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CP violation in charged Higgs production and decays in the Complex Two Higgs Doublet Model

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A. Arhrib, E. Christova, H. Eberl, E. Ginina

High Energy Physics - Phenomenology · Submitted 30 Nov 2010 · 70 references

Pith's verdict: A solid one-loop C2HDM calculation with a genuinely useful FeynArts model file, but the abstract's '≤2–3%' ceiling is a scan statement dressed up as a model-space bound.

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CitationA. Arhrib, E. Christova, E. Ginina, H. Eberl. "CP violation in charged Higgs production and decays in the Complex Two Higgs Doublet Model." arXiv:1011.6560 (2010). https://pith.science/paper/BAJKG3ZA
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The paper

The paper claims

In the complex two-Higgs-doublet model, CP-violating asymmetries in charged Higgs production and decay top out near 2 to 3 percent, roughly ten times smaller than the MSSM's.

The reading

The authors ask how much CP violation the complex two-Higgs-doublet model can imprint on a charged Higgs boson at the LHC, and answer with a one-loop calculation of the rate asymmetries between $H^+$ and $H^-$ in production ($pp$ → $tH^+ + X$), in the decays $H^+$ → $t b$ and $H^+$ → $W^+ H_i^0$, and in the two combined. The CP-violating ingredient is a single complex mass parameter $m_{12}^2$ in the tree-level scalar potential, which makes the three neutral Higgs mass eigenstates mixtures of CP-even and CP-odd states; that mixing then propagates through loops into the couplings that control charged-Higgs production and decay. The headline result is a ceiling: over the parameter region surviving vacuum stability, unitarity, the $B$ → $X_s gamma$ bound $M_{H^+} >= 295$ GeV and the $Delta rho$ window, no asymmetry exceeds roughly 2 to 3 percent, about an order of magnitude below the analogous MSSM numbers. That matters because it says the CP-violating handle on a charged Higgs at the LHC is weak in this model even though CP violation is present already at tree level, and the authors estimate that a 2 percent asymmetry at $M_{H^+} = 350$ GeV would yield a statistical significance of only about 4 with $200$ fb$^{-1}$.

What carries the argument

The load-bearing object is the complex parameter $m_{12}^2$ of the tree-level potential, which after electroweak symmetry breaking forces the neutral Higgs mass eigenstates to be rotated by a general orthogonal matrix $R$ parametrised by three angles $alpha_1, alpha_2, alpha_3$. The elements $R_{j3}$ measure the pseudoscalar admixture of each $H_j^0$, and they enter both the neutral-Higgs Yukawa couplings (which take the form $a + i b gamma_5$) and the $H_j^0 W^+ H^-$ coupling $C(H_j^0 W^+ H^-) = -i (sin beta R_{j1} - cos beta R_{j2}) + R_{j3}$, which is genuinely complex. Nonzero asymmetries then require interference between these CP-odd couplings and the absorptive parts of one-loop amplitudes, whose strong phases come from on-shell intermediate states such as $t$ → $b W^+$ and $H_1^0$ → $b bar b$, plus $H^+$ → $W^+ H_j^0$ and $H^+$ → $t b$ whenever kinematically open. The second piece of machinery is technical and reusable: a complete FeynArts model file (CTHDM.mod, 270 couplings) for the complex 2HDM, together with FormCalc Fortran drivers that compute $M_{H_3^0}$ from the mass relation, evaluate the $lambda_i$ from physical masses and mixing angles, and apply the stability, unitarity and $Delta rho$ constraints.

Extended reading notes

Core claim

The paper establishes that in the type II complex 2HDM with softly broken $Z_2$ symmetry, one-loop CP-violating rate asymmetries in charged-Higgs physics stay small. Concretely: the decay asymmetry in $H^+$ → $t b$ is positive and reaches about 2.5 percent for $tan beta = 4.5$ and $M_{H^+}$ near 400 GeV, with the vertex diagrams dominating and partially cancelling against self-energies; the asymmetry in $H^+$ → $W^+ H_1^0$ is negative and reaches about 1.7 percent for $tan beta = 1.5$ near the 297 GeV threshold, with self-energies dominating; the asymmetry in $H^+$ → $W^+ H_2^0$ is positive and nearly flat at about 3.7 percent for $tan beta = 1.5$. The production asymmetry from $b g$ → $t H^-$ is negative, of order 2 percent at $tan beta = 4$ and $M_{H^+} = 400$ GeV, and therefore nearly cancels against the $t b$ decay asymmetry in the combined process, leaving that combined asymmetry below about 1 percent; no such cancellation occurs in the bosonic channels, where the combined asymmetries reach about 2.5 percent (negative) for $W^+ H_1^0$ and about 3 percent (positive) for $W^+ H_2^0$. A grid scan of 6,415,200 parameter points leaves only 67,861 after constraints (about 1 percent), and finds the asymmetry distribution bunched asymmetrically around zero, with isolated points reaching 3.5 percent negative.

Load-bearing premise

The claim that no asymmetry exceeds 2 to 3 percent rests on a finite grid scan of a restricted parameter box combined with a specific set of theoretical and experimental cuts, so a finer scan or a region outside that box could in principle produce a larger asymmetry.

Editorial extensions

If this is right

  • Any search strategy that relies on a charge asymmetry in $H^+$ versus $H^-$ production or decay to probe CP violation in the 2HDM faces asymmetries at the few-percent level, so the observable must be extracted from large samples rather than from a rate difference alone.
  • Because the production and $t b$ decay asymmetries carry opposite signs and cancel in the combined $p p$ → $t H^+$ → $t t b$ channel, the $t b$ final state is the least favourable place to look for CP violation, while the $W^+ H_1^0$ and $W^+ H_2^0$ channels add constructively and are the better targets.
  • The CP-violating effects in this model are electroweak in origin, coming from neutral Higgs exchange, rather than QCD-driven as in the gluino-box contributions of the MSSM, which explains the order-of-magnitude gap between the two models.
  • A high-luminosity upgrade is the natural setting for such a measurement: the estimated significance of about 4 for a 2 percent asymmetry at 350 GeV with $200$ fb$^{-1}$ scales roughly with the square root of luminosity.
  • The released FeynArts model file and FormCalc drivers make the complex 2HDM available for one-loop calculations of other processes without rederiving the couplings.

Reading between the lines

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

  • The ceiling of 2 to 3 percent is a statement about the constrained parameter space, not about the model in general; regions where the $Delta rho$ window and the $B$ → $X_s gamma$ bound are relaxed, or where $tan beta$ and $M_{H^+}$ lie outside the scanned box, are the obvious places to check whether the ceiling is real or an artefact of the cuts.
  • Because the neutral Higgs mixing is present at tree level here while in the MSSM it is loop-induced, the smallness of the C2HDM asymmetries is itself informative: it suggests that tree-level CP phases in the scalar potential need not translate into large CP-odd observables once the neutral Higgs couplings are constrained by the $W W$ and $W H$ sum rules.
  • The near-degeneracy of the $H_2^0$ and $H_3^0$ contributions in the $W^+ H_2^0$ channel, combined with the flatness of that asymmetry in $M_{H^+}$, hints that this channel is the most robust of the three for a first experimental extraction, since it does not require precise knowledge of the charged Higgs mass.
  • If a charged Higgs is found and its mass measured, the sign pattern reported here (positive for $t b$ and $W^+ H_2^0$, negative for $W^+ H_1^0$ and for production) would itself be a discriminator between the C2HDM and the MSSM, independent of the magnitudes.
Original abstract

We study the effects of CP violation in charged Higgs boson production $pp\to t H^\pm + X$ at the LHC, as well as in the charged Higgs boson decays $H^\pm \to t b$ and $H^\pm \to W^\pm H_i^0$, $i=1,2,3$. The study is done in the framework of the type II complex Two Higgs Doublet Model (2HDM) with softly broken $Z_2$ symmetry. In this model violation of CP invariance is induced by the complex parameter $m^2_{12}$ of the tree-level Higgs potential. We calculate the CP violating rate asymmetries for $H^+$ and $H^-$ production and decays as well as for the combined processes at one-loop level and perform a detailed numerical analysis. All calculations are done with the automatic amplitude generator FeynArts and the calculational tool FormCalc, for which we have written a complete complex 2HDM model file and relevant fortran drivers. The implementation of the complex 2HDM in FeynArts and FormCalc is described. In comparison with the analogous results in the MSSM, all considered CP violating asymmetries are smaller by an order of magnitude and do not exceed 2 to 3%.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 5,792 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.70 · human participants 0.01 · controlled comparison 0.42 · randomized assignment 0.01 · states quantitative result 0.98 · compares with prior results 0.97 · mentions code or data availability 0.19.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

We study the effects of CP violation in charged Higgs boson production $pp\to t H^\pm + X$ at the LHC, as well as in the charged Higgs boson decays $H^\pm \to t b$ and $H^\pm \to W^\pm H_i^0$, $i=1,2,3$. The study is done in the framework of the type II complex Two Higgs Doublet Model (2HDM) with softly broken $Z_2$ symmetry. In this model violation of CP invariance is induced by the complex parameter $m^2_{12}$ of the tree-level Higgs potential. We calculate the CP violating rate asymmetries for $H^+$ and $H^-$ production and decays as well as for the combined processes at one-loop level and perform a detailed numerical analysis. All calculations are done with the automatic amplitude generator FeynArts and the calculational tool FormCalc, for which we have written a complete complex 2HDM model file and relevant fortran drivers. The implementation of the complex 2HDM in FeynArts and FormCalc is described. In comparison with the analogous results in the MSSM, all considered CP violating asymmetries are smaller by an order of magnitude and do not exceed 2 to 3%.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We study the effects of CP violation in charged Higgs boson production $pp\to t H^\pm + X$ at the LHC, as well as in the charged Higgs boson decays $H^\pm \to t b$ and $H^\pm \to W^\pm H_i^0$, $i=1,2,3$. contribution 0.99 0.74 0.04 asserted 0.69
s1 The study is done in the framework of the type II complex Two Higgs Doublet Model (2HDM) with softly broken $Z_2$ symmetry. method 0.95 0.48 0.02 asserted 0.99
s2 In this model violation of CP invariance is induced by the complex parameter $m^2_{12}$ of the tree-level Higgs potential. method 0.68 0.21 0.03 asserted 1.00
s3 We calculate the CP violating rate asymmetries for $H^+$ and $H^-$ production and decays as well as for the combined processes at one-loop level and perform a detailed numerical analysis. contribution 0.87 0.97 0.14 asserted 0.99
s4 All calculations are done with the automatic amplitude generator FeynArts and the calculational tool FormCalc, for which we have written a complete complex 2HDM model file and relevant fortran drivers. method 0.99 0.91 0.02 asserted 1.00
s5 The implementation of the complex 2HDM in FeynArts and FormCalc is described. method 0.72 0.73 0.02 asserted 0.96
s6 In comparison with the analogous results in the MSSM, all considered CP violating asymmetries are smaller by an order of magnitude and do not exceed 2 to 3%. result 0.99 0.86 0.71 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.59 · evidence from simulation or computation 1.00.

What was examined, and what was not

sources read
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not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures
Figure 1. The tree-level graphs for bg → tH−: a) s-channel, b) t-channel, and charged Higgs decays: c) H− → tb¯ , d) H− → W−H0 1 . 3.2 CP violating asymmetries For the processes listed in section (3.1) we investigate the following CP violating H± rate asymmetries: • Decay rate asymmetries ACP D,f , defined by: A CP D,f (H± → f) = Γ(H+ → f) − Γ(H− → ¯f) 2Γtree(H+ → f) , (3.4) where D stands for decay and f stands for any of the decay modes: f = t ¯b; W±H0 i with i = 1, 2. • Production rate asymmetry ACP P , related only to the process (3.2) and defined by: A CP P = σ(pp → H+t¯) −
Figure 2. Generic CP violating selfenergy and vertex contributions to H− → tb¯ . F denotes a generic fermion, S a generic neutral or charged scalar field, and V a generic vector boson. In the C2HDM, the CP violating phases arise from: • Neutral Higgs couplings to a fermion pair • Charged Higgs – Neutral Higgs – gauge bosons couplings • Charged Higgs – Neutral Higgs – Goldstone bosons couplings The parts of the C2HDM Lagragian needed for this study are given in the appendix C. The CP conserving phases originate from various on-shell intermediate states of the one-loop amplitudes. For the…
Figure 3. Generic CP violating selfenergy and vertex contributions to H− → W−H0 1 . violating one-loop contributions to the decay H± → t ¯b are shown in figure 2 and to the decay H± → W±H0 1 in figure 3. Furthermore, we have three types of possible generic CP violating loop contributions to the partonic cross sections of the production processes (1.1): selfenergy contributions, shown in figure 4; vertex contributions shown in figure 5 and box diagram contributions shown in figure 6. All diagrams have been generated with FA [16] package, for which we – 11 –
Figure 4. Generic CP violating selfenergy contributions to charged Higgs boson production ¯b g → H+t¯. a b g t H F F S F b b g t H F S F S c b g t H F S F V d b g t H F V F S e b g t H F F S F f b g t H F S F S g b g t H F S F V h b g t H F V F S k b g t F H F F S l b g t F H F S F
Figure 5. Generic CP violating vertex contributions to charged Higgs boson production ¯b g → H+t¯. a b g t H F S F F b b g t H F S F S c b g t H F S F V d b g t H F V F S e b g t H S F F F
Figure 6. Generic CP violating box contributions to charged Higgs boson production ¯b g → H+t¯. – 12 –
Figure 7. Left: CPV asymmetry ACP D,tb as a function of MH+ for four values of tan β. The other parameters are: MH0 1 = 120 GeV, MH0 2 = 220 GeV, Re(m12) = 170 GeV, α1 = 0.8, α2 = −0.9 and α3 = π/3. Right: CPV vertex and selfenergy contributions to ACP D,tb, as functions of the charged Higgs mass for tan β = 1.5. -0.018 -0.014 -0.01 -0.006 -0.002 295 310 330 350 370 390 410 ACP(H + →WH1 ) mH + (GeV) tanβ=1.5 =2.0 =3.0 =4.5 -0.04 -0.03 -0.02 -0.01 0 0.01 0.02 295 310 330 350 ACP(H + →WH1 ) mH + (GeV) total vertex selfenergies
Figure 8. Left: CPV asymmetry ACP D,WH0 1 as a function of MH+ for four values of tan β. The other parameters are the same as for figure 7. Right: CPV vertex and selfenergy contributions to ACP D,WH0 1 , as functions of the charged Higgs mass for tan β = 1.5. As we already commented in section 4.1 large values of tan β are excluded, except for some small areas in the region MH0 1 < µ which require fine-tuning of the parameters [35]. Moreover, we have checked that very often for large tan β the mass of the heaviest Higgs boson MH0 3 becomes tachyonic. Therefore in most of the cases we sh
Figure 9. CPV asymmetry ACP D,WH0 2 (3.4), as a function of MH+ for four values of tan β. The other parameters are: MH0 1 = 120 GeV, MH0 2 = 220 GeV, Re(m12) = 170 GeV, α1 = 0.8, α2 = −0.9 and α3 = π/3. here the dominant contribution in the CPV asymmetry comes from the vertex diagrams. For the bosonic channel H± → W±H0 1 , the CPV asymmetry is shown in figure 8. It is seen that ACP D,W H0 1 is negative and can reach ∼ 1.7% for tan β = 1.5 and MH+ close to the lower limit ≈ 297 GeV. In this channel there is also a cancellation between the selfenergy and the vertex contributions, which
Figure 10. The allowed parameter regions in the (α1, α2) plan in the C2HDM together with the absolute value of the CPV asymmetry ACP D,tb. We have taken MH0 1 = 120 GeV, MH0 2 = 220 GeV, MH± = 350 GeV, Re(m12) = 170 GeV, and α3 = π/3. On the top left plot tan β = 1.5, top right: tan β = 2, down left: tan β = 3, and down right: tan β = 4.5. α2 ≈ 0 and α1 ≈ π/3 (yellow color). The position of this region shifts to the right for larger values of tan β. The coupling C(H0 1H±W∓) is complex. Therefore, the condition C(H0 1H±W∓) → 0 also implies that its imaginary part R13 → 0, which furthermore m
Figure 11. The allowed parameter regions in the (α1, α2) plan in the C2HDM together with the absolute value of the CPV asymmetry ACP D,WH0 1 . The other parameters are the same as for figure 10. W±H0 1 ) → 0 and consequently the CPV asymmetry will increase considerably. However, the large rate asymmetry we would obtain in this case, would go together with a small BR of the H± → W±H0 1 decay. In figure 12 we show the BR of H+ → W+H0 1 as a function of α1 for various values of tan β and the other parameters fixed as in figure 10. It can be seen in the plots that in some cases the BR of H+
Figure 12. The BR(H+ → W+H0 1 ) as a function of α1 with α2 in the allowed parameter range. The other parameters are the same as for figure 10. 4.3 CP violation in H±-production We also study the CPV asymmetry ACP P , given by eq. (3.5), for charged Higgs production (3.2) at the LHC with √ s = 14 TeV. For a direct comparison with the results of section 4.2, in figure 13 we present the asymmetry ACP P as a function of the charged Higgs mass MH+ for the same parameter set as used for figure 7. One can see that here the asymmetry is of the same order of magnitude or smaller than in the H± → t
Figure 13. CPV asymmetry ACP P (3.5); Left: as a function of charged Higgs mass for four values of tan β and the other parameters are as in figure 7: MH0 1 = 120 GeV, MH0 2 = 220 GeV, Re(m12) = 170 GeV, α1 = 0.8, α2 = −0.9 and α3 = π/3; Right: vertex, selfenergy and box contributions to ACP P as a function of MH+ for tan β = 1.5. In figure 13 we show the vertex, selfenergy and box contributions to ACP P for tan β = 1.5. The vertex contribution is negative and dominating, especially for smaller masses of the charged Higgs. The selfenergies and box contributions are both positive, but their
Figure 14. The allowed parameter regions in the (α1, α2) plan in the C2HDM together with the absolute value of the CPV asymmetry ACP P . The other parameters are the same as in figure 10. The total number of the scanned parameter points is quite large: 6415200. After having applied the theoretical and experimental constraints, see section 2.5 and section 4.1, the allowed number of parameter points relegates to 67861, which is only 1% of the scanned parameter space. The numerical results based on the parameter scan (4.6) show that in most of the cases the asymmetry is very small, practically…
Figure 15. The maximal value of the asymmetry |ACP P | as a function of α1 and α2 – left; and MH+ and tan β – right, based on the parameter scan (4.6). show that the CPV asymmetry ACP P can reach 3.5 % (negative) for single isolated points of the parameter space. In figure 15 we show the maximal value of |ACP P | as a function of α1 and α2 – left; and MH+ and tan β – right, based on the parameter scan (4.6). One sees small regions where the asymmetry can go up to ∼ 3%. These are roughly: (α1, −α2) ∈ (π/6 ÷ π/3) and relatively large MH+ and tan β: MH+ ∈ (460 ÷ 550) and tan β ∈ (2 ÷ 4). Howev
Figure 16. CPV asymmetry ACP t¯b (3.6) as a function of the charged Higgs mass for four values of tan β and the other parameters are as in figure 7: MH0 1 = 120 GeV, MH0 2 = 220 GeV, Re(m12) = 170 GeV, α1 = 0.8, α2 = −0.9 and α3 = π/3. -0.027 -0.026 -0.025 -0.024 -0.023 -0.022 -0.021 -0.02 -0.019 -0.018 -0.017 295 310 330 350 370 390 410 ACP(pp →tWH1 ) mH + (GeV) tanβ=1.5 =2.0 =3.0 =4.5 -0.015 -0.01 -0.005 0 0.005 0.01 0.015 0.02 0.025 0.03 300 320 340 360 380 400 ACP(pp →tWH 2 ) mH + (GeV) tanβ=1.5 =2.0 =3.0 =4.5
Figure 17. CPV asymmetries ACP WH1 and ACP WH2 (3.6) as functions of MH+ for four values of tan β. The other parameters are: mH0 1 = 120 GeV, mH0 2 = 220 GeV, m12 = 170 GeV, α1 = 0.8, α2 = −0.9, and α3 = π/3. (3.6) as functions of MH+ for four values of tan β. As one can see, here the effect is bigger and the asymmetry ACP W H1 can reach up to 2.5% (negative), while the asymmetry ACP W H2 can go up to 3% (positive). In the analogous study performed in the MSSM [13] the main contribution for the case with the decay H± → tb is due to box graphs with gluino exchange which involves the st

Figures reproduced from arXiv:1011.6560 by the authors.

References
How the literature uses it

36 arXiv papers cite this in 53 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

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  • In the analogous study performed in the MSSM [ref] the main contribution for the case with the decay $H^±→t b$ is due to box graphs with gluino exchange which involves the strong coupling constant.

    CP violation in $H^\pm t$ production at the LHC · CP violation in $H^±$-production and subsequent decays · 0.89

Cites as background 22 papers

Discussion

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