Measurement and effective field theory interpretation of the photon-fusion production cross section of a pair of W bosons in proton-proton collisions at $\sqrt{s}$ = 13 TeV

Using 138 fb$^{-1}$ of proton-proton collision data at $\sqrt{s}$ = 13 TeV, the CMS collaboration measured the photon-fusion production cross section of W boson pairs, finding results consistent with Standard Model predictions and establishing stringent constraints on anomalous quartic gauge couplings within an effective field theory framework.

The Gist

The Big Picture: Catching Ghosts in a Storm

Imagine the Large Hadron Collider (LHC) at CERN as a massive, high-speed highway where two streams of protons (tiny particles) zoom toward each other at nearly the speed of light. Usually, when these streams crash, it's like a massive pile-up: thousands of particles fly everywhere, creating a chaotic "storm" of debris.

However, sometimes, instead of a crash, the protons act like polite drivers who just flash their headlights at each other as they pass. They exchange a flash of light (a photon) but don't actually hit each other. This is called photon fusion.

This paper is about the CMS team successfully "catching" a very rare event where two protons flashed their headlights, and that flash of light turned into a pair of W bosons (heavy particles that carry the weak nuclear force). It's like two cars flashing their lights, and suddenly, two heavy trucks appear out of thin air between them, while the cars themselves keep driving away without a scratch.

The Challenge: Finding a Needle in a Haystack

The problem is that the "haystack" (the normal collisions where protons smash together) is huge and messy. The "needle" (the photon fusion event) is very quiet. In a normal crash, you see a lot of extra tracks (debris) flying around the collision point. In a photon fusion event, the area around the new particles is eerily empty.

The Strategy:
The scientists decided to look for events that were "clean." They set up a filter with two main rules:

1. The Signature: They looked for exactly two specific particles: one electron and one muon (a heavy cousin of the electron).
2. The Silence: They demanded that there be zero other tracks (debris) coming from the exact spot where the electron and muon were born. If there was even one extra speck of dust, they threw the event out.

This is like looking for a specific conversation in a crowded room by only listening to people who are whispering in a completely silent corner. If you hear anyone shouting or clinking glasses nearby, you ignore that corner.

The Results: A Perfect Match

Using data collected over three years (2016–2018), the team found enough of these "clean" events to say, "We have seen this happen!"

• The Count: They measured how often this happened. The number they found (643 events per unit of time) matched almost perfectly with what the Standard Model (the rulebook of physics) predicted (631).
• The Confidence: The match was so good that they could say with high confidence that their observation is real and not just a fluke. It's like flipping a coin 1,000 times and getting 500 heads; you know the coin is fair.

Why Does This Matter? The "Rulebook" Check

The main reason scientists do this isn't just to count particles; it's to check if the "Rulebook" (the Standard Model) has any hidden errors or missing pages.

In physics, there are "forces" that hold particles together. Sometimes, scientists suspect there might be "new physics" (Beyond the Standard Model) that makes these forces act slightly differently at high energies. They use a mathematical framework called Effective Field Theory (EFT) to test this. Think of EFT as a set of "what-if" scenarios.

• The Test: The team asked, "What if the rules for how these W bosons interact are slightly different than we think?"
• The Outcome: They ran the numbers and found that the "what-if" scenarios didn't fit the data. The data fits the current rulebook perfectly.
• The Constraint: Because the data matches the standard rules so well, they were able to put very tight "fences" around the possible size of any new, unknown forces. They effectively said, "If there is any new physics here, it must be very, very weak, because we didn't see it."

Summary

In short, this paper is a victory lap for the "clean collision" strategy.

1. They found a rare event: Two protons flashed light at each other, creating a pair of heavy W bosons without crashing.
2. They proved it works: By looking for "empty" collision zones, they successfully separated this rare signal from the noisy background.
3. They checked the rules: The event happened exactly as the current laws of physics predicted.
4. They set limits: They used this perfect match to rule out many theories about "new physics," tightening the constraints on what the universe can and cannot do.

It's a confirmation that our current understanding of how light and matter interact is solid, at least for this specific, rare dance of particles.

Technical Summary

Technical Summary: Measurement and Effective Field Theory Interpretation of Photon-Fusion $W^+W^-$ Production

Problem and Motivation
Photon-induced processes in proton-proton ($pp$) collisions at the Large Hadron Collider (LHC) offer a unique testing ground for the Standard Model (SM), complementary to the dominant quark- and gluon-initiated interactions. Specifically, the photon-fusion production of $W$ boson pairs ($\gamma\gamma \to W^+W^-$) proceeds through interactions involving trilinear and quartic gauge boson couplings. While evidence for this process was previously reported by CMS at $\sqrt{s} = 7$ and $8$ TeV, and observed by ATLAS at 13 TeV, a precise measurement using the full Run 2 dataset allows for stringent constraints on Beyond-the-Standard-Model (BSM) physics. The primary goal of this analysis is to measure the total and fiducial cross sections of $\gamma\gamma \to W^+W^-$ and to interpret these results within a dimension-8 Effective Field Theory (EFT) framework to constrain anomalous quartic gauge couplings (aQGCs), including CP-odd operators for the first time in this channel.

Methodology
The analysis utilizes $pp$ collision data collected by the CMS detector at $\sqrt{s} = 13$ TeV during 2016–2018, corresponding to an integrated luminosity of $138 \text{ fb}^{-1}$.

• Signal Selection: The signal is characterized by the exclusive nature of photon-fusion events, where the protons either remain intact or dissociate into remnants that fall outside the detector acceptance. Consequently, the selection requires a final state with one isolated electron and one isolated muon of opposite charge, with no additional tracks associated with the electron-muon production vertex ($N_{\text{tracks}} = 0$).
• Kinematic Cuts: Leptons are required to have transverse momentum $p_T > 24$ GeV (leading) and $15$ GeV (subleading), with pseudorapidity $|\eta| < 2.5$ (electron) and $2.4$ (muon). An acoplanarity requirement ($A = 1 - |\Delta\phi|/\pi > 0.015$) is applied to suppress the $\gamma\gamma \to \tau\tau$ background, which produces back-to-back decay products.
• Background Estimation:
  • Dominant Backgrounds: Inclusive diboson production ($pp \to WW$) and Drell-Yan ($Z/\gamma^* \to \tau\tau$) processes are the primary backgrounds. These are estimated using Monte Carlo (MC) simulations corrected with data-driven methods.
  • Track Multiplicity Correction: A critical systematic challenge is the accurate modeling of pileup and hard-scattering track multiplicities. Corrections are derived using a control region (CR) enriched in inclusive backgrounds ($1 \le N_{\text{tracks}} \le 5$) and validated in a $\mu\mu$ final state.
  • Non-prompt Leptons: Backgrounds from jets misidentified as leptons are estimated using a same-sign (SS) charge method, reweighted by an OS-to-SS scale factor derived from data.
• Statistical Analysis: A binned maximum likelihood fit is performed on the vectorial sum of the transverse momenta of the electron and muon ($p_T^{e\mu}$) in both the Signal Region (SR, $N_{\text{tracks}}=0$) and the Control Region (CR). The signal strength is the parameter of interest, while background normalizations and track multiplicity corrections are treated as nuisance parameters.

Key Contributions and Results

• Observation: The analysis reports the first observation of photon-fusion $W^+W^-$ production using CMS data, with a signal significance well above $5\sigma$ against the background-only hypothesis.
• Cross Section Measurements:
  • The inclusive cross section is measured to be $643^{+82}_{-78}$ fb. This is in agreement with the SM prediction of $631 \pm 126$ fb (generated with SUPERCHIC 4).
  • The fiducial cross section (matching the analysis selection criteria) is measured to be $3.96^{+0.53}_{-0.51}$ fb, consistent with the SM prediction of $3.87 \pm 0.77$ fb.
• EFT Interpretation: The results are interpreted as constraints on dimension-8 EFT operators describing anomalous quartic gauge couplings. The analysis varies one operator at a time while fixing others to zero.
  • CP-Even and CP-Odd Operators: The study derives 95% confidence level (CL) intervals for a comprehensive set of operators ($fM_i/\Lambda^4$ and $fT_i/\Lambda^4$, including CP-odd $\tilde{f}$ variants).
  • Significance of Constraints: The measured limits are competitive with, and in some cases superior to, previous CMS measurements in other final states (e.g., $W\gamma$, $Z\gamma$, and vector boson scattering). Notably, this analysis provides the first constraints on CP-odd dimension-8 operators using the $\gamma\gamma \to W^+W^-$ channel.

Significance
The paper claims that the excellent agreement between the measured cross sections and SM predictions validates the description of photon-fusion processes involving trilinear and quartic gauge couplings. By successfully isolating the exclusive signal in a high-pileup environment and applying rigorous data-driven background corrections, the analysis establishes a robust baseline for probing BSM physics. The derived constraints on dimension-8 operators represent the most stringent limits to date for several aQGCs in this specific channel, effectively testing the unitarity of the electroweak sector at high energies. The inclusion of CP-odd operators expands the sensitivity of the EFT interpretation to new sources of CP violation in gauge boson interactions.