STAR focus: Precise Measurement of the Mass Difference and the Binding Energy of the Hypertriton and Antihypertriton at STAR

In March 2020, the STAR Collaboration published "Measurement of the mass difference and the binding energy of the hypertriton and antihypertriton" in Nature Physics.

In this paper, we present two measurements from gold-gold collisions at a center-of-mass energy per nucleon pair of $\sqrt{s_{NN}} = 200$ GeV: the relative mass difference between $\rm^3_\Lambda H$ (the hypertriton) and $\rm^3_{\bar{\Lambda}}\overline{H}$ (the antihypertriton) (see Fig. 1), as well as the $\Lambda$ hyperon binding energy for $\rm^3_\Lambda H$ and $\rm^3_{\bar{\Lambda}}\overline{H}$ (see Fig. 2). The hypernucleus $\rm^3_{\Lambda}H$ is reconstructed through its mesonic decay channels $\rm^3_{\Lambda}H \rightarrow {^3}He + \pi^-$ (2-body decay) and $\rm^3_{\Lambda}H \rightarrow$ $ d + p + \pi^-$ (3-body decay). The significance $S/ \sqrt{S+B}$, where $S$ is signal counts and $B$ is background counts in the invariant mass window $2.986 - 2.996$ GeV$/c^{2}$, is 11.4 for $^3_\Lambda$H and 6.4 for $\rm^3_{\bar{\Lambda}}\overline{H}$. The signal counts from 2-body/3-body decay channels are about 121/35 for $^3_\Lambda$H and 36/21 for $\rm^3_{\bar{\Lambda}}\overline{H}$, respectively.

According to the CPT theorem, which states that the combined operation of charge conjugation, parity transformation and time reversal must be conserved, particles and their antiparticles should have the same mass and lifetime but opposite charge and magnetic moment. Here, we test CPT symmetry in a nucleus containing a strange quark, more specifically in the hypertriton. A comparison of the masses of the hypertriton and the antihypertriton allows us to test CPT symmetry in a nucleus with strangeness for the first time, and we observe no deviation from the expected exact symmetry with precision of 10$^{-4}$.

This hypernucleus is the lightest one yet discovered and consists of a proton, a neutron, and a $\Lambda$ hyperon. We measure the $\Lambda$ hyperon binding energy $B_{\Lambda}$ for the hypertriton, and find that it differs from the widely used value and from predictions, where the hypertriton is treated as a weakly bound system. Our results place stringent constraints on the hyperon-nucleon interaction, and have implications for understanding neutron star interiors, where strange matter may be present.

Fig 1: Measurements of the relative mass-to-charge ratio differences between nuclei and antinuclei. The current measurement of the relative mass difference ${\Delta m}/m$ between $^3_\Lambda$H and $\rm^3_{\bar{\Lambda}}\overline{H}$ constrained by the existing experimental limits for decay daughters is shown by the red star marker. The green point is the new $^{3}$He result after applying the constraint provided by the present $^{3}_{\Lambda}$H result. The differences between $d$ and $\bar{d}$ and between $^3$He and $\rm^3\overline{He}$ measured by the ALICE collaboration are also shown. The two $^3$He - $\rm^3\overline{He}$ points are staggered vertically for visibility. The dotted vertical line at zero is the expectation from CPT invariance. The horizontal error bars represent the sum in quadrature of statistical and systematic uncertainties.

As shown in Fig. 1, the mass difference between $^3_\Lambda$H and $\rm^3_{\bar{\Lambda}}\overline{H}$ observed in the present data is consistent with zero, and the precision is an order of magnitude improved over prior data with same mass number, published by the ALICE collaboration. The current measurement extends the validation of CPT invariance to a nucleus containing a strange quark. We can place a new constraint on the relative mass difference between $\rm^{3}He$ and $\rm^{3}\overline{He}$ based on the current STAR measurement, namely $\rm\Delta m_{{\rm^{3}He}}/m_{{\rm^{3}He}}$ = [-1.5 $\pm$ 2.6 (stat.) $\pm$ 1.2 (syst.)]$\times 10^{-4}$.

Fig 2: Measured $\Lambda$ binding energy in the hypertriton compared to earlier results and theoretical calculations. The black points and their error bars (which are the reported statistical uncertainties) represent $B_\Lambda$ (see text for exact definition) for $^3_\Lambda$H based on earlier data. The current STAR measurement plotted here is based on a combination of $^3_\Lambda$H and $\rm^3_{\bar{\Lambda}}\overline{H}$ assuming CPT invariance. Error bars show statistical uncertainties (standard deviations) and caps show systematic errors. The green solid circles and green vertical line in the right panel represent theoretical calculations of $B_\Lambda$ values. The horizontal blue lines in both panels indicate a reference energy corresponding to zero binding of the $\Lambda$ hyperon.

The $\Lambda$ binding energy $B_\Lambda$ for $^3_\Lambda$H and $\rm^3_{\bar{\Lambda}}\overline{H}$ is $B_\Lambda =0.41\pm 0.12 {\rm(stat.)}\pm 0.11{\rm (syst.)~MeV}$. This binding energy is presented in Fig. 2 (left panel) along with earlier measurements from nuclear emulsion and helium bubble chamber experiments. The current STAR result differs from zero with a statistical significance of 3.4$\sigma$ and the central value of the current STAR measurement is larger than the commonly used measurement from 1973. Theoretical calculations of $B_\Lambda$ for $^3_\Lambda$H are also available (see right panel of Fig. 2). For example, Dalitz reported the calculation $B_\Lambda = 0.10$ MeV in 1972. In recent calculations, $B_\Lambda = 0.262$ MeV was obtained through SU(6) quark model baryon-baryon interactions, and $B_\Lambda$ was calculated to be 0.23 MeV using auxiliary field diffusion Monte Carlo (AFDMC). A span of values ranging from 0.046 MeV to 0.135 MeV was obtained in SU(3) chiral effective field theory. The divergence of results among different calculations emphasizes the need for a precise determination of $B_\Lambda$ from experiment. In a model based on effective field theory is used to extract a scattering length of $13.80^{+3.75}_{-2.03}$ fm from the earlier average value of $\rm 0.13\pm 0.05(stat.)\,MeV$; when applied to our value of $\rm 0.41\pm 0.12(stat.)\,MeV$ it yields a significantly smaller value of $7.90^{+1.71}_{-0.93}$ fm. The larger $B_\Lambda$ and shorter effective scattering length suggest a stronger $YN$ interaction between the $\Lambda$ and the relatively low-density nuclear core of the $^3_\Lambda$H. This, in certain models, requires SU(3) symmetry breaking and a more repulsive $YN$ interaction at high density, consistent with implications from the range of masses observed for neutron stars.

Posted Mar 10, 2020

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