Sub-TeV H + Boson Production as Probe of Extra Top Yukawa Couplings

We suggest searching for the charged Higgs boson at the Large Hadron Collider (LHC) via cg → bH + → bt ¯ b . In the general two Higgs Doublet Model, extra top Yukawa couplings ρ tc and ρ tt can drive the disappearance of antimatter from the Universe, while ¯ cbH + and ¯ tbH + couple with strength ρ tc V tb and ρ tt V tb , respectively. For ρ tc , ρ tt ∼ 0 . 5 and m H + ∼ 300–500 GeV, evidence could emerge from LHC Run 2 data at hand, and discovery by adding Run 3 data in the near future.

We suggest searching for the charged Higgs boson at the Large Hadron Collider (LHC) via cg → bH + → btb. In the general two Higgs Doublet Model, extra top Yukawa couplings ρtc and ρtt can drive the disappearance of antimatter from the Universe, whilecbH + andtbH + couple with strength ρtcV tb and ρttV tb , respectively. For ρtc, ρtt ∼ 0.5 and m H + ∼ 300-500 GeV, evidence could emerge from LHC Run 2 data at hand, and discovery by adding Run 3 data in the near future.
Introduction.-The discovery of the Higgs boson h(125) at the LHC [1] suggests a weak scalar doublet, but there is no principle that precludes the existence of a second doublet. Having two Higgs doublets (2HDM), one has a charged H + boson plus the CP -even/odd scalar bosons H, A [2].
We propose a novel process, cg → bH + (see Fig. 1) followed by H + → tb, that may lead to the discovery of the exotic H + boson in the near future.
In the popular 2HDM type II (2HDM-II), up-and down-type quark masses arise from separate doublets [2], hence mass and Yukawa matrices are simultaneously diagonalized, just like in the Standard Model (SM). The model motivates an H + search at the LHC via the processbg →tH + [3,4] which goes through thetbH + coupling, while the cg → bH + process is suppressed by the Cabibbo-Kobayashi-Maskawa (CKM) matrix element ratio |V cb /V tb | 2 ∼ 1.6 × 10 −3 . But in the general 2HDM (g2HDM) with extra Yukawa couplings [5],cbH + and tbH + couple with strength ρ tc V tb and ρ tt V tb , respectively, and cg → bH + is not CKM-suppressed.
The extra top Yukawa couplings [5] ρ tc and ρ tt are not well constrained. If both are O(1), i.e. the top Yukawa coupling strength λ t in SM, they facilitate the production and decay in cg → bH + → btb [6,7], with the signature of lepton plus missing energy and three b-jets. It is known [8] that ρ tc and ρ tt at O(1) can each drive electroweak baryogenesis (EWBG), hence account for the disappearance of antimatter shortly after the Big Bang, one of the biggest mysteries. Perhaps equally interesting, when the ACME 2018 bound [9] on electron electric dipole moment (eEDM) seemed to rule out the ρ tt parameter space of Ref. [8], a second paper [10] brought in the extra electron Yukawa coupling, ρ ee , and showed that a natural cancellation mechanism can survive the ACME18 bound, and with expanded parameter space for EWBG. This gives strong motivation for the cg → bH + → btb search.
The recent CMS hint of an "excess" [11] in gg → A → tt at m A ∼ 400 GeV could also arise from ρ tt ∼ O(1) [12].
In this Letter, we first show that the H, A and H + bosons in g2HDM can be sub-TeV in mass while satisfying all known constraints. This is in contrast with the absence of beyond SM (BSM) signatures so far at the LHC, with bounds often reaching multi-TeV in scale.
We then show that ρ tc , ρ tt at O(1) is allowed by current bg →tH + and other search bounds. Full Run 2 data could already give evidence for cg → bH + → btb, and discovery is possible by adding Run 3 data. Dimension-4 Higgs Couplings.-Besides gauge couplings, Higgs bosons uniquely possess two additional sets of dimension-4 couplings: Higgs quartic and Yukawa interactions. In the Higgs basis, one can write the most general CP -conserving potential [13,14] in g2HDM as where all quartic couplings η i are real, Φ induces spontaneous symmetry breaking by the vacuum expectation value v, i.e. µ 2 11 = − 1 2 η 1 v 2 < 0, while Φ = 0 hence µ 2 22 > 0. The minimization condition µ 2 12 = 1 2 η 6 v 2 reduces the parameter count to nine. From Eq. (1) one finds m 2 Finally, η 6 mixes h (0) and H (0) into h and H. The emergent alignment phenomenon, that h resembles the Higgs boson of the SM so well [15][16][17], implies that the h-H mixing angle c γ ≡ cos γ (denoted usually as − cos(β − α)) is rather small.
The Yukawa couplings to quarks are [13,14] where λ f i =   while in the alignment limit of c γ → 0, h couples diagonally and H carries the extra Yukawa couplings ρ f ij . Thus, besides mass-mixing hierarchy protection [18][19][20] of flavor changing neutral Higgs (FCNH) couplings, alignment provides [14] further safeguard, without the need of Natural Flavor Conservation [21]. The importance of ρ tt and ρ tc was emphasized [5] already at the h(125) discovery, and was subsequently shown [8] to possibly drive EWBG.
From Eq. (2) one finds that the leadingcbH + and tbH + couplings are ρ tc V tb and ρ tt V tb , respectively [22], where there is no CKM-suppression of the former [23] as in 2HDM-II. In this Letter, we take m H + > m t [24] and focus on the cg → bH + → btb process at the LHC. Note that the gg →cbH + process discussed in Ref. [7] bears some similarity, but Fig. 1(left) was not mentioned explicitly, and a detailed collider study was not performed, hence the promise was not sufficiently demonstrated. Constraints on Higgs Parameters.-Higgs quartics need to satisfy positivity, perturbativity and tree-level unitarity, which we implement via 2HDMC [25]. We express [13,14] η 1 , η 3−6 in terms of µ 22 , m h, H, A, H + (all normalized to v) and cos γ, plus η 2 , η 7 that do not enter Higgs masses. Since H + Yukawa couplings do not depend on c γ , which is known to be small, we set c γ = 0 for simplicity while fixing m h ∼ = 125 GeV, hence [14] η 6 = 0 and η 1 = m 2 h /v 2 . Thus, e.g. t → ch does not constrain ρ tc . In the common Higgs basis, we identify η 1−7 with the input parameters Λ 1−7 to 2HDMC.
For fixed m H + , we randomly generate the parameters in the ranges |η 2−5, 7 | ≤ 3 (positivity requires η 2 > 0), µ 22 ∈ [0, 1] TeV, and m A, H ∈ [m H + − m W , 650 GeV] to forbid H + → AW + , HW + . We then use 2HDMC for scanning, where the electroweak oblique parameter constraints (including correlations) are imposed, e.g. the 2σ range of −0.17 < T < 0. 35 [26], which restricts [27,28] the scalar masses hence the η i s. Scan points satisfying these constraints are plotted in Fig. 2 in the m H -m A plane for m H + = 300, 500 GeV, illustrating that finite parameter space exist. We choose a benchmark for each η2 η3 η4 η5 η7 m H + value and list the parameters in Table I. More details of our scanning procedure is given in Ref. [29]. Flavor Constraints.-Flavor constraints on ρ tt and ρ tc are not particularly strong [5,30]. For m H + 500 GeV, B q mixings (q = d, s) provide the most stringent constraint. An H + effect from ρ ct to the M q 12 amplitude is enhanced by |V cq /V tq | ∼ 25, hence ρ ct must be turned off [30]. Assuming all ρ ij vanish except ρ tt , we have M q 12 /M q 12 | SM = C Bq , with negligible phase. Allowing 2σ error on C B d = 1.05 ± 0.11 and C Bs = 1.11 ± 0.09 [31], we find the blue shaded exclusion region (extending to upper-right) in Fig. 3, where the left (right) panel is for BP1 (BP2). The constraint from H + effects via charm loops [32] gives ρ tc 1 (1.7) for BP1 (BP2).
B → X s γ puts a strong constraint on m H + in 2HDM-II, but weakens for g2HDM due to extra Yukawa couplings. In fact, an m t /m b enhancement factor constrains ρ bb more strongly [30] than ρ tt . Taking ρ bb as small, the constraint on ρ tt falls outside the range of Fig. 3. The B → X s γ constraint on ρ tc via charm loop is weaker than B q mixing [30]. Note that flavor constraints would grow weaker for m H + heavier than our benchmarks. Collider Constraints.-To focus on our signal process, we set all ρ ij = 0 except ρ tt and ρ tc for simplicity.
Heavy Higgs searches via gg → H/A → tt can constrain ρ tt . ATLAS [37] searched at 8 TeV for m A/H > 500 GeV; with 36 fb −1 at 13 TeV, CMS constrains the "coupling modifier" [11] for m A/H = 400-750 GeV for various Γ A/H /m A/H values. Both ranges are above BP1, while for BP2 the bounds are weaker than results shown  [3] and CMS [4] for ρtc = 0 are overlaid (purple and red shaded), which is weakened for ρtc = 0.4 (dash) and 0.8 (dots). See text for details.
Based on 137 fb −1 at 13 TeV, the CMS 4t search [38] constrains ρ tc and ρ tt . We first note that the direct limits from σ(pp → ttA/ttH) B(A/H → tt) for m A/H ∈ [350, 650] GeV are again weaker than results shown Fig. 3. With both ρ tc and ρ tt finite, the cg → tH/tA → ttt process [39] can feed the Signal Region, SR12, of the CMS 4t search if all three top quarks decay semileptonically. As cg → tH/tA → ttt barely occurs for BP1 because of low m A, H values, this applies only to BP2. SR12 requires [38] at least three leptons, four jets with at least three b-tagged, plus missing p T . Following Ref. [12], we generate events and interface with PYTHIA 6.4 [40] for showering and hadronization, adopt MLM merging [41] of matrix element and parton shower, then feed into Delphes 3.4.2 [42] for CMS-based fast detector simulation, including b-tagging and c-and light-jet rejection. We find ρ tt 1 is excluded if ρ tc ∼ 0.8 for BP2. Noting that H + → cb decay from finite ρ tc would dilute B(H + → tb) and soften the bg →t(b)H + constraint, we illustrate this effect by the dash (dot) curves in Fig. 3(right) for ρ tc = 0.4 (0.8).
The cg → tH/tA → ttc process [39] can feed the Control Region for ttW (CRW) background of CMS 4t study when both tops decay semileptonically. With CRW defined by same-sign dileptons (e or µ), p miss T , and up to five jets with at least two b-tagged, we follow Refs. [12,43] and find ρ tc 0.4 is excluded for BP1, which is stronger than the B q mixing bound, and with little dependence on ρ tt . For BP2, we find that CRW gives comparable limit as SR12. Thus, we illustrate in Fig. 3(left) the softened bg →t(b)H + constraint only for ρ tc = 0.4.
We remark in passing that the ATLAS search for samesign di-leptons and b-jets [44], or search for supersymmetry in similar event topologies [45], impose stronger cuts and in general do not give relevant constraints. Collider Signature for cg → bH + → btb.-We now show that the cg → bH + → btb process, or pp → bH + + X → btb + X, is quite promising.
Signal and background samples are generated at LO for 14 TeV as before by MadGraph, interfaced with PYTHIA and fed into Delphes for fast detector simulation adopting default ATLAS-based detector card. The LO tt+jets background is normalized to NNLO by a factor 1.84 [47], and factors of 1.2 and 1.47 [48] for t-and s-channel singletop. The LO W t+jets background is normalized to NLO by a factor 1.35 [49], whereas the subdominant tth, ttZ receive factors of 1.27 [50], 1.56 [51]. The DY+jets background is normalized to NNLO by a factor 1.27 [52]. Finally, the 4t and ttW − (ttW + ) cross sections at LO are adjusted to NLO by factors of 2.04 [34] and 1.35 (1.27) [53]. The tW h and W +jets backgrounds are kept at LO. Correction factors for other charge conjugate processes are assumed to be the same, and the signal cross sections are kept at LO.
Events are selected with one lepton, at least three jets with three b-tagged, and E miss T > 35 GeV. Jets are reconstructed by anti-k t algorithm using radius parameter R = 0.6. The lepton p T should be > 30 GeV, with all three b-jet p T > 20 GeV, and pseudo-rapidity (|η|) of lepton and b-jets < 2.5. The ∆R separation between a b-jet and the lepton, or any b-jet pair, should be > 0. 4 sum of the lepton and three leading b-jet transverse momenta H T should be > 350 (400) GeV for BP1 (BP2). We have not optimized the selection cuts for H T , p T , E miss T , etc. The total background cross section B tot after selection cuts and its various components, together with the signal cross section Sig, are given in Table II.
Discussion and Summary.-A 3.5σ local (1.9σ global) excess at m A ≈ 400 GeV was reported by CMS [11] in gg → A → tt search. The excess can be explained [12] with sizable ρ tt ∼ 1.1, ρ tc ∼ 0.9 for m H 500 GeV, m H + 530 GeV. The bound on m H is from the cg → tH → ttt process, while the slightly higher bound on m H + arises from combining B q mixing and bg →tH + constraints and the opening of H + → AW + decay. Although not our benchmark, for m A = 400 GeV, m H , m H + = 500, 530 GeV and ρ tt ∼ 1.1, ρ tc ∼ 0.9, we find that cg → bH + could reach up to 11σ significance with full Run 2 data! While exciting if the excess is confirmed, it could also become problematic for the g2HDM if cg → bH + is not seen.
One may have same-sign top signature via cg → tA/tH → ttc. Following the same analysis of Refs. [39,43], we find BP1 may have ∼ 3.5σ significance with full Run 2 data, but below ∼ 1σ for BP2 due to dilution from A/H → tt decay and falling parton luminosity.
Single-top studies may contain cg → bH + events. For ρ tc = 0.4 and ρ tt = 0.6, we find the combined cross sections for pp → H + [tb]j, H + [cb]t can contribute 15.2 (2.9) pb for BP1 (BP2), well within the 2σ error of current t-channel single-top [57,58] measurements. The situation is similar for Run 1 with s-channel single-top.
We have not included uncertainties from scale dependence and PDF [59,60], where the latter is sizable for processes initiated by heavy quarks. Using LO signal cross sections can also bring in some uncertainties, e.g. higher order corrections [49,61] to σ(bg → tH + ) may be 30-40% for m H + ∼ 300-500 GeV. A detailed study of such uncertainties is left for the future, and is part of the reason why we adopt conservative ρ tc , ρ tt values.
Finally, our 300-500 GeV mass range is not just for its promise. Significance can still be high at higher masses for larger ρ tc , ρ tt , but the decoupling µ 2 22 would have to become larger [14] (as can be seen from µ 2 22 /v 2 3.78 for BP2 in Table I), which would start to damp the EWBG motivation. But the cg → bH + process can certainly be pursued for heavier m H + at higher luminosities.
In summary, extra top Yukawa couplings ρ tc and ρ tt entercbH + andtbH + couplings without CKM suppression, leading to the cg → bH + → btb signature of lepton plus missing energy and three b-jets. For conservative ρ tc , ρ tt ∼ 0.5, evidence could already emerge with full LHC Run 2 data for m H + = 300-500 GeV, with discovery at 300 fb −1 and beyond, which would unequivocally point to physics beyond the Standard Model.