REVIEW 4 major objections 4 minor 11 references
Fermionic decay of light charged pseudoscalar in Georgi Machacek model
T0 review · 4 major / 4 minor · reviewed 2026-08-07 · deepseek-v4-flash
Pith's one-line read This paper claims that ATLAS and CMS searches for H±→cs and H±→τν, reinterpreted in the Georgi-Machacek model, set a new upper limit on the triplet vev v2 that is much stronger than the b→sγ bound for charged pseudoscalar masses below 160…
desk verdict A plausible update of the GM-model v2 bound that never shows the conversion, so the green line in Fig. 1 is a claim, not a result you can check. read the letter →
The pith
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
The reading
What carries the argument
The central object is the light charged pseudoscalar $H_3^\pm$ of the Georgi-Machacek model, a member of the custodial triplet whose production in top decay $t\to H_3^\pm b$ and dominant fermionic decays $H_3^\pm\to c\bar{s}$ (BR $\approx 0.57$) and $H_3^\pm\to \tau\nu$ (BR $\approx 0.39$) are the levers of the analysis. The machinery is the conversion of experimentally measured upper limits on $\mathrm{BR}(t\to H^+ b)\times \mathrm{BR}(H^+\to X)$ into an upper bound on $v_2$: since the physical states are expressed through the relation $\tan\beta = 2\sqrt{2}\,v_2/v_1$, the production rate at fixed $m_3$ is fixed by $v_2$, so a null result in a channel $X$ maps directly onto a boundary in the $v_2$--$m_3$ plane. The paper takes the branching fractions as constants over the whole scanned region and uses the theoretical constraints and LHC Higgs signal strengths quoted in the literature to select the plotted points.
What would settle it
For a point just above the green line, for instance $m_3 \approx 120$ GeV and $v_2 \approx 15$ GeV, compute the GM-model predictions for $\mathrm{BR}(t\to H_3^\pm b)\times \mathrm{BR}(H_3^\pm\to c\bar{s})$ and $\mathrm{BR}(t\to H_3^\pm b)\times \mathrm{BR}(H_3^\pm\to \tau\nu)$ using the model calculator cited in [2], and compare them with the observed 95% CL upper limits from the four searches; if the predicted products never exceed those limits for any $m_3$, then the green-line exclusion is not actually implied by the data.
Extended reading notes
Core claim
The paper's central claim is that the low-mass charged pseudoscalar $H_3^\pm$ of the GM model is constrained more strongly by direct LHC searches than by the indirect $b\to s\gamma$ measurement. It combines the CMS [8] and ATLAS [9] upper limits on $\mathrm{BR}(t\to H^+ b)\times \mathrm{BR}(H^+\to c\bar{s})$ with the CMS [10] and ATLAS [11] limits on $\mathrm{BR}(t\to H^+ b)\times \mathrm{BR}(H^+\to \tau\nu)$, and interprets them as exclusions on the triplet vev $v_2$, which controls the $t\to H_3^\pm b$ coupling. Using the GM-model branching ratios $\mathrm{BR}(H_3^\pm\to c\bar{s})=0.57$ and $\mathrm{BR}(H_3^\pm\to \tau\nu)=0.39$, it finds that every point above the green line in the $v_2$--$m_3$ plane is disfavoured by at least one of the four searches. The strongest bound comes from ATLAS $\tau\nu$ data for $m_3$ below 160 GeV. The author concludes that the LHC has already overtaken $b\to s\gamma$ as the prime constraint on $v_2$ in this mass window.
Load-bearing premise
The load-bearing premise is that the ATLAS and CMS upper limits on $\mathrm{BR}(t\to H^\pm b)\times \mathrm{BR}(H^\pm\to X)$, measured for a benchmark charged scalar, apply directly to the GM pseudoscalar $H_3^\pm$ with the same production acceptance, and that $\mathrm{BR}(H_3^\pm\to c\bar{s})=0.57$ and $\mathrm{BR}(H_3^\pm\to \tau\nu)=0.39$ stay constant over the scanned mass range; if the GM production rate or these branching fractions differ from what the paper silently assumes, the green line shifts or disappears.
Editorial extensions
If this is right
- For $m_3$ below 160 GeV, the $v_2$--$m_3$ space that survived the $b\to s\gamma$ limit is further cut, so the LHC fermionic searches become the dominant direct constraint on the triplet vev.
- The ATLAS $H^\pm\to \tau\nu$ result alone is the strongest single bound in that mass window; future runs of the same search with more data would deepen the exclusion without needing new channels.
- The green region is the part of the parameter space consistent with all four searches at once, so it gives a concrete target for subsequent searches, including doubly charged and $H_5^\pm$ states, in the same model.
- Because $v_2$ feeds the custodial-symmetry relation $v_1^2+8v_2^2=v^2$, a lower allowed $v_2$ shifts the doublet vev $v_1$ accordingly, which alters the $h\to\gamma\gamma$ and Higgs-signal-strength predictions used to filter the plotted points.
Reading between the lines
- The paper silently treats the two branching ratios as constants; a mass-dependent scan with the model calculator cited in [2] would test whether the green line stays at the same $v_2$ values or moves, which would change the headline bound.
- The same reinterpretation, taking ATLAS and CMS limits on $t\to H^\pm b$ production and mapping them onto $v_2$, could be applied to other triplet or doublet-extended models, with the only model-dependence entering through the $H^\pm$ production coupling and decay fractions.
- A direct comparison of the cs-channel and $\tau\nu$-channel exclusions might eventually distinguish a scalar $H^\pm$ from a pseudoscalar $H_3^\pm$, since their fermionic couplings, and hence the ratios of the branching ratios, differ even at fixed mass and $v_2$.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The paper considers the Georgi-Machacek (GM) model and claims to derive a new upper bound on the triplet vacuum expectation value v2 as a function of the charged pseudoscalar mass m3. The bound is obtained by using ATLAS and CMS searches for t→H±b with H±→cs and H±→τν, combined with fixed branching ratios of BR(H3±→cs)=0.57 and BR(H3±→τν)=0.39. Figure 1 shows a green exclusion line that the paper claims is much stronger than the existing b→sγ constraint (red line), with the ATLAS H±→τν search being most restrictive for m3 below 160 GeV.
Significance. If the claimed bound is correct, it would be a useful phenomenological constraint on the GM model parameter space, sharper than b→sγ in the low-mass region and directly derived from public LHC data. The paper addresses an interesting question and identifies a potentially important channel. However, the central result is currently not reproducible from the manuscript: the production-rate calculation, the coupling normalization, the branching-ratio variation, and the reinterpretation of the experimental limits are not shown, so the significance of the claim cannot yet be assessed.
major comments (4)
- [Section 3] The central exclusion in Fig. 1 is obtained without showing the GM-model prediction for the quantity constrained by ATLAS and CMS, namely BR(t→H3±b)×BR(H3±→X). No formula for the t-H3±-b coupling in terms of v2 and m3 is given, no normalization convention (e.g., the doublet component of H3± and tanβ) is stated, and no scan specification over the GM parameters is provided. Consequently an independent reader cannot reproduce the green line or verify that it is more stringent than the b→sγ curve. The paper must present the production-rate formula (or the product used), the recasting of the experimental upper limits, and the scan ranges over all relevant parameters.
- [Section 3] The branching ratios BR(H3±→cs)=0.57 and BR(H3±→τν)=0.39 are quoted as constants over the whole v2-m3 region. In the GM model these branching ratios depend on the scalar mass spectrum, mixing angles, and v2 through the partial widths. The paper should either demonstrate that these branching ratios are indeed constant over the allowed region or include their mass and parameter dependence; without this, the conversion of the experimental limits into a v2 exclusion is not justified.
- [Section 3] The ATLAS and CMS searches cited in [8]-[11] were optimized for a charged scalar produced in top-quark decays. The H3± in the GM model is a pseudoscalar, which changes the spin correlations and hence the signal acceptance. No acceptance correction is discussed, and no argument is given that the acceptance for a pseudoscalar is identical to the scalar case. This can shift the derived v2 limit by an amount comparable to the claimed exclusion and must be quantified or explicitly justified.
- [Section 3] The paper does not state whether the experimental limits used are the observed 95% confidence-level upper limits, and it does not propagate experimental or theoretical uncertainties into the green line in Fig. 1. Since the central claim is a numerical bound, the absence of any uncertainty treatment makes the precision and robustness of the limit unclear.
minor comments (4)
- [Abstract and Section 1] The phrase "v2 for GM model pseudoscalar mass below 160 GeV" is awkward; it should read "for GM model pseudoscalar masses below 160 GeV" or similar.
- [Figure 1] The caption of Fig. 1 is minimal; it should identify the meaning of the red and green lines and of the colored points, and state that the lines represent the new and old limits.
- [Section 3] The notation "BR of t→H+b times the BR of H+→cs" is used interchangeably with BR(t→H±b)×BR(H±→cs); the experimental papers use specific conventions (e.g., for the charged-Higgs mass and the top-quark branching), and these conventions should be spelled out.
- [References] Reference [7] is the author's own earlier work and appears to contain the branching-ratio and possibly the recasting information; it should be clearly flagged where the input values come from and, if [7] is crucial, the relevant formulas should be reproduced in this paper.
Circularity Check
No significant circularity: the v2 exclusion is a reinterpretation of independent ATLAS/CMS limits, not a definitional reduction.
full rationale
The derivation chain in arXiv:2506.03772 starts from the GM model definitions and masses (Sec. 1), external theory and unitarity constraints (Sec. 2), and independent ATLAS/CMS upper limits on BR(t→H+b)×BR(H→X) (Sec. 3). The claimed new limit on v2 is obtained by comparing these experimental exclusion curves with the GM prediction for t→H3±b production and the quoted H3± branching fractions. None of the paper's equations define the output v2 limit in terms of the experimental input alone; the output is a model-dependent projection of externally measured limits. The main weakness is that the paper does not display the conversion formula BR(t→H3±b)(v2,m3) or the mass and mixing dependence of BR(H3±→cs,τν), which makes the green line in Fig. 1 unreproducible, but this is a transparency and correctness gap rather than circularity. The only self-citation, [7], is invoked for h→γγ constraints and is not load-bearing for the new H±→cs,τν bound. The branching ratios are asserted as constants without derivation, but there is no evidence they were fitted to the same LHC data, so the claim does not reduce to its inputs by construction.
Assumptions & free parameters
free parameters (3)
- BR(H3±→cs) =
0.57 (quoted constant)
- BR(H3±→τν) =
0.39 (quoted constant)
- Scan region in (v2, m3) =
v2 up to about 30 GeV, m3 from 90 to 160 GeV (Figure 1 range)
assumptions (4)
- domain assumption The GM model field content and custodial-symmetric vacuum (vξ = vχ = v2) reproduce the stated mass spectrum and couplings.
- domain assumption The theoretical constraints (perturbative unitarity, vacuum stability) and LHC Higgs signal-strength measurements define the allowed parameter space plotted in Fig. 1.
- ad hoc to paper The ATLAS/CMS upper limits on BR(t→H±b) x BR(H±→X) apply directly to the GM-model pseudoscalar with the same production kinematics and acceptance.
- ad hoc to paper The partial widths for H3±→cs and H3±→τν are independent of the scanned parameters, so the branching ratios are the quoted constants.
Cite this review
Pith. "Pith review of Fermionic decay of light charged pseudoscalar in Georgi Machacek model." pith.science (2026). https://pith.science/paper/C6QFPB76
@misc{pith2026250603772,
author = {Pith},
title = {Pith review of: Fermionic decay of light charged pseudoscalar in Georgi Machacek model},
year = {2026},
howpublished = {\url{https://pith.science/paper/C6QFPB76}},
note = {Machine review of arXiv:2506.03772}
}
abstract
The Georgi Machacek (GM) model is a triplet extension of the scalar sector of the Standard Model (SM) containing charged and neutral scalars and pseudoscalars with alluring phenomenology. The CMS and ATLAS collaborations of the LHC at $\sqrt{s}=13$ TeV already searched for various decays of the charged Higgs boson in low as well as high mass region. The low mass charged Higgs are produced by the decay of top quarks or antiquarks. $H^{\pm}\rightarrow \tau\nu,\, cs$ are the main fermionic decay channels of light charged scalars or pseudoscalars. For low mass region of the charged pseudoscalars, the triplet vev is restricted from above from the indirect search coming from the $b\rightarrow s \gamma$ decay. Here, I consider the observed data from the ATLAS and CMS both for the light charged Higgs decaying into $cs$ and $\tau\nu$. The ATLAS data observed for $H^{\pm}\rightarrow \tau\nu$ offers a more stringent bound on $v_2$ for GM model pseudoscalar mass below $160$ GeV.
Figures
Reference graph
Works this paper leans on
-
[9]
G. Aadet al.[ATLAS] : “Search for a light charged Higgs boson int→H ±bdecays, withH ± →cs, inpp collisions at √s= 13 TeV with the ATLAS detector,” [arXiv:2407.10096 [hep-ex]]
-
[7]
Fermionic decay of charged Higgs boson in low mass region in Georgi Machacek Model
S. Ghosh : “Fermionic decay of charged Higgs boson in low mass region in Georgi Machacek Model,” doi:10.1142/S0217751X24501392 [arXiv:2205.03896 [hep-ph]]
-
[8]
A. M. Sirunyanet al.[CMS] : “Search for a light charged Higgs boson in the H ± →cs channel in proton- proton collisions at √s= 13 TeV,” Phys. Rev. D102, no.7, 072001 (2020) doi:10.1103/PhysRevD.102.072001 [arXiv:2005.08900 [hep-ex]]
arXiv 2020
-
[11]
M. Aaboudet al.[ATLAS] : “Search for charged Higgs bosons decaying viaH ± →τ ±ντ in theτ+jets and τ+lepton final states with 36 fb −1 ofppcollision data recorded at √s= 13 TeV with the ATLAS experiment,” JHEP09, 139 (2018) doi:10.1007/JHEP09(2018)139 [arXiv:1807.07915 [hep-ex]]. 4
arXiv 2018
-
[1]
H. Georgi and M. Machacek : “DOUBLY CHARGED HIGGS BOSONS,” Nucl. Phys. B262, 463-477 (1985) doi:10.1016/0550-3213(85)90325-6
-
[2]
GMCALC: a calculator for the Georgi-Machacek model,
K. Hartling, K. Kumar and H. E. Logan : “GMCALC: a calculator for the Georgi-Machacek model,” [arXiv:1412.7387 [hep-ph]]
-
[3]
The decoupling limit in the Georgi-Machacek model,
K. Hartling, K. Kumar and H. E. Logan : “The decoupling limit in the Georgi-Machacek model,” Phys. Rev. D 90, no.1, 015007 (2014) doi:10.1103/PhysRevD.90.015007 [arXiv:1404.2640 [hep-ph]]
arXiv 2014
-
[4]
Indirect constraints on the Georgi-Machacek model and implications for Higgs boson couplings,
K. Hartling, K. Kumar and H. E. Logan : “Indirect constraints on the Georgi-Machacek model and implications for Higgs boson couplings,” Phys. Rev. D91, no.1, 015013 (2015) doi:10.1103/PhysRevD.91.015013 [arXiv:1410.5538 [hep-ph]]
arXiv 2015
Show all 11 references
-
[5]
Combined measurements of the Higgs boson’s couplings at √s= 13 TeV,
[CMS] : “Combined measurements of the Higgs boson’s couplings at √s= 13 TeV,” CMS-PAS-HIG-17-031
-
[6]
Combined measurements of Higgs boson production and decay using up to 80 fb −1 of proton-proton collision data at √s= 13 TeV collected with the ATLAS experiment,
[ATLAS] : “Combined measurements of Higgs boson production and decay using up to 80 fb −1 of proton-proton collision data at √s= 13 TeV collected with the ATLAS experiment,” ATLAS-CONF-2019-005
2019
-
[10]
Search for charged Higgs bosons in the H ± →τ ±ντ decay channel in proton-proton collisions at √s= 13 TeV,
A. M. Sirunyanet al.[CMS] : “Search for charged Higgs bosons in the H ± →τ ±ντ decay channel in proton-proton collisions at √s= 13 TeV,” JHEP07, 142 (2019) doi:10.1007/JHEP07(2019)142 [arXiv:1903.04560 [hep-ex]]. 3
2019 arXiv
Reviewed August 7, 2026 · model on record in the stance chip above.
Discussion (0). Sign in to comment.