Oxygen-doping dependence of the in-plane effective mass in the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si2.svg"> <mml:mrow> <mml:mi mathvariant="normal">H</mml:mi> <mml:mi mathvariant="normal">g</mml:mi> <mml:msub> <mml:mrow>

• The Casimir–Kempf framework is applied to describe oxygen-doping effects in H g B a 2 C u O 4 + δ . • An analytical relation links m ab ∗ to lattice parameters, carrier density, and T c . • The calculated m ab ∗ ( δ ) (3.9–9 m e ) increases smoothly with oxygen enrichment. • Geometric confinement and dielectric screening jointly govern the superconducting response. The superconducting properties of high- T c cuprates are extremely sensitive to oxygen doping, which strongly modifies their lattice geometry and carrier dynamics. In this work, analytical relations derived within the Casimir–Kempf framework are applied to describe the doping dependence of the in-plane effective mass m ab ∗ in H g B a 2 C u O 4 + δ (Hg-1201). The model connects superconducting parameters to the Casimir energy of confined vacuum electromagnetic modes between adjacent C u O 2 planes, establishing a geometric link among m ab ∗ , the interlayer spacing c , the lattice constant a , the number of doped holes per Cu site n h , and the critical temperature T c . Using experimentally reported structural and transport data, m ab ∗ ( δ ) values in the range 4–9 m e were obtained, showing a gradual increase with oxygen content and a sharp rise in the heavily overdoped region. The results indicate that the Casimir–Kempf geometric contribution provides a complementary, phenomenological scaling link between lattice geometry and the inferred in-plane effective mass. We emphasize that the extracted m ab ∗ ( δ ) trends may also reflect conventional electronic mechanisms (band-structure renormalization, correlations, and scattering-rate effects), which are not disentangled in the present analysis.