SU(5) effective potential including Higgs loop contribution and bounds for the Higgs masses

Fine-tuning and the doublet-triplet splitting problem in the minimal $SU(5)$ GUT

“…Gauge boson loops can induce a H † Φ 2 H term, leading to a non-zero value for β. This can be seen from the SU (5) effective potential [15] 1 . Moreover, beyond leading order the reason for requiring β = 0 may be absent altogether, since there might be other terms that contribute to Eq.…”

“…Note there must be an error in Eq. 2.4 of[15] because there is a non-zero contribution to the H † Φ 2 H term from Higgs loops even when β = 0. This is impossible, since there are no terms present in the Higgs potential that mix components of H. It was checked that the gauge boson loop really does give rise to an effective β parameter…”

Aspects of fine-tuning in theories with extended scalar sectors

“…Beyond leading order, gauge boson loops will induce a H † Φ 2 H term, leading to a non-zero value for β. This can be seen from the SU (5) effective potential [123]. 2 Hence, beyond leading order the above argument may not apply, because the minimum equations will be different and the Goldstone bosons may be absent.…”

“…Note there must be an error in Eq. 2.4 of Ref [123]. because there is a non-zero contribution to the H † Φ 2 H term from Higgs loops even when β = 0.…”