A new 700 GeV scalar in the LHC data?

As an alternative to the metastability of the electroweak vacuum, resulting from perturbative calculations, one can consider a non-perturbative effective potential which, as at the beginning of the Standard Model, is restricted to the pure $\Phi^4$ sector yet consistent with the known analytical and numerical studies. In this approach, where the electroweak vacuum is now the lowest-energy state, besides the resonance of mass $m_h=$ 125 GeV defined by the quadratic shape of the potential at its minimum, the Higgs field should exhibit a second resonance with mass $(M_H)^{\rm Theor}=690\,(30)$ GeV associated with the zero-point energy determining the potential depth. In spite of its large mass, this resonance would couple to longitudinal $W$s with the same typical strength as the low-mass state at 125 GeV and represent a relatively narrow resonance, mainly produced at LHC by gluon-gluon fusion. In this Letter, we review LHC data suggesting a new resonance of mass $(M_H)^{\rm EXP} \sim 682\,(10)$ GeV, with a statistical significance that is far from negligible.


INTRODUCTION
The discovery [1,2] of a narrow scalar resonance with mass m h = 125 GeV and the phenomenological consistency with the expectations for the Higgs boson have confirmed spontaneous symmetry breaking (SSB) through the Higgs field as a fundamental ingredient of current particle physics.Yet, in our opinion, the present perturbative description of symmetry breaking is not entirely satisfactory.Indeed, once we start to look farther than the Fermi scale, such a calculation predicts that the effective potential of the Standard Model (SM) should have a new minimum, well beyond the Planck scale and being much deeper than the electroweak (EW) vacuum; see e.g.[3,4].While it is reassuring that the most accurate calculation [5] gives a tunnelling time that is larger than the age of the universe, still the idea of a metastable vacuum raises several questions: the role of gravitational effects, the mechanism explaining why the theory remains trapped in our EW vacuum, . . . .This would require a cosmological perspective and to control the properties of matter in the extreme conditions of the early universe.
As an alternative, one can consider [6,7,8,9] a non-perturbative effective potential which, as at the beginning of the SM, is restricted to the pure Φ 4 sector but is also consistent with the known analytical and numerical studies.In this approach, where the EW vacuum is now the lowest-energy state, besides the resonance of mass m h = 125 GeV defined by the quadratic shape of the potential at its minimum, the Higgs field should exhibit a second resonance with a mass (M H ) Theor = 690 (30) GeV, associated with the zero-point energy (ZPE) determining the potential depth.This large M H stabilises the potential, because including the ZPEs of all known gauge and fermion fields would now represent just a small radiative correction. 1 Like in the early days of the SM, one could thus adopt the perspective of explaining SSB within the pure scalar sector.Checking this picture then requires to observe the second resonance and its phenomenology. 1 By subtracting quadratic divergences or using dimensional regularisation, the logarithmically divergent terms in the ZPEs of the various fields are proportional to the fourth power of the mass.Thus, in units of the pure scalar term, one finds (6M In this respect, the hypothetical H is not like a regular Higgs boson of 700 GeV, because it would couple to longitudinal Ws with the same typical strength as the low-mass state at 125 GeV [6,7,8,9].In fact, it is m h = 125 GeV (and not M H ∼ 700 GeV) which fixes the quadratic shape of the potential and the interaction with the Goldstone bosons.Thus, the large conventional widths H would be suppressed by the small ratio (m h /M H ) 2 ∼ 0.032, leading to the estimates Γ(H → ZZ) ∼ M H /(700 GeV) × (1.6 GeV) and Γ(H → WW) ∼ M H /(700 GeV) × (3.3 GeV).As such, the heavy H should be a relatively narrow resonance of total width Γ(H → all) = 25 ÷ 35 GeV, decaying predominantly to t t quark pairs, with a branching ratio of about 70÷80 %.Due to its small coupling to longitudinal Ws, H production through vector-boson fusion (VBF) would also be negligible as compared to gluon-gluon fusion (ggF), which has a typical cross section σ ggF (pp → H) ∼ 1100 (170) fb [14, 15], depending on the QCD and H-mass uncertainties.
After this brief review, in this Letter we will present LHC data suggesting a new resonance in the expected mass and width range, with a non-negligible statistical significance.Partial evidence was already presented in Refs.[10,11,12,13], but in Sec. 2 we will consider a larger data set and also refine the analysis of some final states.Finally, Sec. 3 will contain a summary and our conclusions.

EXPERIMENTAL SIGNALS FROM LHC
Having a definite prediction (M H ) Theor = 690 (30) GeV, we will look for signals in the expected region of invariant mass 600÷800 GeV, so that local deviations from the background should not be downgraded by the"look elsewhere" effect.In this search, one should also keep in mind that, with the present energy and luminosity of LHC, the second resonance is too heavy to be seen unambiguously in all possible channels.(Recall the h(125) discovery, which initially was producing no signals in the important b b and τ + τ − channels).Now, with an expected large branching ratio B(H → t t) = (70 ÷ 80) %, the natural starting point would be the t t channel.However, in the relevant region m(t t) = 620 ÷ 820 GeV, CMS measurements [16] give a background cross section σ(pp → t t) = 107 ± 7.6 pb, which is about 100 times larger than the expected signal σ(pp → H → t t) ≲ 1 pb.Therefore, in Refs.[10,11,12,13] ii) ATLAS high-mass inclusive γγ events; iii) ATLAS and CMS (b b + γγ) events; iv) CMS γγ pairs produced in pp diffractive scattering.

The ATLAS ggF-like 4-lepton events
To start with, we will review ATLAS work [17,18] dedicated to the charged 4-lepton channel and to the search for a heavy scalar resonance H decaying through the chain H → ZZ → 4l.This is important because, for this particular channel, there is a precise prediction characteristic of our picture.Indeed, for a relatively narrow resonance, the resonant peak cross section σ R (pp → H → 4l) can be well approximated as with 4B2 (Z → l + l − ) ∼ 0.0045.Thus, in our case, where to be compared with the ATLAS data.
In the ATLAS search, the 4-lepton events were divided into ggFlike and VBF-like events.By expecting our second resonance to be produced through gluon-gluon fusion, we have considered the ggFlike category.The only sample that satisfies the two requirements, viz.a) being homogeneous from the point of view of the selection and b) having sufficient statistics, is the so called ggF-low category, which contains a mixture of all three final states.Since for an invariant mass around 700 GeV, the energy resolution of these events varies considerably, 2 it is natural to adopt a large-bin visualisation to avoid spurious fluctuations between adjacent bins.The numbers of events are reported in Table 1 [17,18].Now, subtracting the background from the observed events gives a considerable excess, at about 680 GeV, and then a sizable defect, around 740 GeV.A simple explanation for these two simultaneous features would be the existence of a resonance of mass M H ∼ 700 GeV which, above the Breit-Wigner peak, produces the characteristic negative-interference pattern proportional to (M 2 H − s).To check this idea, we have exploited the basic model where the ZZ pairs, each subsequently decaying into a charged l + l − pair, are produced by various mechanisms at the parton level.For E ≡ m(4l), this produces a smooth distribution of background events N b (E), proportional to a background cross section σ b (E), which can interfere with a resonance of mass M H and total decay width Γ H .The total cross section σ T (E) can then be expressed as [8] σ where we have introduced the resonant peak cross section σ R at s = M 2 H .Then, by simple redefinitions, the theoretical number of events can be expressed as where denotes the extra events at the resonance peak for an acceptance A. The data in Table 1 were fitted with Eq. ( 4) in [12,13].
The quality of the fit is good, but error bars are large and a test of our picture is not very stringent.Still, with our Γ(H → ZZ) ∼   2.
After this first comparison from Refs.[12,13], we will now consider the other ATLAS paper Ref. [19,20] for the differential 4lepton cross section dσ/dE, with E = m(4l).From Fig. 5 of this other Ref. [19], one finds the same excess-defect sequence as in Table 1 and additional support for a new resonance.The corresponding data are given in Table 2 and in Fig. 2. Besides, by comparing with Ref. [19,20], we can sharpen our analysis.In fact, the ggF-low events considered above contain a large contribution from q q → 4l processes.Although the initial state is pp in all cases, our H resonance would mainly be produced through gluon-gluon fusion, so that, strictly speaking, the interference should only be computed with the non-resonant gg → 4l background.Obtaining this refinement is now possible, because, in Ref. [19,20], the individual contributions to the background are reported separately.Denoting by σ gg B the pure nonresonant gg → 4l background cross section, we can thus consider a corresponding experimental cross section σEXP after subtracting out preliminarily the "non-ggF' background: The corresponding values and background are given in Table 3.
We then compare the resulting experimental σEXP with the theoretical σ T in Eq. ( 3  GeV, and σ R = 0.40 +0.62 −0.34 fb.The comparison for the optimal parameters is shown in Table 4. The quality of our fit is good, but error bars are large.Yet, by restricting again to the central values, there is good agreement with our expectations.Indeed, by rescaling the partial width from Γ(H → ZZ) ∼ 1.6 GeV to 1.55 GeV (for M H from 700 to 677 GeV), and fixing ⟨Γ H ⟩ = 21 GeV, we find a branching ratio B(H → ZZ) ∼ 0.073.For the theoretical value σ ggF (pp → H) ∼ 1100 fb of Ref. [15] (at M H = 677 GeV), this would then imply a theoretical peak cross section (σ R ) Theor = 1100 × 0.073 × 0.0045 ∼ 0.36 fb, which only differs by 10% from the central value ⟨σ R ⟩ = 0.40 fb of our fit.Moreover, from the central values of the fit ⟨σ R ⟩ = 0.40 fb and ⟨γ H ⟩ = 0.031, we find ⟨σ R ⟩ × ⟨γ H ⟩ ∼ 0.012 fb, again in good agreement with our Eq.( 2).
Summarising: from the two ATLAS papers Refs.[17] and [19], we find consistent indications of a new resonance in our theoretical mass range (M H ) Theor ∼ 690 (30) GeV.By comparing with Ref. [19], we identify more precisely the non-resonant background gg → 4l, which can interfere with a second resonance H produced via gluon-gluon fusion.Thus, the determinations obtained with our Eq.( 3) are more accurate, from a theoretical point of view.In practice, there is not too much difference with the previous Refs.[12,13] based on the ggF-low events of [17].Indeed, the two mass values (M H ) EXP = 677 +30 −14 GeV vs. (M H ) EXP = 706(25) GeV and the two decay widths Γ H = 21 +28 −16 GeV vs. Γ H = 29 ± 20 GeV are well consistent within their uncertainties.Most notably, our crucial correlation Eq. ( 2) is well reproduced by the central values of the fits to the two sets of data.3) and σ R = 0 to the ATLAS data [21] shown in  The ATLAS number N = N(γγ) of events, in bins of 16 GeV and for luminosity 139 fb −1 , for the range of invariant mass µ = µ(γγ) = 600 ÷ 770 GeV.These values were extracted from Fig. 3 of Ref. [21], because the relevant numbers are not reported in the companion HEPData file.

The ATLAS high-mass γγ events
References [12,13] also considered the invariant-mass distribution of the inclusive diphoton events observed by ATLAS [21]; see Table 5.By parametrising the background with a power-law form σ B (E) ∼ A × (685 GeV/E) ν , a fit to the data in Table 5 gives a good description of all data points, except for a sizable excess at 684 GeV (estimated by ATLAS to have a local significance of more than 3σ); see Fig. 3.This isolated discrepancy shows how a (hypothetical) new resonance might remain hidden behind a large background nearly everywhere.For this reason, apart from the mass M H = 696 (12) GeV, the total decay width is determined very poorly, namely Γ H = 15 +18 −13 GeV, but still consistent with the other loose determinations from the 4-lepton data.In Fig. 4 we show three fits with the full Eq.( 3), for Γ H = 15, 25, and 35 GeV.quark pair and a γγ pair.In particular, in Ref.
[22] one considered the cross section for the full process For a spin-zero resonance, the 95% upper limit σ(full) < 0.16 fb, for an invariant mass of 600 GeV, was found to increase by about a factor two, up to σ(full) < 0.30 fb in a plateau 650 ÷ 700 GeV, and then to decrease for larger energies; see Fig. 5.The local statistical significance is modest, about 1.6σ, but the relevant mass region M X ∼ 675 (25) GeV is precise and agrees well with our prediction.
The analogous ATLAS plot is depicted in Fig. 6 (which is the same   as Fig. 15 of the ATLAS paper Ref. [23]).Again, one finds a modest 1.2σ excess at 650 (25) GeV immediately followed by a 1.4σ defect, which could indicate a negative above-peak (M 2 H − s) interference effect as found in the ATLAS 4-lepton data.

CMS-TOTEM γγ events produced in pp diffractive scattering
The CMS and TOTEM Collaborations have also been searching for high-mass photon pairs produced in pp diffractive scattering, i.e. when both final protons are tagged and have large x F .For our scope, the relevant information is contained in Fig. 7, taken from Ref. [24].
In the range of invariant mass 650 (40) GeV and for a statistics of 102.7 fb −1 , the observed number of γγ events is N EXP ∼ 76 (9), to be compared with an estimated background N B ∼ 40 (9).In the most conservative case, viz.N B = 49, this is a local 3σ effect and is the only statistically significant excess in the plot.

SUMMARY AND CONCLUSIONS
Let us summarise our review of LHC data: i) The ATLAS ggF-like four-lepton events [17] reported in Table 1 show a definite excess-defect sequence, suggesting the existence of a new resonance.The same pattern is also visible in the AT-LAS cross section [19]; see Table 2 and the ∆σ in Fig. 2. The combined statistical deviation in the latter analysis is at the 3σ level and indicates a resonance mass M H = 677 +30 −14 GeV.
iii) An overall +2σ effect in the (b b + γγ) channel is obtained by combining the excess of events observed by ATLAS at 650 (25) GeV and the corresponding excess observed by CMS at 675 (25) GeV.iv) A +3σ excess is present at 650 (40) GeV in the distribution of CMS-TOTEM γγ events produced in pp diffractive scattering.By combining the above determinations i)-iv), the resulting estimate (M H ) EXP ∼ 682 (10) GeV, is in very good agreement with our expectation (M H ) Theor = 690 (30) GeV.We stress again that, when comparing with a definite prediction, one should look for deviations from the background nearby, so that local significance is not downgraded by the so called "look elsewhere" effect.Therefore, since the correlation of the above measurements is small, the combined statistical evidence for a new resonance in the expected mass range is far from negligible and close to (if not above) the traditional 5σ level.We also emphasise that the determinations i) and ii) above were obtained by fitting the numerical data reported in Refs.[17,19,21] to the general expressions Eqs. ( 3) and ( 4).This is very different from comparing with other Beyond-Standard-Model scenarios (such as supersymmetry, extra-dimensions, . . .), whose exclusion limits assume built-in constraints (such as mass-width and/or mass-couplings relations) that are not valid in our approach.For this reason, we look forward to new precise data on which we can carry out the same general analysis as with the ATLAS papers [17,19,21].

FIGURE 2 :
FIGURE 2:The quantity ∆σ = (σ EXP − σ B ) given for each bin in the last column of Table2.

FIGURE 3 :
FIGURE 3:The fit with Eq. (3) and σ R = 0 to the ATLAS data[21] shown in Table5, transformed into cross sections in fb.The χ 2 value is 14, with the background parameters A = 1.35 fb and ν = 4.87.

2. 3 .
ATLAS and CMS (b b + γγ) events The ATLAS and CMS Collaborations have also searched for new resonances decaying, through two intermediate h(125) scalars, into a b b

FIGURE 6 :
FIGURE 6: Expected and observed 95% upper limit for the cross section σ(pp → X → h(125)h(125)) extracted by the ATLAS Collaboration from the final state (b b + γγ).The figure is taken from the talk given by Bill Balunas at Higgs-2022 and is the same as Fig. 15 of the ATLAS paper Ref. [23].

TABLE 4 :
Comparing the experimental cross section in Table3with the theoretical Eq. (3) for the optimal set of parameters M H = 677 GeV, Γ H = 21 GeV, σ R = 0.40 fb.

Table 5 ,
transformed into cross sections in fb.The χ 2 value is 14, with the background parameters A = 1.35 fb and ν = 4.87.