A Final Word on FCNC-Baryogenesis from Two Higgs Doublets

Electroweak baryogenesis in a two-Higgs doublet model is a well-motivated and testable scenario for physics beyond the Standard Model. An attractive way of providing $CP$ violation is through flavor-changing Higgs couplings, where the top-charm coupling is hardly constrained. This minimal scenario can be tested by searching for heavy charged and neutral Higgs bosons at the LHC. While the charged Higgs signature requires a dedicated analysis, the neutral Higgs signature will be covered by a general search for same-sign top pairs. Together, they provide a conclusive test of this kind of baryogenesis.

If we use baryogenesis [23] as a guiding principle to new physics searches at the LHC, a 2HDM is an attractive and minimal choice. It can provide both, new scalar degrees of freedom [24,25] and CP -violation. In the general [26,27] or type-III [28] 2HDM, the new particles can be close in mass to the SM-Higgs [29,30]. Sufficiently large CP -violation is nontrivial to achieve, in our model we rely on the Yukawa sector. If both doublets couple to uptype and down-type quarks, they define two separate Yukawa matrices. After diagonalizing the quark mass matrices we find the real, diagonal couplings λ ii = √ 2m i /v and the complex, nondiagonal couplings ρ ij . While flavor-changing neutral couplings are generally well-constrained, it is possible to have electroweak baryogenesis (EWBG) driven by a single, order-one, complex coupling ρ tc [31], Im ρ tc 0. 5 and | cos γ| 0.1 , where γ is the mixing angle between the two CP -even Higgs states.
It has been shown [32][33][34][35][36] that the coupling ρ tc can be discovered in the LHC process where this process retains a very mild dependence on cos γ and is especially useful for small values of cos γ. To attribute this signal to EWBG requires information on the mixing angle cos γ, for instance through b-associated charged Higgs production [37] cg → bH + → b (W + h) .
Here the production process is induced by ρ tc [38,39], while the decay amplitude is proportional to the mixing angle cos γ. Even in the absence of complex phase information, such a search can test the required particle content and parameter space for the ρ tc -EWBG scenario. Finally, the exotic top decay is induced by the coupling ρ tc combined with non-vanishing cos γ [28] and is searched for by CMS [40] and ATLAS [41].
In this paper we show how the two LHC searches for charged and neutral heavy Higgs bosons can conclusively probe the parameter region required for ρ tc -EWBG in the general 2HDM (g2HDM). The paper is organized as follows: in Sec. 2 we discuss the model and its preferred parameter space, and then compare it to the reach of the charged Higgs channel in Sec. 3. Section 4 is dedicated to same-sign top production from neutral Higgs production and its complementarity to the charged Higgs signature. We summarize our results in Sec. 5.
On the other hand, given experimental constraints and a possible order-of-magnitude correspondence in the values of ρ F and λ F lead us to consider ρ U tj or ρ U tt . In principle, a complex ρ tt can robustly drive EWBG [31], which motivates search for channels like gg → H → tt or gg → Htt → 4t [52][53][54]. In this paper we focus instead on complex off-diagonal entries ρ tj , specifically ρ tc . With a large phase, this FCNC coupling can also account for the observed baryon asymmetry [31]. One of its merits is that ρ tc does not 400 500 600 300 400 500 600 generate an electron EDM through the Barr-Zee [55] two-loop mechanism, and can therefore more easily [56] evade the ACME bound [57] d e < 1.1 × 10 −29 e cm. Moreover, if we assume ρ ct to be small, the constraint on ρ tc from the charm chromo-EDM also vanishes [58]. We therefore define our specific baryogenesis scenario as [31] |ρ tc | 0.5 and |c γ | 0.1 , with a sufficiently large complex phase. A strong first-order phase transition is then possible for [59][60][61][62][63][64][65][66][67][68] m A,H,H + ∼ 300 ... 600 GeV.
This mass range is allowed by perturbativity, positivity, unitarity, and electroweak precision data. We rely on 2HDMC [69] to provide the results of Fig. 1  As the first constraint on c γ and the set of ρ ij we consider measurements of the SM-like Higgs. Higgs coupling measurements constrain the Higgs mixing angle to c γ ≤ 0.3 and 95%CL. Our choice of ρ tc as the source of CP -violation is motivated by its much weaker constraints, because it hardly affects SM-like Higgs production and decay. The relevant constraints on ρ tc are indirect. For flavor observables, ρ tc enters through loops with charm quarks and a charged Higgs into B s − B s mixing and B(B → X s γ). Reinterpreting the limit from Ref. [73] we find |ρ tc | 1, for m H + = 300 GeV, and its counterpart for m H + = 500 GeV is illustrated in Fig. 2, alongside with the EWBGregion. The limit is relatively weak in our general model, in contrast to the type-II 2HDM, and for larger m H + it rapidly becomes irrelevant. Finally, finite c γ in combination with ρ tc [26]  leads to anomalous top decays t → ch [28], forbidden at tree level in the SM. The current Run 2 limits at 95%CL are They get weaker for smaller c γ and vanish in the alignment limit. We illustrate the stronger ATLAS [41] constraint also in Fig. 2, along with the projected HL-LHC 95%CL upper limit B(t → ch) < 1.0 × 10 −4 [74]. While an observation of this anomalous decay could point to a large value of |ρ tc |, if would not provide a link to baryogenesis. A natural step towards solving the baryogenesis puzzle would be to search for new scalar degrees of freedom related to this flavor-changing coupling.
While we will focus on ρ tc throughout this paper, we point out that ρ tu can be tested using a very similar strategy. For the LHC processes discussed in the coming sections, there is always a corresponding process with an up-quark replacing the charm-quark. One difference between the two FCNC scenarios is that ρ tu can induce observable effects in B(B → µν) [75], within the reach of Belle-II [76]. The combination of ρ tc and ρ tu is subject to very strong constraints from D-D mixing [73], and we will assume only one of the two, but not both at the same time.

Charged Higgs production
In the EWBG parameter region of Eq.(9), the partonic process at LHC probes ρ tc in H + -production and c γ in the decay H + → W + h. The production benefits from the relatively large charm density in the proton, as well as the combination [39] with the CKM matrix element V tb following Eq. (7). The leading-order Feynman diagrams are presented in Fig. 3. While we will require a tagged b-jet, the b-inclusive production process could also be defined as cb → H + [77,78]. For a clean analysis, we assume that all three W -bosons decay to either electrons or muons. The same process is induced by ρ ct , but this coupling is constrained to be much smaller [79] by flavor constraints.
The H + W − h coupling, modulated by c γ , arises from [13,14] L where g 2 is the SU (2) gauge coupling. To estimate the reach of our charged Higgs signal, we choose two allowed benchmark points, ρ tc = 0.35, c γ = 0.25, m H + = 350, 500 GeV, (15) as given in Tab. 1. For the branching ratios, we ignore the loop-induced decays H + → W + γ and H + → W + Z. We generate signal and background events for √ s = 14 TeV at leading order with MadGraph5 aMC@NLO [80]. The effective model is implemented in the FeynRules [81] framework, and for parton densities we use NN23LO1 [82]. The events are showered and hadronized with PYTHIA6.4 [83] and then handed to Delphes 3.4.2 [84] for a fast detector simulation with the default ATLAS card. Jets are reconstructed with an R = 0.6 anti-k T algorithm [85] in FastJet [86]. For b-tagging as well as c-jet and light-jet rejections, we also rely on the default ATLAS card. To allow for extra jets we apply MLM matching [87,88] with the default MadGraph5 aMC run card. The signal is generated with up to two additional jets, do account for higher-order effects in the event kinematics.
The dominant SM-backgrounds are ttW and ttZ production, followed by W Z + jets, 4t, tth, tZj, tW Z, and ZZ + jets. Furthermore, we find the backgrounds 3t, 3t+W , and 3W to be negligible, so we ignore them in our analysis. However, given a mis-identification probability  Table 2: Background cross sections for the charged Higgs process after cuts.
for a jet as a lepton around 10 −4 [89,90], tt production will lead to non-trivial background contributions. For all backgrounds, we use the same simulation chain as for the signal, with up to one additional jet for ttW , ttZ, W Z + jets, ZZ + jets, tZ + jets, tt+ jets, and no QCD jets for the high-multiplicity backgrounds 4t, tW Z and tth. To approximately account for QCD corrections in addition to the jet emission, we attach NLO K-factors to the dominant ttV backgrounds, namely 1.35 (W − ), 1.27 (W + ) [91], and 1.56 (Z) [92]. We also correct the W Z + jets and tt+ jets background normalizations to NNLO by factors 2.07 [93] and 1. 84 [94] respectively. Furthermore, we adjust the 4t, tth, andtZ + jets rates to NLO through the Kfactors 2.04 [80], 1.27 [95] and 1.44 [80]. The cross sections for the signal and tW Z are kept at LO for simplicity. Here, we simply assume the QCD correction factors for the W + Z + jets and tZ + jets processes to be the same as their respective charge-conjugate processes.
To suppress the backgrounds, we adopt a simple set of requirements. We start with events containing at least three charged leptons and at least one tagged b-jet passing p T, > 20 GeV, |η | < 2.5, The same-flavor opposite-sign dilepton veto reduces the dominant ttZ background. In case more than one such + − pair exists, we select the combination closest to the Z-mass for rejection. The remaining signal rate is given in Tab. 1, while the background rates are summarized in Tab. 2.
For discovery reach and exclusion limits, we compute the significance using the likelihood for a simple counting experiment [96]. If we observe n events with n pred predicted, the agreement between observation and prediction is given by For discovery, we compare the observed signal plus background with the background prediction and require Z(s + b|b) > 5. For exclusion, we assume a background-consistent measurement after predicting a signal on top of the background, such that Z(b|s + b) > 2. For instance, assuming an HL-LHC data set with 3000 fb −1 and the signal and background cross sections in Tabs. 1 and 2, we find a significance of ∼ 5.6σ for m H + = 350 GeV and ∼ 5σ for m H + = 500 GeV.
We illustrate in Fig. 4 the Run 3 and HL-LHC reach for the charged Higgs signature in the |ρ tc |-c γ plane. We see from the left panel that Run 3 can exclude |ρ tc | > 0. 3  m H ± = 350 GeV, while the HL-LHC will be sensitive to |ρ tc | > 0.2 and |c γ | = 0.14. For larger Higgs masses, the expected limits become only slightly weaker. The b-associated charged Higgs channel covers the |ρ tc | range preferred by EWBG, but there remains a slice of EWBG parameter space with |c γ | 0.14. This follows as an effect of decreasing B(H ± → W ± h) with smaller c γ . Unfortunately, this hole is unlikely to be filled by other charged Higgs decays, because for instance the standard signature H + → tb requires large production rates. Here, utilizing the expression from Ref. [73], the limit from B s in the left panel of Fig. 4 is plotted for m H + = 350 GeV to conform with the benchmark charged Higgs mass for pp → bH + → bW + h signature.

Neutral Higgs production
To cover the parameter region |c γ | < 0.14, left open by the charged Higgs signature, we turn to the neutral Higgs channel, also given in Fig. 3, where production and decay are both mediated by ρ tc . A very slight c γdependence of the cg → tH/tA → ttc process arises from the heavy Higgs branching ratios. Non-resonant and t-channel diagrams with H/A exchange leading to cc → tt scattering as well as gg → ttcc, though small, are included in our signal analysis.
For small c γ , the neutral Higgs production process currently leads to the most stringent limit on ρ tc [33,97], because it affects the SM control region of the Run 2 tttt (4t) analysis by CMS [98]. Based on the number of b-jets and leptons, CMS divides its analysis into several signal and two control regions. The most stringent constraint on ρ tc arises from the ttW control region (CRW) [32,33]. The CMS baseline selection includes two same-sign leptons with p T, > 25, 20 GeV and |η e | < 2.5, where the charge-misidentified Drell-Yan background is reduced by vetoing same-sign electron pairs with m ee < 12 GeV. The CRW then requires two to five jets, two of them b-tagged. All jets have to fulfill |η j | < 2.4, and events are selected if they fulfill any one of Finally, the analysis requires [98] H T = jets p T,j > 300 GeV and / E T > 50 GeV.
With this selection, CMS observes 338 events with 335 ± 18 events expected from SMbackgrounds plus 4t signal. To estimate the CRW limits on ρ tc , we generate both neutral Higgs processes with the decay H/A → tc, followed by lepton-hadron combinations of the top decays at √ s = 13 TeV. We use the same setup as for the charged Higgs simulations, except that we use the default CMS detector card in Delphes 3.4.2. Remaining uncertainties on our simulation affect the c-initiated processes cg → bH + and cg → tA/tH, such as from parton densities and scale dependence [78,[99][100][101]. We expect them to be small, and do not include them, just as we do not account for non-prompt and fake backgrounds.
There exist a similar ATLAS search [102], but it is less constraining [103]. This is primarily due to the definition of signal regions and selection criteria. Furthermore, searches for squark pair production in R-parity violating supersymmetry [104] and exotics searches for same-sign dileptons and b-jets [105] involve similar final states, but their selection cuts are too modelspecific to be applied to our signature.
To judge the impact of the existing CMS CRW limits from 4t search, we focus on the border of the EWBG-region with c γ = 0.1 and |ρ tc | = 0.5. We stick to our two charged Higgs masses, assume m A ≈ m H ± = 350, 500 GeV for the pseudoscalar, and decouple the heavy scalar H. In this scenario, the same-sign top contribution to the CRW arises from cg → tA → ttc. We demand that the combination of SM-backgrounds and heavy neutral Higgs production agree with observed within 2σ and give the excluded regions in Fig. 5. To scan the parameter space we use a simplified scaling |ρ tc | 2 B(A → tc), such that Γ A = 3.05 (6.08) GeV for m A = 350 (500) GeV. The exclusion covers most of the EWBG-region except for small values of |ρ tc |.
A dedicated same-sign top search, such as the pp → tA + X → ttc + X study of Ref. [103], can probe the nominal parameter space of ρ tc -EWBG. This process can be searched for in events containing same-sign dileptons (ee, µµ, eµ), at least three jets with at least two b-tag, and some / E T . The dominant backgrounds are ttZ, ttW , 4t, while tth, with tZ + jets, 3t + W and 3t + j give subdominant contributions, and the non-prompt background can be 1.5 times the rate of ttW . In addition, if a lepton charge gets misidentified, the tt + jets and Z/γ * + jets processes will also contribute. For further details of the QCD correction factors for different backgrounds, we refer to Ref. [103]. To reduce backgrounds, we applied an event selection  For the reference values |ρ tc | = 0.5 and c γ = 0.1, we generate the same-sign top cross sections for m A = 350 and 500 GeV. Based on the background rates of Tab. 3 and Eq. (17), rescaling the signal cross section by |ρ tc | 2 B(A → tc), we find the exclusion (green dashed) and discovery (green solid) contours in the |c γ |-|ρ tc | plane as given in Fig. 5.
A loop hole in the neutral Higgs analysis appears though the destructive interference of cg → tH → ttc and cg → tA → ttc. If the widths and masses of the two heavy neutral Higgses become degenerate, the two production processes completely cancel [32,33] and the same-sign top signature vanishes. Our limits derived from A-production would be similar for H-production with /v 2 = 1.189 (3.516), in agreement with perturbativity, positivity, unitarity, and electroweak precision data [69]. The relevant decays are A → tc, Zh and H → tc, hh, ZZ, W W , with mild contributions from the λ f c γdependent fermionic decays to bb and tt. For ρ tc = 0.5 and c γ = 0.1, the total widths are Γ A = 3.28 (7.37) GeV and Γ H = 2.91 (6.56) GeV, and the combined contributions to the CRW rates are 0.467 fb and 0.261 fb, corresponding to 64 and 35.8 events. Demanding that the combination of events expected in the SM and from the neutral Higgs channels agree within 2σ of the observed number, we find that |ρ tc | = 0.5 is already excluded for m H ± = 350 GeV and c γ = 0.1, and barely allowed for m H ± = 500 GeV. We see that, due to the choice of parameters, the cancellation between cg → tH → ttc and cg → tA → ttc is not exact, and the CRW limit is stronger than the H (or A) decoupled case.
As mentioned in the introduction, we ignore all ρ ij couplings except for ρ tc , so before closing we should discuss the impact of this assumption. It may well be that the ρ U,D,L matrices share the flavor-ordering of the Yukawa couplings, ρ tt ∼ λ t , ρ bb ∼ λ b and ρ τ τ ∼ λ τ . Current data still allows ρ tt 0.5 [39] and ρ bb ∼ 0.1 [71,72] for sub-TeV scalars, and both parameters can account for the observed baryon asymmetry. The extra top Yukawa coupling ρ tt can be searched for in signatures such as gg → A/H → tt [106,107] gg → A/Htt → tttt [98] and gb →tH + →ttb [77,78,108,109], while rare decays B(B → X s γ) and B d,s mixing provide indirect probes [79]. In general, a large value for ρ tt dilutes the decays A/H → tc and H + → (gray shades), as well as HL-LHC expectations from a dedicated same-sign top search [103] (green). We also show the EWBG region and the indirect constraints from Fig. 2 and the HL-LHC charged Higgs reach from Fig. 4.
W + h through A/H → tt and H + → tb. However, the combination with ρ tc opens additional discovery modes such as cg → tA/tH → ttt [32] and cg → bH + → btb [39]. There also exist several direct and indirect constraints on ρ bb [71,72]. Finally, a large allowed value of ρ tu [103] combined with non-vanishing ρ tc will be constrained by D-meson mixing [73,79]. Similarly, constraints on ρ tt , ρ bb , ρ τ τ from flavor physics and low energy observables as discussed in Refs. [38,72,73,79], and their detailed impact on the ρ tc -EWBG would be an interesting future direction.

Outlook
Electroweak baryogenesis is an attractive target for experimental analysis, because it can be tested by a variety of measurements. Specific models typically combine new bosonic degrees of freedom with extra CP -violation. In our case, the new degrees of freedom are provided by a general or type-III 2HDM. If the Higgs self-couplings are sufficiently large, the heavy Higgs states can be relatively heavy, so we use m H + = 350 and 500 GeV as benchmark scenarios. The complex phase is given by an FCNC top-charm coupling with |ρ tc | 0.5, combined with a CP -even Higgs mixing angle c γ 0.1. At the LHC, ρ tc has the advantage that we can test it in processes mediated by this large top Yukawa, but with a charm quark in the initial state, while it easily evades EDM constraints.
In the allowed 2HDM parameter space, the charged Higgs has to be relatively light, which means we can search for it via cg → bH + with a subsequent H + → W + h decay. Our proposed analysis is relatively straightforward and probes most of the EWBG parameter space at the HL-LHC, with the exception of small values of c γ ∼ 0.1 ... 0.12, when H + → W + h decay becomes too suppressed by CP -even Higgs boson mixing.
A complementary channel that can survive small CP -even Higgs boson mixing is heavy neutral Higgs production, cg → tA/tH, together with A/H → tc decay. In this case, production and decay are both mediated by ρ tc without being suppressed by small c γ , providing strong limits on ρ tc even for small c γ values.The search channel at the LHC is same-sign top pairs, allowing us to extract limits already from Run 2. At the HL-LHC, the decay t → ch, charged heavy Higgs searches, and neutral heavy Higgs searches guarantee a comprehensive coverage of the ρ tc -EWBG parameter space in the general 2HDM, leaving us with the challenge of observing the CP -violating phase in a dedicated analysis.