A bulk axion in flat or warped extra dimensions cannot produce displaced 'QCD maxion' patterns; only a canonical QCD axion plus a decoupled KK plateau survives the combined gravitational, unitarity, and astrophysical constraints.
(IV.13) Hence, for the zero mode, we have: λ0 ≈ y 2 , (IV.14) g0 ≈ π2 2y2 , (IV.15) f0 ≈ f4× √ 2 π2 y2
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Extra-dimensional axion patterns
A bulk axion in flat or warped extra dimensions cannot produce displaced 'QCD maxion' patterns; only a canonical QCD axion plus a decoupled KK plateau survives the combined gravitational, unitarity, and astrophysical constraints.