Differential measurements of $\gamma\gamma\to\tau\tau$ and constraints on $\tau$-lepton electromagnetic moments in Pb+Pb collisions at $\sqrt{s_{_\text{NN}}} = 5.02$ TeV with ATLAS

Using 1.93 nb$^{-1}$ of Pb+Pb collision data at $\sqrt{s_{_\text{NN}}} = 5.02$ TeV, the ATLAS collaboration presents the first differential fiducial measurements of $\gamma\gamma\to\tau\tau$ production and extracts constraints on the $\tau$-lepton's anomalous magnetic and electric dipole moments, marking the first time the latter has been measured in heavy-ion collisions.

The Gist

The Big Picture: A "Ghostly" Collision

Imagine two massive, heavy trains (Lead ions) speeding toward each other on parallel tracks at the Large Hadron Collider (LHC). Usually, if they get too close, they crash, creating a massive explosion of debris (hadronic collisions).

But in this experiment, the ATLAS scientists set the tracks so the trains pass each other at a safe distance. They don't crash. Instead, because they are so huge and charged, they create a massive "wind" of invisible energy around them. In physics, this wind is made of photons (particles of light).

When these two trains pass, their "winds" of light crash into each other. This is called a photon-photon collision. It's like two people waving giant flashlights at each other; the beams cross, and something new is created out of pure light.

What They Were Looking For: The "Ghost" Particles

When these light beams crash, they can create pairs of tau leptons. Think of a tau lepton as a heavy, unstable cousin of the electron. It's like a "ghost" because it exists for a tiny fraction of a second before vanishing and turning into other particles.

The scientists wanted to study these ghosts to see if they behave exactly as our current rulebook (the Standard Model of physics) says they should, or if they have some "secret tricks" (new physics) that we haven't discovered yet.

The Three "Rooms" of the Experiment

Since the tau particles vanish so quickly, the scientists can't see them directly. They have to look at what the tau turns into. The paper describes sorting the events into three different "rooms" based on what the tau leaves behind:

1. The Muon Room: One tau turns into a muon (a heavy electron) and some invisible neutrinos. The other tau turns into a single charged particle (a track).
2. The Three-Track Room: One tau turns into a muon, and the other tau turns into three charged particles.
3. The Electron Room: One tau turns into a muon, and the other turns into an electron.

By looking at these specific combinations, the scientists can be sure they are seeing the right "ghosts" and not just random noise.

The "Silent" Requirement

A crucial part of the experiment was ensuring the heavy trains (Lead ions) didn't break apart. If the ions broke, they would shoot out neutrons like shrapnel.

The scientists used special detectors at the very ends of the hall (Zero Degree Calorimeters) to check for this shrapnel. They only kept the data where no neutrons were found. This is like saying, "We only want to study the game if the players stayed in their seats and didn't throw anything." This ensures the collision was purely a "light vs. light" event and not a messy crash.

What They Measured

The team measured seven different things about the particles that came out, such as:

• How fast they were moving (Momentum).
• How heavy the system was (Mass).
• How wide apart they were flying (Acoplanarity).

They compared these measurements to computer simulations. Think of it like a weather forecast: they ran the simulation to predict what the "storm" of particles should look like, and then checked if the real data matched the forecast.

The Result: The real data matched the predictions very well. The "weather forecast" was accurate.

The Main Discovery: Checking the "Magnetic Personality"

The most exciting part of the paper is about the electromagnetic moments of the tau particle.

Imagine the tau particle is a tiny bar magnet.

• The Anomalous Magnetic Moment ($a_\tau$): This measures how strong the magnet is compared to what we expect. It's like checking if a compass needle is slightly bent.
• The Electric Dipole Moment ($d_\tau$): This measures if the magnet has a "lopsided" charge distribution. It's like checking if the magnet is slightly tilted or twisted in a way that violates the laws of symmetry (specifically CP symmetry).

Why does this matter?
If these values are slightly different from what the Standard Model predicts, it's a huge clue that there is "new physics" hiding somewhere—perhaps a new force or a new particle we don't know about yet.

The Final Verdict

The scientists performed a complex statistical fit (like tuning a radio to find the clearest signal) to see what values for these "magnetic personalities" best explained their data.

• For the Magnetic Moment ($a_\tau$): They found a range of values that are consistent with what we already know. They didn't find a "smoking gun" for new physics, but they tightened the rules on what is possible.
• For the Electric Dipole Moment ($d_\tau$): This is a first for heavy-ion collisions. They set a new limit, saying, "If this 'tilt' exists, it must be smaller than this specific number."

Summary in One Sentence

Using the "light winds" from passing lead trains, the ATLAS collaboration successfully measured how tau particles behave, confirming that they mostly follow the known rules of physics, while setting the strictest limits yet on their "magnetic tilt" in heavy-ion collisions.

Technical Summary

Technical Summary: Differential Measurements of $\gamma\gamma \to \tau\tau$ and Constraints on $\tau$-Lepton Electromagnetic Moments in Pb+Pb Collisions

Problem and Motivation
This paper addresses the measurement of photon-induced $\tau$-lepton pair production ($\gamma\gamma \to \tau\tau$) in ultra-peripheral collisions (UPC) of lead ions (Pb+Pb) at the Large Hadron Collider (LHC). In UPCs, the electromagnetic fields of the relativistic ions act as intense fluxes of quasi-real photons. Due to the $Z^4$ enhancement for di-photon processes (where $Z=82$ for lead), these collisions provide a high-luminosity environment to study $\gamma\gamma$ interactions with minimal hadronic background.

The primary physics goals are twofold:

1. To perform the first differential fiducial measurements of the $\gamma\gamma \to \tau\tau$ process in heavy-ion collisions, probing kinematic distributions of the visible decay products.
2. To constrain the anomalous magnetic moment ($a_\tau$) and the electric dipole moment ($d_\tau$) of the $\tau$-lepton. While the Standard Model (SM) predicts small non-zero values for $a_\tau$ and a negligible $d_\tau$, deviations could signal physics beyond the Standard Model (BSM), such as new sources of CP violation or unparticle/leptoquark models. Previous constraints on these moments in heavy-ion collisions were limited to integrated cross-sections; this analysis aims to improve sensitivity through differential measurements and fits to kinematic distributions.

Methodology
The analysis utilizes 1.93 nb$^{-1}$ of Pb+Pb data recorded by the ATLAS detector at $\sqrt{s_{NN}} = 5.02$ TeV during Run 2 (2015 and 2018).

• Event Selection: Events are selected where both lead ions remain intact (no nuclear breakup) and no neutrons are emitted in the forward direction ($0n0n$ topology). This requirement suppresses photonuclear backgrounds and ensures the interacting photons have near-zero virtuality ($q^2 \sim 0$ GeV$^2$), a necessary condition for defining electromagnetic moments.
• Signal Regions (SRs): Events are categorized into three mutually exclusive regions based on the decay topology of the two $\tau$-leptons, where one $\tau$ always decays to a muon ($\tau \to \mu \nu \nu$):
  • $\mu1T$-SR: One muon and one charged track (from $\tau \to \pi \nu$ or leptonic decay with low $p_T$).
  • $\mu3T$-SR: One muon and three charged tracks (from $\tau \to 3\pi \nu$).
  • $\mu e$-SR: One muon and one electron (both $\tau$s decay leptonically).
• Background Estimation: The dominant backgrounds are $\gamma\gamma \to \mu\mu(\gamma)$ and diffractive photonuclear processes.
  • $\gamma\gamma \to \mu\mu(\gamma)$ is estimated using Monte Carlo (MC) samples (STARlight/SuperChic) corrected by a data-driven Global Residual Flux Factor (GRFF) derived from a dedicated di-muon control region ($2\mu$-CR).
  • Diffractive photonuclear backgrounds are estimated using a fully data-driven method with control regions ($\mu2T$-CR and $\mu4T$-CR) that relax the track multiplicity and topocluster veto requirements.
• Unfolding: Differential cross-sections are measured at the particle level for seven kinematic variables (muon $p_T$, visible system $p_T$, invariant mass, pseudorapidity, etc.) in each fiducial region. Detector effects are corrected using an iterative Bayesian unfolding (IBU) procedure with a migration matrix derived from nominal signal MC.
• Moment Extraction: Constraints on $a_\tau$ and $d_\tau$ are extracted via a maximum-likelihood fit to the detector-level muon transverse momentum ($p_T$) distributions in the three SRs. The fit utilizes event-level reweighting of the MC signal to simulate non-zero values of $a_\tau$ and $d_\tau$ based on form factors in the $\gamma\tau\tau$ vertex. Spin correlation effects are included via bin-by-bin correction factors.

Key Contributions

1. First Differential Measurements: This work presents the first differential fiducial cross-sections for $\gamma\gamma \to \tau\tau$ in Pb+Pb collisions, covering seven kinematic variables across three distinct decay topologies.
2. First $d_\tau$ Constraints in Heavy Ions: While previous ATLAS analyses constrained $a_\tau$ in UPCs, this paper reports the first constraints on the $\tau$-lepton electric dipole moment ($d_\tau$ derived from Pb+Pb collision data.
3. Improved Photon Flux Modeling: The analysis employs a data-driven correction (GRFF) to the photon flux modeling, addressing discrepancies between STARlight predictions and data observed in control regions. It also compares results against various photon flux models (STARlight, SuperChic, and gamma-UPC with different form factors).
4. NLO Comparison: For the $\mu e$-SR, the measured cross-sections are compared against Next-to-Leading-Order (NLO) electroweak predictions, which retain full spin correlation effects.

Results

• Cross-Sections: The measured differential cross-sections are generally compatible with Standard Model predictions within uncertainties. The nominal predictions (incorporating the GRFF and spin correlations) show reasonable agreement with data. Predictions using the original STARlight photon flux or specific form factor assumptions (e.g., electric dipole form factor) show poorer agreement in certain kinematic regions.
• Electromagnetic Moments:
  • The best-fit value for the anomalous magnetic moment is $a_\tau = -0.037$.
  • The 95% confidence level (CL) interval for $a_\tau$ is $-0.057 < a_\tau < 0.035$.
  • The best-fit value for the electric dipole moment is $|d_\tau| = 1.7 \times 10^{-16} \, e\cdot\text{cm}$.
  • The 95% CL interval for $d_\tau$ is $|d_\tau| < 2.7 \times 10^{-16} \, e\cdot\text{cm}$.
• Precision: The constraints on $a_\tau$ are of similar precision to previous results from LEP and Pb+Pb collisions. The constraints on $d_\tau$ are competitive with the most precise existing limits from LEP (DELPHI, OPAL, L3) and represent the first such limits from heavy-ion collisions.

Significance
The paper claims that these results provide a rigorous test of the SM in the $\tau$-lepton sector using the unique high-photon-flux environment of heavy-ion collisions. The measurement of differential cross-sections allows for a more granular comparison with theoretical models, particularly regarding photon flux descriptions and spin correlations. The extraction of $d_\tau$ in Pb+Pb collisions is highlighted as a significant milestone, demonstrating the capability of ultra-peripheral heavy-ion collisions to probe CP-violating parameters with sensitivity comparable to traditional lepton colliders. The results are consistent with the SM, placing tight bounds on potential BSM contributions to the $\tau$-lepton's electromagnetic structure.