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Measurement of the $\gamma\gamma \to \tau \tau$ cross section and constraints on the anomalous magnetic moment of the $\tau$ lepton in ultraperipheral PbPb collisions at $\sqrt{s_\mathrm{NN}}$ = 5.02 TeV

Using 1.70 nb $^{-1}$ of 2018 CMS data from ultraperipheral PbPb collisions at 5.02 TeV, this study presents the most precise LHC measurement of the $\gamma\gamma \to \tau\tau$ fiducial cross section and establishes the tightest constraints to date on the anomalous magnetic moment of the $\tau$ lepton, finding results consistent with next-to-leading-order QED predictions.

Original authors: CMS Collaboration

Published 2026-07-23

📖 4 min read🧠 Deep dive

CC BY 4.0

Original authors: CMS Collaboration

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Cosmic Billiard Hall and the Wobbly Tau

Imagine the universe as a giant, invisible billiard hall where the smallest particles in existence are the balls. In this hall, scientists are obsessed with understanding how these balls spin and wobble as they move. One of the most important rules of the game is how a particle's "magnetic moment" works—essentially, how strongly it acts like a tiny magnet. For the lightest particles, like the electron, we know this rule almost perfectly. But for the heaviest of the three charged "lepton" family members, the tau, things get fuzzy. Because the tau is so heavy, it should be much more sensitive to hidden, unknown forces that might be lurking in the universe, potentially revealing new physics beyond what we currently know.

The problem is that the tau is incredibly shy and short-lived. It exists for only a fleeting instant before it decays into other particles, making it impossible to catch and study directly in a storage ring like a muon. To study it, physicists have to be clever. They use a technique called "ultraperipheral collisions," which is like rolling two massive, charged bowling balls (lead nuclei) past each other without actually hitting them. As they zoom by, their intense electric fields act like flashlights, shooting out beams of light (photons). When two of these light beams crash into each other, they can briefly turn into a pair of tau particles. It's a rare, ghostly event where light becomes matter, and by watching how these tau pairs behave, scientists can measure their magnetic wobble and see if it matches the predictions of our current rulebook, the Standard Model.

The CMS Experiment: Catching Ghosts in the Lead

In this new study, the CMS collaboration at CERN's Large Hadron Collider (LHC) decided to take a closer look at these ghostly tau pairs. They analyzed data collected in 2018 from lead-lead collisions, a dataset equivalent to watching 1.70 billionths of a barn of interactions (a unit of area used in nuclear physics, known as 1.70 nb⁻¹). The team didn't just look for one type of tau decay; they cast a wide net, examining four different ways the tau pairs could break apart: a muon plus a single charged track, a muon plus three tracks, an electron plus three tracks, and a mix of a muon and an electron.

To find the signal, the scientists had to filter out the noise. They looked for events where the lead ions survived the encounter and flew away without breaking apart, leaving the detector mostly empty except for the specific decay products of the tau pair. They used a sophisticated statistical method, a "simultaneous likelihood fit," which acted like a master detective. This tool didn't just count the number of tau pairs found; it analyzed the exact shape of their energy distributions and how many were found in total. By comparing the real data against millions of computer simulations, they could determine the most likely value for the tau's anomalous magnetic moment, denoted as $a_\tau$ .

The Findings: A Tighter Net and a Clearer Picture

The results of this massive effort are twofold. First, the team measured the probability of this light-to-matter conversion happening, known as the cross section. They found that for tau leptons with a transverse momentum greater than 1 GeV and within a specific range of angles, the cross section is $555^{+60}_{-14} \mu b$ . This is the most precise measurement of this process at the LHC to date, and it aligns perfectly with the predictions made by next-to-leading-order quantum electrodynamics (QED), the theory describing how light and matter interact.

Second, and perhaps more exciting, is the constraint placed on the tau's magnetic wobble. The analysis yielded a 95% confidence interval for the anomalous magnetic moment of the tau lepton: $-0.039 < a_\tau < 0.032$ . This means that if the tau's magnetic moment deviates from the Standard Model prediction, it must be within this narrow range. This new limit is more than three times more precise than the previous best measurement from the same experiment. While it doesn't yet prove the existence of new physics, it significantly narrows the search area, bringing us closer to the level of precision needed to potentially spot the first crack in our current understanding of the universe. The study confirms that, for now, the tau behaves exactly as the Standard Model predicts, but the window for discovering something new is getting smaller and more defined.

Technical Summary: Measurement of the $\gamma\gamma \to \tau^+\tau^-$ Cross Section and Constraints on the Anomalous Magnetic Moment of the $\tau$ Lepton in Ultraperipheral PbPb Collisions

Problem and Motivation
The magnetic moments of charged leptons serve as stringent tests of the Standard Model (SM) and quantum field theory. While the electron's anomalous magnetic moment ( $a_e$ ) agrees with SM predictions to better than one part per billion, and the muon's ( $a_\mu$ ) shows tensions with certain theoretical calculations, the tau lepton ( $\tau$ ) remains less constrained. Due to the tau's short lifetime, direct measurements in storage rings are impossible. Consequently, constraints on the tau anomalous magnetic moment ( $a_\tau$ ) are derived primarily from photon-fusion production ( $\gamma\gamma \to \tau^+\tau^-$ ) in high-energy collisions. Previous measurements, including those from LEP and early LHC runs, have left $a_\tau$ constraints roughly a factor of three less precise than required to probe the SM prediction ( $a_\tau^{SM} \approx 0.001177$ ). This paper addresses the need for improved precision by analyzing a larger dataset and incorporating multiple decay channels in ultraperipheral collisions (UPCs) of lead ions.

Methodology
The analysis utilizes data collected by the CMS experiment in 2018 during ultraperipheral lead-lead (PbPb) collisions at a nucleon-nucleon center-of-mass energy of $\sqrt{s_{NN}} = 5.02$ TeV, corresponding to an integrated luminosity of $1.70 \text{ nb}^{-1}$ . The study focuses on the exclusive production of tau pairs, $PbPb \xrightarrow{\gamma\gamma} Pb^{(*)} \tau^+\tau^- Pb^{(*)}$ , where the lead ions remain intact or are electromagnetically excited but escape detection at low angles.

Signal Channels: The analysis extends previous work by examining four distinct $\tau^+\tau^-$ decay final states:
1. $\mu + 1\text{-prong}$ (one muon, one charged hadron): Highest branching fraction ( $\approx 17.4\%$ ) but higher background.
2. $\mu + 3\text{-prong}$ (one muon, three charged hadrons): Benefits from excellent muon identification and efficient background suppression.
3. $\mu + e$ (one muon, one electron): Lowest background contamination but lower yield due to trigger thresholds.
4. $e + 3\text{-prong}$ (one electron, three charged hadrons): Included despite lower yields compared to muon channels.
  The $e + 1\text{-prong}$ channel was excluded due to substantial background contamination.
Event Selection and Reconstruction: Events are selected using a combination of single-muon and electron triggers with specific transverse momentum ( $p_T$ ) thresholds. Offline selection requires exactly the number of tracks expected for each decay mode, strict "high-purity" track quality, and exclusivity criteria (e.g., no additional activity in Forward Hadron (HF) calorimeters or Zero Degree Calorimeters (ZDCs) to suppress non-exclusive backgrounds). A key discriminant is the acoplanarity ( $A_{\phi}$ ) between the decay products, which distinguishes the signal (characterized by larger acoplanarity due to neutrinos) from exclusive dilepton backgrounds like $\gamma\gamma \to \mu^+\mu^-\gamma$ .
Simulation and Background Estimation: Signal events are simulated using gamma-UPC and UPCGEN generators, incorporating variations in $a_\tau$ from $-0.1$ to $+0.1$ . Backgrounds from exclusive $\gamma\gamma \to \mu^+\mu^-\gamma$ and $\gamma\gamma \to e^+e^-$ are estimated via simulation, while residual backgrounds are derived from data using the "ABCD" method in control regions defined by track multiplicity and HF activity.
Statistical Analysis: A simultaneous binned likelihood fit is performed on the transverse momentum ( $p_T$ ) distributions of the decay leptons across all four channels. This fit simultaneously extracts the fiducial cross section ( $\sigma_{\text{fid}}$ ) and the anomalous magnetic moment ( $a_\tau$ ), incorporating systematic uncertainties as nuisance parameters.

Key Contributions

Expanded Dataset and Channels: This analysis increases the integrated luminosity by more than a factor of four compared to the first CMS observation of this process and includes three additional decay channels ( $\mu+1\text{-prong}$ , $\mu+e$ , $e+3\text{-prong}$ ) alongside the previously studied $\mu+3\text{-prong}$ mode.
Simultaneous Fit Strategy: The paper introduces a simultaneous likelihood fit that combines spectral shape and normalization information from all four channels, improving the precision of the extracted parameters.
Improved Constraints: The analysis achieves a significant improvement in the precision of the $a_\tau$ constraint compared to previous CMS PbPb results.

Results

Anomalous Magnetic Moment ( $a_\tau$ ): The measured 95% confidence level (CL) interval for the anomalous magnetic moment is:
$-0.039 < a_\tau < 0.032$
This result is consistent with the SM prediction and represents a sensitivity comparable to existing constraints from electron-positron collisions at LEP, improving upon the previous CMS PbPb measurement by more than a factor of three. The limit is derived from the low-mass region ( $m_{\tau\tau} \gtrsim 5$ GeV).
Fiducial Cross Section: The measured fiducial cross section for $\tau$ leptons with $p_T^\tau > 1$ GeV and $|\eta^\tau| < 3$ is:
$\sigma_{\text{fid}}^{\gamma\gamma \to \tau\tau} = 555^{+60}_{-14} \, \mu\text{b}$
(when $a_\tau$ is left free in the fit). When $a_\tau$ is fixed to the SM value, the cross section is $589^{+43}_{-40} \, \mu\text{b}$ . This measurement is the most precise for this process at the LHC to date.
Theoretical Agreement: The measured cross section agrees with next-to-leading-order (NLO) quantum electrodynamics (QED) predictions ( $\sigma_{\text{NLO}} = 570 \pm 3 \, \mu\text{b}$ ) and leading-order (LO) predictions ( $\sigma_{\text{LO}} = 568 \pm 3 \, \mu\text{b}$ ).

Significance
The paper claims that this measurement extends the utility of PbPb collisions beyond traditional heavy-ion physics topics, enabling the study of QED processes under experimental conditions as clean as those in $e^+e^-$ collisions. By providing the most precise measurement of the $\gamma\gamma \to \tau^+\tau^-$ cross section at the LHC and tightening constraints on $a_\tau$ , the work demonstrates the capability of ultraperipheral heavy-ion collisions to probe fundamental electromagnetic properties of the tau lepton. The results are consistent with the Standard Model and provide a robust baseline for future searches for new physics contributions to the tau magnetic moment.

The Cosmic Billiard Hall and the Wobbly Tau

The CMS Experiment: Catching Ghosts in the Lead

The Findings: A Tighter Net and a Clearer Picture

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