Dark photon searches in the photon channel

Imagine you are trying to find a ghost in a crowded room. Usually, you look for the ghost by seeing what it bumps into or how it disturbs the furniture. But what if the ghost is invisible and doesn't bump into anything? You'd have to look for something else: the absence of a sound, or a strange shadow where a light should be.

This paper proposes a new way to hunt for a mysterious particle called the Dark Photon. Think of the Dark Photon as a "shadow twin" of the regular light particle (photon) we know. It might exist, but it barely interacts with normal matter, making it very hard to catch.

Here is the simple breakdown of their idea:

1. The Setup: A High-Speed Collision

The researchers imagine firing a beam of protons (tiny, fast-moving particles) like a cannonball into a very thin sheet of tungsten metal (a heavy metal foil).

The Analogy: Imagine shooting a stream of marbles at a thin sheet of paper. When the marbles hit the paper, they smash into the atoms inside, creating a chaotic explosion of smaller particles.
The Result: One of the main things created in this explosion is a Neutral Pion ( $\pi^0$ ). This is a short-lived particle that immediately falls apart.

2. The Two Ways the Particle Falls Apart

Normally, when a Neutral Pion falls apart, it splits into two regular photons (light particles). This is like a firecracker exploding into two sparks that fly off in opposite directions. Scientists have seen this a million times.

But, if Dark Photons exist, the Neutral Pion might fall apart differently:

The "Semi-Invisible" Split: Instead of two regular sparks, it might split into one regular photon and one Dark Photon.
The Clue: Because the Dark Photon is heavy (unlike a regular photon which has no weight), the single regular photon it leaves behind will be "tired." It will have less energy than the sparks from a normal explosion.

3. The Detective Work: Looking at the Energy

The paper suggests that if we can measure the energy of these photons very precisely, we might see a difference.

The Analogy: Imagine you are listening to a choir. Usually, everyone sings a perfect high note (the normal two-photon decay). But if a few singers are secretly carrying heavy backpacks (the Dark Photons), their voices will be slightly lower and weaker.
The Goal: The researchers want to build a detector that can hear that "lower note." If they see a bunch of photons with slightly less energy than expected, it's a sign that a Dark Photon was created and flew away unseen.

4. The Filter: Two Thin Foils

To make this work, they propose a clever setup using two thin tungsten foils separated by a tiny gap (200 micrometers—thinner than a human hair).

Foil 1 (The Target): The proton beam hits this first. It creates the explosion of particles.
Foil 2 (The Detector): The photons fly across the gap and hit the second foil.
The Trick: When a high-energy photon hits the second foil, it can turn into a pair of particles: an electron and a positron (the "anti-electron").
Why Positrons? The researchers realized that by measuring the energy of these positrons, they can work backward to figure out the energy of the original photon. If the positrons have a specific "low energy" pattern, it proves the original photon came from the "Dark Photon" split, not the normal split.

5. Why This Matters

Most current experiments look for Dark Photons by seeing what they do (like hitting a detector directly). But if the Dark Photon only talks to "Dark Matter" and ignores normal matter, those experiments can't see it.

This new method is different. It doesn't care what the Dark Photon does after it's created. It only cares about the shape of the light (the energy spectrum) it leaves behind.

The Advantage: It's like finding a thief not by catching them in the act, but by noticing that the money in the safe is missing a specific amount.
The Result: The authors used computer simulations (GEANT4) to show that with a powerful enough beam, this setup could find Dark Photons in a range of masses and strengths that other experiments have missed, especially in models where the Dark Photon doesn't interact with electrons at all.

Summary

The paper proposes a "shadow hunting" strategy. By smashing protons into a thin metal foil and carefully measuring the energy of the light particles that escape, we might spot the subtle "tired" signature of a Dark Photon that flew away into the dark sector, invisible to our eyes but detectable through the gap it left in the energy spectrum.

Technical Summary: Dark Photon Searches in the Photon Channel

Problem Statement
Current searches for dark photons ( $A_D$ ) in vector portal models typically rely on detecting visible decays (to Standard Model fermions) or invisible decays (to Dark Matter pairs) via missing energy signatures. While experiments like NA64, DarkQuest, and SHiP have placed stringent constraints on these scenarios, limits are often model-dependent, particularly regarding the dark photon's coupling to leptons. In scenarios where the dark photon decays predominantly to Dark Matter (invisible) and has suppressed couplings to electrons (e.g., $U(1)_{L_\mu-L_\tau}$ models), existing constraints weaken, leaving significant regions of the parameter space ( $m_{A_D} \lesssim m_{\pi^0}$ ) unexplored. The authors propose that the spectral shape differences between photons produced in the standard $\pi^0 \to \gamma + \gamma$ decay and the semi-invisible $\pi^0 \to \gamma + A_D$ decay offer a new, model-independent avenue for detection.

Methodology
The authors propose an experimental configuration inspired by $\pi^0$ lifetime measurements at CERN SPS, utilizing a low-energy, moderate-intensity proton beam striking a thin tungsten target.

Experimental Setup: A 1 GeV proton beam (10–50 $\mu$ A) impinges on a 70 $\mu$ m thick tungsten foil. A second identical foil is placed 200 $\mu$ m downstream.
Detection Mechanism: The first foil acts as the production target for $\pi^0$ mesons. The second foil serves as a converter. Photons emerging from the first foil interact with the nuclei in the second foil via pair production ( $\gamma \to e^+e^-$ ). The resulting positron spectrum is the observable signal.
Simulation: A two-stage GEANT4 model was developed to simulate:
1. Proton interactions with the first foil to generate $\pi^0$ spectra (validated against COHERENT collaboration data).
2. The propagation of photons to the second foil and their conversion into positrons.
3. Background estimation from non- $\pi^0$ sources (proton/neutron inelastic scattering, electron Bremsstrahlung) and standard $\pi^0$ decays.
Theoretical Framework: The analysis utilizes the Lagrangian for kinetic mixing. The signal is defined by the shift in the photon energy spectrum in the $\pi^0$ rest frame due to the massive $A_D$ , which translates to a shift in the laboratory frame positron spectrum compared to the Standard Model (SM) $\pi^0 \to \gamma\gamma$ background.
Sensitivity Estimation: Sensitivities were projected by scaling simulation results to benchmark Protons-on-Target (POT) values of $10^{21}$ and $10^{22}$ . A $\chi^2$ analysis was performed on the positron energy bins to determine exclusion limits on the kinetic mixing parameter ( $\epsilon$ ) versus dark photon mass ( $m_{A_D}$ ).

Key Contributions

Novel Detection Strategy: The paper introduces a method to search for dark photons by analyzing the photon channel (specifically the spectral distortion in $\pi^0$ decays) rather than relying solely on missing energy or visible resonance searches.
Background Suppression: The authors demonstrate that by using thin tungsten foils and imposing a kinematic cut ( $E_\gamma \gtrsim 20$ MeV), the photon flux can be effectively filtered to be dominated by $\pi^0$ decays, suppressing contamination from nuclear de-excitation and Bremsstrahlung.
Model Independence: The proposed technique relies on the kinematic shift caused by the dark photon mass and does not depend on the dark photon's coupling to electrons, making it uniquely sensitive to leptophobic models where traditional electron-beam experiments (like NA64) lose sensitivity.
Feasibility Analysis: The study provides a detailed thermal and radiation damage assessment, concluding that beam currents in the tens of microampere range are sustainable for the proposed foil thickness, citing rotating/cooled foil systems (e.g., SHiP) as a viable engineering solution.

Results

Spectral Distinction: The simulation confirms that the photon spectrum from $\pi^0 \to \gamma + A_D$ is distinct from $\pi^0 \to \gamma + \gamma$ . As $m_{A_D}$ increases, the photon line shifts to lower energies, resulting in a measurable shift in the positron energy spectrum after conversion in the second foil.
Background Characterization: The dominant background is identified as the standard $\pi^0 \to \gamma\gamma$ decay and the Dalitz decay ( $\pi^0 \to \gamma e^+e^-$ ). Other sources (neutrons, protons) produce primarily low-energy photons ( $E_\gamma \lesssim 20$ MeV) which are effectively cut.
Projected Sensitivity: The projected 90% CL limits (Fig. 5) indicate that with $10^{21}$ to $10^{22}$ POT, this setup can probe regions of the $m_{A_D} - \epsilon$ parameter space currently unexplored, specifically in the mass range $20 \text{ MeV} \lesssim m_{A_D} \lesssim 100 \text{ MeV}$ .
Comparison to Existing Limits: In scenarios where the dark photon does not couple to electrons, the proposed method offers competitive or superior sensitivity compared to NA64 and BaBar results, which rely on electron couplings.

Significance and Claims
The authors claim that this work represents a "first step" toward developing new strategies for uncovering dark sectors using photon spectral measurements. They emphasize that the approach is highly model-independent regarding the dark sector's coupling to leptons. The paper does not claim to have discovered a dark photon but rather demonstrates the feasibility of an experimental arrangement that could access previously unexplored parameter space. The authors suggest that facilities with suitable proton beams and target capabilities, such as ISIS and LANSCE, are well-suited to implement this measurement. The significance lies in providing a complementary search channel that remains effective even when standard visible or invisible decay searches are constrained by specific model assumptions.