Discovery prospects for photophobic axion-like particles at a 100 TeV proton--proton collider

This paper investigates the discovery potential for heavy photophobic axion-like particles at a future 100 TeV proton-proton collider with 20 ab$^{-1}$ luminosity, demonstrating that electroweak-driven production and decay channels (specifically $a \to Z\gamma$ and $a \to W^+W^-$) offer significant sensitivity to the ALP-W coupling through detector-level analyses utilizing boosted decision trees.

The Gist

Imagine the universe is a giant, bustling city. For decades, we've been looking for a specific type of "ghost" that lives there: a particle called an Axion-Like Particle (ALP).

Usually, when physicists look for these ghosts, they expect them to leave a very bright, obvious trail: a flash of two photons (light particles) crashing together. It's like looking for a ghost by the bright spotlight it leaves behind. But what if this ghost is "photophobic"—meaning it's afraid of light and refuses to turn on that spotlight?

This paper is a blueprint for a new, super-powerful search for these "light-fearing" ghosts, but instead of looking for a spotlight, we are looking for the shadows they cast on the city's infrastructure.

Here is the breakdown of the research in simple terms:

1. The Setting: Building a Super-Telescope

The authors are planning to use a future particle collider called the SppC or FCC-hh.

• The Analogy: Think of the current Large Hadron Collider (LHC) as a standard race car. The new 100 TeV collider is a Formula 1 car going at seven times the speed.
• Why it matters: At these speeds, we aren't just smashing things harder; we are unlocking a completely different neighborhood of physics. The paper argues that simply "turning up the volume" on the old machine isn't enough. The new machine changes the rules of the road, creating new types of collisions that were impossible before.

2. The Target: The "Photophobic" Ghost

Most searches look for ALPs that decay into two photons ($\gamma\gamma$). This paper says, "Let's assume the ALP is shy and hates photons."

• The Twist: If the ALP doesn't talk to light, it must talk to something else. In this scenario, it talks to the Weak Force (the force behind radioactivity and the sun's energy).
• The Strategy: Since the ghost won't show us its face (light), we have to look for the footprints it leaves on the Weak Force particles (W and Z bosons).

3. The Three Detective Stories (Search Channels)

The team designed three different "detective stories" to catch this ghost, each looking for a different set of footprints.

Story A: The "Z-Photon" Trail ($Z\gamma + \text{jets}$)

• The Scene: The ghost is created alongside two jets (sprays of particles) and immediately decays into a Z boson (a heavy cousin of the photon) and a photon.
• The Clue: The Z boson splits into two charged particles (electrons or muons).
• Why it's good: This is the "cleanest" crime scene. The particles are easy to track, and you can reconstruct the exact mass of the ghost very precisely. It's like finding a fingerprint that matches the suspect perfectly.
• Result: This is the most powerful method for finding the ghost across almost all mass ranges.

Story B: The "Triple W" Chase ($W^\pm W^\pm W^\mp$)

• The Scene: The ghost is created alongside a W boson. The ghost then splits into two more W bosons.
• The Clue: Two of the W bosons decay into muons with the same electric charge (like two positive charges). This is a very rare event in nature, like finding two identical twins who are both wearing red hats in a crowd of people wearing blue.
• Why it's good: Because same-charge muons are so rare in nature, if we see them, it's almost certainly a signal. It's a "smoking gun."
• Limitation: It's harder to do at very high masses because the "gun" gets harder to fire as the ghost gets heavier.

Story C: The "Jet-Heavy" Hunt ($W^+W^- + \text{jets}$)

• The Scene: The ghost is created with two jets and decays into two W bosons, which then turn into an electron and a muon.
• The Clue: This is the "heavy hitter." At very high energies (when the ghost is very heavy), the universe starts producing a lot of "forward jets" (particles shooting out the sides).
• The Surprise: The paper found a crossover point. For lighter ghosts, Story B (Triple W) was better. But once the ghost gets heavier than 1 TeV (about the weight of a proton, but packed into a tiny space), Story C takes over.
• Why? At 100 TeV, the "Vector Boson Fusion" (a specific way particles collide) becomes dominant. It's like realizing that for heavy cargo, a cargo ship (Story C) is much faster than a speedboat (Story B).

4. The Tools: The "AI Detective"

The data from these collisions is messy. There are billions of background events (noise) that look like the signal.

• The Solution: The team used a Boosted Decision Tree (BDT).
• The Analogy: Imagine a security guard at a club. A human guard might just check IDs. But an AI guard (the BDT) looks at everything: the way you walk, the color of your shoes, your height, your voice, and how you hold your drink. It combines thousands of tiny clues to decide, "This person is definitely a VIP (Signal)" or "This person is a regular (Background)."
• Result: This AI allows them to filter out the noise and find the ghost even when it's hiding in a crowd.

5. The Big Picture: Why This Matters

• Beyond the LHC: The current LHC (14 TeV) is like looking for a needle in a haystack with a flashlight. This 100 TeV machine is like using a magnet to pull the needle out.
• The "Photophobic" Limit: By focusing on the "light-fearing" scenario, they are covering a blind spot that other experiments might miss. If the ALP exists but hates light, this is the only way to find it.
• The Verdict: If this ghost exists with a mass between 100 GeV and 7,000 GeV, this future collider has a very high chance of finding it. The paper provides a "map" for the next generation of physicists, telling them exactly where to look and what tools to use.

In summary: This paper is a guidebook for hunting a shy, light-avoiding ghost in a super-fast city. It tells us that while the ghost might hide from the spotlight, it leaves very clear footprints on the heavy machinery of the universe, and with a 100 TeV collider and some smart AI, we can finally catch it.

Technical Summary

1. Problem Statement and Motivation

• Context: Axion-like particles (ALPs) are pseudo-scalar states often searched for via their coupling to photons ($a\gamma\gamma$). However, existing astrophysical and laboratory constraints have severely limited the parameter space for this diphoton coupling ($g_{a\gamma\gamma}$).
• The "Photophobic" Limit: This paper investigates the "photophobic" scenario where $g_{a\gamma\gamma} \simeq 0$. In this limit, ALP production and decay via photons are suppressed, and the phenomenology is driven entirely by electroweak couplings ($aWW$, $aZ\gamma$, $aZZ$).
• The Challenge: While previous studies (e.g., at the HL-LHC, $\sqrt{s}=14$ TeV) have explored these channels, simply rescaling results from 14 TeV to a future 100 TeV collider (SppC/FCC-hh) is insufficient. The shift in center-of-mass energy fundamentally alters:
  • Parton luminosities (shifting to smaller momentum fractions).
  • The relative importance of production topologies (Vector Boson Fusion vs. s-channel).
  • Kinematic distributions (increased boosting and forward jet activity).
  • Background compositions and rejection efficiencies.
• Goal: To perform a dedicated, detector-level study of heavy photophobic ALPs ($m_a \in [100, 7000]$ GeV) at $\sqrt{s}=100$ TeV with an integrated luminosity of $L=20$ ab$^{-1}$, optimizing analysis strategies for each mass point.

2. Methodology

The study employs a comprehensive simulation and analysis chain:

• Theoretical Framework: An Effective Field Theory (EFT) description is used where the ALP couples to $SU(2)_L$ and $U(1)_Y$ field strengths. The photophobic condition ($g_{a\gamma\gamma}=0$) imposes specific relations between the remaining couplings: $g_{aZ\gamma} = \tan\theta_W g_{aWW}$ and $g_{aZZ} = (1-\tan^2\theta_W)g_{aWW}$.
• Signal Topologies: Three complementary channels are analyzed:
  1. $pp \to jj a (\to Z\gamma)$: Associated production with two jets (s-channel and VBF), with $Z \to \ell^+\ell^-$.
  2. $pp \to W^\pm a (\to W^+W^-)$: Associated production via s-channel, with same-sign dimuons ($W^\pm \to \mu^\pm\nu$) and a hadronic $W$ ($W^\mp \to jj$).
  3. $pp \to jj a (\to W^+W^-)$: Associated production with two jets (s-channel and VBF), with opposite-sign, different-flavor dileptons ($e^\pm\mu^\mp$).
• Simulation Tools:
  • Event Generation: MadGraph5_aMC@NLO (v2.6.7) for hard scattering; PYTHIA 8.3 for parton showering and hadronization.
  • Detector Simulation: Delphes 3.4.2 (CMS configuration) to model detector effects.
  • Backgrounds: High-statistics Monte Carlo samples generated for all relevant SM processes (e.g., $ZW\gamma$, $t\bar{t}\gamma$, $W^\pm W^\pm jj$, $t\bar{t}$).
• Analysis Strategy:
  • Preselection: Tight kinematic cuts on leptons, jets, photons, and missing transverse energy ($E_T^{miss}$), including $b$-jet vetoes.
  • Multivariate Analysis (MVA): A Boosted Decision Tree (BDT) classifier is trained using TMVA. Input variables include kinematic observables (momenta, $\eta$, $\phi$), angular separations ($\Delta R$, $\Delta \eta$), invariant masses, and specific topological variables (e.g., dijet mass and separation for VBF).
  • Optimization: The BDT threshold is optimized independently for each ALP mass hypothesis ($m_a$) to maximize the statistical significance ($S/\sqrt{S+B}$ or the Asimov significance).

3. Key Contributions

• Detector-Level Realism: Unlike simplified scaling studies, this work provides a full detector-level simulation for both signal and high-statistics backgrounds, accounting for realistic acceptance and reconstruction efficiencies.
• Mass-Dependent Optimization: The analysis recognizes that the optimal kinematic variables and BDT performance change with $m_a$. For instance, VBF topologies become dominant at high masses, requiring specific dijet variables in the MVA.
• Identification of Channel Crossover: The study explicitly identifies a regime change where the VBF-assisted $pp \to jj a (\to W^+W^-)$ channel overtakes the purely s-channel $pp \to W^\pm a (\to W^+W^-)$ channel for $m_a \gtrsim 1$ TeV. This is driven by the rapid growth of electroweak vector-boson luminosities at 100 TeV.
• Model-Independent Results: Beyond coupling limits, the paper provides discovery thresholds in terms of the fiducial cross-section times branching ratio ($\sigma \times \text{Br}$), allowing direct reinterpretation for other new physics models.

4. Key Results

• Discovery Reach on Coupling ($g_{aWW}$):
  • Best Channel: The $jj a (\to Z\gamma)$ channel (Channel I) offers the best sensitivity across the entire mass range ($100-7000$ GeV) due to the fully reconstructible resonance ($m_{\ell\ell\gamma}$) and low irreducible backgrounds.
  • High Mass Performance: For $m_a \gtrsim 1$ TeV, the $jj a (\to W^+W^-)$ channel (Channel III) becomes more sensitive than the $W^\pm a$ channel (Channel II).
  • Improvement over HL-LHC: The 100 TeV collider improves the reach on $g_{aWW}$ by roughly an order of magnitude compared to HL-LHC projections and extends the mass reach by several TeV.
• Cross-Section Sensitivity ($\sigma \times \text{Br}$):
  • $Z\gamma$ Channel: Sensitivity reaches the sub-fb level for multi-TeV masses.
  • $W^\pm a$ Channel: Sensitivity improves from $\mathcal{O}(10^2)$ fb near threshold to $\mathcal{O}(1)$ fb at multi-TeV masses, benefiting from the rare same-sign dilepton signature.
  • $jj a (W^+W^-)$ Channel: Sensitivity improves from $\mathcal{O}(10)$ fb to a few fb in the multi-TeV regime.
• Systematic Robustness: The three channels probe the same underlying physics from different experimental angles (different production modes and decay signatures). This allows for over-constraining the photophobic relations and provides robust cross-checks against channel-specific systematic uncertainties.

5. Significance

• Physics Reach: This study demonstrates that a 100 TeV collider is essential for probing heavy photophobic ALPs in the multi-TeV regime, a region largely inaccessible to the 14 TeV HL-LHC.
• Strategic Insight: It highlights that simply increasing luminosity is not enough; the shift in kinematics and the emergence of VBF-dominated topologies at high energies require tailored analysis strategies.
• Comprehensive Coverage: By covering $Z\gamma$ and $WW$ final states with both s-channel and VBF production, the study provides a complete "program" to test the gauge structure of photophobic ALPs. If a signal is found, the combination of these channels would allow for a precise determination of the ALP's electroweak couplings and CP properties.
• Reusability: The provided model-independent $\sigma \times \text{Br}$ limits serve as a benchmark for future searches for other resonant new physics in these specific final states.