Phenomenology of scalar particles assisted by machine learning

E. A. Herrera-Chac\'on

REVIEW 4 major objections 5 minor 118 references

Phenomenology of scalar particles assisted by machine learning

T0 review · 4 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read Machine learning could make new scalars visible at the HL-LHC: a thesis claims 5σ discovery for charged-Higgs pairs and a flavon once boosted decision trees suppress background.

desk verdict Solid thesis, shaky headline numbers: the two published analyses hold up, but the new h→eµ projection and the 5σ claims rest on unreported post-cut yields and a numerical inversion in Sec. 5.1.1. read the letter →

arxiv 2507.15019 v1 pith:DIFPWXDW submitted 2025-07-20 hep-ph

E. A. Herrera-Chacón This is my paper

classification hep-ph

keywords chargedHiggspairproductiontwo-Higgs-doubletmodeltypeIIIflavour-symmetryflavonboosteddecisiontreesHL-LHCdiscoverypotentiallepton-flavourviolationh→eµdecaysignalsignificance

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 thesis tries to establish that two scalar extensions of the Standard Model produce signals large enough to be discovered at the High-Luminosity LHC, provided machine-learned classifiers are used to suppress background. In the Type-III two-Higgs-doublet model, charged-Higgs pairs decaying to a muon, a neutrino, and a charm-bottom jet pair are claimed to reach over 5σ statistical significance for charged-Higgs masses between 110 and 250 GeV with roughly 300 to 1000 inverse femtobarns, depending on the scenario. In the flavour-symmetry (flavon) model, the process where a heavy flavon decays to a Higgs boson and a bottom-quark pair, with the Higgs decaying to two bottom quarks, is claimed to reach 3 to 5.6σ at 3000 inverse femtobarns, and the lepton-flavour-violating decay h→eμ is claimed to reach 5σ at 1300 inverse femtobarns in one benchmark scenario. The common device in all three searches is a boosted-decision-tree score cut at 0.95 that separates the sparse signal from Standard Model backgrounds that are orders of magnitude larger. If right, these numbers give concrete luminosity targets for when the LHC's full dataset could turn these speculative scalars into established particles.

What carries the argument

The load-bearing object is a boosted-decision-tree classifier trained on kinematic observables (transverse momenta, missing energy, transverse and invariant masses) that outputs a single score the thesis calls xgb; the analysis cuts at xgb>0.95 to separate signal from background. The other central machinery is the four-zero-texture Yukawa structure of the Type-III two-Higgs-doublet model, whose off-diagonal parameters χij control the charged-Higgs branching ratios, and the flavour-symmetry model's effective interactions where the flavon couples to a Higgs boson plus fermion pairs through a 1/Λ-suppressed operator.

What would settle it

Reproduce the analysis and print the number of signal and background events passing the xgb > 0.95 cut for each benchmark at the quoted luminosity; if more than a handful of background events survive at the claimed luminosity, or if systematic uncertainties are included, Z = S/√(S+B) will no longer reach 5σ. Alternatively, a null result from a dedicated 14 TeV search in the μνcb final state with 300 fb−1 in the 110–250 GeV mass window would contradict the claim.

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Extended reading notes

Core claim

The central claim is that the process pp→H+H−→μνμcb in the Type-III two-Higgs-doublet model can be observed above 5σ for charged-Higgs masses in the window 110<M_H±<250 GeV at the HL-LHC, with scenario S2 needing about 250–300 fb−1 for the lower mass range and scenario S3 up to about 1000 fb−1 for the upper end; the dominant production is the on-shell decay of a heavy neutral scalar H of mass 500 GeV. In the same framework, a heavier neutral scalar (M_H=800 GeV) would require at least 2400 fb−1 and is sensitive to charged-Higgs masses between roughly 180 and 360 GeV. For the flavour-symmetry model, the thesis claims that the process pp→HF→hb\bar{b} with h→b\bar{b} reaches a signal significance of 3–5.6σ for flavon masses around 800–950 GeV at 3000 fb−1, and that the lepton-flavour-violating decay h→eμ reaches 5σ at 1300 fb−1 in scenario S6 (and 3σ at 700 fb−1 in scenario S5). The significance is computed as Z=S/√(S+B) after a boosted-decision-tree cut at xgb>0.95.

Load-bearing premise

The 5σ estimates assume that a machine-learning cut can suppress Standard Model backgrounds to the implied level without any systematic uncertainty entering the significance, and the thesis does not report how many background events remain after the cut.

Editorial extensions

If this is right

Charged Higgs bosons with masses between 110 and 160 GeV would be discoverable with 250–300 fb−1 in scenario S2, so data already being collected at the LHC could start probing the parameter region that explains the t→H±b→cb excess.
If scenario S3 holds, the search window extends to M_H±≈250 GeV with 220–1000 fb−1, covering the low-mass range where production proceeds through an on-shell heavy neutral scalar.
For a heavier neutral scalar (M_H=800 GeV), the same final state needs at least about 2400 fb−1 and is sensitive only for M_H± between roughly 180 and 360 GeV.
In the flavour-symmetry model, the four-bottom final state from HF→hb\bar{b} with h→b\bar{b} would be visible at 3–5.6σ for flavon masses just below 1 TeV at 3000 fb−1, giving a concrete target for HL-LHC searches.
The h→eμ channel is the most striking: scenario S6 reaches 5σ at 1300 fb−1, which is within reach of the HL-LHC, and would be evidence for charged-lepton-flavour violation in Higgs decays.

Reading between the lines

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

Editorial inference: the claimed significance depends entirely on the classifier rejecting more than seven or eight orders of magnitude of background, and the thesis does not tabulate post-cut event counts; a re-analysis that reports those counts would be the decisive check.
Editorial inference: if the low-mass charged-Higgs excess is real, the pair-production channel provides an independent cross-check, because the same χ_cb and χ_tb couplings that fit t→H±b→cb predict a measurable pp→H+H−→μνμcb rate in the same mass window.
Editorial inference: the h→eμ analysis, with its resonance peak in the eμ invariant mass, is nearly free of hadronic background; if the quoted 5σ at 1300 fb−1 survives a full treatment with systematic uncertainties, it would constitute a discovery of lepton-flavour violation rather than just a hint.

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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

Quick take: this is a competent PhD thesis that repackages two already-published PRD analyses and adds a new h→eµ sensitivity study with a BDT. The declared provenance is honest, the models are well-motivated, and the simulation chain is standard. The genuinely new result is the h→eµ projection; the rest re-presents work that already passed peer review. But the central 5σ claims are not supported by the text: no post-cut signal and background yields are reported anywhere, and Section 5.1.1 contains a numerical inversion that makes you doubt the numbers.

What is good: the two published analyses (charged Higgs pairs and Flavon) are solid reproductions, the constraints chapter is thorough, and the public code framework (PrakritiMLPrep) is a useful tool. The h→eµ study is a routine extension of the FNSM, but it is the paper's only new physics output.

The soft spots are serious and concentrated. The significance formula (4.0.1) omits systematic uncertainties, which is normal in a first pass but should be stated. The real problem: the reader is told that xgb>0.95 is the optimal cut, but the surviving S and B are never tabulated. From Tables 5.1 and 5.2, at 300 fb^-1 and MH±=150 GeV, you get ~97 signal events, so a 5σ significance requires B≲280 against a raw background of ~10^9 events—a rejection factor of order 10^7. That might be achievable with two resonant handles, but the thesis has to show it, and it doesn't. The h→eµ analysis does the same thing, with Zeµ tuned until ~5σ appears.

There is also a direct contradiction in §5.1.1: the text says the signal cross-section exceeds the background by up to seven orders of magnitude, while Tables 5.1 and 5.2 show the opposite. It reads like a slipped sentence, but in a thesis carrying 5σ discovery claims, this is exactly the kind of error that erodes confidence.

I partly disagree with the reader's circularity charge: picking benchmark points to exhibit reach is standard practice in BSM phenomenology, and the FNSM constraints are honestly applied. The problem is not that the parameters are chosen; it is that the resulting significance is presented as a discovery claim without the event-level evidence to back it.

Who is this for? A phenomenologist working on 2HDM or Froggatt-Nielsen models might want the code and the constraint summary. The h→eµ projection, once the yields are added and systematics addressed, could be a citable sensitivity limit. As it stands, the thesis is not publishable in its current form, but it is a heavy revision away from a useful contribution. I would send it to a referee: the flaws are fixable and the underlying work is real, not a desk reject.

Referee Report

4 major / 5 minor

Summary. This thesis (arXiv:2507.15019) studies the collider phenomenology of two scalar extensions of the Standard Model. For the 2HDM-III it analyzes pp→H+H−→μνμcb after applying flavour and electroweak constraints, and claims a statistical significance above 5σ for charged Higgs masses around 100–250 GeV in benchmark scenarios S2 and S3 at L≈250–1000 fb−1. For the Froggatt-Nielsen singlet model it analyzes pp→HF→hbb with h→bb and h→γγ, and the LFV decay h→eμ, claiming up to 5σ at HL-LHC luminosities. The analysis uses MadGraph5/Pythia8/Delphes simulations, a BDT implemented with XGBoost, and a custom Python framework for LHCO processing.

Significance. If the numerical results were established, the work would provide concrete, testable targets for the HL-LHC and a reusable ML-based analysis pipeline. The thesis is also valuable for its systematic scan of low-energy constraints (B0s,d→μ+μ−, ℓi→ℓjγ, ℓi→3ℓj, b→sγ, oblique parameters) and for making the PrakritiMLPrep framework available. However, the central discovery claims are not derivable from the manuscript as written: the post-cut signal and background yields are absent, the significance formula is purely statistical, and the h→eμ benchmarks are chosen to produce the claimed significances. The quantitative conclusions therefore remain to be substantiated.

major comments (4)

[§5.1.2, Eq. (4.0.1)] The 5σ claims for scenarios S2 and S3 are not reproducible because the post-cut yields S and B are never reported. Tables 5.1 and 5.2 provide only raw cross-sections; for example, for M_H±=150 GeV and L=3000 fb−1 the signal expectation is about 972 events while the raw Wjj+Wbb background is about 1.1×10^10 events, so the xgb>0.95 cut would need to suppress the background by roughly seven orders of magnitude. No acceptance, efficiency, or post-cut count is given for the 2HDM-III analysis (or for the h→eμ analysis in §5.2.2), so the reader cannot verify that Z=S/√(S+B) actually reaches 5.
[§5.1.1] The text following Tables 5.1 and 5.2 states that for M_H±=100 GeV and M_H=500 GeV 'the signal cross-section exceeds the corresponding background production cross-section by up to seven orders of magnitude.' This is opposite to the numbers in the tables: σ(pp→μνμcb)≈0.189 fb while σ(Wjj+Wbb)≈3.75×10^6 fb, i.e., the background exceeds the signal by about seven orders of magnitude. This internal contradiction must be corrected or explained before the significance estimates can be evaluated.
[§5.2.2, Table 5.8] For the h→eμ analysis, the LFV coupling Zeμ in scenarios S4, S5 and S6 is selected (subject only to the bound BR(h→eμ)<6.2×10−5) so that the event rate yields 3–5σ. The quoted significances are therefore the result of benchmark construction rather than a prediction from external constraints; this should be stated explicitly, or the analysis should be reframed as a sensitivity scan in the (vs, Zeμ) plane.
[Eq. (4.0.1), §§5.1.2, 5.2.1, 5.2.2] The significance estimator Z=S/√(S+B) ignores systematic uncertainties. Since the 2HDM-III projection relies on background rejection by a factor of order 10^7, a small relative error on the background normalization can change the estimated significance substantially; a treatment of dominant systematic uncertainties (or an explicit statement that the quoted numbers are statistical only) is needed for the discovery claims to be meaningful.

minor comments (5)

[Table 5.8] Table 5.8 appears to list two blocks of the same scenarios with different luminosities and significance levels; clarify the labeling (e.g., separate 3σ and 5σ tables) so the reader does not mistake the duplicated rows for separate benchmarks.
[Chapter 6 vs §5.1.2] The Conclusions state that the charged Higgs reach extends to M_H±≈250 GeV with 300–1000 fb−1, while §5.1.2 quotes 250–300 fb−1 for S2 and 220–1000 fb−1 for S3; harmonize these statements.
[Chapter 4] Chapter 4 contains long listings of LHCO examples and Python code that are not used in subsequent chapters; condensing this material would improve readability.
[Eq. (5.2.4)] In Eq. (5.2.4), the lower/upper limits of x_b are written with an apparent typesetting artifact ('2(1−xa+xt, )'); please correct the formula and define the variables consistently.
[Figure captions] Some figure captions, e.g. Fig. 5.8 ('scenarios S21') and Fig. 5.12 ('acceptance cuts'), should be checked for typos.

Circularity Check

1 steps flagged · score 6.0 of 10

Partial circularity: the h→eµ 5σ 'discovery' result is obtained by tuning the LFV coupling Zeµ and the luminosity to hit 5σ; the 2HDM-III and FNSM channels are benchmark calculations, with an additional unstated missing-yield limitation.

fitted input called prediction [Sec. 5.2.2 (Lepton-Flavour-Violating Decays h→eµ), text immediately before and around Table 5.8]
"By scanning over different values of the model parameters (such ascosα, vs, and LFV couplings likeZeµ), as well as varying the assumed integrated luminosity, we can identify regions in which the LFV decayh→ eµ that could be observed with evidence-level (3σ) or discovery-level (5σ) significance. ... These parameters correspond to a significance of∼ 5σ."

The scenarios S4-S6 are not fixed, externally derived benchmarks: Zeµ is scanned/varied, and the luminosity is varied, until a 3σ/5σ significance is found. Since Z=S/sqrt(S+B) grows with the signal cross-section, and the text states that higher LFV couplings lead to larger cross-sections and thus higher significance, the quoted discovery significances (e.g., ~5σ for S6 at 1300 fb^-1) are the selection targets, not outputs of a model with independently fixed parameters. The experimental upper bound BR(h→eµ)<6.2e-5 only caps the scan; it does not determine Zeµ. The claimed discovery potential is therefore partly constructed from the desired significance.

full rationale

Only one step meets the exhibition standard for circularity. In Sec. 5.2.2 the LFV benchmarks are obtained by scanning Zeµ and luminosity until evidence-level or discovery-level significances appear, and the chosen parameters are then said to 'correspond to a significance of ~5σ'. This is a fitted input presented as a prediction. The 2HDM-III charged-Higgs analysis and the FNSM h→bb/γγ analyses are not circular under the strict definition: their benchmark points are selected from scans subject to LHC, flavour, and oblique constraints, and the significances are computed from simulated cross-sections and Eq. (4.0.1). One may question whether the BDT cut xgb>0.95 can actually suppress the seven-to-ten-order-larger backgrounds, but that is a validation and reporting gap, not an input-output equivalence; the thesis never tabulates the post-cut S and B for the 2HDM-III or h→eµ significances. The internal contradiction in Sec. 5.1.1, where the text says the signal exceeds the background by up to seven orders of magnitude while Tables 5.1 and 5.2 show the reverse, is a correctness/reproducibility issue rather than circularity. Citation [78] is peer-reviewed work by the same collaboration but is used only to motivate the FNSM mass range; it is not the load-bearing derivation of any significance claim. The score reflects only the h→eµ tuning step.

Assumptions & free parameters 6 free parameters · 7 assumptions · 2 invented entities

The central 5-sigma projections rest on many scanned model parameters, including chi_cb, chi_tb, chi_mu_mu, Z_e_mu, masses and mixing angles, plus a simplified significance formula and fast detector simulation. The most consequential free inputs are the benchmark scenarios themselves, which are chosen after scanning to yield large cross-sections. No parameter is derived from an independent first-principles constraint.

free parameters (6)

chi_cb (2HDM-III off-diagonal Yukawa) = 5 (S2), 1 (S3), scan [-10,10]
Controls H+->cb; scanned to match the ATLAS t->H±b, H±->cb excess, then benchmarked to maximize significance.
chi_tb (2HDM-III) = scan [-10,10], benchmark unspecified
Controls t->H±b coupling; chosen in benchmark scenarios S1-S3.
chi_mu_mu (2HDM-III) = 5 (S2), 1 (S3), scan [-10,10]
Controls the H+->mu nu coupling in the charged Higgs pair signal.
chi_tt, chi_bb (2HDM-III) = chi_tt=0.1, scan [-1,1] for both
Attenuate H+ couplings to top and bottom quarks to satisfy b->s gamma constraints.
Z_e_mu (FNSM LFV coupling) = 0.0025 (S4), 0.005601 (S5), 0.009781 (S6)
LFV coupling in h->eµ; values chosen so scenarios reach 3 to 5 sigma under the B(h->eµ) < 6.2e-5 constraint, effectively selected to produce the claimed significance.
cos(alpha), v_s, Lambda, M_HF (FNSM) = cos(alpha)=0.995 or -0.89/-0.95; v_s=1-2.5 TeV; Lambda=1-2.5 TeV; M_HF=800-1500 GeV
Free scalar sector parameters scanned within theoretical and experimental constraints; benchmark scenarios hand-picked for large cross-sections.

assumptions (7)

standard math Standard Model gauge structure and particle content
Used throughout Chapters 2 and 3 to define the SM and its extensions; accepted background quantum field theory.
domain assumption Four-zero texture ansatz and Hermitian Yukawa matrices in the 2HDM-III
Section 3.1.2 imposes this texture to control tree-level flavour-changing neutral currents; it is a modeling assumption, not derived.
domain assumption CP conservation in the 2HDM-III scalar potential
Section 3.1.1 takes all scalar potential parameters real, so CP is conserved in the scalar sector; the thesis acknowledges this is a choice.
domain assumption U(1)_F Froggatt-Nielsen mechanism with soft breaking
Section 3.3 introduces a global U(1)_F with a complex singlet S_F, a soft breaking term, and higher-dimensional operators suppressed by Lambda; this is the model definition, not independently evidenced.
ad hoc to paper Z2-derived theoretical constraints applied to Type-III
Section 3.2 states that perturbativity, unitarity and oblique constraints are adopted from Z2-symmetric models with lambda6=lambda7=0 even though Type-III does not impose the Z2 symmetry.
domain assumption Significance formula Z=S/sqrt(S+B) with negligible systematic uncertainties
Equation (4.0.1) is used for all discovery claims; this ignores systematic uncertainties in background normalization and BDT shapes, a strong unstated premise.
domain assumption Fast detector simulation with Delphes ATLAS-like cards approximates real ATLAS and CMS performance
Used in Sections 5.1.1 and 5.2; fast simulation cannot capture full reconstruction efficiencies and systematic correlations.

invented entities (2)

Flavon H_F (and CP-odd A_F)
purpose: Spontaneously breaks U(1)_F, generates fermion mass hierarchy, and produces the H_F -> h b bbar signal studied in Chapter 5.
Pre-existing Froggatt-Nielsen model content, not introduced by this thesis. The paper provides no new falsifiable handle, such as a new predicted mass outside the model scan, and relies on indirect constraints.
Extra 2HDM-III scalars H, A and H±
purpose: Extend the scalar sector and give the charged Higgs pair signal.
Pre-existing model content; the thesis scans their masses and couplings but finds no new independent evidence.

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Cite this review

Pith. "Pith review of Phenomenology of scalar particles assisted by machine learning." pith.science (2026). https://pith.science/paper/DIFPWXDW

@misc{pith2026250715019,
  author       = {Pith},
  title        = {Pith review of: Phenomenology of scalar particles assisted by machine learning},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/DIFPWXDW}},
  note         = {Machine review of arXiv:2507.15019}
}

abstract

In this thesis, we explore the phenomenology of scalar particles within Beyond Standard Model frameworks, using Machine Learning (ML) techniques to enhance sensitivity and discovery potential at current and future collider experiments, the Large Hadron Collider (LHC) and the High-Luminosity LHC (HL-LHC). Specifically, we study scalar extensions of the Standard Model such as the Two Higgs Doublet Model Type-III (2HDM-III) and the Froggatt-Nielsen Flavon model. We perform a detailed collider analysis focusing on charged Higgs boson pair production within the 2HDM-III, examining final states involving muons, neutrinos and quark jets. Our studies identify parameter regions consistent with recent experimental anomalies reported by ATLAS collaboration, particularly in charged Higgs decays involving charm-bottom quark transitions, and suggest concrete scenarios for achieving statistically significant signals of 5$\sigma$ at future luminosities. In the context of the Flavon model, we analyse potential signatures of a new scalar called Flavon decaying into a Higgs boson and a pair of bottom quarks, followed by the channels where the Higgs decays into a pair of bottom quarks or a pair of photons. Additionally, we analyse Lepton-Flavour-Violating processes, both of them achieving discovery level significances of up to $5\sigma$ at the HL-LHC. Using multivariate analysis techniques, specifically Boosted Decision Trees, we demonstrate a significant improvement in signal discrimination. Throughout this thesis, ML methodologies have been integral, notably enhancing the signal from background separation and significantly improving the robustness of phenomenological predictions. The methods and analyses presented here contribute to clarifying the flavour structure mysteries of the SM and offer actionable targets for future experimental searches.

Figures

Figures reproduced from arXiv: 2507.15019 by the authors.

**Figure 3.1.** Generic Feynman diagram for the decays of a neutral meson M (such as B 0 , K 0 , or D 0 ) into µ + µ − . The black circle indicates a Flavour-changing vertex in the quark sector. The decay of B 0 s,d mesons into a µ + µ − pair is both compelling and highly constraining, given its sensitivity to BSM physics. Within the theoretical framework of the SM, [PITH_FULL_IMAGE:figures/full_fig_p053_3_1.png] view at source ↗

**Figure 3.2.** Feynman diagrams contributing to aµ. Here ϕ represents a CP-even scalar, CP-odd scalar, or the SM-like Higgs boson. H ± denotes charged scalar bosons. In these diagrams ℓi = µ [PITH_FULL_IMAGE:figures/full_fig_p056_3_2.png] view at source ↗

**Figure 3.3.** Feynman diagram for process ℓi → ℓjγ at one-loop level induced by ϕ = h, H, A. case in which ℓi = τ and ℓj = µ, we adopt the approximations gϕµµ ≪ gϕττ and mµ ≪ mτ ≪ mϕ. Based on these assumptions, the one-loop Wilson coefficients CL, R simplify as follows [62, 63] C 1−loop L ≃ X ϕ gϕττ gϕτµ 12m 2 ϕ   − 4 + 3 log m 2 ϕ m 2 τ  , C 1−loop R ≃ X ϕ gϕττ gϕτµ 12m 2 ϕ   − 4 + 3 log m 2 ϕ m 2 τ  . (3.2.16) The nume… view at source ↗

Figures from the paper (44 more)

**Figure 3.4.** Figure 3.4: Feynman diagrams contributing to the process ℓi → ℓj ℓk ¯ℓk. Panel (a) shows the tree-level and (b) one-loop level, where the black circle denotes a loop of the type as Feynman diagram of [PITH_FULL_IMAGE:figures/full_fig_p059_3_4.png]

**Figure 3.5.** Figure 3.5: Feynman diagram for the tree-level decay [PITH_FULL_IMAGE:figures/full_fig_p059_3_5.png]

**Figure 3.6.** Figure 3.6: In the cos(α−β)−tan β plane, the blue points represent parameter values allowed by all signal strength modifiers µX, whereas the orange points indicate those consistent with the LFV processes. The dataset was generated using the SpaceMath framework. Further details o…

**Figure 3.** Figure 3: a shows the production cross-section [PITH_FULL_IMAGE:figures/full_fig_p061_3.png]

**Figure 3.7.** Figure 3.7: Feynman diagram for the production of ϕ in association with a bottom quark at the LHC, followed by its decay into a τ τ pair. Additionally, the green (yellow) shaded bands illustrate the ±1σ (±2σ) intervals around the expected limits, providing a visual measure of th…

**Figure 3.8.** Figure 3.8: Observed and expected 95% CL upper limits on the production cross-section multiplied by the di-tau BR for a scalar boson produced in association with a bottom quark. The results are shown as a function of (a) MA and (b) MH, where we consider tanβ = 5, 10, 20 and cosα…

**Figure 3.9.** Figure 3.9: Feynman diagram illustrating the production process of H and its subsequent decay into a pair of Higgs bosons hh. limit (blue line). These results, reported by the ATLAS collaboration [45], are compared with the theoretical predictions of the 2HDM-III for tan β = 5, …

**Figure 3.10.** Figure 3.10: The 95% CL upper limits on the production crosssection multiplied by the di-Higgs BR are presented for a scalar boson produced in pp collisions as a function of MH. We observed and expected limits are shown, considering tan β = 5, 10, 20 and cos(α − β) = 0.01. MH ±…

**Figure 3.11.** Figure 3.11: Radiative decay b → sγ mediated by charged Higgs bosons. The loop involves up-type quarks (u, c, t), with the dominant contribution coming from the top quark. The photon is emitted from the charged scalar line. form C (L) 7 = v 2 λtmb X j Γ RLH+ ∗ ujd2 Γ LRH+ ujd3 m…

**Figure 3.12.** Figure 3.12: Scatter plot in the MH ± − tan β plane. (a) Red points stand for these regions allowed by Rquark for the mass interval 114 ≤ MH ± ≤ 140 GeV. (b) The same as in (a) but for the mass range mt + mb ≤ MH ± ≤ 1000. The Rquark is defined in Eq. (3.2.27). resenting paramet…

**Figure 3.13.** Figure 3.13: Scatter plot in the χbb−χtt plane. Red points represent parameter combinations allowed by allowed by Rquark as defined in Eq. (3.2.27). Parameter Scanned range tan β [0.1, 20] χtt [−1, 1] χbb [−1, 1] MH ± [114, 140] GeV [PITH_FULL_IMAGE:figures/full_fig_p069_3_13.png]

**Figure 3.14.** Figure 3.14: χcb–χtb plane. The coloured points indicate the values of χ parameters that accommodate the current excess of events reported by the ATLAS collaboration. (a) Blue points represent parameter values that explain the excess for MH ± = 120 GeV. (b) and (c) show the same…

**Figure 3.15.** Figure 3.15: Allowed points (simultaneously) for the difference of scalar masses by oblique parameters. outlined in [PITH_FULL_IMAGE:figures/full_fig_p073_3_15.png]

**Figure 3.** Figure 3: displays the [PITH_FULL_IMAGE:figures/full_fig_p080_3.png]

**Figure 3.16.** Figure 3.16: displays the cos α–vs plane, where each point represents a parameter combination that satisfies all the theoretical constraints, including perturbativity and the unitarity conditions imposed on the S-matrix. For this analysis, we generated a set of random points tha…

**Figure 3.17.** Figure 3.17: This plot shows the ultraviolet mass scale Λ as a function of the VEV of the complex singlet vs . The area enclosed by the solid black lines corresponds to the intersection of all constraints, while the different points represent the individual RX measurements. Th…

**Figure 5.2.** Figure 5.2 [PITH_FULL_IMAGE:figures/full_fig_p106_5_2.png]

**Figure 5.1.** Figure 5.1: Branching Ratios (a) BR(H + → cb), (b) BR(H + → µν), as a function of the charged scalar mass MH + . • BACKGROUND: The dominant SM background comes from the final state bjℓνℓ , which is produced by – W jj + W b¯b, – tb + tj, – tt¯. In the case of the tt¯ background p…

**Figure 5.** Figure 5: provides an overview of the production cross-section as a function of [PITH_FULL_IMAGE:figures/full_fig_p108_5.png]

**Figure 5.3.** Figure 5.3: Production cross-section of a charged Higgs pair with their subsequent decays into µνµcb for MH = 500 GeV. For the three scenarios, we can observe that the cross-sections are significantly higher when the charged Higgs boson masses lie in the range of 100 ≤ MH ± ≤ 25…

**Figure 5.4.** Figure 5.4: Production cross-section for a pair of charged Higgs bosons followed by their subsequent decays into µνµcb, for MH = 800, 1000 GeV in scenario S2. In our computational framework we begin by implementing the full model using FeynRules [96] within MadGraph5 [82], emplo…

**Figure 5.5.** Figure 5.5: Plot of the discriminant for signal and background data [PITH_FULL_IMAGE:figures/full_fig_p111_5_5.png]

**Figure 5.7.** Figure 5.7: Kinematic distributions for the signal and SM background processes are shown for the following observables: (a) transverse momentum of the b-jet, (b) missing transverse energy E/ T , (c) transverse momentum of the c-jet, (d) transverse mass of the muon MT [µ] and …

**Figure 5.** Figure 5: presents contour plots of the [PITH_FULL_IMAGE:figures/full_fig_p115_5.png]

**Figure 5.8.** Figure 5.8: Signal Significance as a function of the charged Higgs boson mass MH ± and the integrated luminosity for the following scenarios: (a) S2, (b) S3 with MH = 500 GeV, and (c) S2 with MH = 800 GeV [PITH_FULL_IMAGE:figures/full_fig_p116_5_8.png]

**Figure 5.9.** Figure 5.9: Feynman diagrams inducing the HF → ¯ffh decay in the FNSM. Diagram (a) shows an effective vertex corresponding to a dimension-5 operator suppressed by 1/Λ. Such interactions are non renormalisable and are treated within the effective field theory framework, where hi…

**Figure 5.10.** Figure 5.10: Production cross-section of the signal pp → HF → hb¯b. The centre-of-mass energy was set to 14 TeV. On the other hand, we analyse two specific decay channels of the Higgs boson: (i) pp → HF → hb¯b(h → b ¯b) and (ii) pp → HF → hb¯b(h → γγ). The identification of b-je…

**Figure 5.12.** Figure 5.12: b-jet transverse momentum normalised distributions for the signal and total background following the application of the acceptance cuts [PITH_FULL_IMAGE:figures/full_fig_p123_5_12.png]

**Figure 5.13.** Figure 5.13: Normalised distribution of the reconstructed invariant mass Minv(b1b2b3b4) for the signal and background processes. Meanwhile, [PITH_FULL_IMAGE:figures/full_fig_p124_5_13.png]

**Figure 5.15.** Figure 5.15: Normalised pT distributions for photons (γ) and b-jets, comparing signal and total background after acceptance cuts. For this framework, we train the BDT classifiers using variables associated with the kinematics of both final-state and intermediate-state particles…

**Figure 5.16.** Figure 5.16: Normalised distribution of the reconstructed invariant mass Minv(γ1γ2b1b2) for the signal and background processes. The training of the BDT classifier is carried out using Monte Carlo simulated samples. The dataset comprises 200,000 signal events and an equivalent …

**Figure 5.** Figure 5: presents the ROC curve for the [PITH_FULL_IMAGE:figures/full_fig_p129_5.png]

**Figure 5.17.** Figure 5.17: Density plot showing the Signal Significance for the h → b ¯b channel as a function of the integrated luminosity and the Flavon mass MHF , the subplots correspond to the following benchmark scenarios: (a) S1, (b) S2, and (c) S3 [PITH_FULL_IMAGE:figures/full_fig_p1…

**Figure 5.** Figure 5: illustrates the [PITH_FULL_IMAGE:figures/full_fig_p131_5.png]

**Figure 5.18.** Figure 5.18: ROC curve for h → b ¯b channel showing the model’s ability to predict training data (used to fit the model) and independent test data (evaluating performance on new, unseen data). Each plot corresponds to a different Flavon mass as indicated [PITH_FULL_IMAGE:figure…

**Figure 5.19.** Figure 5.19: 1/Background Acceptance against the Signal Acceptance for the h → b ¯b channel. Each plot corresponds to a different Flavon mass as indicated [PITH_FULL_IMAGE:figures/full_fig_p133_5_19.png]

**Figure 5.20.** Figure 5.20: Density plot displaying the Signal Significance as a function of the integrated luminosity and the Flavon mass MHF for the h → γγ decay channel, the subplots correspond to the following benchmark scenarios: (a) S1, (b) S2, and (c) S3 [PITH_FULL_IMAGE:figures/full_f…

**Figure 5.21.** Figure 5.21: Feynman diagram of the LFV process h → eµ. After training, the BDT outputs a single discriminant variable (xgb), which we can cut on in order to isolate a high purity signal region [PITH_FULL_IMAGE:figures/full_fig_p136_5_21.png]

**Figure 5.22.** Figure 5.22: Feature importances from the XGBoost classifier, showing which variables contribute most strongly to separate signal from background for h → eµ. (Correlated features were removed prior to training, as discussed in the dataset preparation section of the previous c…

**Figure 5.23.** Figure 5.23: Parameter space in the plane (vs , Zeµ) for h → eµ. Since this decay has not been observed, no signal strength is measured for this channel. Instead, only upper limits on the BR are available. In this analysis, we impose the experimental constraint B(h → eµ) < 6.2 ×…

**Figure 5.24.** Figure 5.24: BDT classifier distribution for S6, comparing signal (blue) and background (red) events in both training and test samples. The legend shows the KS p-values for each distribution [PITH_FULL_IMAGE:figures/full_fig_p139_5_24.png]

**Figure 5.25.** Figure 5.25: ROC curve for S6, illustrates purity vs. efficiency for both, the training (blue) and test (red) datasets. The AUC values are ∼ 0.996 (train) and ∼ 0.996 (test), reflecting strong discrimination [PITH_FULL_IMAGE:figures/full_fig_p139_5_25.png]

**Figure 5.26.** Figure 5.26: Signal Significance as a function of the integrated luminosity and the XGB cut for the decay h → eµ in the scenarios: (a) S4, (b) S5, and (c) S6 [PITH_FULL_IMAGE:figures/full_fig_p141_5_26.png]

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