There is no 690 GeV resonance

Once again, a long standing, but sub-five sigma "bump" in particle accelerator results turns out to be explained by better analysis of what the background expectation without the new predicted particle should look like, and not "new physics". The low significance bump is also suspiciously close to four times the top quark mass at that energy scale.

I full expect the search for the X17 boson to end the same way.

Sadly, these pet ideas are zombies that persist in preprints, experimental efforts, and published papers long after they should have been abandoned.

In a series of ∼30 papers starting in 1991, it has been claimed that the Higgs field should be heavier than its now-measured value. To reconcile this idea with reality, it was modified to the assertion that the Higgs field describes two physical degrees of freedom, one of which corresponds to a second Higgs particle with mass 690 GeV. Here I summarize the lack of theoretical and experimental evidence for these claims.

James M. Cline, "There is no 690 GeV resonance" arXiv:2509.20115 (September 24, 2025). 

The paper is only three pages, half of which contains 33 references and the first page's heading and abstract, so I'll take the liberty of reproducing the entire short and punchy paper here:

Recently Ref. [1] reiterated the claim, already made in Refs. [2–14], that the Higgs field has an excited state with mass 690 GeV. This appears to be a modification of an earlier idea [15–28], pursued by one of the same authors, that the Higgs mass could or should be above the perturbative unitarity limit ∼ 700 GeV, as heavy as 2 TeV, depending upon the year of publication. The theoretical motivation for this prediction was the claim [29, 30] that λϕ^4 is not trivial, as is usually believed, but rather has a radiatively generated spontaneous symmetric phase (as predicted by the Coleman-Weinberg one-loop potential), in which it is asymptotically free.1 

1 The triviality of ϕ^4 theory, long believed to be the case, was proven in Ref. [31].

It was also claimed that the vacuum expectation value (VEV) of the scalar field gets renormalized by a different factor Z(v) than the fluctuations around the VEV, Z(ϕ), so that the usual relation between the Higgs mass and the VEV is modified by a factor Z(ϕ)/Z(v) which must be determined by lattice simulations, and predicts m(h) = 760 ± 20 GeV [17]. 

With the experimental discovery of the Higgs with mass m(h) = 125GeV, one might have hoped for such claims to be put to rest, but a way to have one’s cake and eat it too was found. It somehow goes back to the aforementioned idea, that pure λϕ^4 theory has spontaneous symmetry breaking `a la Coleman-Weinberg, despite the usual reservations that the perturbative calculation leading to that result cannot be trusted. The authors argue that now there are two mass scales in the potential: one is m(h)^2, the curvature of the potential V at its minimum, and the other is M(H)^4 = ∆V, from the depth of the potential minimum, which was generated by radiative symmetry breaking. It is not clear why this extra scale should correspond to an additional propagating degree of freedom. 

In order for a single field to describe two degrees of freedom, the propagator must have two poles, which usually arises from a higher derivative action containing ghosts. In the present case, the authors claim that nonperturbative effects generate the propagator structure 

G= i/(p^2 − M(H)^2*A(p^2)) (1) 

where A is a function such that A(m(h)^2) = m(h)^2/M(H)^2 and A(M(H)^2) = 1. The detailed form of A(p) is not disclosed, so we are forced to guess.2 

2 Ref. [1] says that this behavior was verified on the lattice in Ref. [13], but that reference purports to show that the form of the inverse propagator is (p^2 − m(h)^2)f(p), where f(p) has the same properties as A(p) in Eq. (1). This is puzzling since f(p) corresponds to wave function renormalization, while A(p) is the self-energy. 

It cannot be linear in p^2 since that would give G = i/0; hence the next simplest analytic possibility is quartic, A = 1 + (p^4/M(H)^4)(M(H)^2/m(h)^2 − 1). With this choice, we find for m(h) ≪ M(H)

G ∼ = −iM(H)^2/((p^2 − M(H)^2)(p^2 − m(h)^2)),  (2) 

which has the wrong sign for the heavy degree of freedom. The heavy particle is a ghost, as expected from a theory with a higher-derivative Lagrangian. The theoretical motivations for the “resonance” (unaptly named, since it is supposed to be coming from an elementary Higgs field, not a composite particle) are problematic. 

Let us turn then to the experimental evidence, which the LHC collaborations must have been very excited to discover. In Ref. [12] the authors discerned a bump in the ATLAS search [32] for heavy resonances decaying to ZZ → 4ℓ at m(H) ∼700GeV. The authors note that H should be dominantly produced through the gluon-gluon fusion (ggF) process, with negligible production from vector boson fusion (VBF). Fig. 1 reproduces the main results from the two papers. The ATLAS ggF limit has a 2-σ excess at 662GeV, which receives no comment in the ATLAS paper, and only upper limits are quoted.

The CMS collaboration took note of Ref. [12]’s prediction of an excess in this channel in their later search [33]. They also reported no significant excess. 

Since the original suggestion [12], there have been an additional ten papers [1–10] by various combinations of the authors emphasizing the predicted excess, lest we should forget. None of them are referred to by the experimental collaborations. In fact, of the 44 citations to these papers, all but 11 are self-cites. The authors find an equally convincing bump in the H → hh channel, leading them to “spell out a definite experimental signature of this resonance that is clearly visible in various LHC data.” A Nobel prize is sure to follow.