Searching for additional bottom Yukawa coupling via $bg\to b A \to b Z H$ signature

The recent discovery of the bottom quark Yukawa coupling ($hbb$) of the 125 GeV scalar motivates one to search for extra bottom Yukawa coupling that may exist in the nature. The two Higgs doublet model without a discrete $Z_2$ symmetry allows the possibility of additional bottom Yukawa coupling $\rho_{bb}$. We show that $\rho_{bb}$ can be searched directly at the LHC via $bg\to b A \to b Z H$ and $gg \to b \bar b A \to b \bar b Z H$ processes, where $A$ and $H$ are the CP-odd and CP-even scalars respectively. We find that the $bg\to b A \to b Z H$ process could be discovered with $\sim300$ fb$^{-1}$ integrated luminosity if $ m_A \sim 300$ GeV, while the latter process may emerge in the high luminosity LHC (HL-LHC) data. A discovery might touch upon the parameter space required for the electroweak baryogenesis.


I. INTRODUCTION
The discovery of the 125 GeV scalar boson h [1] and its properties corroborate that the Standard Model (SM) is the correct effective theory at around weak scale. Although, no clear evidence of new physics (NP) has been found, the Run-2 era of LHC witnessed one of the most intriguing discovery, that is the bottom quark Yukawa coupling hbb [2,3]. The observation was announced simultaneously by the ATLAS and CMS collaborations. Both the experiments performed searches mainly in the process where h is produced in association with a Z or W boson and followed by the h → bb decay. When combined with the results from other searches in the Run-1 and Run-2 with the h → bb decay, the observed signal strengths relative to the SM expectation were reported to be 1.01 ± 0.12(stat.) +0. 16 −0.15 (syst.) at ATLAS [2], while 1.04±0.14(stat.)±0.14(syst.) at CMS [3]. Although they are consistent with the SM prediction, both the measurements are quite accommodating for NP contribution. In the backdrop of these recent observations, it is timely to ask whether there exists any additional bottom Yukawa coupling in the nature. In this article we explore the possibility of direct detection and identification of such extra bottom Yukawa coupling at the LHC.
The context is the two Higgs doublet model (2HDM). In the absence of discrete Z 2 symmetry, which was invoked to ensure Natural Flavor Conservation (NFC) [4] of Glashow and Weinberg to forbid flavor changing neutral Higgs couplings, both the doublets couple to upand down-type quarks. After the diagonalization of the fermion mass matrices two independent Yukawa matrices λ F ij = ( √ 2m F i /v) δ ij (with v 246 GeV) and ρ F ij emerge, where F denotes up-and down-type quarks and, leptons. The Yukawa matrices λ F ij are real and diagonal, where as, ρ F ij are in general non-diagonal and complex. Our focus of interest is the the extra bottom Yukawa coupling ρ bb . In this paper, we analyze the prospect its direct detection at the LHC via bg → bA → bZH and gg → bbA → bbZH processes (charge conjugate processes are implied) with b-tagging.
We investigate the discovery potential of ρ bb via pp → bA + X → bZH + X (X is inclusive activity) with Z → + − ( = e, µ) and H → bb (denoted as bZH process) at the 14 TeV LHC. In finding the discovery potential we assumed the extra top Yukawa coupling ρ tt to be relatively small to avoid the direct search constraints from gg → A/H. A sizable ρ bb would also induce gg → bbA → bbZH which provides additional probe for ρ bb . We study this process via pp → bbA+X → bbZH+X followed by Z → + − and H → bb (denoted as bbZH process). Recently, ρ bb received additional significance as it can drive electroweak baryogenesis (EWBG) rather efficiently [5]. It was shown that O(0.1) imaginary ρ bb (Im(ρ bb )) can successfully generate the observed Baryon Asymmetry of the Universe [5]. Although, the information of the phase could not be captured in the bZH and bbZH processes, however, a discovery might indicate ρ bb driven EWBG.
The paper is organized as follows. We outlined the formalism in the Sec. II, followed by discussion on the relevant constraints and available parameter space in the Sec. III. The Sec. IV is dedicated to the collider signatures of the bZH and bbZH processes respectively. We summarized our results with some discussions in the Sec. V.
Our process of interest is bg → bA → bZH , where the production process is initiated by ρ bb and the decay A → ZH is conformed by with g 2 is the SU (2) L gauge coupling and c W is Weinberg's angle. A search can be performed in bg → bA → bbb mode, although, the process suffers from the overwhelming QCD multijets backgrounds.
The relations between the parameters in the two bases can be found out in Ref. [6]. bH + W − is possible, but if searched in H + → tb (induced by ρ bb ) with t → b + ν one loses the mass reconstruction capability of A and, hence, controlling of the tt background. In general, backgrounds are even higher if searched in the hadronically decaying t mode. Notice that, the ρ tt coupling, which also can induce H + → tb decay, obfuscates the role of ρ bb . We remark that the bg → bA → bZH process, which can only be induced via ρ bb , offers a unique probe for the ρ bb coupling 2 . The process bg → bA → bZh is indeed possible, however suppressed by the mixing angle c β−α . It should be clear from Eq. (7) that the decay A → ZH is proportional to s β−α . As a result, a discovery is plausible even in the approximate alignment (i.e. for small c β−α ), which is observed at the LHC [9]. Further, ρ bb can initiate bb → A → ZH and loop induced gg → A → ZH [10], however, the coupling information is lost in the pp collision. Besides, as ρ tt can also get involved in the loop, the role of ρ bb is obscured in gg → A → ZH. One can also have gg → A → Zh (see e.g. Refs. [11,12] and references therein) and gg → bbA → bbZh (see e.g. Refs. [11][12][13][14]), however, again both processes are suppressed by the mixing angle c β−α .

III. ALLOWED PARAMETER SPACE
Having already set up the formalism we now focus on the relevant constraints and the available parameter space for our study. We first scrutinize the constraints on ρ bb . For simplicity, we set all ρ ij = 0 except for ρ bb and ρ tt in this section. We assume small ρ tt in order to avoid direct search limits from gg → A/H. In particular we choose ρ tt = 0.1 for illustration. The most stringent constraints arise from the Higgs signal strength measurements, the branching ratio of B → X s γ (B(B → X s γ)), the asymmetry of the CP asymmetry between the charged and neutral B → X s γ decays (∆A CP ), electron electric dipole moment (EDM) measurement and the upper limit on the h decay width.
The couplings ρ ij modify the h boson couplings to the fermions for moderate values of c β−α , as can be seen from Eq.(6). Therefore, ρ bb receives meaningful constraint from the Higgs boson coupling measurements, unless c β−α is vanishingly small. We utilized Run-2 AT-LAS [15] and CMS [16] measurements which are based on 80 fb −1 and 35.9 fb −1 data respectively. The results summarize the values of different signal strengths µ f i and corresponding errors to a particular decay mode i → h → f . Following the Refs. [15,16], we define a signal strength µ f i as: where σ i is denoted as the production cross section of i → h and B f is the branching ratio for h → f . The production modes considered are i = ggF (gluon-fusion), V BF (vector-boson-fusion), Zh, W h, tth, and the branching ratios are f = γγ, ZZ, W W, τ τ, bb, µµ. For simplicity we utilized the LO µ f i in our analysis and followed Refs. [17][18][19][20] for their explicit expressions. In particular, we focused on two different production modes, the ggF and the V BF in our analysis. We find that for the ggF category, the most relevant signal strengths for our analysis are µ ZZ ggF , µ W W ggF , µ γγ ggF and µ τ τ ggF , while in the V BF category µ W W V BF , µ γγ V BF and µ τ τ V BF ; we refer them together as "Higgs signal strength measurements". In addition, we further considered the recent observation of the h → bb in the V h production by ATLAS [2] and CMS [3]. The parameter space excluded by the Higgs signal strength measurements are shown by the red (ATLAS) and green (CMS) shaded regions in Fig. 1 for m H ± = 350 GeV (left) and 450 GeV (right). In generating Fig. 1, we allowed 2σ errors on each signal strength measurements and, assumed c β−α = 0.5.
The branching ratio measurement of B → X s γ provide another stringent constraint on ρ bb . The coupling ρ bb enters in the B(B → X s γ) via charged Higgs and top quark loop. At the matching scale µ = m W , the modified leading order (LO) Wilson coefficients C with, m t (m W ) is the MS running mass of top quark at m W , x t = (m t (m W )/m W ) 2 , while the expression for can be found out in the Refs. [21,22]. The second term in Eq. (9), which originates from the charged Higgs contribution, expressed at LO as [23] δC (0) where Here we have followed Ref. [21], for the expression of F 7,8 (y H + ). The current world average of B(B → X s γ) exp , which is extrapolated to the photon energy cut E 0 = 1.6 GeV is found to be (3.32 ± 0.15) × 10 −4 [24]. The SM prediction of B(B → X s γ) at next-to-next-to LO (NNLO) for the same photon energy cut is (3.36±0.23)×10 −4 [25]. In order to find the constraint on ρ bb , we adopted the prescription of Ref. [26] and defined Based on our LO calculation we further defined and took m W and m b (m b ) as the matching scale and lowenergy scales respectively. We finally demanded R theory should not exceed 2σ error of R exp . The excluded regions are displayed by the blue shaded regions in Fig. 1. The direct CP asymmetry A CP [27] of B → X s γ is sensitive to Im(ρ bb ). However, it has been proposed [28] that ∆A CP , defined as the asymmetry of the CP asymmetry between the charged and neutral B → X s γ decay provides even more powerful probe for the CP violating effects. The ∆A CP is defined as [28] where, α s is the strong coupling constant calculated at m b (m b ) andΛ 78 is a hadronic parameter. It is expected that hadronic parameterΛ 78 ∼ Λ QCD and estimated to be in the range of 17 MeV <Λ 78 < 190 MeV [28]. We take the average value ofΛ 78 = 89 MeV as a reference value for illustration. A recent Belle measurement report ∆A CP = (+3.69 ± 2.65 ± 0.76)% [29], where the first and second uncertainties are statistical and systematic respectively. Utilizing Eq. (13) and allowing 2σ error on the Belle measurement of ∆A CP we find the red dotted lines (the regions above are excluded) in Fig. 1 for m H ± = 350 GeV and 450 GeV. As a first approximation we have utilized the LO Wilson coefficients as in Eq. (9) in our analysis. We stress that the constraint heavily depends on the value ofΛ 78 and becomes stronger for the larger values ofΛ 78 . The most stringent constraint on Im(ρ bb ) comes from the electron EDM (d e ) measurements. The two-loop Barr-Zee diagrams [30], which is studied widely in the context of 2HDM [31], are the leading contributions to d e . A recent result from ACME Collaboration finds |d e | < 1.1 × 10 −29 e cm [32], which excludes even the nominal value (i.e. |Im(ρ bb )| 0.058) required for ρ bb driven EWBG [5]. The constraint could be relaxed by either turning on ρ ee , or even could vanish in the alignment limit. In the former scenario non-zero ρ ee and ρ bb induce other Barr-Zee diagrams with opposite sign, where as in the the latter case all the contributions to the EDM are simply decoupled. In particular, Ref. [5] finds for Re(ρ ee ) = 0, The current upper limit of the h boson decay width, which is extracted to be < 0.013 GeV (95% CL) [33], can provide some limit on |ρ bb | if c β−α = 0. Besides, the presence of the additional scalars modify the Zbb vertex [34] at one-loop and in principle can constrain the ρ bb coupling. However, we found these limits to be weaker and lie beyond the plotted ranges in Fig. 1.
Let us understand Fig. 1. In generating Fig. 1 we set c β−α = 0.05 and ρ tt = 0.1 for illustration. The constraint from the Higgs signal strength measurements depend primarily on the value of c β−α and vanish in the alignment limit. Same is true for the constraint from the electron EDM, which also disappears in the alignment limit. On the other hand, bounds from B(B → X s γ) and ∆A CP alleviate if ρ tt is small, and/or H ± is heavy. It is clear from Fig. 1 that |ρ bb | ∼ 0.1 is still allowed, however, c β−α and ρ tt should not be very large. In the following we would assume the alignment limit and set ρ tt = 0 for the sake of simplicity, however their impacts will be discussed in the latter part of the paper. In passing we remark that there exist several direct searches which can also constrain ρ bb , even for c β−α = 0 and ρ tt = 0. We defer a detailed discussion of them for the next section.
For the dynamical parameters in Eq. (1), one needs to satisfy the perturbativity, positivity and tree-level unitarity conditions, for which we utilized 2HDMC [35]. The quartic couplings η 1 , η 3−6 can be expressed in terms of m h , m A , m H , m H ± , µ 22 and mixing angle β − α, all normalized to v [7]: The mixing angle β − α and the quartic couplings η 2 and η 7 are not related to masses. Hence, we take v, m h , m A , m H , m H ± , c β−α , η 2 , η 7 and µ 22 as the phenomenological parameters. However, in order to save computation time, we randomly generated these parameters in the following ranges: In general, heavier m A is possible, however the discovery potential would be alleviated due to the rapid fall in the parton luminosity. These randomly generated parameters are then passed to 2HDMC, which uses the input parameters [35] m H ± and Λ 1−7 in the Higgs basis, and with v as implicit parameter while scanning. We identify Λ 1−7 with η 1−7 and take −π/2 ≤ β−α ≤ π/2 to match the convention of 2HDMC. We further conservatively require all |η i | ≤ 3, however, η 2 > 0 is demanded by the positivity of the potential in Eq. (1), in addition to other involved conditions in 2HDMC.
We further imposed the stringent oblique T parameter [36] constraint, which restricts the scalar masses m H , m A and m H ± [37,38], and hence η i s. Utilizing the expression given in Ref. [37] the points that passed unitarity, perturbativity and positivity conditions from 2HDMC, were further required to satisfy the T parameter constraint within the 2σ error [39]. These points are denoted as "scanned points". Finally the scanned points are plotted as gray dots in Fig. 2 Fig. 2 implies that finite parameter space exist for 300 GeV m A 500 GeV 3 .

IV. COLLIDER SIGNATURES
In this section we analyze the discovery potential of pp → bA+X → bZH+X and pp → bbA+X → bbZH+X  processes, followed by H → bb and Z → + − decays. In general Z → νν and Z → τ + τ − are possible, however, we found these modes to be not as promising. In order to illustrate the discovery potential we took three benchmark points (BPs) from the scanned points in Fig. 2, which are summarized in Table I. As discussed earlier, the phase information of ρ bb is lost in the bg → bA → bZH and gg → bbA → bbZH processes. Therefore, the only meaningful quantity in this section is the absolute value of ρ bb (|ρ bb |). Unless otherwise specified we would only consider |ρ bb | from here on.
There exist several direct search limits from ATLAS and CMS that may restrict the parameter space of ρ bb , even for c β−α = 0 and ρ tt = 0. We find that the searches of heavy Higgs boson, in particular Refs. [41][42][43][44] are the relevant ones for our study. The most stringent bound arises from the CMS search for a heavy Higgs boson production in association with least one additional b quark and decaying into bb pair [41]. The search is performed with 13 TeV 35.7 fb −1 data. It sets model-independent 95% CL upper limits on the σ(pp → bA/H + X) · B(A/H → bb) for m A /m H ranging from 300 to 1300 GeV. Utilizing this result we have extracted [45] 95% CL σ(pp → bA/H + X) · B(A/H → bb) upper limit for BP1, BP2 and BP3. We then calculated the production cross sections (pp → bA/H + X) at the leading order (LO) for the three BPs for a reference |ρ bb | value using Monte Carlo event generator Mad-Graph5 aMC@NLO [47] with the default NN23LO1 parton distribution function (PDF) set [48]. Since, CMS does not veto additional activity in the event, we also included contributions from gg → bbA/H along with bg → bA/H in the cross-section estimation. The cross sections are then rescaled by |ρ bb | 2 ×B(A/H → bb) to get the corresponding 95% CL upper limits on |ρ bb |. The upper limits for the BPI is |ρ bb | 0.5, where as |ρ bb | 0.26 and |ρ bb | 0.24 for BPII and BPIII respectively. A similar search has been performed by ATLAS [42] however the limits are somewhat weaker than that of Ref. [41]. The limits extracted from Ref. [43], which searches for a light scalar decaying into bb pair, are weaker except for BPI. For BPI, we found the upper limit to be |ρ bb | 0.51 (at 95% CL), which is roughly similar to the one from Ref. [41]. Moreover, ATLAS search for H ± in association with a t quark and a b quark with H + /H − → tb/tb decay [44] is relevant, but the constraints are milder for all three BPs. The effective model is implemented in the FeynRules 2.0 [49].
We choose |ρ bb | = 0.1 as a representative value for illustration in this section. Since our working assumptions are alignment limit with all ρ ij = 0 except ρ bb , the total decay width of A is nicely approximated as the sum of the partial widths of A → bb and A → ZH, while H only decays to bb. The corresponding branching ratios of A for the three BPs are given in Table I [50] for showering and hadronization. We adopted MLM matching scheme [51] for matrix element and parton shower merging. The event samples are finally fed into fast detector simulator Delphes 3.4.0 [52] for detector effects (ATLAS based). We do not include backgrounds from the fake and non-prompt sources. Such backgrounds are not properly modeled in Monte Carlo simulations and requires data to estimate such contributions.
The LO tt+jets and W t+jets cross sections are normalized to NNLO+NNLL cross sections by factors 1.84 [53] and 1.35 [54] respectively. The DY+jets background cross section is adjusted to the NNLO QCD+NLO EW one by a factor 1.2, which is obtained utilizing FEWZ 3.1 [55]. The ttZ,tZ+ jets, tth, 4t and ttW − (ttW + ) cross sections at LO are normalized to NLO ones by the K-factors 1.56 [56], 1.44 [47], 1.27 [57], 2.04 [47] and 1.35 (1.27) [58] respectively, while tW h and tW Z are kept at LO. Further, the W − Z+jets background is normalized to NNLO cross section by factor 2.07 [59]. For simplicity, we assumed the QCD correction factors for the tZj and W + Z+jets to be the same as their respective charge conjugate processes. The signal cross sections are kept at LO.
In order to distinguish the signal from the background processes, we have applied following event selection criteria: Each event should contain two same flavor opposite sign leptons (e and µ), at least three jets with at least three of them are b-tagged. The minimum transverse momenta (p T ) of the leading and subleading leptons are required to be > 28 GeV and > 25 GeV respectively, where as the p T of all three b-jets should be > 20 GeV. The absolute value of the pseudo-rapidity (|η|) of the leptons and all three b-jets are needed to be < 2.5. The jets are reconstructed by anti-k T algorithm with radius parameter R = 0.6. The separations ∆R between any two b-jets, any two leptons and, any b-jet and lepton in an event are required be > 0.4. In order to reduce the tt+jets background we vetoed events with missing transverse energy (E miss T ) > 35 GeV. The invariant mass of the two leading same flavor opposite charge leptons (m ) is required to be within the Z boson mass window i.e. 76 < m < 100 GeV. To reduce backgrounds further, we finally demanded the invariant mass of the two leading leptons and two leading b-jets (m bb ) to remain within |m A −m bb | < 100 GeV. We adopted the η and p T dependent b-tagging efficiency and, c-and light-jets misidentification efficiencies of Delphes. The background cross sections of the three benchmark points after selection cuts are summarized in Table. III, while the signal cross sections along with their corresponding significances with the integrated luminosity L = 300 fb −1 are given in Table IV for |ρ bb | = 0.1. We remark that in our exploratory study we have not optimized the selection cuts such as m and m bb , and kept them unchanged for all three benchmark points for simplicity.  The statistical significances in Table IV are determined by using Z = 2[(S + B) ln(1 + S/B) − S] [60], where S and B are the number of signal and background events after selection cuts. The achievable significances for BPI, BPII and BPIII are ∼ 6.6σ, ∼ 4.0σ and ∼ 2.2σ with 300 fb −1 integrated luminosity. We find that even the collected Run-2 data (∼ 150 fb −1 ) would lead to ∼ 4.7σ, ∼ 2.8σ significances for the BPI and BPII respectively, where as lower than 2σ for BPIII. As for the parameter space of EWBG, |Im(ρ bb )| should be 0.058 [5], which leads to ∼ 12.1σ, ∼ 4.5σ and ∼ 2.5σ significances for the BPI, BPII and BPIII with the full HL-LHC dataset (i.e. 3000 fb −1 integrated luminosity). This implies that the bZH process can fully probe the parameter space required for ρ bb driven EWBG if m A 300 GeV, where as a evidence (3σ) could be found for 300 GeV m A 400 GeV.
Before closing we remark that the scope for discovery of the bZh process (i.e. pp → bA 50 and m H = 236.34 4 , the significance lies below ∼ 1σ, even for the full HL-LHC dataset 5 . The significance improves substantially if m A < m H +m Z and/or ρ bb is large. A larger c β−α would also help, however in such cases the significance would be balanced by more severe bounds from Higgs signal strength measurements. For c β−α ∼ 0.05, H → ZZ, H → W + W − would open up, although we do not find them to be very promising even for HL-LHC.

B. The bbZH process
As for the bbZH process, the SM backgrounds are essentially same as in the preceding subsection however with one extra b-jet in the final state. We have adopted similar procedure for the signal and background events generation and, followed the event selection cuts as in the bZH process except the additional b-jet is required to have p T > 20 GeV and |η| < 2.5. The separation ∆R between any two b-jets, any two leptons and, any b-jet and lepton should be > 0.4. All other cuts are kept same as in bZH. Finally, we applied the m and m bb selection cuts as before. The background and signal cross sections after the selection cuts are summarized in Table V and Table VI respectively. We assumed the QCD correction factors for the different backgrounds as in the bZH process and kept the signal cross sections at LO. Therefore, we remark that, there are slightly greater uncertainties involved in the background cross sections.  As can be seen from Table VI, the cross sections of the bbZH process is suppressed due its to 2 → 4 body nature. Hence, the significances are provided only for 3000 fb −1 integrated luminosity, which can reach up to ∼ 4.2σ, ∼ 2.8σ and ∼ 1σ for the BPI, BPII and BPIII respectively. Hence, a discovery is beyond the HL-LHC, that is unless ρ bb is large. The significances can be higher if the upper limits of |ρ bb | for the corresponding BPs are saturated, which can rise up to ∼ 6.5σ, ∼ 13.8σ and ∼ 4.5σ for BPI, BPII and BPIII respectively with the full HL-LHC data. As before, pp → bbA + X → bbZh + X is possible, however, the significances are even smaller than the bZh process.

V. DISCUSSION AND SUMMARY
Motivated by the recent observation of hbb coupling, we have investigated the possibility of probing extra bottom Yukawa coupling ρ bb at the LHC. We first looked for the existing constraints on ρ bb , mainly from the Higgs signal strength measurements, B(B → X s γ), ∆A CP of B → X s γ, electron EDM, as well as several direct searches at the LHC. We found that O(0.1) |ρ bb | is allowed by the current data, however c β−α and ρ tt should not be large. We remark that additional constraints can come from the A CP and isospin violating asymmetry (∆ 0+ ) of B → K * γ measurement by Belle [61], and could be comparable to the inclusive one, however, they both suffer from sizable uncertainties in their theoretical predictions [62].
We have shown that bg → bA → bZH with Z → + − and H → bb offers excellent probe for ρ bb . Discovery seems plausible with 300 fb −1 integrated luminosity for O(0.1) ρ bb however m A needs to be 300 GeV. For 400 GeV m A 500 GeV one may need the HL-LHC data. The process could be followed by gg → bbA → bbZH, although we find that a discovery is unlikely even with the full HL-LHC dataset if |ρ bb | 0.1. We focused on the scenario where m H + m Z < m A . However, for m A + m Z < m H our study can be extended to bg → bH → bAZ (and gg → bbH → bbZA) process where a complimentary search strategy as in bZH (and bbZH) can be adopted. Note that, ρ bb also invokes gg →tbH + →tbtb, which we leave out for future study. We have not included QCD corrections for the signal and neglected systematic uncertainties in our analysis. These would induce some uncertainties in our results.
A discovery might indicate EWBG driven by ρ bb . With the full HL-LHC dataset the bZH process can probe the entire parameter space required for the EWBG if m A 300 GeV. Although, a discovery would be intriguing, however it would not be sufficient to establish it to the EWBG without the information of the phase of ρ bb . This would need further scrutiny and perhaps angular analysis of the bZH (or bbZH) process would be indicative. Information of the phase can also be extracted from the future measurement of ∆A CP of B → X s γ at Belle-II, if H ± is not too heavy.
In principle, ρ bd , ρ db , ρ bs and ρ sb all can replicate bZH and bbZH signatures at the LHC, however, their impacts are inconsequential due to severe bounds from B d and B s mixings. If the charm quark gets misidentified as b-jet, a sizable ρ cc can mimic bZH signature in pp collision via cg → cA → cZH. However, such possibilities can be excluded with the simultaneous application of c-and b-tagging on the final state event topologies [63].
While determining the discovery potential we set all ρ ij = 0 except ρ bb for the sake of simplicity. In general non-zero ρ ij s suppress B(A/H → bb) and hence the discovery potential of the bZH and bbZH. E.g., if ρ tt ∼ 0.1, we find that the statistical significances of the BPII and BPIII are reduced by ∼ 15% − 20% for both the processes. A larger ρ tt would alleviate the significances further if m A /m H > 2m t . Besides, ρ τ τ is likely O(λ τ ) [7], although, the impact is negligibly small for both the processes in all three BPs. Here, we assumed the flavor changing neutral Higgs coupling ρ tc to be small, however, a O(1) value is still allowed by the current data [64,65] (see also Ref. [66]), and could potentially reduce the significances of both the processes.
We assumed small ρ tt in order to avoid strong constraints arising from the gg → A/H searches. Notwithstanding, O(1) ρ tt with complex phase provides another robust mechanism for EWBG [67] (see also Ref. [68]), which can be probed by the conventional search programs such as gg → A/H → tt or gg → A/Htt → tttt [69]. The former process suffers from large interference [70] with the overwhelming gg → tt background, however a recent ATLAS study [71] found some sensitivity. If both ρ bb and ρ tt are sizable bg → bA/H → btt as well as gg → bbA/H → bbtt [72] are possible and would provide complimentary information.
In summary, we have explored the possibility of discovering and identifying additional bottom Yukawa coupling that might exist in the nature via bg → bA → bZH and gg → bbA → bbZH processes at √ s = 14 TeV LHC. We found that the former process could be discovered with 300 fb −1 integrated luminosity if m A ∼ 300 GeV, which could be extend up to ∼ 500 GeV but the full HL-LHC dataset would be required. The latter process could also be discovered at the HL-LHC, however ρ bb needs to be large. A discovery would not only confirm physics beyond the Standard Model, but may also indicate the EWBG driven by ρ bb .