Probing the neutrino trident process using the Scattering and Neutrino Detector at HL-LHC and SHiP

This paper investigates the potential of the Scattering and Neutrino Detector (SND) at the HL-LHC and the SHiP experiment to observe the rare neutrino trident scattering process by presenting cross-section predictions and demonstrating their complementary sensitivity across different energy ranges.

The Gist

Imagine the Large Hadron Collider (LHC) and the upcoming SHiP experiment as two massive, ultra-fast particle factories. They smash protons together at incredible speeds, creating a shower of new particles. Among these particles are neutrinos—ghostly, tiny particles that almost never interact with anything. They can pass through light-years of lead without stopping.

Usually, scientists just watch these ghosts fly by. But this paper asks a bold question: What if we could catch one of these ghosts and force it to crash into a wall, creating a spectacular "trident" (a three-pronged fork) of new particles?

Here is a simple breakdown of what the authors are proposing:

1. The "Ghost" and the "Wall"

Neutrinos are like invisible ninjas. They slip through everything. However, if a ninja (neutrino) flies fast enough and hits a heavy, dense wall (a nucleus of a heavy metal like Tungsten or Iron), it might occasionally bounce off and create a pair of charged particles (like an electron and a positron, or a muon and an antimuon).

This specific event is called Neutrino Trident Scattering. It's a rare event in the Standard Model of physics. Finding it is like trying to catch a specific, rare firefly in a hurricane.

2. The Two Hunting Grounds

The paper looks at two different places where we might catch these events:

• The HL-LHC (High-Luminosity LHC): Think of this as a supersonic jet. The neutrinos here are incredibly energetic, moving at near-light speed with energies in the Tera-electronvolt (TeV) range. They are fast, powerful, and rare. The detector here is called SND@LHC.
• SHiP (Search for Hidden Particles): Think of this as a heavy freight train. It uses a beam dump (smashing protons into a block of material) to create a massive, steady stream of neutrinos. These neutrinos are slower, with energies in the Giga-electronvolt (GeV) range, but there are way more of them. The detector here is similar to the one at the LHC but designed for this different environment.

3. The Two Ways to Hit the Wall

When a neutrino hits the target, it can do so in two ways, which the authors call Coherent and Incoherent:

• Coherent (The Team Huddle): The neutrino hits the entire atomic nucleus as a single, solid unit. The nucleus stays intact, like a bowling ball hitting a stack of bricks without knocking them apart. This is more likely to happen with heavy nuclei (like Tungsten) and produces a clean signal.
• Incoherent (The Scattered Crowd): The neutrino hits just one proton or neutron inside the nucleus. This is like hitting a single brick in the stack, causing the whole structure to shatter. This creates a messier signal with more debris.

4. The Big Discovery: Complementary Hunting

The authors ran the numbers and found something exciting: These two experiments are perfect partners.

• At the LHC (The Jet): The neutrinos are so fast that they mostly produce "Coherent" hits. The most common result is seeing an electron and a muon (two different types of charged particles) appear together. They predict about 19 events over the entire run. It's rare, but doable.
• At SHiP (The Train): Because there are so many more neutrinos, even though they are slower, the numbers are huge. They predict over 550 events for that same electron-muon pair! However, because the energy is lower, it's much harder to produce heavy particles like Taus (a heavy cousin of the electron). If a Tau is involved, the event rate drops to almost zero.

5. Why This Matters

Think of this research as mapping a new territory.

• If we only looked at the LHC, we'd see the high-energy, rare events.
• If we only looked at SHiP, we'd see the high-volume, lower-energy events.
• Together, they cover the whole spectrum.

The paper concludes that with the upgraded detectors coming online, we have a very good chance of actually seeing this rare "trident" process for the first time in these specific setups. It's like finally having a camera fast enough and sensitive enough to snap a photo of a ghost doing a backflip.

In short: The authors are saying, "We have two different types of particle factories. One is fast and rare, the other is slow and abundant. If we use both, we can finally catch the elusive neutrino trident process, especially when it creates a mix of electrons and muons."

Technical Summary

1. Problem Statement

The neutrino trident process is a rare Standard Model (SM) interaction where a neutrino scatters off a heavy nucleus in the Coulomb field, producing a pair of charged leptons ($\nu + A \to \nu + \ell^+ \ell^- + A'$). While theoretically well-understood, this process has not yet been observed in collider environments due to its low cross-section and the difficulty of distinguishing it from background noise.

With the recent discovery of collider neutrinos by the FASER and SND@LHC collaborations, there is a new opportunity to test the SM and search for New Physics in the forward region of high-energy collisions. The paper addresses two primary objectives:

1. To evaluate the feasibility of observing neutrino trident scattering at the upgraded Scattering and Neutrino Detector (SND) during the High-Luminosity LHC (HL-LHC) run.
2. To provide the first predictions for neutrino trident scattering at the SHiP (Search for Hidden Particles) experiment, located at the new SPS Beam Dump Facility (BDF).

2. Methodology

The authors employ a phenomenological approach combining Monte Carlo simulations with specific detector configurations and flux models.

• Theoretical Framework:

  • The calculation utilizes a Monte Carlo generator (based on Ref. [15] and modified in Ref. [9]) that treats the full $2 \to 4$ kinematics of the trident process without relying on the equivalent photon approximation.
  • The process is modeled via $W^\pm$ and $Z^0$ exchange (Feynman diagrams shown in Fig. 1).
  • The analysis distinguishes between two interaction types:
    • Coherent Scattering: The leptonic system interacts with the entire nucleus (remains intact). The cross-section scales with $Z^2$ (square of nuclear charge).
    • Incoherent Scattering: The leptonic system interacts with individual nucleons, causing nuclear dissociation. The cross-section scales with $Z$.

• Detector Configurations:

  • SND@HL-LHC: Assumes an extended configuration with a tungsten target consisting of 58 plates (7 mm each).
  • SND@SHiP: Assumes a detector with a $40 \text{ cm} \times 40 \text{ cm}$ transverse area. It includes a tungsten target (120 plates, 3.5 mm thick, $\approx 1.3$ tons) and an iron target (42 plates, 5 cm thick, $\approx 2.6$ tons).

• Flux and Luminosity Assumptions:

  • HL-LHC: Uses the neutrino flux predicted for $\sqrt{s} = 14$ TeV with an integrated luminosity of $3 \text{ ab}^{-1}$. The flux is characterized by TeV-scale energies.
  • SHiP: Uses the flux derived from the CERN SPS accelerator delivering $6 \times 10^{20}$ protons on target (PoT) of 400 GeV over 15 years. This flux is characterized by energies in the range of tens of GeV.

• Cross-Section Calculation:

  • The number of events is calculated as $N = \Phi \times (\sigma_{\nu A} \rho L / m_A)$, where $\Phi$ is the integrated flux, $\sigma_{\nu A}$ is the cross-section, $\rho$ is density, $L$ is target length, and $m_A$ is nuclear mass.
  • Form factors based on the Woods-Saxon nuclear charge distribution are used for the tungsten target.

3. Key Contributions

• First SHiP Predictions: This work presents the first quantitative estimates for neutrino trident event rates at the SHiP experiment.
• Complementary Energy Ranges: The study demonstrates that SND@HL-LHC and SND@SHiP probe complementary energy regimes (TeV vs. tens of GeV), offering a comprehensive test of the trident process across different kinematic scales.
• Detailed Breakdown of Final States: The authors provide granular predictions for all possible leptonic final states ($e^+e^-$, $\mu^+\mu^-$, $\tau^+\tau^-$, and mixed flavors like $e^\pm\mu^\mp$), separating coherent and incoherent contributions.
• Detector Specificity: The analysis explicitly accounts for the different nuclear targets (Tungsten vs. Iron) and their impact on coherent vs. incoherent scattering probabilities.

4. Results

A. SND@HL-LHC (High-Luminosity LHC)

• Event Rates: For an integrated luminosity of $3 \text{ ab}^{-1}$, the total predicted events are low but observable.
  • Dominant Channel: The mixed flavor state $e^\pm + \mu^\mp$ yields the highest rate (18.90 events).
  • Same Flavor: $e^+e^-$ (6.30 events) and $\mu^+\mu^-$ (4.97 events).
  • Tau Channels: $\tau^+\tau^-$ is very rare (0.12 events).
• Coherence: Coherent scattering dominates for light leptons (e.g., $e^+e^-$ is ~95% coherent).
• Comparison: The event rate is approximately one order of magnitude lower than predictions for the FASER$\nu$2 detector, but still feasible for observation.
• Energy Spectrum: The event distribution peaks at TeV energies, consistent with the LHC neutrino flux.

B. SND@SHiP (Beam Dump Facility)

• Event Rates: Over a 15-year run, the event rates are significantly higher than at HL-LHC.
  • Dominant Channel: $e^\pm + \mu^\mp$ yields 553.81 events.
  • Same Flavor: $e^+e^-$ (228.93 events) and $\mu^+\mu^-$ (104.17 events).
  • Tau Channels: $\tau^+\tau^-$ remains extremely rare (0.20 events).
• Energy Spectrum: The peak distribution occurs at $E_\nu \approx 20$ GeV for light lepton pairs.
• Coherence vs. Incoherence:
  • For light leptons, coherent scattering (scaling with $Z^2$) dominates, particularly in the Tungsten target.
  • For final states involving a tau lepton, the incoherent contribution becomes dominant due to the higher mass threshold and kinematic suppression of the coherent process.
• Comparison: The annual event rate for light lepton pairs at SHiP is approximately 2 times larger than the projected rate at SND@HL-LHC.

5. Significance

• Feasibility of Observation: The study confirms that the neutrino trident process is observable in both upcoming experiments, particularly for the $e^\pm + \mu^\mp$ final state.
• Standard Model Validation: Observing these rates will provide a stringent test of the SM in a regime involving neutrino-nucleus scattering, potentially constraining New Physics models (e.g., $Z'$ bosons or non-standard neutrino interactions).
• Experimental Strategy: The results suggest that while HL-LHC offers high-energy data, the SHiP experiment offers a higher statistical yield for light lepton pairs due to the intense flux and optimized target geometry. However, detecting tau tridents remains a significant challenge in both setups.
• Future Physics Program: These predictions serve as a baseline for experimental collaborations (SND@LHC and SHiP) to design analysis strategies, optimize trigger conditions, and separate coherent signals from incoherent backgrounds based on hadronic activity in the final state.