Operator identification in charged lepton-flavor violation: Global EFT analysis with RG evolution, polarization observables, and Bayesian model discrimination at future colliders

Charged lepton-flavor violation is a null-test frontier of the Standard Model and a direct probe of physics beyond it. We present a global effective field theory (EFT) analysis across FCC-ee, ILC, CLIC, HL-LHC, HE-LHC, and muon colliders at 3 and 10 TeV, with operator identification as the primary target rather than exclusion reach alone. The analysis combines low-energy constraints, collider differential observables, and Dalitz-level <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mrow> <a:mi>μ</a:mi> <a:mo stretchy="false">→</a:mo> <a:mn>3</a:mn> <a:mi>e</a:mi> </a:mrow> </a:math> information in a common profile-likelihood framework. Key hadron-collider and muon-collider signal/background samples are generated at the event level and propagated through Delphes detector simulation, while clean <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"> <d:msup> <d:mi>e</d:mi> <d:mo>+</d:mo> </d:msup> <d:msup> <d:mi>e</d:mi> <d:mo>−</d:mo> </d:msup> </d:math> benchmark channels are modeled with a parametric response calibrated to published detector-performance benchmarks. We include one-loop renormalization group (RG) running and operator mixing between UV matching and measurement scales, finding 10–30% shifts in selected operator-correlation entries when comparing tree-level and RG-evolved coefficient mappings at multi-TeV matching scales. Polarization asymmetries are used to separate <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"> <f:msub> <f:mi>c</f:mi> <f:mrow> <f:mi>H</f:mi> <f:mo>ℓ</f:mo> </f:mrow> </f:msub> </f:math> and <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"> <h:msub> <h:mi>c</h:mi> <h:mrow> <h:mi>H</h:mi> <h:mi>e</h:mi> </h:mrow> </h:msub> </h:math> directions, and UV discrimination is quantified with Bayes factors for benchmark leptoquark and heavy-neutral-lepton hypotheses. The full code chain for event generation, detector response, inference, and figure reproduction is provided.