Probing loop effects in wrong-sign Yukawa coupling region of Type-II 2HDM

In the framework of 2HDM, we explore the wrong-sign Yukawa region with direct and indirect searches up to one-loop level. The direct searches include the latest H/A→ff¯,VV,Vh,hh\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H/A \rightarrow f{\bar{f}}, VV, Vh, hh$$\end{document} reports at current LHC, and the study of indirect Higgs precision measurements works with current LHC, future HL-LHC and CEPC. At tree level of Type-II 2HDM, for degenerate heavy Higgs mass mA=mH=mH±<800\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$m_A=m_H=m_{H^\pm }<800$$\end{document} GeV, the wrong-sign Yukawa regions are excluded largely except for the tiny allowed region around cos(β-α)∈(0.2,0.3)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\cos (\beta -\alpha )\in (0.2,0.3)$$\end{document} under the combined Higgs constraints. The excluded region is also nearly independent of parameter m12\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$m_{12}$$\end{document} or λv2=mA2-m122/(sinβcosβ)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda v^2=m_A^2-m_{12}^2/(\sin \beta \cos \beta )$$\end{document}. The situation changes a lot after including loop corrections to the indirect searches, for example mA=1500GeV\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$m_A=1500 \text {~GeV}$$\end{document}, the region with λv2<0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda v^2<0$$\end{document} will be stronger constrained to be totally excluded. Whilst parameter space with λv2>0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda v^2>0$$\end{document} would get larger survived wrong-sign region for mA=800GeV\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$m_A=800 ~\text {~GeV}$$\end{document} compared to it at tree level. We also conclude Higgs direct searches works better on constraining λv2≈0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda v^2 \approx 0$$\end{document} GeV range than theoretical constraints. We also find that the loop-level wrong-sign Yukawa limit only occurs at mass decoupling scale.


Introduction and motivation
Since the discovery of Standard Model (SM) -like Higgs boson at LHC Run-I [1,2], SM is confirmed to be one selfconsistent theory, and exploring Higgs boson properties especially Higgs couplings becomes a promising window to study new physics beyond-the-SM (BSM). Meanwhile motivated by various experimental and theoretical hits, to extend SM Higgs sector becomes necessary to address them.
Among numerous extensions, Two Higgs Doublet Model (2HDM) is a well motivated framework [3][4][5][6]. After electroweak symmetry breaking (EWSB), the general 2HDM will generate 5 mass eigenstates, a pair of charged Higgs H ± , one CP-odd Higgs boson A and two CP-even Higgs bosons, h, H . Here we take the lighter h as the measured SM-like Higgs.
Since the improvements of various experiments, the wrong-sign region have attracted fruitful researches [7][8][9][10][11][12][13][14][15][16]. This work focuses on testing the so-called wrong-sign Yukawa region up to one-loop level with both indirect and direct searches at current LHC. For the direct searches, we constrain the parameter space with various heavy Higgs decays, taking the cross section times branching ratio σ × Br limits of various channels, including A/H → μμ [17][18][19] [32] and CPEC [33] up to one-loop level. The results show that the wrong-sign Yukawa region for m A < 800 GeV is strongly constrained. But the constraints get weaker afer including the loop correction to Higgs precision studies for λv 2 > 0. While for m A = 1500 GeV with λv 2 > 0, the constraints get stronger compared to it at tree level.
Our paper is structured as follows. In Sect. 2, we will give a brief introduction to 2HDMs, concentrated on the wrongsign Yukawa analysis. We give a brief summary of study methods and the relevant experimental reports in Sect. 3. Then at Sects. 4 and 5 we present our analyses and results at tree and one-loop level respectively. Finally we will give our main conclusions in Sect. 6.
The 2HDM Lagrangian for the Higgs sector can be written as with a Higgs potential of where we have assumed C P conservation, and a soft Z 2 symmetry breaking term m 2 12 . For the neutral CP-even Higgs, with α as the rotation angle diagonalizing the CP-even Higgs mass matrix, In this work we set m H > m h = 125 GeV, and by convention, here we set 0 ≤ β ≤ π 2 , 0 ≤ β − α ≤ π . The most general Yukawa interactions of 1,2 with the SM fermions under the Z 2 symmetry is where u,d,e are either 1 or 2 . Depending on the interactions of i coupling to the fermion sector, there are typically four types of 2HDM (Table 1): For a review on different types of 2HDM as well as the phenomena, see Ref. [34]. Table 2 is Higgs couplings to the SM fermions in the four different types of 2HDM, normalized to the corresponding SM values, for a better analysis at following sections.
In the following sections, we will take κ x = κ x h . For normalized SM-like Higgs gauge couplings, V = Z , W ± , with sign(κ V ) = 1 by convention. After EWSB, three Goldstone bosons are absorbed by the SM gauge bosons Z , W ± , providing their masses. The remaining physical mass eigenstates are h, H, A and H ± . Instead of the eight parameters appearing in the Higgs potential m 2 11 , m 2 22 , m 2 12 , λ 1,2,3,4,5 , a more convenient choice of the parameters is v, tan β, α, m h , m H , m A , m H ± , m 2 12 .

Wrong-sign Yukawa of 2HDM
Taking the notations in [35], we define, When sin(β − α) = 1, all the SM-like Higgs boson couplings in four types will be exact same as them in SM respectively, which is the usual case called as alignment limit. These terms also can be written in the other mode, +O(cos 2 (β + α)) (9) κ D = − sin(β + α) + cos(β + α) tan β = ∓1 + cos(β + α) tan β ± 1 2 cos 2 (β + α) Here we can get sin(β + α) = 1, κ U = −κ D = 1, whilst sin(β + α) = −1, κ U = −κ D = −1, which is usually called "wrong-sign" Yukawa limit in 2HDM. Wrong-sign Yukawa Regime As defined in [35], the wrong-sign Yukawa regime requires at least one of sign of Yukawa couplings is opposite to Higgs vector boson coupling, in physics which can be expressed as, for any up-type or down-type quark. Physically this definition is suitable for both tree-and loop-level study. For the gauge couplings κ V = sin(β − α), it is always positive in our notaion. Through Table 2, Type-I 2HDM only has the wrong κ U = −1 case, and other three types would have both κ U = −1 or κ D = −1 cases. It would deviate from 1 significantly, which could be one important constraint for parameter space of the wrong-sign Yukawa region.
But even at future lepton colliders, the wrong-sign Yukawa region at tree level will be allowed as shown in Fig. 3, even the allowed | cos(β − α)| is less than 0.007. This situation can be changed once the loop level corrections are included,
At one-loop level, to reach at wrong-sign limit at Eq. (13), mass decoupling and sin(β + α) = 1, cos(β + α) = 0 are all in need. At this limit, loop U/D are negligible and all values become same as them at tree level. Under current measurements, there are allowed regions deviated from this exact limit at loop level.
In this work, we will address one-loop level 1−loop effects to the global fit results around wrong-sign Yukawa region before the decoupling scale, with Higgs precision measurement at current LHC Run-II and future HL-LHC, CEPC.

Study method
Since the discovery of 125 GeV Higgs boson at LHC Run-I, the study of Higgs sector, both the SM-like Higgs boson precision measurements and direct search of additional Higgs boson, has fruitful results. To have a complete study of wrong-sign Yukawa region of 2HDM, here we will explore its properties with both direct and indirect experimental reports at LHC Run-II.
To interpret the experimental direct search reports, we take the cross section times branching ratio σ × Br limits of various channels, including A/H → μμ [17][18][19] About the indirect search, we transfer the errors of SMlike Higgs boson couplings to the constraints on the model parameters at one-loop level, adopting the on-shell renormalization scheme [38] for Higgs masses, α, β, vacuum expectation value v, and minimal substraction scheme for parameter m 12 . The conventions for the renormalization constants, and conditions follows Refs. [38,39], which are two-point functions of Higgs field. More details are discussed at our previous work [40], and our numerical results keeps consistent with package H-coup [41]. We make a global fit by constructing the χ 2 with the profile likelihood method Here μ BSM i = (σ ×Br) BSM (σ ×Br) SM for various Higgs search channels and σ μ i is the experimental precision on a particular channel. μ BSM i is predicted in each specific model, depending on model parameters. For the LHC Run-II, the measured μ obs i and corresponding σ μ i are given by ATLAS at 13 TeV up to 80 f b −1 [31]. In our analyses of the future colliders, μ obs i are set to be the SM value: μ obs i = 1, assuming no deviation to the SM observables are observed. For the corresponding σ μ i of the HL-LHC and CEPC, we take the precision measurements from [32,33]. The future FCC-ee [42] has similar performance to CEPC [43], thus here we will only show the results with CEPC. For one or two parameter fit, the corresponding χ 2 = χ 2 − χ 2 min for 95% C.L. is 3.84 or 5.99, respectively.
In 2HDMs, the additional Higgs sector involves several Higgs self-couplings, which are constrained by various theories considerations, such as vacuum stability, perturbativity and unitarity. For the detailed study, we refer to the results in works [40,43]. The general idea is −(125 GeV) 2 ≤ √ λv 2 ≤ (600 GeV) 2 , and we will study inside of this region.

Results at tree level
Based on the discussion above, first we will show our study results at tree level. It includes the current LHC direct and indirect searches, as well as the indirect searches at future HL-LHC and CEPC.

Indirect search at LHC and future colliders
With the global fit methods in Sect. 3, here we will utilize the SM-like Higgs precision measurement from LHC Run-II [31], HL-LHC [32] and CPEC [33]. In details, for LHC Run-II we work with the ATLAS results ATLAS at 13 TeV up to 80 f b −1 , and for HL-LHC, we work with combined results from future ATLAS and CMS, up to 6 ab −1 . For CPEC, the latest designed luminosity is 5.6 ab −1 at √ S = 240 GeV. We give our global fit results in Fig. 1, the allowed region in the plane of tan β -cos(β−α) at 95% C.L. for the four types of 2HDM, given LHC Run-II (green), HL-LHC (blue) and CEPC (red) Higgs precision measurements. For the Type-I 2HDM, all the SM-like Higgs fermion couplings are κ U type in Eq. (7) with cot β-enhanced corrections when deviates from alignment limit cos(β − α) = 0. Thus at large tan β region, the Yukawa couplings would not contribute much in constraining the parameter space, and the main restriction is from gauge couplings. The detailed values are displayed in Table 3.
For the other three types, they include both κ U and κ D type Yukawa couplings, as a result both large and small tan β are strongly constrained apart for the wrong-sign Yukawa regions. The relevant the maximally allowed | cos(β − α)| ranges are also shown in Table 3. We also note the Type-LS is less restricted at small tan β compared to Type-II and Type-F, because only lepton couplings of Type-LS have κ D type and the precisions of δκ b is better than δκ τ , for example in CPEC, δκ b = 1.3%, δκ τ = 1.5%.
The gray represent the wrong-sign Yukawa regions as Sect. 2.2, with κ U κ V < 0 for Type-I, κ b κ V < 0 for Type-II and Type-F, κ τ κ V < 0 for Type-II and Type-LS.

Wrong-sign region and disappeared up-type
From Eqs. (9) and (10), even cos(β − α) 0 there are still allowed regions to get |κ U,D | = 1, which is the so called wrong-sign Yukawa region of 2HDM as defined (Eq. 12). As shown in Fig. 1, gray regions are of wrong-sign Yukawa couplings defined in Eq. (12). Since κ V > 0 keeps always, Eq. (12) means κ U/D < 0, with the lower left region for Type-I, and the upper right regions for Type-II/L/F. The later three types all have κ U -type wrong-sign Yukawa region as Type-I, which are not shown out.
In details the κ D -type wrong-sign Yukawa in Eq. (10) only occurs at tan β > 1. For the exact wrong-sign limit at tree level κ U = −κ D = 1, sin(β − α) = − cos 2β, and at large tan β, we have Thus even at CEPC, where we will have δκ Z = |1 − sin(β − α)| ≤ 0.25%, the wrong-sign Yukawa is still allowed around cos(β − α) ≈ 2/ tan β for cos(β − α) < 0.07 at tree level. κ U -type wrong-sign Yukawa in Eq. (10) only occurs at tan β < 1. For the exact wrong-sign limit κ D = −κ U = 1, sin(β − α) = cos 2β, and at small tan β, Usually κ U and κ D are estimated in the form of κ 2 U,D , except for if there is any interference. The two sensitive parameters [32] are Here Eqs. (17) and (18) tell us the sign of κ b does not make an important enough difference to χ 2 (κ b → 1) and χ 2 (κ b → −1) through the global fit method Eq. (14) at tree level [35], while the sign of κ t makes an important difference to both κ γ , κ g . For κ U -type wrong-sign region, corrected κ γ γ Fig. 1 The allowed region in the plane of tan β -cos(β − α) at 95% C.L. for the four types of 2HDM, given LHC Run-II (green), HL-LHC (blue) and CEPC (red) Higgs precision measurements. For future measurements, we assume that the measurements agree with SM predictions. The gray represent the wrong-sign Yukawa regions discussed at Sect. 2.2, with κ U κ V < 0 for Type-I, κ b κ V < 0 for Type-II and Type-F, κ τ κ V < 0 for Type-II and Type-LS. . The colored "arm" regions for the Type-II, L and F are the allowed wrong-sign Yukawa regions correspondingly deviated from SM values too large to be excluded. The colored "arm" regions for the Type-II, L and F are the allowed wrong-sign Yukawa regions correspondingly at 95% C.L. under various Higgs precision measurements.

Current LHC direct search
Afte r the indirect searches, here we will take the Type-II 2HDM as an example to compare with the direct LHC searches, and to explore the combined constraint ability to the wrong-sign Yukawa region. As shown in Fig. 2, the excluded region by current LHC direct search in the plane m H/A − tan β, including Fig. 1, to study the the wrong-sign Yukawa region, we take the benchmark parameter cos(β − α) = 0 (left), 0.2 (middle) , and 0.4 (right), with degenerate heavy Higgs mass m A = m H , m H ± = max{600 GeV, m H } ,m 2 H = m 2 12 /s β c β . For the constraints from charged Higgs, on one hand, both the B-physics requiring m H ± > 580 at tan β > 0.7 [44,45] and direct searches at LHC [46] do not have strong probe ability on wrong-sign Yukawa region as channels about heavy neutral ones. On the other hand, mass splittings between heavy Higgs are allowed [40]. Therefore charged Higgs constraints do not affect wrong-sign Yukawa regions from direct searches or affecting neutral heavy Higgs indirectly. After all in our studies, we take m A = m H , m H ± = max{600 GeV, m H }.
In the left panel of Fig. 2, only H/A → ff channels have constraint since H hh, H V V, Ah Z couplings at tree level are proportional to cos(β − α). Generally the region m A ∈ (130, 800), tan β > 10 is excluded by τ τ decay channel, and for larger heavy Higgs mass, the excluded tan β limit will be larger, to limitless around 1.5 TeV. Also a small region m A ∈ (130, 2m t ), tan β ∈ (0.5, 2) is excluded by A/H → τ τ . For middle and right panels of Fig. 2, all channels here would make a difference with non-zero cos(β − α). For cos(β − α) = 0.2, at large tan β the regions of m A < 700, tan β > 5, m A < 800, tan β > 10 are excluded. Similarly the restriction ability goes down until 1.5 TeV. At small tan β region, m A < 800, tan β < 0.3 is strongly constrained. The excluded region can reach 1.2 TeV for tan β ∈ (0.9, 2). For larger cos(β − α) = 0.4, when m A < 800, tan β > 3 are strongly constrained since the more powerful A → Zh channel. This channel gets larger decay rates with larger cos(β − α). But it can only reach 1.4 TeV around tan β = 30. The excluded region of cos(β −α) = 0.4 at small tan β region is similar as cos(β − α) = 0.2. Another important feature is, the covered regions on tan β are nearly similar for m A ∈ (2m t , 800) GeV.
The strong constraints at large tan β and non-zero cos(β − α) can contribute to exclude the wrong-sign Yukawa region. To have a more straightforward idea, we will compare the direct and indirect searches in the plane cos(β − α) − tan β.
As in Fig. 3 √ λv 2 = 100 GeV , the wrong-sign region at large tan β > 20 is totally covered by A/H → τ τ channel, and at small tan β region, it is strongly constrained by A → Zh channel. The small allowed region is around 8 < tan β < 10, 0.2 < cos(β − α) < 0.3. At small tan β region, LHC direct searches give weak constraints resulting from too wide A/H and current searches are not valid in this region. Compared the middle panel with √ λv 2 = 600 GeV, the general results around wrong-sign Yukawa region are quite similar. This tells us the independence on √ λv 2 or m 12 in the considered regions. For the right panel with m A = 1500 GeV, √ λv 2 = 100 GeV , the LHC direct search can nearly give no constraints there, which is Generally the central region between the two lines around cos(β − α) = 0 are allowed except for the "arm" of Type-II, the wrong-sign Yukawa region as discussed detailed in Fig. 1 also shown in Fig. 2. Also from middle and right panels of Fig. 2, where the LHC direct search constraints are similar for m A < 800 GeV and large tan β region, we can say the wrong-sign region with m A < 800 GeV are strongly constrained by the combined indirect and direct searches at tree level.
For direct searches, channels like H → bb, τ τ can make differences if their couplings are tan β-enhanced as from Table 2. For H τ τ of Type-L, and Hbb of Type-F are also same as Type-II, and other channels are tan β-reduced. Thus the constraints on wrong-sign region for Type-L/F would be same as Type-II, or weaker than Type-II.

Results at one-loop level
From last section, the combined indirect and direct searches at current LHC can give strong constraints on wrong-sign Yukawa region for m A < 800 GeV while for large heavy Higgs mass such m A = 1500 GeV, direct searches nearly has no restrictions. The conclusion will be modified to a large extent when including the loop-level corrections to Higgs precision measurement study [40,43].

Loop effects in cos(β − α) − tan β plane
To explore loop effects on the wrong-sign Yukawa region, here we first analyze the individual Higgs couplings cosntraints in details in Type-II 2HDM. In [40,43], we have detailed studies about the normal Yukawa regions around cos(β − α) = 0, and the studies method here are similar, thus here we only display the wrong-sign regions.
As the Fig. 4, we show the allowed wrong-sign Yukawa region in the plane of tan β -cos(β −α) at 95% C.L. for Type-II 2HDM, given LHC Run-II Higgs precision measurements at one-loop level. The benchmark parameters in the left panel is m A = m H = m H ± = 800 GeV, λv 2 = −100 2 . The gray regions are of κ b < 0 as in Fig. 1. The blue region is allowed at one-loop level, and the red and green lines are for δκ b = ±0.19 and δκ Z = ±0.08 taken from current LHC reports [32].
The allowed region by h Z Z coupling at one-loop level are always around cos(β − α) = 0 displayed by green line, similar to tree level. For hbb the case becomes parameter dependent, with κ b = −1 ± 0.19 represented by red lines. In the left panel with λv 2 = −100 2 GeV 2 , region with κ b < 0 gets reduced compared to it at tree level, as well as the allowed wrong-sign Yukawa "arm". In the middle panel with λv 2 = 0 GeV 2 , the upper right regions has κ b > 0, resulting to two regions of κ b = −1 ± 0.19. For right panel with λv 2 = 600 2 GeV 2 , κ b < 0 region gets larger, and the allowed wrong-sign Yukawa "arm" shifts a lot compared to themselves at tree level. Generally we can conclude, the blue allowed wrong-sign Yukawa regions are mainly dependent on hbb, h Z Z channels at one-loop level at Type-II.
In Fig. 5, based on the analysis in Fig. 4, we show the allowed wrogn-sign Yukawa regions of various λv 2 values at one-loop level in the plane of tan β -cos(β − α) at 95% C.L. for Type-II 2HDM, given LHC Run-II Higgs precision measurements at one-loop level. Here we work with the bench- Fig. 4 The blue allowed region in the plane of tan β -cos(β − α) at 95% C.L. for Type-II 2HDM, given LHC Run-II Higgs precision measurements at one-loop level. Here we take the benchmark parameters m A = m H = m H ± = 800 GeV, λv 2 = −100 2 (left), 0 (middle), abd 600 2 (right) GeV 2 . The gray regions are of κ b < 0 as in Fig. 1. We also show the current precision δκ b = ±0.19 and δκ Z = ±0.08 with red and green lines respectively, whose overlap parts are blue allowed regions Fig. 5 The summarized allowed wrogn-sign Yukawa region in the plane of tan β -cos(β − α) at 95% C.L. for Type-II 2HDM, given LHC Run-II Higgs precision measurements at one-loop level. Here we take the benchmark parameters m A = m H = m H ± = 800 GeV (left) and 1500 GeV (right). The diffenet colorful regions are for λv 2 = −100 2 (blue), 0 (light red), 50 2 (magenta), 200 2 (green), 400 2 (cyan) and 600 2 (orange) GeV 2 . We also show the allowed wrong-sign Yukawa region at tree level with black solid lines. For m A = 800 GeV, we show the larger allowed region in the subplot, upper right corner of the left panel mark parameters m A = m H = m H ± = 800 GeV (left), 1500 GeV (right), λv 2 = −100 2 , 0, 50 2 , 200 2 , 400 2 , 600 2 GeV 2 displayed by blue, light red, magenta, green and cyan regions respectively. At the left panel, the main plot shows cos(β − α) ∈ (−0.02, 0.2), and the larger region is in the subplot for cos(β − α) ∈ (−0.02, 0.4) . The allowed wrong-sign Yukawa region at tree level is displayed by black solid lines. Here the light red region for λv 2 = 0 is the most similar one to the tree level region, and regions of smaller λv 2 would locate at right while regions of larger λv 2 would shift to the left of black lines. Thus this range would be less constrained by current LHC direct searches as shown in Fig. 3. For m A = 1500 GeV, region of λv 2 ≤ 0 is totally excluded, and for large λv 2 the allowed region is shifted to the left of black lines as m A = 800 GeV. Here we also see, the allowed cos(β − α) range at loop level is larger than it at tree level, for both cases. Usually theoretical constraints can restrict large |λv 2 | strongly, especially for |λv 2 | > 100 GeV, while Higgs precision measurements is complementary on constraining small λv 2 for large mass.

Loop effects in m − m 12 plane
Since there are weak theoretical constraints around λv 2 = m 2 H/A − m 2 12 /(sin β cos β) = 0, here we explore this special region carefully, in the plane of m A − m 12 .
In Fig. 6, performing the global fit at 95% C.L. for Type-II 2HDM, we show the allowed region in the plane of m A m 12 after including the loop corrections to SM-like Higgs couplings. For the benchmark parameters, we still take heavy Higgs mass m A = m H , m H ± = 600 GeV, with cos(β − α) = 0.05 (left), 0.07 (right), tan β = 30 (blue), 35 (green), 45 (red). The global fit results with current LHC and future HL-LHC Higgs precision measurements are displayed with light and dark colors respectively. With the future CEPC reports, the allowed region is strongly constrained, and since the χ 2 of best point is larger than 100 for these cases, we would not show them here.
Generally for a pair of fixed cos(β − α) and tan β, the allowed wrong-sign Yukawa regions at one-loop level are divided into two parts based on tan β = 20. For m 12 > 20 GeV, the allowed region tends to have √ λv 2 = m 2 A − m 2 12 (1 + tan 2 β)/ tan β ≈ 0 GeV, where there is weak constraints from theory, and m A < (1.5 − 2) TeV. Larger m A range is excluded because of too large loop corrections. In the plots, we also show the dashed line indicating the tiny regions allowed by theoretical constraints for corresponding parameters. The allowed region partially are same as the colored region allowed by Higgs precision measurements. For m 12 < 20 GeV, the allowed region has large | √ λv 2 | > 100 GeV, to excluded by theoretical constraints [40]. Therefore we can conclude, constraints from Higgs precision measurements works better than theoretical constraints at small λv 2 , and the two together could constrain the whole λv 2 stronger.
Based on Eq. (15), the wrong-sign Yukawa region at tree level has a simple relationship cos(β − α) ≈ 2/ tan β when tan β 1 . This relationship at one-loop level would not keep anymore, since for a specific cos(β −α), different tan βs are allowed.

Conclusions
Since the discovery of SM-like Higgs boson at LHC Run-I, exploring its properties especially Higgs couplings become a promising method to study new physics. In the framework of 2HDM, this work focuses on testing the so-called wrongsign Yukawa region up to one-loop level. It is known that wrong-sign limit of Type-II is κ D = −1, and κ U = 1. sin(β + α) = 1 can reach it at tree level. We pointed out that, the limit at one-loop level requires heavy Higgs mass decoupling as well.
Our study worked with both indirect and direct searches at current LHC, to search the region before decoupling scale. For the direct searches, we constrained the parameter space with various heavy Higgs decays, A/H → ff , V V, V h, hh at tree level. For the indirect searches, we perform the global Generally as shown in Figs. 1, 2, 3, for heavy Higgs mass m A = m H < 800 GeV, m H ± = max{m H , 600 GeV}, the wrong-sign Yukawa regions at tree level are excluded largely for Type-II 2HDM, except for the tiny allowed region around tan β ∈ (8, 10) under the combined direct and indirect searches of current LHC data at tree level. The excluded region is also nearly independent of parameter m 12 or λv 2 = m 2 A − m 2 12 /(sin β cos β). For larger m A , the constraints get weaker, and direct searches can not put any more constraints on the wrong-sign region for m A = 1500 GeV.
The excluded region would change much after including loop corrections to the indirect Higgs precison measuremetns studies. Comparing Fig. 1 and Fig. 4, the sign(κ b ) = −1 region and the allowed wrong-sign Yukawa region could be corrected magnificently in some parameter space, which is mainly depedent on hbb, h Z Z channels for Type-II. Unlike the results at the tree level, m 12 or λv 2 could also make a difference. From Fig. 5, we can conclude that the wrongsign region with λv 2 > 0 will be less constrained by heavy Higgs direct searches at Fig. 2 for small mass such as m A = 800 GeV. For large mass, such as our case study with m A = 1500 GeV where is no constraints from direct searches at tree level, region of λv 2 ≤ 0 is totally excluded, and for large λv 2 > 50 GeV 2 the allowed region is shifted to the left of the tree-level region. In general we can conclude that with loop corrections, wrong-sign Yukawa regions of small λv 2 will be more constrained, while the range of large λv 2 is less constrained under current LHC direct and indirect limits. These features are quite different to the results at tree level. Since theoretical constraints put weak restriction on small |λv 2 |, at Fig. 6 we explored the λv 2 = m 2 A − m 2 12 /(sin β cos β) ≈ 0 GeV. We found Higgs measurements works better here than theoretical constraints. There are still allowed regions under current LHC form m A < 1500 GeV, but when considering the future CEPC, it is difficult to find out the survived points.

Data Availability Statement
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