Directed flow (v1) of the hypernuclei ${}_{\Lambda }^3\text{H}$ and ${}_{\Lambda }^4\text{H}$ have been observed in mid-central Au+Au collisions at $\sqrt{s_{\text{NN}}}$ = 3 GeV 3 at RHIC. This measurement opens up a new possibility for studying hyperon-nucleon (Y-N) interaction under finite pressure. In addition, multi-strangeness hypernuclei provide a venue to probe hyperon-nucleon-nucleon (Y-N-N) and even hyperon-hyperon-nucleon (Y-Y-N) interactions. Hypernuclei are important for making connection between nuclear collisions and the equation of state which governs the inner structure of compact stars.

Hypernucleus, a bound state of hyperon(s) and nucleons, is a “laboratory” to study the hyperon-nucleon (Y-N) interactions. The strength of Y-N interaction is fundamentally important for understanding the nature of strong interaction. Based on simple kinematics, the theory predicts that the hyperon would exist in the interior of neutron star, which is the collapsed core of a massive star (around 10–25 solar mass), and has a typical mass of 1–2 solar mass and a radius of 10–12 km. However, the equation of state (EoS) with including strangeness were essentially excluded by the observations of massive neutron stars (e.g. PSR J0740-6620 [1]), due to that the presence of hyperons in the core of neutron star would soften the EoS. This inconsistency of theory and observations is the so-called "hyperon puzzle". To allow the existence of observed two-solar-mass neutron star with including hyperons, theory suggests that Y-N and Y-N-N interaction at high baryon density can create a stiffer EoS which can compensate the mentioned soften effect. Therefore, nuclear matter density dependent Y-N and Y-N-N interaction deduced experimentally is highly expected to the communities of nuclear physics and astrophysics.

High energy heavy-ion collision provides an effective tool to create hot dense nuclear matter [2, 3] which finally evolves to form various particles and rare nuclei in the laboratory [4-9], providing a venue to study the strong interaction [10-14]. Thermal model [15] and hadronic transport model with coalescence afterburner [16, 17] calculations have predicted abundant production of light hypernuclei in high-energy nuclear collisions, especially at high baryon density. Collective flow is driven by pressure gradients created in such collisions, which has been commonly used for studying the properties of nuclear matter created in collisions. Due to its genuine sensitivity to early collision dynamics [18-28], the first order coefficient of the Fourier-expansion of the azimuthal distribution in the momentum space, v₁, also called the directed flow, has been analyzed for many particles species ranging from π-mesons to light nuclei for a long time [29-34], see a carton picture in Fig. 1. Hence, measurements of hypernuclei collective flow help to study the Y-N interactions in the QCD equation of state at high baryon density.

Fig. 1Full-screen View

(Color online) A carton for hypernuclei collective flow in high-energy heavy ion collisions.

Now publishing in Physical Review Letters [35], the STAR Collaboration has reported the first observation of directed flow, v₁, of ${}_{\Lambda }^3\text{H}$ and ${}_{\Lambda }^4\text{H}$ in center-of-mass energy $\sqrt{s_{\text{NN}}}$ = 3 GeV 3 Au + Au collisions. The work was mainly contributed by a joint team of Institute of Modern Physics (IMP@CAS) and Lawrence Berkeley National Laboratory, led by Xin Dong, Xionghong He, Chenlu Hu, Yuanjing Ji, Yue-Hang Leung, Nu Xu, Yapeng Zhang, and Fengyi Zhao.

The data were collected by the STAR experiment at Relativistic Heavy-Ion Collider (RHIC) with the fixed-target (FXT) setup in 2018. A gold beam of energy at 3.85A GeV is bombarded on a gold target of thickness 1% interaction length. After colliding vertex selection, a total of 2.6×10⁸ minimum bias (MB) events are used for this analysis. ${}_{\Lambda }^3\text{H}$ is reconstructed via both two-body and three-body decays ${}_{\Lambda }^3\text{H}{\to }^{\text{3}}\text{He}+{\pi }^{-}$ and ${}_{\Lambda }^3\text{H}\to d+p+{\pi }^{-}$ while ${}_{\Lambda }^4\text{H}$ is reconstructed via the two-body decay channel, ${}_{\Lambda }^4\text{H}{\to }^{\text{4}}\text{He}+{\pi }^{-}$. For this analysis, a relatively wide centrality range, 5–40%, is selected where both the event plane resolution and the yields of hypernuclei are maximized.

The Time-Projection Chamber (TPC) [36] is the main sub-detector for identifying above decay daughters, which is the main tracking detector in STAR, is 4.2 m long and 4 m in diameter, positioned inside a 0.5 T solenoidal magnetic field along the beam direction. Charged particles, including π^-, p, d, ³He and ⁴He, are selected based on the ionization energy loss (dE/dx) measured in the TPC as a function of rigidity (p/|q|), where p and q are the momentum and charge of the particle. In order to ensure high track quality, the number of TPC points used in the track fitting are required to be larger than 15 (out of a maximum of 45). Λ, ${}_{\Lambda }^3\text{H}$ and ${}_{\Lambda }^4\text{H}$ were reconstructed using the KFParticle package based on a Kalman filter method [37, 38].

Signal candidates of Λ, ${}_{\Lambda }^3\text{H}$ and ${}_{\Lambda }^4\text{H}$ were obtained via their invariant mass distributions reconstructed from decay daughters. The directed flow of Λ, ${}_{\Lambda }^3\text{H}$ and ${}_{\Lambda }^4\text{H}$ are extracted with the event plane method [39]. In transverse momentum (p_t) interval of $0.4<p_{\text{t}}/A<0.8$ GeV/c (hypernucleus is very close to this p_t interval due to the statistical reason), Λ, ${}_{\Lambda }^3\text{H}$ and ${}_{\Lambda }^4\text{H}$ v₁ as a function of rapidity (y) is obtained from 5–40% mid-central Au + Au collisions at $\sqrt{s_{\text{NN}}}$ = 3 GeV 3. In the Ref. [35], the v₁(y) of p, d, t, ³He and ⁴He from the same data are also analyzed in the p_t interval of $0.4<p_{\text{t}}/A<0.8$ GeV/c. Due to limited statistics, the v₁(y) distributions of hypernuclei are fitted with a linear function v₁(y) = a·y, in the rapidity range -1.0<y<0.0. v₁(y) of Λ, p, d, t, ³He and ⁴He are fitted with a third-order polynomial function v₁(y) = a·y+b·y³ in the rapidity regions, where a stands for the mid-rapidity slope dv₁/dy|_y=0, and b are fitting parameters.

The mid-rapidity slopes dv₁/dy for Λ, ${}_{\Lambda }^3\text{H}$ and ${}_{\Lambda }^4\text{H}$ as a function of particle mass are shown in Fig. 2. In same 5–40% data, v₁ slopes of p, d, t, ³He and ⁴He are presented by open circles. The slopes dv₁/dy of hypernuclei are all systematically lower than these of nuclei with the same mass number. Linear fits are performed on the mass dependence of dv₁/dy for both light nuclei and hypernuclei. The obtained slope parameters are 0.3323 ± 0.0003 for light nuclei and 0.27 ± 0.04 for hypernuclei, respectively. Two transport models (JAM and UrQMD) plus coalescence afterburner calculations are in agreement with data within uncertainties. These observations suggest that coalescence of nucleons and hyperon Λ could be the dominant mechanism for the hypernuclei ${}_{\Lambda }^3\text{H}$ and ${}_{\Lambda }^4\text{H}$ production in the 3 GeV collisions.

Fig. 2Full-screen View

(Color online) Mass dependence of the mid-rapidity v₁ slope, dv₁/dy, for Λ, ${}_{\Lambda }^3\text{H}$ and ${}_{\Lambda }^4\text{H}$ from the $\sqrt{s_{\text{NN}}}$ = 3 GeV 3 5–40% mid-central Au+Au collisions. Transport models (JAM model and UrQMD model) plus coalescence afterburner can describe the data. The figure is taken from Ref. [40].

With the uncertainties, it is seems that the mass dependence of the hypernuclei v₁ slope is similar to that of light nuclei although it may not necessarily be so due to the differences in N-N and Y-N interactions. In future, precision data on hypernuclei collectivity will yield invaluable insights on in-medium Y-N interaction. This work opens up a new direction for studying Y-N interaction under finite pressure [41]. This is important for making connection between heavy-ion collisions and the equation of state which governs the inner structure of compact stars. The excitation function of hypernuclei collective flow would provide valuable information for understanding in-medium Y-N interactions, which can be achieved in STAR BES-II program in future.

Last but not least, it is worthy to mention that the production of multi-strangeness hypernuclei is another important probe to understand Y-N as well as Y-Y interactions. In a recent work on multi-strangeness hypernuclei production by Zhang et al. [42], nucleon and Ω which has triple strange quarks, are coalesced into Ω NN and ΩΩ N based on the phase-space information generated by the blast-wave model. It is found that with the growing of constituent baryon number, e.g. $\Omega \to N\Omega \to NN\Omega$ as well as $N\to N\Omega \to \Omega \Omega N$, the production rates appear to follow the exponential function $\exp (-cA)$ where c is the reduction factor. This kind of baryon number dependent trend is similar to that for light nuclei of $p\to d\to t{(}_{\Lambda }^3\text{H})$ in Fig. 3. In general, two classes for these production chains are observed. One is for $N\to d\to t{(}_{\Lambda }^3\text{H})$, $\Omega \to N\Omega \to NN\Omega$ and $\Omega \Omega \to N\Omega \Omega$ (solid lines). Another is for $N\to N\Omega \to N\Omega \Omega$, $\Omega \to \Omega \Omega$ and $d\to NN\Omega$ chains (dash lines). The fact that much larger reduction of dN/dy for the second class than the first class illustrates that much less yield for adding one more Ω than one more nucleon, which mainly results from the different interactions between N-Ω and Ω-Ω. Thus, the production of hypernuclei could provide another method to understand the hyperons and nucleons interactions. Interestingly, different magnitude and slopes for baryon number dependence of hypernuclei production [42] as well as mid-rapidity v₁ slope between light nuclei and hypernuclei [35] are exhibited, demonstrating rich information on N-N, Y-N and Y-Y-N interactions. Overall, systematic studies on hypernuclei will build a connection between nuclear collisions and the equation of state which governs the inner structure of compact stars.

Fig. 3Full-screen View

(Color online) The exponential decay relation of dN/dy versus the constituent mass number (A) for Pb + Pb collisions at 2.76 TeV. There are basically two-class production chains, i.e. the one is: $N\to d\to t{(}_{\Lambda }^3\text{H})$ (red), $\Omega \to N\Omega \to NN\Omega$ (blue), $\Omega \Omega \to N\Omega \Omega$ (pink), and the another is: $N\to N\Omega \to N\Omega \Omega$ (green), $\Omega \to \Omega \Omega$ (brown) and $d\to N\Omega N\to NN\Omega \Omega$ (violet). Lines show the exponential decay fits. The figure is adapted from Ref. [42].