---
title: Photon-Fusion Production of W Boson Pairs
url: https://www.emergentmind.com/topics/photon-fusion-production-of-w-boson-pairs
type: topic
---

# Photon-Fusion Production of W Boson Pairs

Photon-fusion production of $W$ boson pairs refers to the process in which two quasi-real photons, radiated by the incoming protons in high-energy proton-proton ($pp$) collisions, interact to produce a $W^+W^-$ pair. This mechanism, fundamentally electroweak, provides a unique probe of Standard Model (SM) gauge structure—especially the triple and quartic gauge-boson self-interactions, including the $\gamma WW$ and $\gamma\gamma WW$ vertices. While subdominant to the leading Drell–Yan $q\bar q\to W^+W^-$ process in inclusive $WW$ production, photon-induced $WW$ represents a rare channel whose clean experimental signature and sensitivity to new-physics effects (notably anomalous quartic gauge couplings, aQGCs) are essential at the precision frontier of the LHC.

## 1. Theoretical Framework of Photon-Fusion $WW$ Production

Photon-fusion $W^+W^-$ production in $pp$ collisions is modeled as $pp\to p^{(*)}(\gamma\gamma\to W^+W^-)p^{(*)}$, where $p^{(*)}$ denotes either an intact proton (elastic emission) or a proton that dissociates into a hadronic system (inelastic emission). The process proceeds via three tree-level topologies:
  - $t$-channel and $u$-channel $W$-exchange diagrams: characterize the SM $\gamma WW$ trilinear coupling.
  - Quartic $\gamma\gamma W^+W^-$ vertex: genuine four-gauge-boson interaction, central for aQGC studies.

The Equivalent Photon Approximation (EPA), both in collinear and $k_T$-factorized formulations, is used to describe the emission spectrum of quasi-real photons from high-energy protons. The unintegrated photon fluxes $f_\gamma^{(el)}(x,q_T^2)$ (elastic) are governed by proton electromagnetic form factors, while $f_\gamma^{(in)}(x,q_T^2)$ (inelastic) rely on deep inelastic structure functions $F_2$ and $F_L$. The dominant contribution at LHC energies comes from the inelastic–inelastic ($in$–$in$) channel.

The inclusive (total) cross section is schematically:
$$
\sigma_{tot}(pp \to p^{(*)}W^+W^-p^{(*)}) = \sum_{i,j=el,in}\int dx_1\,dx_2\, f_\gamma^{(i)}(x_1) f_\gamma^{(j)}(x_2) \hat{\sigma}_{\gamma\gamma\to W^+W^-}(\hat{s}=x_1x_2s)
$$
where $\hat{\sigma}$ is the hard $\gamma\gamma\to W^+W^-$ partonic cross section, calculable using the gauge-boson self-interaction vertices.

## 2. Experimental Strategies and Event Topology

Photon-fusion $WW$ events are experimentally selected by identifying final states characterized by:
  - Two oppositely charged, isolated leptons ($e^\pm\mu^\mp$), arising from $W$ decays.
  - Minimal additional hadronic activity near the interaction vertex—enforced by a strict zero-track requirement to isolate events without additional charged particles, enhancing purity against Drell–Yan and other backgrounds.
  - Lepton $p_T$ and $\eta$ thresholds reflecting detector acceptance (for instance, leading $p_T>24$ GeV, subleading $p_T>15$ GeV, $|\eta_e|<2.5$, $|\eta_\mu|<2.4$ in CMS at 13 TeV [2601.21574]).
  - Additional kinematic selections, including dilepton mass $m_{e\mu}>20$ GeV and acoplanarity $A>0.015$, help suppress backgrounds.

The fiducial cross section, $\sigma_{fid}$, is defined in the generator-level phase space matching these selection criteria.

CMS and ATLAS analyses both mandate no extra tracks ($N_{trk}=0$) at the dilepton vertex, which suppresses non-exclusive production and ensures a high-purity $\gamma\gamma\to W^+W^-$ sample [2010.04019, 2601.21574]. In exclusive measurements using dedicated forward proton spectrometers, detection of both outgoing protons further ensures exclusivity and enables full event kinematics reconstruction [2009.08331].

## 3. Cross Section Measurements and Differential Properties

Comprehensive measurements at $\sqrt{s}=13$ TeV using the CMS and ATLAS detectors have provided the first observation of photon-fusion $W^+W^-$ at the LHC:
- CMS (138 fb$^{-1}$, 2016–2018): 
  - Inclusive cross section: $\sigma_{tot}=643^{+82}_{-78}$ fb
  - Fiducial cross section: $\sigma_{fid}=3.96^{+0.53}_{-0.51}$ fb
  - Standard Model predictions: $631\pm126$ fb (total), $3.87\pm0.77$ fb (fiducial)
  - Both measurements are consistent with the SM [2601.21574].
- ATLAS (139 fb$^{-1}$): $\sigma_{fid}=3.13\pm0.31(\text{stat})\pm0.28(\text{syst})$ fb [2010.04019].

These cross sections represent about 1–2% of the inclusive $W^+W^-$ rate at central rapidities and low $p_T$, but contribute 10% or more of the total at high $p_T$ ($>200$ GeV) and high invariant mass ($M_{WW}$ above 800 GeV) [1410.5848, 1409.1803, 1208.3147]. The differential spectra are characterized by:
- A relatively flat rapidity distribution for the $W$ bosons over $|y_W|<2.5$.
- Harder $p_T$ spectra than $q\bar q$-initiated modes—photon fusion dominates the $p_T$ and $M_{WW}$ tails.

Cross section uncertainties are dominated by the modeling of photon fluxes, experimental efficiencies, and the treatment of rapidity-gap survival factors, especially in the presence of proton dissociation and pileup [2601.21574, 2004.01111].

## 4. Elastic, Inelastic, and Exclusive Production: Modeling and Rapidity Gap Survival

Photon emission can occur elastically or with proton dissociation:
- Elastic–elastic: both protons remain intact.
- Elastic–inelastic (or inelastic–elastic): one proton remains intact, the other dissociates.
- Inelastic–inelastic: both protons dissociate.
- Central exclusive production: both protons remain intact with no additional hadronic activity; can be directly tagged with forward proton detectors [2009.08331].

Inelastic photon emission dominates the total $\gamma\gamma\to W^+W^-$ cross section at LHC energies, but these events often produce hadronic remnants that populate the forward detector regions. Imposing large central rapidity gaps (absence of charged particles in $|\eta|<2.5$) suppresses inelastic channels:
- Rapidity-gap survival factors $S_{R,SD}$ (single dissociation) and $S_{R,DD}$ (double dissociation) quantify the signal loss due to secondary hadron activity.
- Approximate factorization holds: $S_{R,DD}\approx S_{R,SD}^2$ [2004.01111, 1907.08936].
- For $|\eta|<2.5$ at 13 TeV, $S_{R,SD}\approx0.80$, $S_{R,DD}\approx0.65$; the overall taming of the cross section due to rapidity-gap requirements is in the $20$–$30$% range.
- Proton-dissociative fluxes rely critically on up-to-date structure function parametrizations (ALLM97, LUX-like, MNSZ2017), with resulting cross section uncertainties at the $\pm$20% level [1802.03244, 1907.08936].

Forward proton tagging allows for the clean isolation of exclusive $\gamma\gamma\to W^+W^-$ processes, reducing background and enhancing the sensitivity to anomalous couplings [2009.08331].

## 5. Sensitivity to Anomalous Quartic Gauge Couplings and Effective Field Theory Interpretation

Photon-fusion $W^+W^-$ is uniquely sensitive to quartic gauge boson couplings, especially the $\gamma\gamma WW$ vertex. Constraints are set in the context of both dimension-6 (operators $a_0^W$, $a_C^W$) and dimension-8 (operators $f_{M,i}/\Lambda^4$, $f_{T,i}/\Lambda^4$) effective field theory (EFT) frameworks:
- In CMS at 13 TeV, stringent bounds are placed using profile likelihood scans and reweighting of signal templates [2601.21574]:
  - $f_{T5}/\Lambda^4\in[-0.16,+0.13]$ TeV$^{-4}$ (most stringent among the $f_T$ series)
  - $f_{M2}/\Lambda^4\in[-0.49,+0.50]$ TeV$^{-4}$
  - First-time constraints for CP-odd operators (e.g., $f_{\tilde{T}2}/\Lambda^4\in[-0.03,+0.03]$ TeV$^{-4}$)
- Central exclusive measurements (with forward proton detectors) provide complementary and competitive bounds on $a_0^W$, $a_C^W$ down to $3.7\times10^{-7}$ GeV$^{-2}$ and $9.2\times10^{-7}$ GeV$^{-2}$, respectively, at 14 TeV and 300 fb$^{-1}$ integrated luminosity [2009.08331].
- Sensitivity to aQGCs increases with $W^+W^-$ mass and $p_T$ due to the quadratic and quartic scaling of EFT contributions relative to the SM, making the high-mass kinematic tails crucial for new-physics searches.

Modern studies now incorporate, for the first time, CP-odd operator constraints in this channel at the LHC [2601.21574]. These results are central to global EFT fits of the electroweak sector.

## 6. Numerical Summary and Key Phenomenological Features

A collation of integrated and differential cross-section benchmarks, uncertainties, and topology contributions is given below (at $\sqrt{s}=13$ TeV):

| Channel Topology          | Cross Section (pb) | Relative Fraction (%)    |
|--------------------------|--------------------|--------------------------|
| $q\bar q\to WW$ (total)  | $\sim$80–120       | Dominant                 |
| $\gamma\gamma$-fusion    | 1.3–1.8            | 1–2 in inclusive, up to 10–30 in tails |
| Elastic–elastic          | 0.27               | $\sim$15–20 of $\gamma\gamma$|
| Inel–inel                | 1.1                | $>$60 of $\gamma\gamma$  |

Differentially:
- $d\sigma/dM_{WW}$ falls steeply; by $M_{WW}\sim1$ TeV, $\gamma\gamma$ and $q\bar q$ become comparable.
- $d\sigma/dp_T^W$ peaks at $p_T\sim30$–$50$ GeV for $\gamma\gamma$, but the fraction rises to 10% at $p_T>200$ GeV [1410.5848, 1409.1803, 1208.3147, 1802.03244].
- Polarization fractions are stable, with transversely polarized $W$ pairs dominating.

At very high $p_T$ and $M_{WW}$, omission of this channel significantly biases precision SM and BSM studies [1208.3147].

## 7. Implications for Electroweak Precision Physics and New-Physics Searches

Photon-fusion $WW$ production, though subleading in total rate, is pivotal for:
- Directly probing the SM quartic $\gamma\gamma WW$ coupling;
- Setting stringent constraints on dimension-6 and dimension-8 EFT coefficients for aQGCs, notably in previously unprobed CP-odd directions [2601.21574];
- Complementing other di-boson ($VV$) and vector boson scattering (VBS) observables in global electroweak fits.

Accurate modeling, including inelastic photon fluxes, rapidity-gap survival, and full differential kinematics, is mandatory for exploiting the full sensitivity of LHC data to SM and BSM structures [2004.01111, 1802.03244, 1907.08936, 2009.08331].

Systematic uncertainties are predominantly theory-driven, particularly from the photon PDF/structure function modeling, but recent collider measurements now calibrate many aspects experimentally [2010.04019, 2601.21574].

In conclusion, photon-fusion $W$ boson pair production forms a precision electroweak benchmark, offers a uniquely clean window on gauge-boson self-interactions, and delivers leading sensitivity to anomalous quartic couplings at the LHC [2601.21574, 2009.08331, 2010.04019].

Source: https://www.emergentmind.com/topics/photon-fusion-production-of-w-boson-pairs