Reply to "There is no 690 GeV resonance"

Abstract

A recent paper has criticised the idea that, beside the resonance of mass $m_h=125$ GeV, the Higgs field might exhibit a relatively narrow, second resonance with a mass $M_H\sim 690$ GeV. Without considering the evidence we have provided, the criticism also concerned our claim that experimental signals for this new resonance might already be seen in some LHC data. Since our extensive work is covered by several papers, we will summarise here the whole issue, namely: i) the theoretical motivations for a two-mass structure in cutoff ${\Phi }^4$ theory; ii) the checks from lattice simulations and the prediction $(M_H{)}^{\mathrm{Theor}}=690(30)$ GeV; iii) the present experimental indications of a new, relatively narrow resonance in the expected mass range. This compact presentation will thus give the elements to objectively judge on a relevant question of present-day particle physics.

Comments: Plain LaTeX, Reply to arXiv:2509.20115v1 [hep-ph]; v2: Addendum replying to new arXiv:2509.20115v2 [hep-ph] added; v3: significantly expanded and much more detailed rebuttal of Cline's criticisms, now published in Nucl. Phys. B 1029 (2026) 117526, also submitted to Nuclear Physics B