ALP and $Z^\prime$ boson at the Electron-Ion collider

This paper investigates the sensitivity of the upcoming Electron-Ion Collider to purely electrophilic axion-like particles and $Z^\prime$ bosons in the GeV mass range, demonstrating that the facility can significantly extend exclusion limits on these new physics scenarios through tri-electron and photon final state analyses.

The Gist

Imagine the universe as a giant, complex puzzle. Scientists have a picture of how most of the pieces fit together, called the "Standard Model." But there are missing pieces—mysterious things like dark matter or why the universe has more matter than antimatter. To find these missing pieces, physicists build massive machines called colliders to smash particles together at incredible speeds, hoping to see something new pop out.

This paper is a "blueprint" for how a future machine, the Electron-Ion Collider (EIC), could help find two specific types of missing puzzle pieces: a ghostly particle called an ALP (Axion-Like Particle) and a heavy, invisible messenger particle called a Z' boson.

Here is the breakdown of their plan, using simple analogies:

1. The Setup: A High-Speed Billiard Game

The EIC is like a super-precise billiard table. Instead of just hitting balls against each other, it smashes a beam of electrons (tiny, negatively charged particles) into a beam of protons (heavy particles found in the center of atoms).

• The Goal: The researchers want to see if, during these crashes, new particles appear that only talk to electrons. They call these "electrophilic" (electron-loving) particles.
• The Mass Range: They are looking for these particles in the "GeV" range. Think of this as looking for a specific size of rock—not too heavy, not too light, but right in the middle of the scale where current machines haven't looked very closely.

2. The Two Suspects: The ALP and the Z'

The paper focuses on two hypothetical suspects:

• The ALP: Imagine a very light, ghostly particle that usually hides. In this scenario, it only interacts with electrons.
• The Z' Boson: Imagine a heavy, invisible cousin of the Z boson (a known particle). This new Z' also only interacts with electrons.

3. The Detective Work: Hunting for "Tri-Electron" Clues

How do you catch a ghost that only talks to electrons? You look for a specific signature in the debris after the crash.

• The Signature: The researchers are looking for a crash that produces three electrons flying out (two negative, one positive) along with a spray of other debris (jets).
• The Analogy: Imagine you are at a party. You know that if a specific secret guest (the ALP or Z') shows up, they will always bring exactly three friends (electrons) with them. If you see a group of three friends walking in together, you know the secret guest was there, even if you didn't see the guest directly.
• The Background Noise: The problem is that regular physics (the Standard Model) also sometimes produces three electrons by accident. It's like people at the party occasionally grouping up in threes for no reason. The scientists have to use math and computer simulations to figure out if the groups of three are just random noise or if they are actually the "secret guest" bringing their friends.

4. The Strategy: Filtering the Noise

The paper details a rigorous filtering process:

• The Filter: They use a "Crystal Ball" (a mathematical tool, not a magic one) to analyze the energy and speed of the electrons. If the three electrons have a specific combined energy that matches the mass of the suspected ALP or Z', it's a hit.
• The "Jet" Veto: They also look at the direction of the debris. By ignoring particles flying too far forward (like ignoring the noise from the back of the room), they can make their search cleaner and more sensitive.
• The Photon Hunt: They also considered looking for particles that turn into photons (light particles) instead of electrons, but found that the "three-electron" search is much more effective for this specific type of physics.

5. The Results: A New Frontier

The researchers ran simulations to see what the EIC could achieve if it runs for a specific amount of time (collecting 100 "inverse femtobarns" of data—a fancy way of saying "a huge amount of collision data").

• The Finding: They found that the EIC could spot these "electron-loving" particles in a mass range that current machines (like the LHC) have missed or where the data is too messy to be sure.
• The Comparison: It's like having a new pair of glasses. The LHC is great for seeing very heavy things, but it's a bit blurry when looking for these specific medium-sized, electron-only particles. The EIC, with its cleaner environment, acts like a high-definition lens that can spot them clearly.
• The Limit: They calculated exactly how weak the connection (coupling) between these new particles and electrons could be before the EIC would still be able to find them. They found that the EIC could rule out (or find) these particles in areas where other experiments (like BaBar or LEP) haven't been able to look.

Summary

In short, this paper is a proposal saying: "If we build the Electron-Ion Collider and run it with these specific settings, we have a very good chance of finding new, electron-only particles (ALPs and Z's) that have been hiding in the 'GeV' mass range, a place where other experiments haven't been able to look clearly."

They aren't claiming to have found them yet; they are providing the map and the magnifying glass to show where and how we should look to find them in the future.

Technical Summary

Technical Summary: ALP and Z′ Boson at the Electron-Ion Collider

Problem and Motivation
Despite the success of the Standard Model (SM), fundamental issues such as dark matter, neutrino masses, baryon asymmetry, and the strong CP problem remain unresolved. While the Large Hadron Collider (LHC) has placed stringent constraints on Beyond the Standard Model (BSM) particles, particularly in the TeV regime and regarding interactions with quarks or photons, the effective interactions of Axion-Like Particles (ALPs) and heavy neutral vector bosons ($Z'$) with electrons in the GeV mass range ($\sim 10$–$100$ GeV) remain less explored. Existing experiments like LEP, LHCb, and BaBar have constrained these particles, but a unique opportunity exists to probe "electrophilic" (electron-coupled only) scenarios in a cleaner experimental environment with lower QCD backgrounds. This paper investigates the sensitivity of the upcoming Electron-Ion Collider (EIC) to such electrophilic new physics.

Methodology
The authors employ an Effective Field Theory (EFT) framework to study two specific BSM scenarios where new particles couple exclusively to electrons:

1. Electrophilic ALP: A pseudoscalar particle ($a$) arising from the spontaneous breaking of a global $U(1)$ symmetry, coupled to electrons via a derivative interaction.
2. Electrophilic $Z'$ Boson: A new heavy neutral vector gauge boson coupled to the electron current.

The analysis focuses on electron-proton ($e^-p$) collisions at the EIC with a center-of-mass energy of $\sqrt{s} = 141$ GeV and an integrated luminosity of $100 \text{ fb}^{-1}$. The study utilizes the following methodology:

• Signal Processes: The primary search channel is the tri-electron final state ($e^-p \to e^-e^+e^-j$), where $j$ denotes a light-quark jet. For the ALP, loop-induced couplings to photons ($a\gamma\gamma$) are also considered, leading to additional channels: $e^-p \to e^-\gamma\gamma j$ and $e^-p \to e^-\gamma j$.
• Simulation: Signal and background events are generated using MadGraph5_aMC@NLO at leading order. The SM background for the tri-electron channel arises from $\gamma$ and $Z$ boson production.
• Detector Simulation: Realistic detector effects are incorporated using projected resolutions for tracking and calorimetry (dependent on pseudorapidity $\eta$) as specified in EIC design reports. A flat photon identification efficiency of 70% is applied.
• Analysis Strategy:
  • For the $e^-e^+e^-$ channel, the invariant mass ($m_{ee}$) of the two hardest transverse momentum ($p_T$) electrons is reconstructed. Signal events are expected to form a resonance peak, modeled using a double-sided Crystal Ball function to distinguish them from the smooth SM background.
  • For photon-inclusive channels, kinematic cuts on $p_T$, pseudorapidity, and angular separation ($\Delta R$) are optimized to maximize signal significance ($S$).
  • Statistical significance is calculated using the profile likelihood approximation, accounting for both statistical and systematic uncertainties (tested at 0%, 1%, and 5%).

Key Contributions

• First EIC Projections for Electrophilic Couplings: This work provides the first projected exclusion limits for purely electrophilic ALPs and $Z'$ bosons at the EIC, a parameter space previously unexplored at this facility.
• Comprehensive Channel Analysis: The study systematically evaluates the tri-electron channel ($e^-e^+e^-j$) as the dominant discovery mode, while also quantifying the reach of loop-induced di-photon ($e^-\gamma\gamma j$) and single-photon ($e^-\gamma j$) channels.
• Systematic Uncertainty Impact: The paper quantifies the degradation of sensitivity due to systematic uncertainties, demonstrating that the tri-electron channel remains robust even with 5% systematic errors, particularly at higher masses where background yields are low.
• Forward Jet Veto: The authors investigate the impact of vetoing forward jets (using "far-forward" detector capabilities) and find it improves sensitivity by roughly 10% for cross-section limits and 6% for coupling limits.

Results

• ALP Sensitivity:
  • In the $e^-e^+e^-$ channel, the EIC can exclude ALP-electron couplings ($g_{aee}$) down to $\sim 0.005$ for an ALP mass ($m_a$) of 5.5 GeV, varying between $0.008$ and $0.64$ for masses up to 100 GeV (assuming 0% systematics).
  • The inclusion of loop-induced $a\gamma\gamma$ couplings does not significantly alter the sensitivity in the tri-electron channel.
  • The di-photon and single-photon channels yield significantly weaker constraints compared to the tri-electron channel due to lower production rates and higher backgrounds.
• $Z'$ Sensitivity:
  • For the electrophilic $Z'$, the projected 95% CL exclusion limits on the coupling ($g_{Z'}$) range from $\sim 0.0026$ to $0.60$ for masses between 5.5 and 100 GeV.
  • The sensitivity is strongest in the 10–30 GeV mass range.
• Comparison with Existing Bounds:
  • The projected EIC limits significantly extend the sensitivity to electrophilic ALPs and $Z'$ bosons in the 10–100 GeV mass range, surpassing current constraints from BaBar, LEP, and IceCube in specific regions.
  • Specifically, for $Z'$ masses between 10 and 30 GeV, the EIC projections provide stronger bounds than existing monophoton searches at LEP and $e^+e^-$ searches.

Significance
The paper claims that the EIC offers a unique and powerful environment to probe electrophilic BSM physics in the GeV mass range, a region where the LHC is less sensitive due to high QCD backgrounds and where existing $e^+e^-$ colliders have limited reach. By focusing on the clean tri-electron final state, the EIC can significantly extend the exclusion limits for purely electron-coupled ALPs and $Z'$ bosons, filling a gap in the global search for new physics. The authors emphasize that while UV-complete models often require couplings to other fermions to satisfy anomaly cancellation, the study of the "purely electrophilic" limit serves as a crucial benchmark for understanding these interactions and guiding future model-building.