the decay of 10 billion and 2.7 billion collected at BESIII, the cross sections of several specific elastic and inelastic hyperon-nucleus reactions can be measured via scattering between hyperons and nucleus in the dense objects of the BESIII detector. Subsequently, the cross sections of the corresponding hyperon-nucleon interactions can be extracted from further phenomenological calculations. The interactions between antihyperons and nucleus/nucleon, including scattering and annihilation, can also be studied using the method proposed in this study. The results will definitely benefit the realization of precise probes for hyperon-nuclei/nucleus interactions and establish constraints to study the potential of strong interaction, the origin of color confinement, a unified model for baryon-baryon interactions, and the internal structure of neutron stars. In addition, the desirable prospects of corresponding studies in the future Super Tau-Charm Factory (STCF) are discussed and estimated in this study.

Strangeness S = −2 baryon-baryon interactions and femtoscopic correlation functions in covariant chiral effective field theory* *Supported by the National Natural Science Foundation of China (11735003, 11975041, 11961141004)

We study the baryon-baryon interactions with strangeness and corresponding momentum correlation functions in leading order covariant chiral effective field theory. The relevant low energy constants are determined by fitting to the latest HAL QCD simulations, taking into account all the coupled channels. Extrapolating the so-obtained strong interactions to the physical point and considering both quantum statistical effects and the Coulomb interaction, we calculate the and correlation functions with a spherical Gaussian source and compare them with recent experimental data. We find a good agreement between our predictions and the experimental measurements by using the source radius determined in proton-proton correlations, which demonstrates the consistency between theory, experiment, and lattice QCD simulations. Moreover, we predict the , , and interactions and corresponding momentum correlation functions. We further investigate the influence of the source shape and size of the hadron pair on the correlation functions studied and show that the current data are not very sensitive to the source shape. Future experimental measurements of the predicted momentum correlation functions will provide a non-trivial test of not only SU(3) flavor symmetry and its breaking but also the baryon-baryon interactions derived in covariant chiral effective field theory.

Excitation of the delta-resonance in compressed super heavy neutron-rich doubly magic [formula omitted] nucleus

By using constrained spherical Hartree-Fock approximation (CSHF), nuclear system of the super-heavy spherical U126310bh184 nucleus is investigated. CSHF is applied to no-core shell model, with an effective baryon-baryon interaction. Physical properties are affected by delta excitation under compression. It is shown when the △ resonances have occurred, the nucleus becomes more bound. Also, it can be seen that as the compression is continuous, the formation of △ increases. Under compression, the most of increment in energy of the system is gone to △-mass formation. Therefore, this appears to play a role in nuclear compression in subthreshold pion-production in heavy ions collisions. When the △ degree of freedom is created, reduced compressibility has occurred. In a ground state without nuclear compression, it is seen that the U126310bh184 nucleus is formed from the △ particles as the basic component besides nucleons. Also, there is a radial density distribution of the △ particles at the ground state for the U126310bh184 nucleus. If the nucleus was compressed to twenty-four of the ordinary density, then the △ particle would have been sharply increased to about 14.2% of all particles in the nucleus. The single particle spectra are studied under nuclear compression too. An excellent agreement was happened between the calculations and the shell model for the low levels of the single particle energies. Finally, there is a excellent consistency between the effective Hamiltonian and phenomenological shell model results for the lower single particle energy levels.

Nucleon-nucleon interaction in the [formula omitted]-[formula omitted] coupled channel for a pion mass of 469 MeV

In this work, we apply the relativistic chiral nuclear force to describe the state-of-the-art lattice simulations of the nucleon-nucleon scattering amplitude. In particular, we focus on the S13-D13 coupled channel for a pion mass of 469 MeV. We show that at leading order the relativistic chiral nuclear force can only describe δ3S1 and ε1 up to Tlab.≈10 MeV, while at the next-to-leading order it can do much better up to Tlab=200 MeV. However, at the next-to-next-to-leading order, the description deteriorates, which can be attributed to the fact that the pion-mass dependence of the pion-nucleon couplings c1,2,3,4 may not be negligible. Furthermore, all the studies consistently yield negative δ3D1, contrary to the lattice QCD results which are positive but consistent with zero. The present study is relevant to a better understanding of the lattice QCD nucleon-nucleon force and more general baryon-baryon interactions.

Precise Measurement of Differential Cross Sections of the Σ^{-}p→Λn Reaction in Momentum Range 470-650 MeV/c.

The differential cross sections of the Σ^{-}p→Λn reaction were measured accurately for the Σ^{-} momentum (p_{Σ}) ranging from 470 to 650 MeV/c at the J-PARC Hadron Experimental Facility. Precise angular information about the Σ^{-}p→Λn reaction was obtained for the first time by detecting approximately 100 reaction events at each angular step of Δcosθ=0.1. The obtained differential cross sections show a slightly forward-peaking structure in the measured momentum regions. The cross sections integrated for -0.7≤cosθ≤1.0 were obtained as 22.5±0.68 [statistical error(stat.)] ±0.65 [systematic error(syst.)] mb and 15.8±0.83(stat)±0.52(syst) mb for 470<p_{Σ}(MeV/c)<550 and 550<p_{Σ}(MeV/c)<650, respectively. These results show a drastic improvement compared with past measurements of the hyperon-proton scattering experiments. They will play essential roles in updating the theoretical models of the baryon-baryon interactions.

Status of the hyperon-nucleon interaction in chiral effective field theory

The Jülich-Bonn group aims at an extensive study of the baryonbaryon (BB) interaction involving strange baryons (Λ, Σ, Ξ) within SU(3) chiral effective field theory. An overview of achievements and new developments over the past few years is provided. The topics covered are: 1) Derivation of the leading charge-symmetry breaking (CSB) interaction for the ΛN system and its application in a study of CSB effects in A=4 Λ-hypernuclei. 2) Updated results for the ΞN interaction at NLO and predictions for Ξ−p correlation functions. 3) Extension of the ΛN-ΣN interaction to next-to-next-to-leading order.

Single- &amp; double-strangeness hypernuclei up to A = 8 within χEFT

We investigate S=−1 and −2 hypernuclei with A = 4 − 8 employing the Jacobi-NCSM approach and in combination with baryon-baryon interactions derived within the frame work of chiral effective field theory. The employed interactions are transformed using the similarity renormalization group (SRG) so that the low- and high-momentum states are decoupled, and, thereby, convergence of the binding energies with respect to model space can be significantly speeded up. Such an evolution is however only approximately unitary when the so-called SRG induced higher-body forces are omitted. We first explore the impact of the SRG evolution on the Λ separation energies BΛ in A = 3 − 5 hypernuclei when only SRG-evolved two-body and when both twoand three-body forces are included. For the latter scenario, we thoroughly study predictions of the two almost phase-equivalent NLO13 and NLO19 YN potentials for A = 4 − 7 hypernuclei. We further explore CSB splittings in the A = 7; 8 multiplets employing the two NLO YN potentials that include also the leading CSB potential in the ΛN channel, whose strength has been fitted to the presently established CSB in A = 4. Finally, we report on our recent study for Ξ hypernuclei based on the ΞN interaction at NLO.

Recent progress and future prospects of hyperon nucleon scattering experiment

A new hyperon-proton scattering experiment, dubbed J-PARC E40, was performed to measure differential cross sections of the Σ+p, Σ−p elastic scatterings and the Σ−p → Λn scattering by identifying a lot of Σ particles in the momentum ranging from 0.4 to 0.8 GeV/c produced by the π±p → K+Σ± reactions. We successfully measured the differential cross sections of these three channels with a drastically improved accuracy with a fine angular step. These new data will become important experimental constraints to improve the theories of the two-body baryon-baryon interactions. Following this success, we proposed a new experiment to measure the differential cross sections and spin observables by using a highly polarized Λ beam for providing quantitative information on the ΛN interaction. The results of three Σp channels and future prospects of the Λp scattering experiment are described.

Weakly Bound H Dibaryon from SU(3)-Flavor-Symmetric QCD.

We present the first study of baryon-baryon interactions in the continuum limit of lattice QCD, finding unexpectedly large lattice artifacts. Specifically, we determine the binding energy of the H dibaryon at a single quark-mass point. The calculation is performed at six values of the lattice spacing a, using O(a)-improved Wilson fermions at the SU(3)-symmetric point with m_{π}=m_{K}≈420 MeV. Energy levels are extracted by applying a variational method to correlation matrices of bilocal two-baryon interpolating operators computed using the distillation technique. Our analysis employs Lüscher's finite-volume quantization condition to determine the scattering phase shifts from the spectrum and vice versa, both above and below the two-baryon threshold. We perform global fits to the lattice spectra using parametrizations of the phase shift, supplemented by terms describing discretization effects, then extrapolate the lattice spacing to zero. The phase shift and the binding energy determined from it are found to be strongly affected by lattice artifacts. Our estimate of the binding energy in the continuum limit of three-flavor QCD is B_{H}^{SU(3)_{f}}=4.56±1.13_{stat}±0.63_{syst} MeV.

Measurement of the differential cross sections of the Σ−p elastic scattering in momentum range 470 to 850 MeV/c

A high statistics Σp scattering experiment is performed at the J-PARC Hadron Experimental Facility. Momentum-tagged Σ−s running in a liquid hydrogen target are accumulated by detecting the π−p→K+Σ− reaction with a high intensity π− beam of 20 M/spill. The differential cross sections of the Σ−p elastic scattering were derived with a drastically improved accuracy by identifying approximately 4500 events from 1.72×107Σ−. The derived differential cross section shows a clear forward-peaking angular distribution for a Σ− momentum range from 470 to 850 MeV/c. The accurate data will impose a strong constraint on the theoretical models of the baryon-baryon interactions.12 MoreReceived 28 April 2021Revised 29 July 2021Accepted 1 October 2021DOI:https://doi.org/10.1103/PhysRevC.104.045204©2021 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasHypernuclei & mesic nucleiMeson & hyperon induced nuclear reactionsNucleon induced nuclear reactionsParticle interactionsNuclear Physics

Effects of three-baryon forces on kaon condensation in hyperon-mixed matter

Possibility of kaon-condensed phase in hyperon-mixed matter is considered on the basis of chiral symmetry for kaon-baryon and kaon-kaon interactions, being combined with the relativistic mean-field theory for two-body baryon interaction. In addition, universal three-baryon repulsive force in the string-junction model and phenomenological three-nucleon attractive force are introduced. It is shown that softening of the equation of state stemming from both kaon condensation and mixing of hyperons is compensated with the repulsive effect of the three-baryon force and the relativistic effect for two-body baryon-baryon interaction. The latter effect reflects the density-dependence of scalar and vector meson mean-fields, which is constrained by the contribution of the attractive three-nucleon force to the binding energy at saturation density. The kaon-condensed phase in hyperon-mixed matter becomes stiff enough to be consistent with recent observations of massive neutron stars.

Strangeness S=−3 and S=−4 baryon-baryon interactions in relativistic chiral effective field theory

The strangeness $S=-3$ and $-4$ baryon-baryon interactions are investigated in the relativistic chiral effective field theory at leading order. First, the potentials are derived from the $S=-1$ sector assuming that the corresponding low-energy constants are related to each other via SU(3) flavor symmetry. The comparison with the state-of-the-art lattice QCD simulations, show, however, that SU(3) flavor symmetry breaking effects can not be neglected. In order to take into account these effects, we redetermine two sets of low-energy constants by fitting to the lattice QCD data in the $\Xi\Sigma$ and $\Xi\Xi$ channels respectively. The fitting results demonstrate that the lattice QCD $S$-waves phase shifts for both channels can be described rather well. Without any additional free low-energy constants, the predicted phase shifts for the ${}^3D_1$ channel and the mixing angle $\varepsilon_1$ are also in qualitative agreement with the lattice QCD data for the $S=-3$ channel, while the results for the $S=-4$ channel remain to be checked by future lattice QCD simulations. With the so-obtained low-energy constants, the $S$-wave scattering lengths and effective ranges are calculated for these two channels at the physical point. Finally, in combination with the $S=0$ and $-2$ results obtained in our previous works, we study the evolution of the irreducible representation $27$ in the baryon-baryon interactions as a function of increasing strangeness. It is shown that the attraction decreases dramatically as strangeness increases from $S=0$ to $S=-2$, but then remains relatively stable until $S=-4$. The results indicate that the existence of bound states in the $\Xi\Sigma$ and $\Xi\Xi$ channels is rather unlikely.

Extended-soft-core baryon-baryon model ESC16. III. S=−2 hyperon-hyperon/nucleon interactions

Background: This is the third of a series of papers on baryon-baryon (BB) interactions, where the baryons are the lowest lying baryon states with spin and parity ${J}^{P}={(1/2)}^{+}$. The paper presents the extended-soft-core (ESC) model ESC16 for BB channels with strangeness $S=\ensuremath{-}2$.Purpose: The aim is to describe the ingredients of the $S=\ensuremath{-}2$ ESC16 potentials, to apply these two-body interactions to BB scattering and via $G$-matrix calculations to hypernuclear systems, and to compare with the presently available experimental information.Methods:The potentials for $S=\ensuremath{-}2$ are based on the SU(3) extension of the ESC potentials for the strangeness $S=0$ and $S=\ensuremath{-}1$ sectors, which are fitted to experimental nucleon-nucleon ($NN$), hyperon-nucleon ($YN$), and hyperon-hyperon ($YY$) data. Flavor SU(3) symmetry is broken only `kinematically' by the masses of the baryons and the mesons. For the $S=\ensuremath{-}2$ channels almost no experimental scattering data exist, and the information from hypernuclei is also rather limited. Nevertheless, in the fit to the $S=0$ and $S=\ensuremath{-}1$ sectors information from the Nagara event and the scarce experimental results on the $\mathrm{\ensuremath{\Xi}}N$ cross sections have been used as (mild) constraints to determine the free parameters in the simultaneous fit of the deuteron and the $NN\ensuremath{\bigoplus}YN$ scattering data. Therefore, the potentials for the $S=\ensuremath{-}2$ sectors are almost completely determined by the fits to the $NN, YN$ data, and SU(3) symmetry.Results: Various properties of the $S=\ensuremath{-}2$ potentials are illustrated by giving results for scattering lengths, bound states, phase parameters, and total cross sections. The well-depth ${U}_{\mathrm{\ensuremath{\Xi}}}$ is calculated and $\mathrm{\ensuremath{\Xi}}N G$-matrix interactions are derived and applied to ${\mathrm{\ensuremath{\Xi}}}^{\ensuremath{-}}$-capture reactions. Here, a phenomenological $\mathrm{\ensuremath{\Xi}}N$ interaction is added to describe the experiments. Furthermore, the ESC16 model supplemented with phenomenological SU(3) symmetric gaussian interactions is analyzed, and attractive $\mathrm{\ensuremath{\Xi}}N$ interactions are obtained. Combined with three-body forces derived from the ESC meson-pair vertices and the Fujita-Miyazawa interaction, yields good baryon well depths.Conclusions: The ESC16 $S=\ensuremath{-}2$ potentials, with kinematically broken SU(3) symmetry, provide a basis for realistic calculations in nuclear and hypernuclear physics. For a successful description of the well depth's ${U}_{N},{U}_{\mathrm{\ensuremath{\Lambda}}},{U}_{\mathrm{\ensuremath{\Sigma}}}$, and ${U}_{\mathrm{\ensuremath{\Xi}}}$ and hypernuclear $S=\ensuremath{-}2$ reactions phenomenological additions are needed.

Lattice QCD and Baryon-Baryon Interactions: HAL QCD Method

In this article, we review the HAL QCD method to investigate baryon-baryon interactions such as nuclear forces in lattice QCD. We first explain our strategy in detail to investigate baryon-baryon interactions by defining potentials in field theories such as QCD. We introduce the Nambu-Bethe-Salpeter (NBS) wave functions in QCD for two baryons below the inelastic threshold. We then define the potential from NBS wave functions in terms of the derivative expansion, which is shown to reproduce the scattering phase shifts correctly below the inelastic threshold. Using this definition, we formulate a method to extract the potential in lattice QCD. Secondly, we discuss pros and cons of the HAL QCD method, by comparing it with the conventional method, where one directly extracts the scattering phase shifts from the finite volume energies through the L\"uscher's formula. We give several theoretical and numerical evidences that the conventional method combined with the naive plateau fitting for the finite volume energies in the literature so far fails to work on baryon-baryon interactions due to contaminations of elastic excited states. On the other hand, we show that such a serious problem can be avoided in the HAL QCD method by defining the potential in an energy-independent way. We also discuss systematics of the HAL QCD method, in particular errors associated with a truncation of the derivative expansion. Thirdly, we present several results obtained from the HAL QCD method, which include (central) nuclear force, tensor force, spin-orbital force, and three nucleon force. We finally show the latest results calculated at the nearly physical pion mass, $m_\pi \simeq 146$ MeV, including hyperon forces which lead to form $\Omega\Omega$ and $N\Omega$ dibaryons.

Traces of the nuclear liquid-gas phase transition in the analytic properties of hot QCD

The nuclear liquid-gas transition at normal nuclear densities, $n\ensuremath{\approx}{n}_{0}=0.16\phantom{\rule{4pt}{0ex}}{\mathrm{fm}}^{\ensuremath{-}3}$, and small temperatures, $T\ensuremath{\approx}20\phantom{\rule{4pt}{0ex}}\mathrm{MeV}$, has a large influence on analytic properties of the QCD grand-canonical thermodynamic potential. A classical van der Waals equation is used to determine qualitatively these unexpected features due to dense cold matter. The existence of the nuclear matter critical point results in thermodynamic branch points, which are located at complex chemical potential values, for $T&gt;{T}_{c}\ensuremath{\simeq}20\phantom{\rule{4pt}{0ex}}\mathrm{MeV}$, and exhibit a moderate model dependence up to rather large temperatures $T\ensuremath{\lesssim}100\phantom{\rule{4pt}{0ex}}\mathrm{MeV}$. The behavior at higher temperatures is studied using the van der Waals hadron resonance gas (vdW-HRG) model. The baryon-baryon interactions have a decisive influence on the QCD thermodynamics close to ${\ensuremath{\mu}}_{B}=0$. In particular, nuclear matter singularities limit the radius of convergence ${r}_{{\ensuremath{\mu}}_{B}/T}$ of the Taylor expansion in ${\ensuremath{\mu}}_{B}/T$, with ${r}_{{\ensuremath{\mu}}_{B}/T}\ensuremath{\approx}2--3$ values at $T\ensuremath{\approx}140--170\phantom{\rule{4pt}{0ex}}\mathrm{MeV}$ obtained in the vdW-HRG model.

Baryon–baryon interactions at short distances: constituent quark model meets lattice QCD

The interaction energies between two baryons at short distance in different flavor channels are calculated from the constituent quark model (CQM) and are compared with the recent lattice QCD (LQCD) results for baryon-baryon potentials at short distance. We consider the six-quark system with two strange quarks and focus on the quantum numbers, (Flavor,Spin)=(1,0),(8,1),(10,1),($\overline{10}$,1) and (27,0). The interaction energy is defined by subtracting out isolated baryon masses and relative kinetic energy of two baryons from the total energy of a compact six-quark state. We introduce interaction energy ratio between different flavors as a useful measure to test the prediction of CQM. We find that the ratios in CQM show good agreement with those in LQCD, which indicates that the short range part of the baryon-baryon interaction can be understood qualitatively in terms of the Pauli principle and spin-dependent color interaction among constituent quarks.

Low-lying level structure of Λ hypernuclei and spin dependence of the ΛN interaction with antisymmetrized molecular dynamics

$\Lambda N$ spin-spin and spin-orbit splittings in low-lying excitation spectra are investigated for $p$-shell $\Lambda$ hypernuclei on the basis of the microscopic structure calculation within the antisymmetrized molecular dynamics, where the $\Lambda N$ $G$-matrix interaction derived from the baryon-baryon interaction model ESC (extended soft core) is used. It is found that the ground-state spin-parity is systematically reproduced in the $p$-shell $\Lambda$ hypernuclei by tuning the $\Lambda N$ spin-spin and spin-orbit interactions so as to reproduce the experimental data of $^{4}_\Lambda$H, $^{7}_\Lambda$Li and $^9_\Lambda$Be. Furthermore, we also focus on the excitation energies of the excited doublets as well as the energy shifts of them by the addition of a $\Lambda$ particle.

Quark Models of the Nucleon–Nucleon Interaction

The present chapter aims to provide a review on the relevance of quark degrees of freedom in the description of the nucleon-nucleon and, in general, of the baryon-baryon interaction. After an historical introduction, the second section of the chapter will be dedicated to the first attempts to describe the short-range part of the NN potential in the so-called quark potential models. Here the importance of the symmetries of the 6-quark system will be emphasized. Then, we will discuss the concept of the constituent quark mass as originated by the breakdown of the chiral symmetry, in line with the articles of ~\citep{MANOHAR1984189} and the Instanton Liquid Model of ~\citep{Diakonov:2002fq}, and its consequences on the quark-quark interaction due to the presence of the Goldstone boson exchanges. Once the full quark-quark interaction is established, the description of the bound states (deuteron), the scattering states of the NN system and nuclear matter in constituent quark models will be addressed. In this part a discussion of the influence of $N\Delta$, $\Delta\Delta$ or $NN^*$ components will be included. The rest of the chapter will be devoted to the extension of the model to other baryon-baryon system, namely the triton, hyperon-hyperon and nucleon-antinucleon systems, and references to other possible descriptions of the NN interaction in terms of quark degrees of freedom ( bag models). The chapter will end with a conclusion remarks where the success and limitations of the model described above will be summarized.

Prediction of NΩ -like dibaryons with heavy quarks

Possible $N\Omega$-like dibaryons $N\Omega_{ccc}$ and $N\Omega_{bbb}$ with quantum numbers $IJ^P=\frac{1}{2}2^+$ are investigated within the framework of quark delocalization color screening model. We find both of these two states are bound, and the binding energy increases as the quarks of the system become heavier. The attraction between $N$ and $\Omega_{ccc}$ (or $\Omega_{bbb}$) mainly comes from the kinetic energy term due to quark delocalization and color screening. The effect of the channel-coupling provides more effective attraction to $N\Omega_{ccc}$ and $N\Omega_{bbb}$ systems. Besides, the scattering length, the effective range, and the binding energy, obtained from the calculation of the low-energy scattering phase shifts, also supports the existence of the $N\Omega_{ccc}$ and $N\Omega_{bbb}$ states. All these properties can provide necessary information for experimental search for the $N\Omega$-like dibaryons with heavy quarks. And the experimental progress can also check the mechanism of the intermediate-range attraction of the baryon-baryon interaction in quark models.

Probing ΩΩ and pΩ dibaryons with femtoscopic correlations in relativistic heavy-ion collisions

The momentum correlation functions of baryon pairs, which reflects the baryon-baryon interaction at low energies, are investigated for multi-strangeness pairs ($\Omega\Omega$ and $N\Omega$) produced in relativistic heavy-ion collisions. We calculate the correlation functions based on an expanding source model constrained by single-particle distributions. The interaction potentials are taken from those obtained from recent lattice QCD calculations at nearly physical quark masses. Experimental measurements of these correlation functions for different system sizes will help to disentangle the strong interaction between baryons and to unravel the possible existence of strange dibaryons.