Searching Dark Photons using displaced vertices at Belle II -- with backgrounds

This paper evaluates the sensitivity of searching for dark photons at Belle II via displaced vertices by calculating and analyzing the impact of problematic backgrounds, specifically displaced photon conversions and prompt backgrounds, which challenge the assumption of a background-free search.

The Gist

Imagine you are a detective trying to find a very shy ghost in a crowded, noisy room. This ghost is called a Dark Photon. It's a hypothetical particle that barely interacts with normal matter, making it incredibly hard to spot.

The paper you're asking about is a report from a team of physicists working at Belle II, a giant particle collider in Japan. Their job is to smash electrons and positrons (anti-electrons) together at high speeds to see what new particles pop out.

Here is the story of their search, explained simply:

1. The Plan: Catching the Ghost by its Footprints

Most particles decay (disappear) instantly, right where they are born. But the Dark Photon is special. Because it interacts so weakly, it might travel a tiny bit of space—maybe a few millimeters or centimeters—before it decays into a pair of normal particles (like an electron and a positron).

The physicists' strategy is to look for "Displaced Vertices."

• The Analogy: Imagine throwing a ball in a room. If it explodes immediately, the shrapnel lands right where you threw it. But if the ball rolls a few feet across the floor before exploding, the shrapnel lands in a different spot.
• The Goal: The team wants to find these "exploded balls" (Dark Photons) that landed a few centimeters away from the center of the collision. They also look for a high-energy "flash" (a photon) that balances the energy, like a recoil.

2. The Problem: The Room is Full of Fake Clues

The team realized that while looking for these "exploded balls" is a great idea, the room is full of things that look like exploded balls but aren't. These are background noises.

The paper focuses on two main types of "fake clues":

A. The "Misplaced Spark" (Photon Conversion)

Sometimes, a normal photon (a particle of light) flies through the detector and hits a piece of metal or glass in the machine. When it hits, it can spontaneously turn into an electron-positron pair.

• The Analogy: Imagine a spark flying from a firework and hitting a wall, causing a small explosion on the wall. To a detective looking from far away, it might look like the firework exploded on the wall (a displaced vertex), when it actually just hit the wall and sparked.
• The Issue: The detector is made of layers of material. If a photon hits a layer outside the search area, but the computer reconstructs the data slightly wrong, it might look like the explosion happened inside the search area. This creates a massive amount of "noise" that hides the real ghost.

B. The "Off-Center Throw" (Prompt Backgrounds)

Sometimes, particles are created right at the center (where they should be), but because the beam of particles isn't a perfect pinpoint, or because the computer makes a tiny mistake, the explosion looks like it happened a few millimeters away.

• The Analogy: Imagine throwing a dart. If you miss the bullseye by a tiny fraction of a millimeter, it might look like you aimed for the outer ring.

3. The Investigation: Doing the Math

The authors of this paper (Joerg Jaeckel and Anh Vu Phan) decided to do a very careful calculation of how many of these "fake clues" there actually are.

• Previous Hope: Earlier studies thought that if they looked in the "vacuum zone" (the empty space between the collision point and the first layer of metal), they would see almost no fake clues. They thought the "noise" would be low enough to hear the "ghost."
• The New Reality: The authors calculated that even in the vacuum zone, the "fake clues" from photons hitting the metal further out and being misidentified are much more common than expected.
  • The Result: In the outer regions of the detector (beyond 0.9 cm), the "noise" is so loud that it completely drowns out the signal. You can't hear the ghost because the room is too noisy.
  • The Silver Lining: However, in the very inner region (between 0.2 cm and 0.9 cm), the noise is lower. If the computer is very good at telling the difference between a real "ghost" and a "fake spark," they can still find the Dark Photon.

4. The Conclusion: It's Harder, But Still Possible

The paper concludes that:

1. The Search Area Shrinks: They can't look as far out from the center as they hoped because the background noise is too high. They are now mostly focused on the inner "vacuum" zone.
2. Computer Accuracy is Key: The success of this search depends entirely on how well the computer can reconstruct where the explosion happened. If the computer is slightly sloppy (mis-reconstructs the position), the fake clues will overwhelm the real ones.
3. The Future: If the Belle II experiment can improve its data analysis to filter out these "fake sparks" effectively, they can still discover Dark Photons in a range of masses that no one has tested before.

Summary Metaphor

Imagine you are trying to hear a whisper (the Dark Photon) in a library.

• Old Plan: We thought if we stood in the quietest aisle, we could hear the whisper.
• New Paper: We realized that even in the quiet aisle, people walking in the next aisle over are making enough noise (shuffling papers, coughing) to drown out the whisper.
• The Fix: We can't stand in the back of the library anymore. We have to stand right next to the whisperer (the inner vacuum zone). But, if we can get everyone else to be very quiet (improve the computer algorithms), we might just be able to hear the whisper after all.

This paper is essentially a "reality check" that tells the experimentalists: "Be careful, the background is louder than we thought, but if you tune your ears (algorithms) correctly, the discovery is still possible."

Technical Summary

1. Problem Statement

The search for feebly interacting particles (FIPs), specifically dark photons ($X$), is a major frontier in particle physics. Dark photons in the MeV–GeV mass range with kinetic mixing parameters ($\chi$) of $\sim 10^{-4} - 10^{-3}$ can be produced at the Belle II experiment via the process $e^+e^- \to X\gamma$. If the dark photon has a macroscopic decay length, it decays into a pair of charged particles ($X \to f^+f^-$) at a displaced vertex, providing a clean signature distinct from Standard Model (SM) backgrounds.

Previous studies (e.g., Ref. [1]) proposed that displaced vertex searches at Belle II could probe untested parameter spaces, particularly in regions where beam dump experiments lack sensitivity due to short lifetimes. However, these earlier studies assumed that the region $R > 0.9$ cm (where $R$ is the radial distance from the beam axis) was largely background-free.

The Core Problem: This paper argues that the assumption of a background-free environment is flawed. The authors identify photon conversion ($\gamma \to f^+f^-$) within detector material as a dominant, irreducible background that severely limits the sensitivity of displaced vertex searches, particularly in the outer regions of the detector. Additionally, they address the potential impact of mis-reconstructed prompt events.

2. Methodology

The authors perform a rigorous recalculation of background rates and their impact on sensitivity, improving upon previous models by:

• Signal Modeling:

  • Utilizing the Lagrangian for a massive $U(1)$ vector boson mixing with the SM photon.
  • Calculating signal rates for $X \to e^+e^-$, $\mu^+\mu^-$, and hadronic decays ($\pi, K$) based on the branching ratios and decay widths.
  • Defining search regions: $0.2 \text{ cm} < R < 0.9 \text{ cm}$ (vacuum region) and $0.9 \text{ cm} < R < 60 \text{ cm}$ (outer region).

• Background Simulation (Photon Conversion):

  • Mechanism: Simulating the process $e^+e^- \to \gamma\gamma$, where one photon converts into a lepton pair via interaction with detector material ($\gamma N \to f^+f^- N$).
  • Cross-Section Calculation: The conversion cross-section is computed by summing contributions from Bethe-Heitler (BH) pair production and Timelike Compton Scattering (TCS), including interference terms (which vanish upon integration). The calculation uses nuclear form factors and photoabsorption cross-sections derived from optical theorems.
  • Detector Geometry: The Belle II detector is modeled as concentric cylindrical shells representing specific material layers (silicon, carbon, aluminum, etc.) with thicknesses matching the material budget.
  • Mis-reconstruction: The authors account for the fact that conversion events occurring outside the search region (e.g., in the vertex detector material) can be mis-reconstructed by the tracking algorithm as originating inside the search region. This is parameterized by an exponential decay profile with a characteristic length $\lambda$.

• Selection Criteria:

  • Kinematic cuts are applied based on energy-momentum conservation ($E_{f^+} + E_{f^-} + E_\gamma \approx \sqrt{s}$) and angular correlations.
  • The authors analyze the effect of cutting on the opening angle ($\theta_{ff}$) of the decay products, noting that while signal peaks at a specific kinematic angle, the background has a broader distribution.

3. Key Contributions

• Quantification of Irreducible Backgrounds: The paper demonstrates that for $R > 0.9$ cm, the background from photon conversion is orders of magnitude larger than the dark photon signal for all interesting parameter spaces. This renders the outer region ($0.9 \text{ cm} < R < 60 \text{ cm}$) effectively insensitive for dark photon searches, contradicting previous optimistic estimates.
• Re-evaluation of the Vacuum Region: The authors confirm that the only viable search region is the vacuum gap between the beam pipe and the vertex detector ($0.2 \text{ cm} < R < 0.9 \text{ cm}$). However, even here, the background is not zero; it arises from mis-reconstructed conversion events occurring in the outer detector layers that are pulled inward by the reconstruction algorithm.
• Prompt Background Analysis: The paper evaluates prompt backgrounds (off-center collisions and mis-reconstructed central $e^+e^- \to f^+f^-\gamma$ events). It concludes that while these are theoretically reducible, they require suppression factors of $10^{-4}$ or better to be negligible, necessitating careful experimental validation.
• Updated Sensitivity Projections: By incorporating the realistic background rates and mis-reconstruction probabilities, the authors provide updated exclusion limits for the kinetic mixing parameter $\chi$ as a function of dark photon mass $m_X$.

4. Results

• Background Dominance: In the region $R > 0.9$ cm, the number of background events (from $\gamma \to e^+e^-$ and $\gamma \to \mu^+\mu^-$ conversions) exceeds the signal by a factor of $10^2$ to $10^4$ depending on the mass and luminosity. Consequently, this region cannot constrain dark photon parameters.
• Sensitivity in the Vacuum Region ($0.2 < R < 0.9$ cm):
  • The sensitivity depends critically on the mis-reconstruction length ($\lambda$).
  • If the reconstruction algorithm pulls vertices inward with a decay length $\lambda \approx 0.05$ cm, Belle II can probe kinetic mixing down to $\chi \sim 10^{-5}$ for masses $m_X \sim 100$ MeV with current luminosity ($50 \text{ ab}^{-1}$).
  • If $\lambda$ is larger (worse reconstruction), the sensitivity degrades significantly.
  • Reducing the search region (e.g., $0.2 < R < 0.6$ cm) improves sensitivity by reducing the volume where mis-reconstructed backgrounds can enter.
• Comparison with Previous Work: The new sensitivity curves are generally more conservative (smaller coverage) than those in Ref. [1], particularly for $m_X < 2m_\mu$ and $R > 17$ cm, because the previous work underestimated the conversion background.

5. Significance

This paper is significant because it provides a realistic "stress test" for displaced vertex searches at Belle II.

1. Correction of Optimism: It corrects the overly optimistic view that the outer detector regions are background-free, preventing future experimental efforts from wasting resources on unviable search strategies in those regions.
2. Algorithmic Importance: It highlights that the reconstruction algorithm's performance (specifically its tendency to mis-assign vertex positions) is the limiting factor for sensitivity. Improving the algorithm to reduce $\lambda$ is as crucial as increasing luminosity.
3. Future Guidance: The study establishes that the most promising window for discovery is the narrow vacuum region near the beam pipe, provided that mis-reconstruction backgrounds can be suppressed. It sets a benchmark for the required background rejection levels ($\sim 10^{-6}$ for prompt backgrounds) for future analyses.

In conclusion, while the discovery potential for dark photons at Belle II remains high, it is strictly confined to the inner vacuum region and is highly sensitive to the precise modeling and suppression of photon conversion backgrounds.