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Indications for new scalar resonances at the LHC and a possible interpretation

Anirban Kundu, Poulami Mondal, Gilbert Moultaka

TL;DR

The paper addresses the puzzle of multiple mild scalar hints at the LHC, notably near $95$ GeV and $650$ GeV, by proposing a minimal extension of the scalar sector—the 2-Higgs Doublet extended Georgi–Machacek (2HDeGM) model. It demonstrates that simple singlet/doublet theories cannot accommodate the combined signals and derives stringent unitarity (sum-rule) and custodial-symmetry constraints that shape viable parameter space. By fixing the lightest SM-like Higgs couplings and using experimental inputs for the additional scalars, the authors show that a Type-I Yukawa structure with a sizable triplet VEV $u$ can reconcile the data, predict correlated couplings for $H_{650}$ and other states, and yield testable predictions for charged and CP-odd scalars. The work emphasizes that, even with limited data, the hints impose strong, falsifiable constraints on a multi-multiplet scalar framework, guiding future collider searches toward specific decay channels and mass hierarchies. Overall, the study offers a concrete, testable path to interpret multiple resonance indications within a near-minimal extension of the SM and highlights the critical experimental channels to confirm or refute the scenario.

Abstract

Over the last few years, the CMS and ATLAS collaborations at the Large Hadron Collider (LHC) have reported excesses that could hint at several new scalar resonances. Although none of them has touched the discovery level, at least two of them, at about 95 GeV and 650 GeV, have been indicated by more than one experiments, and have reached statistical significance worthy of a serious investigation. Conservatively using only the numbers given by the experimental collaborations, we find combined global significances around 3$σ$ and 4$σ$ respectively for the 95~GeV and 650~GeV putative resonances. There are some more, like the one at 320 GeV, which have also been hinted at. We show that the data on only the 650 GeV resonance, assuming they stand the test of time, predict the existence of a doubly-charged scalar, and make the more common extensions of the scalar sector like those by gauge singlet scalars, the 2-Higgs doublet models or the Georgi-Machacek model, highly disfavored. We provide the readers with a minimalistic model that may possibly explain all the indications. Such a model can also accommodate the hints of a singly charged scalar at about 375 GeV, and a doubly charged scalar at about 450 GeV, as found by both the major LHC Collaborations, the combined global significance for each of them being above $2.5σ$. We show that even the scant data, with large error bars, have the potential to strongly constrain our model containing four scalar multiplets, which makes the model easily testable and falsifiable. Our analysis comes with the obvious caveat that the allowed parameter space that we find depends on the available data on all the new resonances, and may change in future. One may also note that this is an exploratory exercise that illustrates the difficulties when it comes to fitting several resonances simultaneously, even for next-to-minimal extensions of the SM.

Indications for new scalar resonances at the LHC and a possible interpretation

TL;DR

The paper addresses the puzzle of multiple mild scalar hints at the LHC, notably near GeV and GeV, by proposing a minimal extension of the scalar sector—the 2-Higgs Doublet extended Georgi–Machacek (2HDeGM) model. It demonstrates that simple singlet/doublet theories cannot accommodate the combined signals and derives stringent unitarity (sum-rule) and custodial-symmetry constraints that shape viable parameter space. By fixing the lightest SM-like Higgs couplings and using experimental inputs for the additional scalars, the authors show that a Type-I Yukawa structure with a sizable triplet VEV can reconcile the data, predict correlated couplings for and other states, and yield testable predictions for charged and CP-odd scalars. The work emphasizes that, even with limited data, the hints impose strong, falsifiable constraints on a multi-multiplet scalar framework, guiding future collider searches toward specific decay channels and mass hierarchies. Overall, the study offers a concrete, testable path to interpret multiple resonance indications within a near-minimal extension of the SM and highlights the critical experimental channels to confirm or refute the scenario.

Abstract

Over the last few years, the CMS and ATLAS collaborations at the Large Hadron Collider (LHC) have reported excesses that could hint at several new scalar resonances. Although none of them has touched the discovery level, at least two of them, at about 95 GeV and 650 GeV, have been indicated by more than one experiments, and have reached statistical significance worthy of a serious investigation. Conservatively using only the numbers given by the experimental collaborations, we find combined global significances around 3 and 4 respectively for the 95~GeV and 650~GeV putative resonances. There are some more, like the one at 320 GeV, which have also been hinted at. We show that the data on only the 650 GeV resonance, assuming they stand the test of time, predict the existence of a doubly-charged scalar, and make the more common extensions of the scalar sector like those by gauge singlet scalars, the 2-Higgs doublet models or the Georgi-Machacek model, highly disfavored. We provide the readers with a minimalistic model that may possibly explain all the indications. Such a model can also accommodate the hints of a singly charged scalar at about 375 GeV, and a doubly charged scalar at about 450 GeV, as found by both the major LHC Collaborations, the combined global significance for each of them being above . We show that even the scant data, with large error bars, have the potential to strongly constrain our model containing four scalar multiplets, which makes the model easily testable and falsifiable. Our analysis comes with the obvious caveat that the allowed parameter space that we find depends on the available data on all the new resonances, and may change in future. One may also note that this is an exploratory exercise that illustrates the difficulties when it comes to fitting several resonances simultaneously, even for next-to-minimal extensions of the SM.

Paper Structure

This paper contains 29 sections, 62 equations, 4 figures, 6 tables.

Table of Contents

  1. Introduction
  2. The Indications and Consequences
  3. $h_{95}$
  4. $H_{650}$
  5. $A_{400}$, and $H_{320}$
  6. $h_{151}$, or $A_{151}$
  7. On sum rules
  8. Inadequacy of Higgs doublets, and the canonical Georgi-Machacek model
  9. The 2-Higgs Doublet extended Georgi-Machacek model
  10. Convention
  11. Input strategy
  12. Possible solutions and implications
  13. Type-II Yukawa
  14. Type-X and Type-Y Yukawa
  15. Type-I Yukawa
  16. ...and 14 more sections

Figures (4)

  • Figure 1: $\kappa_t^{h_{95}}$ versus $\kappa_W^{h_{95}}$. The light (dark) green regions correspond to the 2(1)$\sigma$ constraints \ref{['eq:h95gamgam', 'eq:h95tautau']}. Fixing $\kappa_t^{h_{125}}=\kappa_b^{h_{125}}=.99,\kappa_Z^{h_{125}}=1.04,\kappa_W^{h_{125}}=1.02$, the red regions correspond to requiring no complex-valued couplings or mixings, and varying the $H_{320}$ reduced couplings to W and Z in the range $-.45\leq\kappa_W^{H_{320}}, \kappa_Z^{H_{320}} \leq +.45$; the blue regions correspond to overlaying the constraint given by \ref{['eq:h95LEP']} taken at the 2$\sigma$ level: (a) $\kappa_W^{H_{650}} =.89$, $u\simeq 78~{\rm GeV}, v_1 \simeq 16~{\rm GeV}, v_2 \simeq 76~{\rm GeV}$; (b) $\kappa_W^{H_{650}} =.91$, $u\simeq 78~{\rm GeV}, v_1 \simeq 16~{\rm GeV}, v_2 \simeq 76~{\rm GeV}$; (c) $\kappa_W^{H_{650}} =.97$, $u\simeq 78~{\rm GeV}, v_1 \simeq 16~{\rm GeV}, v_2 \simeq 76~{\rm GeV}$; (d) $\kappa_W^{H_{650}} =1.$, $u\simeq 69~{\rm GeV}, v_1 \simeq 14~{\rm GeV}, v_2 \simeq 104~{\rm GeV}$.
  • Figure 2: Parameters and constraints taken from \ref{['fig:ktkW-NEW']}, showing all $\kappa^{H_{650}}$ against $\kappa_t^{H_{650}}$. Figures (a1), (a2), (b1), (b2) correspond to \ref{['fig:ktkW-NEW']} (a): $\kappa_W^{H_{650}} =.89$, $u\simeq 78~{\rm GeV}, v_1 \simeq 16~{\rm GeV}, v_2 \simeq 76~{\rm GeV}$, with (a1), (a2): $c=.82$, (b1), (b2): $c=.75$. Figures (c1), (c2), (d1) ,(d2) correspond to \ref{['fig:ktkW-NEW']} (b): $\kappa_W^{H_{650}} =.91$, $u\simeq 78~{\rm GeV}, v_1 \simeq 16~{\rm GeV}, v_2 \simeq 76~{\rm GeV}$, with (c1), (c2): $c=.85$, (d1), (d2): $c=.78$. In figures (a1), (b1), (c1), (d1) all constraints are imposed except for LEPh95, \ref{['eq:h95LEP']}. Figures (a2), (b2), (c2), (d2) correspond to overlaying the constraint given by LEPh95, \ref{['eq:h95LEP']}, taken at the 2$\sigma$ level. The black circles highlight the location of points that are also consistent with the CMS indication for $H_{650}$, CMS:2022bcb. The corresponding full solutions are given in \ref{['tab:kW650-.91']} for the cases of figures (c1) and (d2).
  • Figure 3: Similar to \ref{['fig:ktkW650']}: parameters and constraints taken from \ref{['fig:ktkW-NEW']}. Figure (a) corresponds to \ref{['fig:ktkW-NEW']} (c): $\kappa_W^{H_{650}} =.97$, $u\simeq 78~{\rm GeV}, v_1 \simeq 16~{\rm GeV}, v_2 \simeq 76~{\rm GeV}$. Figure (b) corresponds to \ref{['fig:ktkW-NEW']} (d): $\kappa_W^{H_{650}} =1.$, $u\simeq 69~{\rm GeV}, v_1 \simeq 14~{\rm GeV}, v_2 \simeq 104~{\rm GeV}$. For both cases $c=1$. The black circles highlight the location of points that are also consistent with the CMS indication for $H_{650}$, CMS:2022bcb. None of these solutions satisfies LEPh95.
  • Figure 4: Figures (a) and (b) show the effect of $H_{650} \to h_{1} h_{2}$ decay: (a) taking $\Gamma_{H_{650} \to h_{1} h_{2}} \simeq 7.7$ GeV illustrates the modification to the solutions given in \ref{['fig:ktkW650']}(b1), where $\kappa_W^{H_{650}} =0.89$, $u\simeq 78~{\rm GeV}, v_1 \simeq 16~{\rm GeV}, v_2 \simeq 76~{\rm GeV}$ and $c=0.75$ ; (b) taking $\Gamma_{H_{650} \to h_{1} h_{2}} \simeq 3.5$ GeV, illustrates the modification to the solution given in \ref{['fig:ktkW650bis']}(b), where $\kappa_W^{H_{650}} =1.0$, $u\simeq 69~{\rm GeV}, v_1 \simeq 14~{\rm GeV}, v_2 \simeq 104~{\rm GeV}$ and $c=1$. Figure (c) illustrates the combined effect of relaxing the constraint $|\kappa_W^{H_{320}}|, |\kappa_Z^{H_{320}}| \lesssim 0.45$, cf. \ref{['tab:inputs']}, with the remaining input as in (b), and $H_{650} \to h_{1} h_{2}$ decays: $\Gamma_{H_{650} \to h_{1} h_{2}} \simeq 5$ GeV, (resp. $\simeq 3.5$ GeV), corresponds to the smaller (resp. larger) black-dotted ellipse. The two black blobs indicate the solutions given in \ref{['tab:finalpoint']}. See also the main text for further discussions.