Fibre Inflation Beyond BHP: Constraints and a BHP-Free Regime

We study a restricted fibre-dependent $\alpha'$-loop sector in Type IIB Large Volume Scenario fibre inflation beyond the conventional Berg-Haack-Pajer (BHP) parametrisation. Motivated by effective-field-theory corrections in K3-fibred Calabi--Yau orientifolds, we analyse BHP-complete, partially BHP-driven and BHP-free configurations. For BHP-driven cases, the additional corrections act as effective deformations of the standard fibre potential and are bounded at the percent level relative to the corresponding BHP structures, with logarithmic terms typically more restricted due to their effects on the slope and curvature. At the effective-field-theory level, we identify a BHP-free fibre-inflation regime, referred to as $\alpha'$-loop inflation, in which the conventional KK- and winding-type BHP channels vanish while the generalized loop sector stabilises the fibre modulus and supports slow-roll inflation. This regime exhibits a characteristic hierarchy between fibre-dependent loop structures controlled by the large-volume suppression and satisfies CMB, K\"ahler-cone, large-volume and heavy-modulus constraints. Our results show that fibre inflation is sensitive to the orientifold and brane configurations, and that corrections beyond the BHP ansatz can generate new controlled inflationary regimes.