Neutrino-induced hyperon final-state interactions as constraints on the in-medium hyperon potential

Technical Summary: Neutrino-Induced Hyperon Final-State Interactions as Constraints on the In-Medium Hyperon Potential

Problem Statement
The "hyperon puzzle" in neutron star physics arises because the appearance of hyperons (specifically $\Lambda$ and $\Sigma^-$) in dense matter relieves nucleon Fermi pressure, softening the Equation of State (EOS) and lowering the maximum neutron star mass ($M_{\text{max}}$) below the observed $\sim 2 M_\odot$ limit. The onset density and softening effect are governed by the in-medium single-particle potentials $U_Y(\rho)$. While the depths of these potentials at nuclear saturation density ($\rho_0$) are loosely constrained by hypernuclear spectroscopy ($U_\Lambda$) and $\Sigma$-atom data ($U_\Sigma$), their behavior at sub-saturation densities and, crucially, their high-density slopes remain poorly constrained. Existing terrestrial constraints (hypernuclei, $\Sigma$-atoms, heavy-ion flow) suffer from model dependencies or probe different density regimes. There is a need for an independent terrestrial handle on $U_Y(\rho)$ at sub-saturation densities to anchor astrophysical extrapolations.

Methodology
The authors propose using charged-current (anti)neutrino interactions on $^{40}\text{Ar}$ nuclei (at SBND and DUNE energies) to probe these potentials. The methodology relies on the following chain:

1. Production: Neutrinos and antineutrinos produce $\Lambda$ and $\Sigma$ hyperons inside the nucleus via Cabibbo-suppressed quasi-elastic ($\bar{\nu}_\mu N \to \mu^+ Y$) and Cabibbo-favoured associated production ($\nu N \to \ell Y K$) channels.
2. Transport: These hyperons propagate through nuclear matter, experiencing the density-dependent potential $U_Y(\rho)$. The authors model this using StrangeMC, an internal multi-channel Monte Carlo generator for strange particle production and intranuclear transport on Argon.
3. Observables: The potential affects the hyperons in four measurable ways:
   • Trapping: Slow $\Lambda$ hyperons may be captured (trapped) if they cannot climb out of the attractive potential well. The trapped fraction is a direct measure of $U_\Lambda$.
   • Momentum Shifts: The kinetic energy of escaping hyperons is shifted by $U_Y$ at the production density. The mean escaping momentum $\langle p_\Sigma \rangle$ is sensitive to $U_\Sigma$.
   • Conversion: Strong interactions ($\Sigma N \to \Lambda N$) convert $\Sigma$ to $\Lambda$, affecting yield ratios.
   • $\Sigma^+$ Tag: In antineutrino quasi-elastic events, $\Sigma^+$ cannot be produced at the weak vertex. Any observed $\Sigma^+$ must arise from Final State Interactions (FSI) (e.g., $\Lambda p \to \Sigma^+ n$). The yield and momentum of these "fake-CCQE" $\Sigma^+$ provide a clean, low-background tag for in-medium dynamics and the potential difference $U_\Sigma - U_\Lambda$.
4. Astrophysical Mapping: The extracted potential parameters are fed into a Relativistic Mean Field (RMF) EOS (specifically the GM1 parameter set) to solve the Tolman-Oppenheimer-Volkoff (TOV) equations, predicting $M_{\text{max}}$ and tidal deformability ($\Lambda_{1.4}$).

Key Contributions

• Novel Probe: The paper establishes a new, independent terrestrial constraint on $U_Y(\rho)$ at sub-saturation densities ($\rho \lesssim \rho_0$) using accelerator neutrinos, distinct from hypernuclear spectroscopy and heavy-ion flow.
• StrangeMC Simulation: Development and application of a dedicated Monte Carlo tool for strange final states and intranuclear transport, calibrated to published cross-sections and validated against inclusive MicroBooNE data.
• Systematic Analysis: A rigorous breakdown of statistical reach versus systematic uncertainties, identifying that the hyperon-nucleon ($YN$) cross-section uncertainty is the dominant systematic for $U_\Sigma$, while the transport prescription (energy shift vs. gradient force) is the leading systematic for $U_\Lambda$.
• Degeneracy Identification: The authors demonstrate that the low-density exponent $\gamma$ (governing the density dependence of the potential) is strongly anti-correlated with the anchor $U_\Lambda(\rho_0)$. Without an external prior on $\gamma$, the precision on $U_\Lambda(\rho_0)$ degrades significantly.

Results

• Sensitivity: The observables respond monotonically to the potentials.
  • Deepening the attractive $U_\Lambda$ increases the trapped $\Lambda$ fraction and hardens the escaping $\Lambda$ spectrum.
  • Making $U_\Sigma$ more repulsive increases the mean escaping $\Sigma$ momentum.
  • The $\Sigma^+$ yield peaks near $U_\Sigma \approx 0$ and drops for both attractive and strongly repulsive potentials.
• Projected Precision (Fixed $\gamma$): At a fixed low-density exponent $\gamma=1$, the Fisher forecast projects a precision of $\delta U_\Lambda \approx 0.3$ MeV and $\delta U_\Sigma \approx 3\text{--}4$ MeV.
• Precision with Marginalization: When marginalizing over the unknown exponent $\gamma$ (which the data alone constrain only to $\delta \gamma \approx 0.8$), the precision on the anchor degrades to $\delta U_\Lambda \approx 5.6$ MeV, while $\delta U_\Sigma$ remains largely unchanged ($\approx 3.2$ MeV).
• Systematics:
  • $U_\Sigma$ is highly sensitive to $YN$ cross-section uncertainties, leading to a bias of $\mathcal{O}(150)$ MeV if not constrained externally.
  • $U_\Lambda$ is robust against $YN$ uncertainties (bias $\lesssim 5$ MeV) but sensitive to the transport prescription (bias $\approx -6$ MeV).
• Astrophysical Inference:
  • Using the GM1 RMF with physical depths ($U_\Lambda = -28$ MeV, $U_\Sigma = +30$ MeV), the model predicts $M_{\text{max}} = 1.94 M_\odot$ and $\Lambda_{1.4} = 1034$. The latter exceeds the GW170817 bound, indicating tension with gravitational wave data for this specific EOS class.
  • A joint fit combining the projected neutrino constraints with terrestrial priors (hypernuclear, $\Sigma$-atom, heavy-ion) yields a posterior $M_{\text{max}} = 2.21^{+0.04}_{-0.15} M_\odot$. The authors emphasize that this central value is driven by the external high-density prior ($c_\Lambda$) and the EOS model choice, not the neutrino data itself. The neutrino data primarily anchor the low-density input.

Significance and Claims
The paper claims that accelerator neutrinos provide a new, largely independent handle on the in-medium hyperon potential at sub-saturation densities. This capability allows for a "terrestrial-to-stellar" mapping that anchors the low-density sector of the neutron star EOS.

However, the authors are modest about the direct impact on the maximum mass puzzle. They explicitly state that:

1. The neutrino data do not constrain the high-density stiffness ($\rho \gtrsim 3\rho_0$) or the maximum mass directly.
2. The precision on the maximum mass is dominated by the EOS model systematic (choice of RMF parametrization and baryon content), which is an order of magnitude larger than the propagated statistical uncertainty from the neutrino measurement.
3. The primary value of this work is constraining the low-density potential function $U_\Lambda(\rho)$ and the transport of hyperons, which serves as a necessary, high-precision input for any future resolution of the hyperon puzzle that relies on a specific high-density extrapolation.

The study concludes that while the neutrino measurement alone cannot solve the hyperon puzzle, it provides a critical, model-independent anchor for the low-density sector, reducing the uncertainty in the initial conditions for astrophysical extrapolations.