CR011 $pp \to W_L W_L W_L W_L; \,\text{experimentally }\, pp \to jj W_L^+/- W_L^+/-$

In custodial RS and composite-Higgs-like completions, longitudinal VBS tests the sector that unitarizes electroweak symmetry breaking: electroweak KK vectors, scalar resonances, and the pattern of couplings to \(W_L\) and \(Z_L\). This is complementary to colored KK-gluon and vectorlike-partner searches. A VBS excess or exclusion constrains the electroweak/composite resonance sector only after specifying the custodial gauge group, the resonance spectrum, the branching fractions into vector bosons versus tops or composite fermions, and the production mechanism. For the RS scan in this repository, CR011 is not expected to be the leading constraint. The quark-scan methodology note quotes \(\Mkk^{\min}(p50,\gs=3)=47.26~\mathrm{TeV}\) from the low-energy \(\Delta F=2\) scan, while direct electroweak VBS reach remains a few-TeV collider cross-check unless a non-anarchic or protected flavor structure weakens the flavor bound. CR011 is therefore useful as a diagnostic of the strong-EWSB sector and as leverage for non-anarchic RS variants, not as a replacement for the active low-energy flavor constraints.

atlas\_2017\_arxiv1611\_02428.txt established the LHC same-sign \(WWjj\) VBS/aQGC program at \(8~\mathrm{TeV}\), separating electroweak and strong production regions and introducing VBS-sensitive anomalous-coupling fiducial selections. atlas\_2020\_arxiv2004\_10612.txt extended the VBS program to rare \(ZZjj\) electroweak production, important because neutral diboson scattering tests a different electroweak channel and different background systematics. cms\_2020\_arxiv2009\_09429.txt was the first CMS polarization measurement in same-sign \(WWjj\), setting the \(1.17~\mathrm{fb}\) longitudinal \(WW\) upper limit used above as the historical comparator. atlas\_2024\_arxiv2312\_00420.txt then provided a full Run-2 ATLAS same-sign \(WWjj\) measurement and aQGC interpretation, including differential information and a same-sign \(H^{\pm\pm}\) VBF search. The current polarization-specific improvement is the ATLAS 2025 result promoted here. For EFT/aQGC context, atlas\_2026\_arxiv2603\_18630.txt is the current ATLAS combined interpretation of measurements sensitive to quartic electroweak gauge couplings. Its coefficient intervals are not quoted in this draft because CR011's promoted observable is the direct longitudinal \(WW\) fiducial cross-section limit; adding coefficient-level values would require a separate table extraction and a choice of unitarity/positivity convention.

The ATLAS/CMS limits are fiducial and polarization-template dependent. They assume the Standard Model electroweak VBS topology, leptonic \(W\)-decay event selection, and fitted longitudinal/transverse polarization templates. They do not directly exclude a universal RS \(M_{KK}\) value. A reinterpretation must simulate the chosen custodial-RS spectrum and account for interference with the SM VBS amplitude, resonance widths, acceptance, and decay branching fractions. For aQGC/EFT statements, the interpretation depends on the operator basis, whether one or several Wilson coefficients are profiled, and whether unitarity constraints are imposed. For explicit RS resonances, the assumptions differ again: a narrow electroweak vector resonance decaying visibly to \(VV\) is much more constrained by VBS-like searches than a broad resonance with dominant decays to top partners, heavy fermions, or other composite-sector states. This entry should therefore be treated as collider-sector cross-check information until a dedicated RS likelihood or recast is attached.

NO. A targeted grep for VBS, longitudinal-polarization, diboson, and aQGC terms across quarkConstraints/, qcd/, flavorConstraints/, neutrinos/, yukawa/, warpConfig/, solvers/, scanParams/, and tests/ returned no matches. Adjacent code evidence shows KK-scale bookkeeping and low-energy flavor evaluation, not collider direct-search filtering: quarkConstraints/scan.py:359 maps \(\Lambda_{\rm IR}\) to \(M_{KK}\), quarkConstraints/scan.py:377 evaluates \(\Delta F=2\) constraints, and scanParams/scan.py:528 passes \(M_{KK}\) into the lepton-flavor-violation check. No ATLAS/CMS, VBS, \(WWjj\), \(ZZjj\), polarization, or collider-likelihood module is present in the searched paths.

HIGH. A live CR011 constraint needs more than a scalar threshold. It requires a collider reinterpretation stack: event generation for the chosen custodial-RS resonance spectrum, showering and detector/selection acceptance, polarization-sensitive templates or an external recast tool such as CheckMATE, MadAnalysis5, or SModelS where applicable, and a likelihood interface for the ATLAS/CMS fiducial regions. EFT/aQGC coefficient comparisons are simpler to record, but mapping them into a concrete RS mass bound is model dependent and not implemented in this repository.

ATLAS2025\_LongitudinalWW; CMS2020\_PolarizedSameSignWW; ATLAS2024\_SameSignWWjj; ATLAS2020\_ZZjj; ATLAS2017\_WWjjAQGC; ATLAS2026\_AQGCCombination; PDG2025\_WZQuarticCouplings; Contino2011\_CompositeHiggsResonances.