Search for the Axion-Like-Particles in the $η\toπ^{+}π^{-}e^{+}e^{-}$ decay with HADES detector

This paper outlines the analysis strategy and event selection methods employed by the HADES collaboration at GSI to search for Axion-Like-Particles in the $η\toπ^{+}π^{-}e^{+}e^{-}$ decay channel using high-statistics data.

The Gist

The Great Particle Hunt: Finding a Ghost in the Machine

Imagine the universe as a giant, incredibly complex puzzle. For decades, scientists have had a picture of the puzzle pieces called the "Standard Model." It explains almost everything we see: how stars shine, how magnets work, and what atoms are made of. But there are still huge gaps in the picture. We can't explain why there is more matter than antimatter, why the universe is expanding faster, or what "dark matter" is (the invisible stuff holding galaxies together).

Scientists suspect there are hidden pieces of the puzzle—new, tiny particles that interact very weakly with the ones we know. One of the most famous suspects is a particle called the Axion (or Axion-Like Particle, ALP). Think of the Axion as a "ghost" particle: it's light, it's shy, and it barely touches anything else, making it incredibly hard to catch.

The Detective Work: HADES and the "Decay"

To find these ghosts, the team behind this paper used a giant particle detector called HADES (High-Acceptance Di-Electron Spectrometer) in Germany. They didn't just look for the ghost directly; instead, they looked for a specific "crime scene" where the ghost might have left a clue.

They focused on a rare event involving a particle called the Eta meson ($\eta$). Imagine the Eta meson as a fragile, unstable balloon. Usually, when it pops (decays), it breaks into specific pieces. But the scientists are looking for a very rare, specific way it pops:

1. The Eta balloon breaks.
2. It releases two pions (like two small marbles).
3. It releases an electron and a positron (a pair of tiny, charged sparks).

The Theory: The scientists suspect that sometimes, instead of just popping into those four pieces directly, the Eta balloon might briefly turn into a "ghost" (the Axion) before turning into the electron-positron pair.

• The Path: Eta $\rightarrow$ Pions + Ghost $\rightarrow$ Pions + Electron + Positron.

If they can find a "bump" or a spike in the data where the electron and positron come from, it would be like finding a footprint of the ghost.

The Challenge: The "Noise" in the Room

The problem is that the HADES detector is like a crowded, noisy concert hall. For every one time the Eta balloon pops the way the scientists want (the signal), it pops millions of other ways (the background noise).

Most of the time, the detector sees:

• Pions crashing into each other.
• Photons turning into electron pairs (like a mirror reflecting light).
• Random combinations of particles that just look like the signal but aren't.

This is the "combinatorial background." It's like trying to hear a single whisper in a stadium full of cheering fans.

The Strategy: Filtering the Signal

To find the whisper, the team built a series of "filters" (cuts) to clean up the data:

1. The ID Check: First, they used a special detector (RICH) to tell the difference between a "lepton" (the electron/positron) and a "hadron" (the pion). It's like a bouncer at a club checking IDs to make sure only the right people get in.
2. The Speed Trap: They checked the speed and momentum of the particles. Real electrons move at a specific speed relative to their weight; pions move differently. They drew a line on a graph and threw out anything that didn't fit the pattern.
3. The Geometry Game: They looked at the angles. If the particles came from the same "parent" (the Eta), they should be flying apart in a specific way. If they were just random noise, their angles would be all over the place.
4. The "Missing Mass" Trick: They calculated what should be there based on energy conservation. If the math adds up perfectly, it's a good candidate. If there's a gap, it's likely background noise.

The Results: Finding the Footprints

After applying all these filters, the team looked at the final data. They found two clear "hills" in the graph:

• The Big Hill: This was the Eta decaying into pions and a neutral pion (which then turned into an electron pair). This is a known, standard process.
• The Smaller Hill: This was the Eta decaying into pions and an electron-positron pair directly. This is the rare event they were hunting.

They successfully isolated about 2,750 of these rare events from their data.

The "Ghost" Search:
Now, they looked closely at the smaller hill to see if there was a tiny, extra spike right in the middle. That spike would be the Axion.

• The Verdict: In this specific report, they haven't found the ghost yet. The data looks smooth, without a mysterious spike.
• The Goal: By proving they can find the rare decay and measure it accurately, they are setting the stage to say, "If a ghost were there, we would have seen it by now." This allows them to set strict limits on how heavy or how common these Axions can be.

Summary

This paper is a report on the setup and cleaning process of a massive scientific experiment. The team has successfully built a high-tech filter to separate a rare, interesting particle decay from a mountain of boring background noise. They have found the rare decay they were looking for, and now they are using this clean data to hunt for the "ghost" Axion particle. If the ghost exists in the mass range they are looking at, they are getting closer to catching it; if not, they are proving it doesn't exist there.

Technical Summary

Technical Summary: Search for Axion-Like-Particles in the $\eta \to \pi^+\pi^-e^+e^-$ Decay with HADES

Problem Statement
The Standard Model (SM) successfully describes particle interactions but fails to explain phenomena such as matter-antimatter asymmetry, neutrino masses, and the acceleration of the universe's expansion. These gaps suggest the existence of physics Beyond the Standard Model (BSM), potentially involving new light particles in the MeV–GeV mass range. Specifically, Axion-Like Particles (ALPs) and QCD axions are hypothesized to couple weakly to the SM. Recent theoretical calculations suggest that ALPs with masses between 1 and 100 MeV could be produced in rare hadronic decays of $\eta$ and $\eta'$ mesons. A specific signature of interest is the decay chain $\eta \to \pi^+\pi^- a$, where the hypothetical isoscalar gauge boson $a$ (an ALP) decays predominantly into an electron-positron pair ($e^+e^-$). While previous experiments like BESIII have set limits on this process, there is a need for high-statistics studies to probe the parameter space for ALPs with masses up to 200 MeV/$c^2$.

Methodology
The authors present a dedicated analysis of high-statistics data collected by the High-Acceptance Di-Electron Spectrometer (HADES) at GSI, Darmstadt. The dataset consists of proton-proton interactions at a kinetic beam energy of 4.5 GeV, corresponding to an integrated luminosity of approximately 5.5 pb$^{-1}$. The analysis focuses on reconstructing the final state $\pi^+\pi^-e^+e^-$.

The methodology involves a multi-stage selection and identification strategy:

1. Particle Identification (PID):
   • Categorization: Candidates are initially categorized as leptons or hadrons based on signals in the Ring Imaging Cherenkov (RICH) detector, which is "hadron blind" but efficient for leptons.
   • Kinematic Cuts: A graphical cut in the velocity ($\beta$) versus momentum ($p \cdot q$) distribution distinguishes charged leptons from pions.
   • Angular Correlations: Leptons are further identified by parameterizing the differences in polar ($\Delta\theta$) and azimuthal ($\Delta\phi$) angles between tracks measured in the Multiwire Drift Chambers (MDC) and the RICH detector.
2. Event Hypothesis and Background Suppression:
   • Events must contain at least one identified $\pi^+$, $\pi^-$, $e^+$, and $e^-$.
   • To estimate combinatorial background, additional hypotheses with like-sign lepton pairs ($\pi^+\pi^-e^+e^+$ and $\pi^+\pi^-e^-e^-$) are analyzed.
   • Kinematic Constraints: A series of cuts derived from Monte Carlo (MC) simulations are applied to suppress the dominant multipion background:
     • Reconstructed vertex $z$-coordinate: $-200$ mm to $0$ mm.
     • Correlation between missing mass and invariant mass of the $\pi^+\pi^-e^+e^-$ system.
     • Opening angle for the $(e^+e^-)(\pi^+\pi^-)$ system: $< 50^\circ$.
     • Invariant mass of the $\pi^+\pi^-$ pair: $< 480$ MeV.
     • Opening angle in the center-of-mass frame for $(e^+e^-)(\pi^+\pi^-)$: $> 140^\circ$.
3. Background Subtraction:
   • Combinatorial Background: The contribution from uncorrelated lepton pairs (e.g., from photon conversions or Dalitz decays) is estimated using the formula $N_{CB} = 2\sqrt{N_{e^+e^+\pi^+\pi^-} \cdot N_{e^-e^-\pi^+\pi^-}}$ and subtracted.
   • Multipion Background: An event-mixing technique is employed to model the smooth background component by combining tracks from different events with similar global properties. This mixed-event spectrum is normalized to the data in the 520–527 MeV range.

Key Results

• Signal Extraction: After applying all selection cuts and subtracting the combinatorial background, the invariant mass spectrum of $\pi^+\pi^-e^+e^-$ reveals distinct structures corresponding to $\eta$ decays.
• Yield Estimation: Using the event-mixing method to estimate the residual background under the $\eta$ peaks, the analysis identifies approximately:
  • 5,000 events in the left peak, corresponding to the $\eta \to \pi^+\pi^-\pi^0$ decay (where $\pi^0 \to e^+e^-\gamma$).
  • 2,750 events in the right peak, corresponding to the $\eta \to \pi^+\pi^-e^+e^-$ decay.
• Background Modeling: The study notes that while the event-mixing method successfully describes the background in the mass region spanned by $\eta$ decays, it fails to reproduce the yield and shape above the $\eta$ peak due to correlations between pions from resonance decays (e.g., $N^*/\Delta$).

Significance and Claims
The paper presents the foundational analysis strategy and initial event selection results for a search for Axion-Like Particles in the $\eta \to \pi^+\pi^-e^+e^-$ channel using HADES data. The authors claim that the developed procedures for particle selection and multipion background suppression successfully enhance the identification of $\eta$ mesons, yielding a statistically significant sample of reconstructed $\eta \to \pi^+\pi^-e^+e^-$ events.

The work is described as a "first attempt" and "currently being developed." The primary significance lies in establishing the basis for a more precise evaluation of potential ALP signatures. The authors state that the ongoing work will focus on optimizing selection criteria and validating the background description with extended data samples. The ultimate goal is to determine the upper limit for ALP production in the 0–200 MeV mass range. The paper does not yet present a final exclusion limit or a discovery claim, but rather the methodology required to achieve these goals.