Two-baryon Systems Research Articles

Low-energy scattering and effective interactions of two baryons at mπ∼450 MeV from lattice quantum chromodynamics

The interactions between two octet baryons are studied at low energies using lattice quantum chromodynamics (LQCD) with larger-than-physical quark masses corresponding to a pion mass of ${m}_{\ensuremath{\pi}}\ensuremath{\sim}450\text{ }\text{ }\mathrm{MeV}$ and a kaon mass of ${m}_{K}\ensuremath{\sim}596\text{ }\text{ }\mathrm{MeV}$. The two-baryon systems that are analyzed range from strangeness $S=0$ to $S=\ensuremath{-}4$ and include the spin-singlet and triplet $NN$, $\mathrm{\ensuremath{\Sigma}}N$ ($I=3/2$), and $\mathrm{\ensuremath{\Xi}}\mathrm{\ensuremath{\Xi}}$ states, the spin-singlet $\mathrm{\ensuremath{\Sigma}}\mathrm{\ensuremath{\Sigma}}$ ($I=2$) and $\mathrm{\ensuremath{\Xi}}\mathrm{\ensuremath{\Sigma}}$ ($I=3/2$) states, and the spin-triplet $\mathrm{\ensuremath{\Xi}}N$ ($I=0$) state. The corresponding $s$-wave scattering phase shifts, low-energy scattering parameters, and binding energies when applicable are extracted using L\"uscher's formalism. While the results are consistent with most of the systems being bound at this pion mass, the interactions in the spin-triplet $\mathrm{\ensuremath{\Sigma}}N$ and $\mathrm{\ensuremath{\Xi}}\mathrm{\ensuremath{\Xi}}$ channels are found to be repulsive and do not support bound states. Using results from previous studies of these systems at a larger pion mass, an extrapolation of the binding energies to the physical point is performed and is compared with available experimental values and phenomenological predictions. The low-energy coefficients in pionless effective field theory (EFT) relevant for two-baryon interactions, including those responsible for $SU(3)$ flavor-symmetry breaking, are constrained. The $SU(3)$ flavor symmetry is observed to hold approximately at the chosen values of the quark masses, as well as the $SU(6)$ spin-flavor symmetry, predicted at large ${N}_{c}$. A remnant of an accidental $SU(16)$ symmetry found previously at a larger pion mass is further observed. The $SU(6)$-symmetric EFT constrained by these LQCD calculations is used to make predictions for two-baryon systems for which the low-energy scattering parameters could not be determined with LQCD directly in this study, and to constrain the coefficients of all leading $SU(3)$ flavor-symmetric interactions, demonstrating the predictive power of two-baryon EFTs matched to LQCD.

Charmed baryon\u2013nucleon interaction

We present a comparative study of the charmed baryon–nucleon interaction based on different theoretical approaches. For this purpose, we make use of (i) a constituent quark model tuned in the light-flavor baryon–baryon interaction and the hadron spectra, (ii) existing results in the literature based both on hadronic and quark-level descriptions, (iii) (2+1)-flavor lattice QCD results of the HAL QCD Collaboration at unphysical pion masses and their effective field theory extrapolation to the physical pion mass. There is a general qualitative agreement among the different available approaches to the charmed baryon–nucleon interaction. Different from hadronic models based on one-boson exchange potentials, quark-model based results point to soft interactions without two-body bound states. They also support a negligible channel coupling, due either to tensor forces or to transitions between different physical channels, Lambda _c N – Sigma _c N. Short-range gluon and quark-exchange dynamics generate a slightly larger repulsion in the ^1S_0 than in the ^3S_1Lambda _c N partial wave. A similar asymmetry between the attraction in the two S waves of the Lambda _c N interaction also appears in hadronic approaches. A comparative detailed study of Pauli suppressed partial waves, as the ^1S_0 (I=1/2) and ^3S_1 (I=3/2)Sigma _c N channels, would help to disentangle the short-range dynamics of two-baryon systems containing heavy flavors. The possible existence of charmed hypernuclei is discussed.

Consistency between L\xfcscher\u2019s finite volume method and HAL QCD method for two-baryon systems in lattice QCD

There exist two methods to study two-baryon systems in lattice QCD: the direct method which extracts eigenenergies from the plateaux of the temporal correlation function and the HAL QCD method which extracts observables from the non-local potential associated with the tempo-spatial correlation function. Although the two methods should give the same results theoretically, there have been reported qualitative difference for observables from lattice QCD simulations. Recently, we pointed out in [1, 2] that the separation of the ground state from the excited states is crucial to obtain sensible results in the former, while both states provide useful signals for observables in the latter. In this paper, we identify the contribution of each state in the direct method by decomposing the two-baryon correlation functions into the finite-volume eigenmodes obtained from the HAL QCD method. As in our previous studies, we consider the ΞΞ system in the 1S0 channel at mπ = 0.51 GeV in (2+1)-flavor lattice QCD using the wall and smeared quark sources with spatial extents, La = 3.6, 4.3, 5.8 fm. We demonstrate that the “pseudo-plateau” at early time slices (t = 1 ∼ 2 fm) from the smeared source in the direct method indeed originates from the contamination of the excited states, and the plateau with the ground state saturation is realized only at t > 5 ∼ 15 fm corresponding to the inverse of the lowest excitation energy. We also demonstrate that the two-baryon operator can be optimized by utilizing the finite-volume eigenmodes, so that (i) the finite-volume energy spectra from the HAL QCD method agree with those from the temporal correlation function with the optimized operators and (ii) the correct finite-volume spectra would be accessed in the direct method only if highly optimized operators are employed. Thus we conclude that the long-standing issue on the consistency between Lüscher’s finite volume method and the HAL QCD method for two baryons is now resolved at least for this particular system considered here: they are consistent with each other quantitatively only if the excited contamination is properly removed in the former.

Calm Multi-Baryon Operators

There are many outstanding problems in nuclear physics which require input and guidance from lattice QCD calculations of few baryons systems. However, these calculations suffer from an exponentially bad signal-to-noise problem which has prevented a controlled extrapolation to the physical point. The variational method has been applied very successfully to two-meson systems, allowing for the extraction of the two-meson states very early in Euclidean time through the use of improved single hadron operators. The sheer numerical cost of using the same techniques in two-baryon systems has so far been prohibitive. We present an alternate strategy which offers some of the same advantages as the variational method while being significantly less numerically expensive. We first use the Matrix Prony method to form an optimal linear combination of single baryon interpolating fields generated from the same source and different sink interpolating fields. Very early in Euclidean time this optimal linear combination is numerically free of excited state contamination, so we coin it a calm baryon. This calm baryon operator is then used in the construction of the two-baryon correlation functions.To test this method, we perform calculations on the WM/JLab iso-clover gauge configurations at the SU(3) flavor symmetric point with mπ~ 800 MeV — the same configurations we have previously used for the calculation of two-nucleon correlation functions. We observe the calm baryon significantly removes the excited state contamination from the two-nucleon correlation function to as early a time as the single-nucleon is improved, provided non-local (displaced nucleon) sources are used. For the local two-nucleon correlation function (where both nucleons are created from the same space-time location) there is still improvement, but there is significant excited state contamination in the region the single calm baryon displays no excited state contamination.

Two-baryon systems from HAL QCD method and the mirage in the temporal correlation of the direct method

Both direct and HAL QCD methods are currently used to study the hadron interactions in lattice QCD. In the direct method, the eigen-energy of two-particle is measured from the temporal correlation. Due to the contamination of excited states, however, the direct method suffers from the fake eigen-energy problem, which we call the “mirage problem,” while the HAL QCD method can extract information from all elastic states by using the spatial correlation. In this work, we further investigate systematic uncertainties of the HAL QCD method such as the quark source operator dependence, the convergence of the derivative expansion of the non-local interaction kernel, and the single baryon saturation, which are found to be well controlled. We also confirm the consistency between the HAL QCD method and the Lüscher’s finite volume formula. Based on the HAL QCD potential, we quantitatively confirm that the mirage plateau in the direct method is indeed caused by the contamination of excited states.

Tetraquark candidateZc(3900) from coupled-channel scattering - how to extract hadronic interactions? -

We present recent progress of lattice QCD studies on hadronic interactions which play a crucial role to understand the properties of atomic nuclei and hadron resonances. There are two methods, the plateau method (or the direct method) and the HAL QCD method, to study the hadronic interactions. In the plateau method, the determination of a ground state energy from the temporal correlation functions of multi-hadron systems is a key to reliably extract the physical observables. It turns out that, due to the contamination of excited elastic scattering states nearby, one can easily be misled by a fake plateau into extracting the ground state energy. We introduce a consistency check (sanity check) which can rule out obviously false results obtained from a fake plateau, and find that none of the results obtained at the moment for two-baryon systems in the plateau method pass the test. On the other hand, the HAL QCD method is free from the fake-plateau problem. We investigate the systematic uncertainties of the HAL QCD method, which are found to be well controlled.On the basis of the HAL QCD method, the structure of the tetraquark candidateZc(3900), which was experimentally reported ine+e-collisions, is studied by the s-wave two-meson coupled-channel scattering. The results show that theZc(3900) is not a conventional resonance but a threshold cusp. A semi-phenomenological analysis with the coupled-channel interaction to the experimentally observed decay mode is also presented to confirm the conclusion.

Baryon-baryon interactions and spin-flavor symmetry from lattice quantum chromodynamics

Lattice quantum chromodynamics is used to constrain the interactions of two octet baryons at the SU(3) flavor-symmetric point, with quark masses that are heavier than those in nature (equal to that of the physical strange quark mass and corresponding to a pion mass of $\approx 806~\tt{MeV}$). Specifically, the S-wave scattering phase shifts of two-baryon systems at low energies are obtained with the application of L\"uscher's formalism, mapping the energy eigenvalues of two interacting baryons in a finite volume to the two-particle scattering amplitudes below the relevant inelastic thresholds. The values of the leading-order low-energy scattering parameters in the irreducible representations of SU(3) are consistent with an approximate SU(6) spin-flavor symmetry in the nuclear and hypernuclear forces that is predicted in the large-$N_c$ limit of QCD. The two distinct SU(6)-invariant interactions between two baryons are constrained at this value of the quark masses, and their values indicate an approximate accidental SU(16) symmetry. The SU(3) irreducible representations containing the $NN~({^1}S_0)$, $NN~({^3}S_1)$ and $\frac{1}{\sqrt{2}}(\Xi^0n+\Xi^-p)~({^3}S_1)$ channels unambiguously exhibit a single bound state, while the irreducible representation containing the $\Sigma^+ p~({^3}S_1)$ channel exhibits a state that is consistent with either a bound state or a scattering state close to threshold. These results are in agreement with the previous conclusions of the NPLQCD collaboration regarding the existence of two-nucleon bound states at this value of the quark masses.

Femtoscopic pair correlations of mesons and baryons at RHIC and LHC from hydrokinetic model

Abstract The femtoscopic scales for identical pions and kaons obtained in hydrokinetic model (HKM) are presented for the top energy RHIC and LHC A + A collisions. The source functions for p Λ ¯ ⊕ p ¯ Λ pairs in Au + Au collisions are found and used for extraction of the scattering length in these two-baryon systems by means of FSI correlation technique. The role of residual correlations in formation of the total baryon–antibaryon correlation function is analyzed.

Two-baryon systems with twisted boundary conditions

We explore the use of twisted boundary conditions in extracting the nucleon mass and the binding energy of two-baryon systems, such as the deuteron, from Lattice QCD calculations. Averaging the results of calculations performed with periodic and anti-periodic boundary conditions imposed upon the light-quark fields, or other pair-wise averages, improves the volume dependence of the deuteron binding energy from ~exp(-kappa*L)/L to ~exp(-sqrt(2)kappa*L)/L. However, a twist angle of pi/2 in each of the spatial directions improves the volume dependence from ~exp(-kappa*L)/L to ~exp(-2kappa*L)/L. Twist averaging the binding energy with a random sampling of twist angles improves the volume dependence from ~exp^(-kappa*L)/L to ~exp(-2kappa*L)/L, but with a standard deviation of ~exp(-kappa*L)/L, introducing a signal-to-noise issue in modest lattice volumes. Using the experimentally determined phase shifts and mixing angles, we determine the expected energies of the deuteron states over a range of cubic lattice volumes for a selection of twisted boundary conditions.

Strangeness−2Hypertriton

We solve for the first time, the Faddeev equations for the bound state problem of the coupled ΛΛN-ΞNN system to study whether or not a hypertriton with strangeness -2 may exist. We make use of the interactions obtained from a chiral quark model describing the low-energy observables of the two-baryon systems with strangeness 0, -1, and -2 and three-baryon systems with strangeness 0 and -1. The ΛΛN system alone is unbound. However, when the full coupling to ΞNN is considered, the strangeness -2 three-baryon system with quantum numbers (I,J(P)) = (1/2,1/2(+)) becomes bound, with a binding energy of about 0.5 MeV. This result is compatible with the nonexistence of a stable (Λ)(3)H with isospin one.

Examination of the H dibaryon within a chiral constituent quark model

We perform a coupled-channel calculation of the H dibaryon within a chiral constituent quark model. The problem is solved within a quark model constrained by the experimental data of strangeness $\ensuremath{-}1$ and $\ensuremath{-}2$ two-baryon systems. We examine in detail the role played by the different contributions of the interacting potential as well as the number of coupled channels considered. Special attention has been paid to the parameter dependence, flavor symmetry breaking, and spatial configurations. The value extracted for the binding energy of the H dibaryon, being compatible with the restrictions imposed by the Nagara event, falls within a plausible extrapolation of recent lattice QCD results.

Strangeness −2 two-baryon systems

We derive strangeness −2 baryon–baryon interactions from a chiral constituent quark model including the full set of scalar mesons. The model has been tuned in the strangeness 0 and −1 two-baryon systems, providing parameter free predictions for the strangeness −2 case. We calculate elastic and inelastic NΞ and ΛΛ cross sections which are consistent with the existing experimental data. We also calculate the two-body scattering lengths for the different spin–isospin channels.

Arguments against one-boson-exchange models of nuclear forces and new mechanism for intermediate-and short-range nucleon-nucleon interaction

Arguments against the traditional Yukawa-type approach to NN intermediate-and shortrange interaction due to scalar-isoscalar and heavy-meson exchanges are presented. Instead of the Yukawa mechanism for intermediate-range attraction, some new approach based on the formation of a symmetric six-quark bag in the state |(0s)6[6]X, L=0〉 dressed owing to strong coupling to π, σ, and ρ fields is suggested. This new mechanism offers a strong intermediate-range attraction, which replaces effective σ exchange (or excitation of two isobars in the intermediate state) in traditional force models. A similar mechanism with the production of a vector ρ meson in the intermediate six-quark state is expected to lead to a strong short-range spin-orbit nonlocal interaction in the NN system, which may resolve the long-standing puzzle of the spin-orbit force in baryons and in two-baryon systems. The effective interaction in the NN channel provided by the new mechanism will be enhanced significantly if the partial restoration of chiral symmetry is assumed to occur inside the six-quark symmetric bag. A simple illustrative model is developed that demonstrates clearly how well the suggested new mechanism can reproduce NN data. Strong interrelations have been shown to exist between the proposed microscopic model and one-component Moscow NN potential developed by the authors previously and also with some hybrid models and the one-term separable Tabakin potential. The new implications of the proposed model for nuclear physics are discussed.

Light and strange baryons, two-baryon systems and the chiral symmetry of QCD

Beyond the scale of spontaneous breaking of chiral symmetry light and strange baryons should be considered as systems of three constituent quarks with confining interaction and a chiral interaction that is mediated by Goldstone bosons between the constituent quarks. The flavor-spin structure and sign of the short-range part of the Goldstone boson exchange interaction reduces the $SU(6)_{FS}$ symmetry down to $SU(3)_F \times SU(2)_S$, induces hyperfine splittings and provides correct ordering of the lowest states with positive and negative parity. A unified description of light and strange baryon spectra calculated in a semirelativistic framework is presented. It is demonstrated that the same short-range part of the Goldstone boson exchange between the constituent quarks induces a strong short-range repulsion in $NN$ system when the latter is treated as $6Q$ system. Similar to the $NN$ system there should be a short-range repulsion in other $NY$ and $YY$ two-baryon systems. We also find that the compact 6Q system with the "H-particle" quantum numbers lies a few hundreds MeV above the $\Lambda\Lambda$ threshold. It then suggests that the deeply bound H-particle should not exist.

THE NUCLEON-NUCLEON FORCE FROM SKYRMIONS

The applications of Skyrmions to the derivation of the nucleon-nucleon force is reviewed with attention to the use of the product ansatz, additional terms in the Lagrangian, baryon resonance admixtures, the instanton ansatz, dilatons, and exact two- or three-dimensional solutions for the B=2 system in order to find the sources of attraction in the central and spin-orbit potentials. We also discuss extensions to two-baryon systems with nonzero strangeness and address possible insights into the behavior of the nucleon in nuclei achieved from the Skyrmion approach.

Electromagnetic properties of one- and two-baryon systems in the quark potential model

These lectures review calculations of the electromagnetic properties of one- and two-baryon systems using the nonrelativistic quark model. We start with a short discussion of spontaneous chiral symmetry breaking, which is essential in understanding the transition from QCD to the constituent quark model. We then discuss the chiral version of the nonrelativistic quark model which simulates the symmetries and dynamical content of the underlying field theory in terms of gluon, pion, and sigma exchange between constituent quarks. In the second lecture, the electromagnetic properties of the one-baryon system are investigated in this framework. In particular, we focus on the effect of gluon and pion degrees of freedom in the electromagnetic current operators. These must be included in order for the electromagnetic current to be conserved. We also study the effect of scalar exchange currents connected with the confinement and sigma exchange potentials. By including these two-body exchange currents we go beyond the single-quark impulse approximation which has mainly been used up to now. The consistent treatment of gluon-, pion-, and scalar-exchange currents in the quark potential model is the new point of the present work. We show that exchange currents have a large effect on various electromagnetic properties, such as magnetic moments, charge and magnetic radii of the nucleon and Δ(1232). We point out that one cannot extract quantitative information about the quark-quark potential from electromagnetic observables without taking two-body exchange currents into account. In the third lecture, we use the quark potential model to study the electromagnetic properties of the deuteron. We emphasize that a quark-model description leads to short-range modifications of the conventional single-nucleon and two-nucleon currents, due to the quark-exchange currents. These appear as a consequence of the Pauli principle at the quark level.

Central Force of the Hyperon-Nucleon Interaction in the SU6 Quark Model

Characteristic properties of the medium·range central attraction of the nucleon·nucleon and hyperon-nucleon interactions are studied in the (3q)-(3q) resonating-group formulation. The SUs properties of two-baryon systems are extensively incorporated with the explicit flavor symmetry breaking of the full Fermi-Breit residual interaction. It is found that, for a realistic quark-model description of the hyperon-nucleon interaction compatible with the present low-energy experimental data, it is necessary to introduce phenomenological medium-range attraction which is much less than that for the nucleon-nucleon system. Effective meson-exchange potentials from the scalar-meson nonet exchange in the Nijmegen model-F are conveniently employed to generate the needed flavor­ dependent central attraction with few parameters determined for each flavor exchange symmetry.

Central Force of the Hyperon-Nucleon Interaction in the SU6 Quark Model

Characteristic properties of the medium-range central attraction of the nucleon-nucleon and hyperon-nucleon interactions are studied in the (3q)-(3q) resonating-group formulation. The SU6 properties of two-baryon systems are extensively incorporated with the explicit flavor symmetry breaking of the full Fermi-Breit residual interaction. It is found that, for a realistic quark-model description of the hyperon-nucleon interaction compatible with the present low-energy experimental data, it is necessary to introduce phenomenological medium-range attraction which is much less than that for the nucleon-nucleon system. Effective meson-exchange potentials from the scalar-meson nonet exchange in the Nijmegen model-F are conveniently employed to generate the needed flavor-dependent central attraction with few parameters determined for each flavor exchange symmetry.

Exchange currents in one- and two-baryon systems

We study the effect of two-body exchange currents on the electromagnetic properties of the nucleon, Δ-isobar and the deuteron in the nonrelativistic quark model. In the deuteron we emphasize the short-range modifications of standard exchange currents due to quark exchange currents. In particular, we study the gluon and pion quark exchange currents which are the electromagnetic counterparts of the processes which generate the short-range repulsion in the NN system.

Study of hyperon-nucleon and hyperon-hyperon interaction in the flip-flop model

The non-relativistic quark cluster model is employed to study two-baryon systems including hyperons such as Λ,Σ and Ξ. The quark confinement is described in terms of the flip-flop model. For a description of long- and medium-range parts of the baryon-baryon interaction, the exchanges of pseudoscalar mesons and a scalar meson σ are taken into account in the present calculation. Adjusting the parameters so as to fit the nucleon-nucleon scattering data, we obtain a strongly bound state di-hyperon which is about 60–120 MeV lower than the ΛΛ threshold.