V.T194 — Neutrino Phase Shift on CMB Peaks

Bashinsky-Seljak neutrino phase shift φ_ν = 0.191π × N_eff/(N_eff+15/4). For τ (N_eff=3): φ_ν = 0.0849π. For SM (N_eff=3.044): φ_ν = 0.0856π. Differential Δφ_ν = 0.00069π shifts peaks by Δℓ ≈ 0.21, below current sensitivity. Mass-dependent correction Δφ_mass ≈ f_ν×0.19π = 0.004 rad is 1.4% of φ_ν. CMB-S4 sensitivity at ~1.5σ for the N_eff distinction.