Light scalars within the $\mathcal{CP}$-conserving Aligned-two-Higgs-doublet model

Anirban Karan; Antonio M. Coutinho; Antonio Pich; V\'ictor Miralles

REVIEW 3 major objections 5 minor 3 cited by

Light scalars within the $\mathcal{CP}$-conserving Aligned-two-Higgs-doublet model

T0 review · 3 major / 5 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read The CP-conserving aligned two-Higgs-doublet model can still hide neutral scalars between 60 and 125 GeV and a charged scalar between 95 and 125 GeV, with all seven light-mass patterns surviving global fits to current data.

desk verdict First global low-mass A2HDM fit, useful and mostly sound, but the flavour set omits RD/RD* and the direct-search likelihood is ad hoc, so the size of the claimed allowed regions should be treated with caution. read the letter →

arxiv 2412.14906 v2 pith:74F4MQHT submitted 2024-12-19 hep-ph

Antonio M. Coutinho , Anirban Karan , Víctor Miralles , Antonio Pich This is my paper · ORCID

classification hep-ph

keywords alignedtwo-Higgs-doubletmodellightscalarschargedHiggsbosonglobalBayesianfitLEPandLHCsearchesYukawaalignmentflavourconstraintsmuong-2

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper asks whether the LHC could have missed additional scalars lighter than the 125 GeV Higgs boson, and answers that within the CP-conserving aligned two-Higgs-doublet model (A2HDM), a Standard Model extension with a second scalar doublet whose Yukawa couplings are aligned with fermion masses, they are not excluded. Depending on which of the three new scalars is light, there are seven distinct scenarios; the authors subject each to global Bayesian fits that combine vacuum stability, perturbativity, electroweak precision data, flavour observables, Higgs rates, and direct LEP and LHC searches. In every scenario the posteriors of all observables agree with measurements within two standard deviations, and the fits' information criteria are similar, with the one-light-neutral cases performing slightly better. This matters because it maps which light-mass windows are still open: neutral scalars between roughly 60 and 125 GeV and a charged scalar between 95 and 125 GeV, with the charged scalar's leptonic coupling weakly constrained in the 95-120 GeV region.

What carries the argument

The load-bearing construction is the CP-conserving A2HDM parameter space with ten beyond-Standard-Model parameters: the three new scalar masses $M_H$, $M_A$, $M_{H^\pm}$, the CP-even mixing angle $\tilde\alpha$, three quartic couplings $\lambda_2,\lambda_3,\lambda_7$, and three Yukawa alignment parameters $\varsigma_u,\varsigma_d,\varsigma_l$. The argument is carried by a Bayesian global fit whose likelihood combines theoretical requirements, precision and flavour observables, Higgs signal strengths, and direct searches; experimental upper limits enter through the ratio $O_{\rm direct}=(\sigma\cdot B)_{\rm A2HDM}/(\sigma\cdot B)_{\rm exp}$ with a truncated normal distribution tuned so that $O_{\rm direct}=1$ is excluded at 95% probability. Two features make light scalars viable: the direct searches leave a gap for $M_{H^\pm}\in[95,120]$ GeV where the leptonic coupling is nearly unconstrained, and the oblique parameters force the charged-scalar mass to align with one of the neutral masses, which explains the mass correlations among the seven scenarios.

What would settle it

A dedicated LHC search for $H^\pm\to\tau^\pm\nu$ with $M_{H^\pm}$ between 95 and 120 GeV, with sensitivity to the $\sigma\cdot B$ values predicted by this paper's allowed regions, would either confirm or close the large-$\varsigma_l$ window; equally, an experiment that excludes $\sigma\cdot B$ below the A2HDM prediction across that entire window would falsify the claim that the light-charged-scalar scenarios remain viable.

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Extended reading notes

Core claim

On its own terms, the paper's central claim is that the CP-conserving A2HDM accommodates all seven possible arrangements of light new scalars alongside the 125 GeV Higgs. A global Bayesian fit yields posterior probabilities for every observable that are compatible with the measured values within two standard deviations, so each scenario retains sizeable allowed regions of parameter space. The fit pins the light neutral scalars above roughly 60 GeV, because below half the Higgs mass the decay $h\to\phi\phi$ is strongly constrained by LHC searches, and the light charged scalar above roughly 95 GeV, from LEP pair-production limits. In the 95-120 GeV window the direct-search constraints on the leptonic alignment parameter $\varsigma_l$ are essentially absent, allowing values as large as about 100, while flavour constraints force the quark alignment parameters to be small whenever the charged scalar is light. The paper also shows that using the 2020 white-paper value of $(g-2)_\mu$ degrades the fit substantially, while the newer lattice-based prediction leaves the fit unchanged.

Load-bearing premise

The entire fit's treatment of upper limits assumes that each experimental exclusion can be converted into a truncated Gaussian likelihood centred at zero, with the width chosen so that a prediction equal to the published limit is excluded at 95% probability; the detailed shape and size of every allowed region depends on this mapping.

Editorial extensions

If this is right

All seven light-scalar patterns of the CP-conserving A2HDM are experimentally open; none is excluded by current data at 95% probability.
Neutral scalars must sit above about 60 GeV, because below half the Higgs mass the $h\to\phi\phi$ searches cut the space; this gives a concrete 60-125 GeV window for future searches.
The charged scalar must be heavier than about 95 GeV, and in the 95-120 GeV slice its leptonic alignment parameter can be as large as roughly 100, so tauonic charged-Higgs searches in that slice have unique discovery power.
Whenever at least one new scalar is light, the heavier scalars are pushed below about 560 GeV, and if both neutral scalars are light the charged scalar stays below 226 GeV, setting explicit mass targets for collider searches.
A light-scalar explanation of the 2020 $(g-2)_\mu$ anomaly is strongly disfavoured, whereas the lattice-based prediction is fully consistent with the same fits.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If the 95-120 GeV window is where a charged scalar actually hides, the correlation between $M_{H^\pm}$ and $|\varsigma_l|$ predicted here discriminates the A2HDM from $Z_2$-symmetric two-Higgs-doublet models, where the leptonic coupling is tied to $\tan\beta$.
The near-equal information criteria across the seven scenarios suggest that current data cannot tell which scalar, if any, is light; a future measurement of the $h\to\gamma\gamma$ rate or of triple-Higgs couplings could break this degeneracy.
The reinterpreted slepton searches only start to bite above 115 GeV, so the 95-115 GeV region remains the least explored territory for a light charged Higgs in this model.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

The genuinely new thing here is the first global fit of the CP-conserving A2HDM with scalars lighter than 125 GeV. Seven mass scenarios are mapped separately, all with surviving regions, using a broad and current constraint set in HEPfit. The direct-search catalog is extensive, the slepton reinterpretation is done carefully (left-handed only, with branching-fraction caveats), and the separate treatment of (g−2)μ is sensible. For the 2HDM subfield this is a useful reference map.

The soft spots are real but not fatal. The Sec. 3.6 direct-search likelihood is a truncated normal tuned so that O_direct = 1 is excluded at 95% probability. That is an approximation, not the experimental likelihood, and it can deform the shape and size of allowed regions. Minor point: the configuration files are not deposited, only offered on request.

The bigger issue is the flavour list. The paper claims all flavour observables relevant for CP-conserving NP are included, but RD and RD* are absent. That is a concrete omission, not a modelling choice. Tree-level H± exchange contributes to b→cτν at a level that matters for a light charged scalar with ς_d ~ 1 and ς_l ~ 50–100, exactly the high-ς_l window the paper highlights as weakly constrained. Adding RD/RD* with current HFLAV averages would likely shrink those regions and could close part of the 95–120 GeV gap in ς_l. The core conclusion — that some parameter space survives in all seven scenarios — probably holds, since ς_l can be small, but the 'sizeable' and 'weakly constrained' claims need qualification.

Send this to a serious referee. The referee should ask for RD/RD* to be added, and for the direct-search likelihood to be justified or replaced. With those changes the paper would be a solid, citable result.

Referee Report

3 major / 5 minor

Summary. This paper presents a Bayesian global fit of the CP-conserving Aligned-two-Higgs-doublet model (A2HDM) in the regime where at least one of the additional scalars is lighter than the 125 GeV Higgs. Seven mass scenarios (one, two, or three light scalars) are fitted separately with HEPfit. The constraints include vacuum stability, perturbative unitarity and perturbativity of the cubic couplings, the S and T oblique parameters, a list of flavour observables, Higgs signal strengths, many LEP and LHC direct searches for neutral and charged scalars, and reinterpreted slepton searches. The central finding is that all seven scenarios contain sizeable regions compatible with current data at the 2σ level, with light neutral scalars bounded above 60 GeV and light charged scalars above 95 GeV, leaving a weakly constrained window around 95–120 GeV for the leptonic alignment parameter |ςl|. The implications of the muon anomalous magnetic moment are analysed separately using two different SM predictions.

Significance. If the main claim survives scrutiny, this is the first global analysis covering all light-scalar scenarios of the A2HDM and it provides a useful reference for future collider searches. The strengths of the paper are its use of the public HEPfit code with a specified commit, the broad and up-to-date set of direct search constraints, the transparent prior choices, the separate treatment of (g−2)μ, and the careful handling of slepton reinterpretation. The paper also gives a benchmark for how viable the low-mass A2HDM remains. The main concerns are the ad hoc likelihood used for direct upper limits and the omission of tree-level b→cτν observables, both of which bear directly on the highlighted high-|ςl| window.

major comments (3)

[Sec. 3.4, Eq. (2.12)] The flavour-observable list omits the tree-level semileptonic decays B→Dτν and B→D*τν (RD and RD*). The text in Sec. 3.4 states that all flavour observables relevant for CP-conserving NP are included, but b→cτν receives a tree-level charged-Higgs contribution proportional to (ςd mb or ςu mc) ςl mτ / M_H±^2. In the allowed high-|ςl| window reported in Sec. 5.1 and Fig. 5 (|ςl| up to about 100, M_H± between 95 and 120 GeV, with ςd not forced to be negligible), these contributions can be O(10%) or larger relative to the SM and are comparable to the current experimental precision of RD and RD*. The conclusion that ςl is only weakly constrained and that all scenarios contain sizeable allowed regions is therefore drawn from an incomplete dataset. I recommend adding RD, RD* (and, where relevant, Bc→τν) to the fit, or at least quantifying their impact on the high-|ςl| window.
[Sec. 3.6] The direct-search likelihood is constructed by assigning a truncated normal distribution to Odirect = (σ·B)_A2HDM/(σ·B)_exp, with the variance chosen so that Odirect = 1 is excluded at 95% probability. This is not the experimental likelihood, yet it is used for all direct bounds, including the 60 GeV neutral-scalar lower bound, the 95 GeV charged-scalar lower bound, and the restrictions on |ςl|. The derived mass limits and the shape of the high-|ςl| region are therefore contingent on this modelling choice. I recommend a robustness check with an alternative treatment (for example, a hard 95% CL cutoff with theory uncertainty, or a likelihood based on observed event counts or published p-values) to confirm that the seven scenarios remain compatible and that the 95–120 GeV |ςl| window is not an artifact of the chosen likelihood.
[Sec. 5, Abstract] The claim that the scenarios contain 'sizeable regions' of parameter space is not quantified. The paper reports posterior ranges, 95% probability plots, and IC values, but not the prior-to-posterior volume fraction or any other measure of the size of the allowed region. Since this claim is the headline result, I ask the authors to quantify it (for example, by giving posterior mass fractions, credible-region volumes, or a precise definition of 'sizeable') or to temper the wording so that the qualitative statement is not mistaken for a quantitative result.

minor comments (5)

[Sec. 5.1] The sentence 'the absolute maxima at a 68% probability: ᾱ ≲ 0.05 rad, ςu ≲ 0.1, ςu ≲ 1.7, and ςl ≲ 42' contains a typo: the second 'ςu ≲ 1.7' should be 'ςd ≲ 1.7'.
[Sec. 3.6] The truncated-normal prescription for Odirect is described only in words; a precise definition of the density and its variance would improve reproducibility.
[Sec. 3.4] The CKM inputs are said to follow the procedure of Ref. [100], but the actual numerical inputs are not given; please provide them or an explicit pointer to the relevant appendix in Ref. [100].
[Sec. 6] The phrase 'the A2HDM model is clearly not a great solution' is informal; consider 'the A2HDM does not provide a good solution' or similar.
[Appendix A] The ranges in the tables for heavy neutral scalars are labelled 'Range (TeV)', but many entries are below 1 TeV; please ensure the units are consistent throughout the tables.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the paper is a global fit whose constraints are external data; self-citations to Ref. [100] transfer independent inputs and are not load-bearing.

full rationale

The paper's central claim is that all seven light-scalar scenarios of the CP-conserving A2HDM have sizeable parameter-space regions compatible with current data, established through Bayesian MCMC global fits with HEPfit. This is a fit, not a derivation: the observables used as constraints (electroweak precision parameters, flavour observables, Higgs signal strengths, direct-search limits) come from experimental measurements, and the statement in Sec. 5 that 'all the posterior probabilities of the observables, for all the scenarios, were compatible with the measurements within two standard deviations' is a posterior consistency check, not a prediction of an observable from a formula that already contains that observable. The Sec. 3.6 construction of the direct-search likelihood via a truncated normal distribution on O_direct = (sigma*B)_A2HDM/(sigma*B)_exp with variance adjusted to exclude O_direct=1 at 95% is an ad hoc but explicit statistical mapping of experimental upper limits; it is a modelling choice that could affect the size and shape of allowed regions, but it does not make the fit circular. The self-citations to the authors' previous work [100] for the Rb-free oblique parameters and for the CKM-fit procedure are not load-bearing in a circular sense: those inputs were obtained from independent global fits with the public HEPfit code and are not defined in terms of the light-scalar parameters being fitted here. The (g-2)_mu section is a genuine stress test: adding the 2020 white-paper prediction degrades the fit substantially (IC ~ 129 vs ~ 88), showing the framework can fail against an external observable. The possible omission of b->c tau nu observables (R_D, R_D*) from the flavour list is a concrete completeness concern rather than a circularity: including them might shrink or close the high-|zeta_l| regions, but that would be a correction to the dataset, not a self-referential derivation. Overall, no step reduces to its own input, and no prediction is manufactured from fitted parameters.

Assumptions & free parameters 11 free parameters · 8 assumptions · 0 invented entities

The fits depend on ten BSM parameters (three masses, mixing angle, three quartic couplings, three alignment parameters) all fitted with flat priors, plus a hand-tuned direct-search likelihood variance. The theoretical constraints (vacuum stability, unitarity, perturbativity) and the model assumption of negligible RG-induced FCNCs are taken from prior literature. No new entities are introduced. The main non-standard methodological choice is the truncated-normal mapping of experimental upper limits into a likelihood.

free parameters (11)

MH = posterior 95% ranges in Table 2, e.g., 65-125 GeV for MH<Mh scenario, up to around 500 GeV in other scenarios
Mass of the heavy CP-even scalar; flat prior [10,125] or [125,700] GeV depending on scenario, fitted to all data.
MA = posterior 95% ranges in Table 2, e.g., 168-496 GeV in MH<Mh scenario, down to 69 GeV in MA<Mh scenario
Mass of the CP-odd scalar; flat prior [10,125] or [125,700] GeV depending on scenario, fitted to all data.
MH+ = posterior 95% ranges in Table 2, e.g., 196-500 GeV in MH<Mh scenario, 97-125 GeV in MH+<Mh scenario
Mass of the charged scalar; flat prior [10,125] or [125,700] GeV depending on scenario, fitted to all data.
alpha_tilde = mean (0.8 +/- 34.0) x 10^-3 rad in first scenario; varies across scenarios
Mixing angle between the two CP-even scalars; flat prior [-0.2, 0.2] rad; constrained mainly by Higgs signal strengths.
lambda_2 = 4.969 +/- 1.925 in first scenario
Quartic coupling; flat prior [-1, 10]; only weakly constrained by perturbative unitarity.
lambda_3 = 3.854 +/- 2.067 in first scenario
Quartic coupling; flat prior [-1, 10]; constrained by cubic neutral-charged scalar coupling and perturbativity.
lambda_7 = 0.005 +/- 0.382 in first scenario
Quartic coupling; flat prior [-3.5, 3.5]; constrained by the effective H H+ H- coupling at one loop.
zeta_u = 0.001 +/- 0.073 in first scenario
Up-type Yukawa alignment parameter; flat prior [-0.5, 0.5]; constrained by flavour observables and Higgs data.
zeta_d = 0.017 +/- 1.716 in first scenario
Down-type Yukawa alignment parameter; flat prior [-10, 10]; constrained by flavour and direct searches.
zeta_l = -0.325 +/- 20.100 in first scenario
Lepton Yukawa alignment parameter; flat prior [-100, 100]; loosely constrained, can be very large in the 95-120 GeV charged-scalar gap.
O_direct likelihood variance = tuned so that O_direct = 1 is excluded at 95% probability
Ad hoc normal-distribution likelihood for direct search bounds (Sec. 3.6); chosen by hand rather than derived from experimental likelihoods.

assumptions (8)

standard math Vacuum stability conditions from the Minkowskian bilinear formalism (eigenvalue conditions and the global-minimum determinant condition) are necessary and sufficient for the potential to be bounded from below and to have a stable neutral minimum.
Invoked in Sec. 3.1 to constrain the scalar potential parameters; if the conditions were incomplete, the posterior could include unstable vacua.
domain assumption Tree-level perturbative unitarity requires |e_i| <= 8 pi for eigenvalues of the scalar scattering matrices, and the one-loop correction to cubic couplings must satisfy Delta <= 0.5.
The 8 pi bound is standard; the Delta <= 0.5 criterion is suggested in Ref [55] and imposed in Sec. 3.2, and it restricts lambda_3 and lambda_7.
domain assumption Yukawa alignment with real zeta_f is assumed; radiative corrections induce only negligible FCNCs.
The A2HDM definition (Eq. 2.11) and the claim that RG-induced FCNCs remain below bounds (citing Refs [51-54,57,66-69]) are load-bearing: if FCNCs were significant, the flavour fit would be invalid.
domain assumption The U oblique parameter is negligible and the experimental inputs for S and T taken from Ref [100] (with Rb removed) are uncontaminated.
Sec. 3.3 assumes U is negligible and uses S,T values from the authors' previous fit to avoid double counting Rb; a different treatment could shift the allowed mass splittings.
domain assumption Only left-handed slepton searches can be reinterpreted as charged Higgs searches because they share the same SU(2)_L structure.
Sec. 3.7; if this symmetry argument failed, the reinterpreted bounds would not apply.
ad hoc to paper Flat priors on model parameters with linear mass priors are appropriate; the ranges are wide and the posterior does not populate the boundaries.
Sec. 4.1; the prior choice affects the posterior volume and hence the 'sizeable regions' claim. The authors check that statistics do not accumulate at boundaries, but the prior is still a subjective input.
ad hoc to paper The direct-search likelihood for each search is a truncated normal on O_direct with variance set so that O_direct = 1 is excluded at 95% probability.
Sec. 3.6; this is not the experimental likelihood and may over- or under-estimate the constraints.
domain assumption (g-2)_mu is excluded from the main fit because of the unresolved Standard Model theory discrepancy; the white-paper and BMW variants are considered separately.
Sec. 6; if the SM prediction settles at the white-paper value, the model is disfavoured (IC around 129). The main conclusions are conditional on this exclusion.

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Cite this review

Pith. "Pith review of Light scalars within the $\mathcal{CP}$-conserving Aligned-two-Higgs-doublet model." pith.science (2026). https://pith.science/paper/74F4MQHT

@misc{pith2026241214906,
  author       = {Pith},
  title        = {Pith review of: Light scalars within the $\mathcalCP$-conserving Aligned-two-Higgs-doublet model},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/74F4MQHT}},
  note         = {Machine review of arXiv:2412.14906}
}

abstract

In this article we study the possibility that neutral and charged scalars lighter than the 125 GeV Higgs boson might exist within the framework of the $\mathcal{CP}$-conserving Aligned-two-Higgs-doublet model. Depending on which new scalar (scalars) is (are) light, seven different scenarios may be considered. Using the open-source code HEPfit, which relies on Bayesian statistics, we perform global fits for all seven light-mass scenarios. The constraints arising from vacuum stability, perturbativity, electroweak precision observables, flavour observables, Higgs signal strengths, and direct-detection results at the LEP and the LHC are taken into account. Reinterpreted data from slepton searches are considered too. It turns out that the seven scenarios contain sizeable regions of their parameter space compatible with all current data. Although not included in the global fits, the possible implications of $(g-2)_\mu$ are also addressed.

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