Continuum contribution to charged-current absorption of low-energy $\nu_e$ on $^{40}$Ar

This paper presents refined calculations of low-energy $\nu_e$ absorption on $^{40}$Ar using a hybrid HF-CRPA and statistical de-excitation model, revealing that the standard MARLEY model overestimates DUNE event yields by approximately 20% while potentially improving the feasibility of supernova pointing due to a more pronounced overestimation at backward angles.

The Gist

The Big Picture: Listening to the Stars

Imagine the universe is a giant, dark room, and a supernova (a dying star exploding) is like a massive firework going off in the corner. For decades, we've been able to see the light from these fireworks, but only after a long delay. However, neutrinos are like invisible ghosts that escape the explosion immediately, carrying a secret message about what happened inside the star's core.

To catch these ghostly messages, scientists are building a giant detector called DUNE (Deep Underground Neutrino Experiment). It's a massive tank filled with liquid argon (a noble gas). When a neutrino hits an argon atom, it creates a tiny flash of light and an electron that the detector can see.

The Problem: The Old Map Was Wrong

To understand the message from the supernova, scientists need to know exactly how often a neutrino hits an argon atom and what happens afterward. They use a computer program called MARLEY to simulate these collisions.

Think of the old version of MARLEY (version 1.2.0) as a map drawn with a very rough sketch. It assumed that when a neutrino hits an atom, the atom reacts in a very simple, predictable way (like a billiard ball bouncing off another). The authors of this paper say, "This map is too simple. It's missing the messy, complex details of how the atom actually behaves."

Specifically, the old map:

1. Ignored the "Forbidden" moves: It only looked at the most common, easy reactions and ignored the rare, complex ones that happen when the neutrino hits hard.
2. Overestimated the hits: It thought the neutrino would hit the atom more often and with more energy than it actually does, especially at certain angles.

The Solution: A High-Definition Upgrade

The authors have built a new, much more detailed version of the map (MARLEY version 2.0.0). They did this by using advanced physics math (called HF-CRPA) to calculate exactly how the argon atom wobbles, shakes, and breaks apart when hit by a neutrino.

Here is what they changed, using analogies:

• From a Strobe Light to a Video Camera: The old model treated the atom's energy levels like a strobe light—only seeing specific, frozen points. The new model treats it like a video camera, seeing the smooth, continuous flow of energy as the atom gets excited.
• Adding the "Forbidden" Moves: Imagine a dance floor. The old model only counted the simple waltz steps. The new model counts the complex breakdancing moves (called "forbidden transitions") that happen when the music gets loud (high energy). These moves are rare but important.
• Fixing the "Push": The old model didn't account for how hard the neutrino was pushing the atom (momentum transfer). The new model realizes that as the push gets harder, the atom doesn't react as strongly as the old model predicted.

The Results: What We Learned

When the authors ran their new, detailed simulations, they found some surprising things:

1. Fewer Hits Than Expected: The new model predicts that the detector will see about 20% fewer events than the old model predicted for a typical supernova explosion. The old map was too optimistic.
2. The "Backwards" Problem: The old model thought neutrinos would bounce off the atom in all directions equally. The new model shows that the neutrinos prefer to keep moving forward (like a bullet) rather than bouncing backward.
   • Why this matters: If neutrinos mostly go forward, scientists can use the direction of the hit to pinpoint exactly where the supernova is in the sky. The new model suggests this "pointing" ability might be better than we thought.
3. Breaking Apart: The new model predicts that when the atom gets hit, it is more likely to break into smaller pieces (like a neutron and a proton flying off) than the old model suggested. This changes how we calculate the total energy of the explosion.

The Bottom Line

This paper is a "software update" for how scientists understand neutrino collisions. By replacing a rough sketch with a high-definition, physics-accurate model, they have corrected the numbers.

The main takeaway: We will likely see fewer neutrino events than previously thought, but the events we do see will give us a sharper, more accurate picture of where exploding stars are located in the sky. This ensures that when the Deep Underground Neutrino Experiment (DUNE) turns on, it will be ready to interpret the universe's messages correctly.

Technical Summary

1. Problem Statement

Accurate modeling of low-energy (tens of MeV) electron neutrino ($\nu_e$) absorption on Argon-40 ($^{40}$Ar) is critical for the Deep Underground Neutrino Experiment (DUNE) and other Liquid Argon Time Projection Chamber (LArTPC) detectors. These detectors aim to observe supernova neutrinos, solar neutrinos, and the diffuse supernova neutrino background (DSNB).

The primary issue addressed is the limitation of the current standard interaction model, MARLEY 1.2.0. This version relies on the Allowed Approximation (AA), which makes two significant theoretical simplifications:

1. Long-wavelength limit ($q \to 0$): It neglects the momentum transfer dependence of nuclear matrix elements.
2. Slow-nucleon limit: It ignores terms of order $1/m_N$ in the weak current.
3. Exclusion of Forbidden Transitions: It completely neglects "forbidden" transitions (multipole orders $J > 1$ or parity changes), which become significant at neutrino energies above $\sim 30$ MeV.
4. Discrete Level Treatment: It treats the unbound nuclear continuum as a set of discrete levels, failing to capture the broad distributions of giant resonances.

These approximations lead to an overestimation of the total cross-section and inaccurate predictions for the energy and angular distributions of outgoing electrons, which are vital for neutrino energy reconstruction and supernova pointing.

2. Methodology

The authors present MARLEY 2.0.0, a refined model that replaces the AA with a hybrid strategy combining advanced nuclear theory with data-driven constraints.

A. Discrete Transitions (Bound States)

For transitions to low-lying discrete nuclear levels, the authors retain the connection to experimental data (measured Fermi and Gamow-Teller strengths) but introduce corrections to account for non-zero momentum transfer ($\kappa$):

• Momentum Transfer Corrections: Instead of assuming $j_0(\kappa r) \approx 1$, they use a nuclear form factor $F(\kappa)$ derived from the Klein-Nystrand expression to scale the matrix elements.
• Current Operator Refinement: They include terms of order $1/m_N$ in the weak current operator, moving beyond the strict AA limit.
• Form Factors: Full $Q^2$ dependence is applied to nucleon form factors (using BBBA05 parameterization).

B. Continuum Transitions (Unbound States)

For the unbound continuum (excitation energies above the particle emission threshold), the AA is entirely replaced by a Hartree-Fock Continuum Random Phase Approximation (HF-CRPA) model:

• Mean Field: Uses the Skyrme (SkE2) interaction to generate self-consistent nuclear potentials and wave functions.
• Correlations: CRPA accounts for long-range correlations by treating excitations as coherent superpositions of particle-hole ($ph^{-1}$) and hole-particle ($hp^{-1}$) states.
• Multipole Expansion: Includes all multipoles up to order $J=5$ for both parities, explicitly calculating forbidden transitions (e.g., $1^-$, $2^-$).
• Smearing: A Lorentzian folding procedure is applied to the response functions to account for the finite width of single-particle states, which the CRPA formalism alone underestimates.
• Energy Shift: An effective energy transfer ($\omega_{eff}$) is introduced to correct for the change in nuclear potential between the initial ($^{40}$Ar) and final ($^{40}$K) states.

C. Nuclear De-excitation

The de-excitation model (Hauser-Feshbach formalism) was updated to:

• Use the KDUQFederal evaluation for nuclear optical potentials.
• Redefine the continuum threshold ($E_c^x$) based on the minimum separation energy for all possible fragments ($n, p, d, t, \alpha$), rather than the highest tabulated discrete level. This significantly lowers the threshold for multi-fragment emission.

3. Key Contributions

• Removal of the Allowed Approximation: The paper successfully removes the AA from MARLEY, replacing it with a rigorous HF-CRPA treatment for the continuum and a momentum-transfer-corrected model for discrete states.
• Inclusion of Forbidden Transitions: For the first time in a DUNE-relevant generator, forbidden transitions (up to $J=5$) are fully included, revealing their significant impact on the cross-section at energies $>30$ MeV.
• Consistent Continuum Threshold: The model now consistently handles the transition from discrete levels to the continuum, preventing artificial suppression of multi-fragment emission channels (specifically $1n1p$).
• Updated Nuclear Data: Integration of recent optical potential evaluations and refined separation energies.

4. Results

The authors compare MARLEY 2.0.0 (v2) against MARLEY 1.2.0 (v1) for various neutrino spectra (Supernova, Muon Decay-at-Rest, and monoenergetic 80 MeV).

• Total Cross Section:

  • The refined model predicts a lower total cross-section than v1.
  • For a representative galactic core-collapse supernova burst, v1 overestimates the event yield by approximately 20%.
  • The reduction is driven primarily by the momentum-transfer corrections suppressing the "allowed" strength at higher energies.
  • While forbidden transitions add strength back, they do not fully compensate for the loss of allowed strength at energies below 100 MeV.

• Exclusive Channels:

  • The $1n1p$ (one neutron, one proton) channel is significantly enhanced in v2. This is due to the lowered continuum threshold and the contribution of forbidden multipoles (particularly $1^-$). At 60 MeV, the $1n1p$ channel nearly overtakes the pure $\gamma$-ray emission channel.
  • Single-fragment emission channels (e.g., $1n$, $1p$, $\alpha$) are generally suppressed relative to v1 due to the momentum transfer corrections.

• Angular Distribution:

  • The AA (v1) predicts a nearly uniform angular distribution.
  • The v2 model predicts a stronger forward-peaking of the electron angular distribution.
  • The suppression of allowed transitions is more severe at backward angles (high momentum transfer). Consequently, the forward-peaked Fermi transition and forbidden transitions dominate the shape.

• Energy Resolution:

  • The inclusion of forbidden continuum transitions prevents the saturation of nuclear excitation energy at high neutrino energies. This improves the fractional RMS energy resolution for neutrino energy estimators at high energies ($>35$ MeV), as the model correctly accounts for energy carried away by nuclear fragments.

5. Significance

• DUNE Sensitivity: The 20% reduction in predicted event rates implies that previous sensitivity estimates for supernova neutrinos in DUNE were optimistic. Future analyses must use MARLEY 2.0.0 to avoid biases in flux reconstruction.
• Supernova Pointing: The new prediction of a more forward-peaked angular distribution suggests that using the charged-current $\nu_e$-$^{40}$Ar reaction for supernova pointing (determining the direction of the supernova) may be more feasible than previously thought. The forward peak could allow for better directional reconstruction than the current strategy relying solely on neutrino-electron elastic scattering.
• Theoretical Benchmark: This work provides a high-fidelity theoretical benchmark for low-energy neutrino interactions, bridging the gap between phenomenological models and rigorous many-body nuclear theory. It highlights the necessity of including forbidden transitions and momentum transfer effects for accurate physics in the tens-of-MeV regime.
• Future Validation: The authors note that the model can be tested against future COHERENT experiment data (using muon decay-at-rest neutrinos) and muon capture data on Argon, which share similar nuclear matrix elements.

In conclusion, this paper represents a major upgrade to the theoretical foundation of low-energy neutrino simulations, correcting systematic overestimations in event rates and providing a more realistic description of nuclear response that is essential for the next generation of neutrino astrophysics.