Talk presented at the International Workshop on Future Linear Colliders

(LCWS2018), Arlington, Texas, 22-26 October 2018. C18-10-22.

Implication of Higgs Precision Measurement

on New Physics

Ning Chen,1 Tao Han,2,3 Shufang Su,4 Wei Su,4,5,6 Yongcheng Wu∗7

1School of Physics, Nankai University, Tianjin 300071, China2Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, PA 15260,

USA3Department of Physics, Tsinghua University, and Collaborative Innovation Center of Quan-

tum Matter, Beijing, 100086, China4Department of Physics, University of Arizona, Tucson, Arizona 85721, USA5CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy

of Sciences, Beijing 100190, China6School of Physics, University of Chinese Academy of Sciences, Beijing 100049, China7Ottawa-Carleton Institute for Physics, Carleton University, 1125 Colonel By Drive, Ottawa,

Ontario K1S 5B6, Canada

E-mail: ustc0204.chenning@gmail.com, than@pitt.edu,

shufang@email.arizona.edu, weisv@itp.ac.cn,

ycwu@physics.carleton.ca

Abstract: Future precision measurements of the Standard Model (SM) parameters

at the proposed Z-factories and Higgs factories may have significant impacts on new

physics beyond the Standard Model (BSM). We illustrate this by focusing on the Type-

II two Higgs doublet model. A multi-variable global fitting is performed with full one

loop contributions to relevant couplings. The Higgs signal strength measurement at

proposed Higgs factories can provide strong constraints on new physics and are found

to be complementary to the Z-pole measurements.

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Contents

1 Introduction 2

2 Higgs and Electroweak Precision Measurement 2

2.1 Higgs Measurements 2

2.2 Electroweak Measurement 3

3 Type-II 2HDM 5

3.1 Model Setup 5

3.2 Loop corrections to Higgs couplings 7

4 Global Fitting 8

4.1 Alignment and Mass Degenerate Case 10

4.2 Non-alignment and Mass Degenerate Case 11

4.3 Non-alignment and Non-degenerate Case 12

5 Summary 14

– 1 –

1 Introduction

All the indications from the current measurements seem to confirm the validity of the

Standard Model (SM) and the observed Higgs boson is SM-like. However, there are

compelling arguments, both from theoretical and observational points of view, in favor

of the existence of new physics beyond the Standard Model (BSM) [1]. One of the

most straightforward, but well-motivated extensions is the two Higgs doublet model

(2HDM) [2] which has five massive scalars (h, H, A, H±) after electroweak symmetry

break (EWSB).

Complementary to the direct searches which has been actively carried out at the

LHC, precision measurements of the Higgs properties could also lead to relevant insights

towards new physics. The proposed Higgs factories (CEPC [3, 4], ILC [5] or FCC-

ee [6–8]) can push the measurement of Higgs properties into sub-percentage era. Using

the Type-II 2HDM as example, we perform a global fit to get the prospects of these

measurements in constraining the model parameter spaces [9].

2 Higgs and Electroweak Precision Measurement

2.1 Higgs Measurements

Currently, the ATLAS and CMS have carried out the comprehensive measurements of

the Higgs signal strength in various channels with 7 and 8 TeV combined data [10] as

well as the 13 TeV data [11, 12]. The results are collected in Fig. 1. In the left panel,

we show the signal strength defined as

µi =(σ × Br)i

(σ × Br)SM

(2.1)

for different production and decay channels. While the right panel shows the constraints

from the signal strength measurement on the κi which is defined as

κi =ghiigSMhii

(2.2)

In each figure, the black line represents the RUN-I combined measurement [10], the

red and blue lines represent the RUN-II measurements from ATLAS [12] and CMS [11]

respectively. From these plots, we find that in some channels (such as those in ZH

production mode) the precision has been improved significantly. For the coupling mea-

surement, it still has at least 10% uncertainties as shown in the right panel of Fig. 1.

The measurements can be significantly improved with the proposed Higgs factories.

As an example, the H-20 scenario of ILC [13] will accumulate about 4000 fb−1 at

– 2 –

Figure 1. Current Higgs signal strength measurements for various channels (left) and the

constraints on the κ of different couplings assuming no additional BSM channel for the Higgs

(right). Data is retrieved from [10–12].

√s =500 GeV, 200 fb−1 at

√s =350 GeV and 2000 fb−1 at

√s =250 GeV. The detailed

precisions of the signal strength measurements for different channels and√s are listed

in Tab. 1. Correspondingly, the coupling measurements can be improved considerably

as shown in Fig. 2. With the huge data accumulated in the Higgs factories, sub-percent

precision can be expected for the measurement of the Higgs couplings which will in turn

put stringent constraints on new physics.

2.2 Electroweak Measurement

Beside Higgs related measurements, the proposed Higgs factories will also have their

own Z-pole measurement. The current best precision measurements for Z-pole physics

mostly come from the LEP-I as well as Tevatron and the LHC [14, 15]. These mea-

surements will be significantly improved at future lepton colliders [3, 6–8, 16]. The

anticipated precisions on several measurements for Z-pole program are listed in Tab. 2.

Given the complexity of a full Z-pole precision global fit, we instead use the Peskin-

Takeuchi oblique parameters S, T and U [17] to present the implications of the Z-pole

– 3 –

years0 5 10 15 20

couplin

g p

recis

ion [%

]

­110

1

10

210

HZZ

HWW

Hbb

Hcc

Hgg

ττH

γγH

Htt

HΓ

µµH

model­independentILC Scenario H­20

no hadronic recoil

Figure 2. The precision on various couplings of the Higgs boson in scenario H-20. Figure is

getting from [13].

collider ILC√s 250 GeV 350 GeV 500 GeV∫Ldt 2 ab−1 200 fb−1 4 ab−1

production Zh Zh ννh Zh ννh tth

∆σ/σ 0.71% 2.1% − 1.06 − −decay ∆(σ ·BR)/(σ ·BR)

h→ bb 0.42% 1.67% 1.67% 0.64% 0.25% 9.9%

h→ cc 2.9% 12.7% 16.7% 4.5% 2.2% −h→ gg 2.5% 9.4% 11.0% 3.9% 1.5% −h→ WW ∗ 1.1% 8.7% 6.4% 3.3% 0.85% −h→ τ+τ− 2.3% 4.5% 24.4% 1.9% 3.2% −h→ ZZ∗ 6.7% 28.3% 21.8% 8.8% 2.9% −h→ γγ 12.0% 43.7% 50.1% 12.0% 6.7% −h→ µ+µ− 25.5% 97.6% 179.8% 31.1% 25.5% −

Table 1. Estimated statistical precisions for Higgs measurements obtained at the ILC with

various center-of-mass energies [13].

precision. Corresponding to the precision listed in Tab. 2, the constrained S, T and U

– 4 –

ranges and associated error correlation matrix are listed in Tab. 3, which are obtained

by using Gfitter package [14].

ILC Precision

αs(M2Z) ±1.0× 10−4

∆α(5)had(M2

Z) ±4.7× 10−5

mZ [GeV] ±0.0021

mt [GeV] (pole) ±0.03exp ± 0.1th

mh [GeV] < ±0.1

mW [GeV] (±5exp ± 1th)× 10−3

sin2 θ`eff (±1.3exp ± 1.5th)× 10−5

ΓZ [GeV] ±0.001

Table 2. Anticipated precisions of the EW observables at the future lepton colliders. The

results are mainly from [14, 18–21].

3 Type-II 2HDM

3.1 Model Setup

In 2HDM, two SU(2)L scalar doublets Φi (i = 1, 2) with a hyper-charge assignment

Y = +1/2:

Φi =

(φ+i

vi+φ0i +iGi√2

)(3.1)

The neutral component of each doublet obtains a vacuum expectation value (vev) vi(i=1,2) after EWSB satisfying v2

1 + v22 = v2 = (246 GeV)2, and v2/v1 = tan β.

Current (1.7× 107 Z’s) ILC (109Z’s)

σcorrelation σ correlation

S T U (10−2) S T U

S 0.04± 0.11 1 0.92 −0.68 3.53 1 0.988 −0.879

T 0.09± 0.14 − 1 −0.87 4.89 − 1 −0.909

U −0.02± 0.11 − − 1 3.76 − − 1

Table 3. Estimated S, T , and U ranges and correlation matrices ρij from Z-pole precision

measurements of the current results, mostly from LEP-I [22], and at future lepton colliders

ILC [16]. Gfitter package [14] is used in obtaining those constraints.

– 5 –

The 2HDM Lagrangian for the Higgs sector can be written as

L =∑i

|DµΦi|2 − V (Φ1,Φ2) + LYuk, (3.2)

where the Higgs potential has following form:

V (Φ1,Φ2) =m211Φ†1Φ1 +m2

22Φ†2Φ2 −m212(Φ†1Φ2 + h.c.) +

λ1

2(Φ†1Φ1)2 +

λ2

2(Φ†2Φ2)2

λ3(Φ†1Φ1)(Φ†2Φ2) + λ4(Φ†1Φ2)(Φ22Φ1) +

1

2λ5

[(Φ†1Φ2)2 + h.c.

](3.3)

where we assume the conservation of CP symmetry.

In general, there are four types Yukawa couplings assigning different doublet to dif-

ferent type fermions. In this work, we focus on Type-II of which the Yukawa couplings

is:

−LYuk = YdQLΦ1dR + YeLLΦ1eR + YuQLiσ2Φ∗2uR + h.c. (3.4)

After EWSB, three of the degree of freedom in two doublets are eaten by the SM

gauge bosons, providing their masses. The remaining physical mass eigenstates are two

CP-even neutral Higgs bosons h and H, one CP-odd neutral Higgs boson A, and a pair

of charged scalars H±. Instead of the eight parameters in the potential m211, m2

22, m212,

λ1,2,3,4,5, more physical parameters will be used: (v, tan β, α, mh, mH , mA, mH± , m212).

In term of these mass eigenstates, the effective Lagrangian for the couplings between

these scalars and SM particles is

L = κZm2Z

vZµZ

µh+ κW2m2

W

vW+µ W

µ−h+ κgαs

12πvGaµνG

aµνh+ κγα

2πvAµνA

µνh

+ κZγα

πvAµνZ

µνh−

(κu∑u

mf

vff + κd

∑d

mf

vff + κ`

∑`

mf

vff

)h (3.5)

where, at tree level, we have

κZ = κW = sin(β − α), κu =cosα

sin β, κd,` = − sinα

cos β. (3.6)

Note that κg, κγ and κZγ are generated at one-loop. From above κ’s, the alignment

limit can be identified as cos(β − α) = 01.

It is also important to have a discussion for the triple couplings among scalars. At

the alignment limit, we have

λhΦΦ = −CΦ

2v(m2

h + 2m2Φ −

2m212

sin β cos β). (3.7)

1Another possibility sin(β − α) = 0 is not considered here.

– 6 –

with CΦ = 2(1) for Φ = H±(H,A). With degenerate masses mΦ ≡ mH = mA = mH± ,

we introduce a new parameter λ as

λv2 ≡ m2Φ −

m212

sin β cos β, (3.8)

which is the parameter that enters the Higgs self-couplings and relevant for the loop

corrections to the SM-like Higgs boson couplings. This parameter could be used inter-

changeably with m212. For the rest of our analysis, v = 246 GeV and mh = 125 GeV

are used. The remaining free parameters are

tan β, cos(β − α),mH ,mA,mH± , λ (3.9)

3.2 Loop corrections to Higgs couplings

We define the normalized SM-like Higgs boson couplings including loop effects as

κ2HDMloop ≡

g2HDMtree + g2HDM

loop

gSMtree + gSM

loop

(3.10)

In our calculations, we adopt the on-shell renormalization scheme [23]. The conven-

tions for the renormalization constants and the renormalization conditions are mostly

following Refs. [23, 24]. All related counter terms, renormalization constants and renor-

malization conditions are implemented according to the on-shell scheme and incorpo-

rated into model files of FeynArts [25]2. One-loop corrections are generated using

FeynArts and FormCalc [31] including all possible one-loop diagrams. FeynCalc [32,

33] is also used to simplify the analytical expressions. LoopTool [34] is used to evaluate

the numerical value of all the loop-induced amplitude. The numerical results have been

cross-checked with another numerical program H-COUP [35] in some cases.

Further, the 2HDM contributions to the oblique parameters are given by [36]:

∆S =1

πm2Z

{[B22(m2

Z ;m2H ,m

2A)− B22(m2

Z ;m2H± ,m2

H±)]

+[B22(m2

Z ;m2h ,m

2A)− B22(m2

Z ;m2H ,m

2A) + B22(m2

Z ;m2Z ,m

2H)− B22(m2

Z ;m2Z ,m

2h)

−m2ZB0(mZ ;mZ ,m

2H) +m2

ZB0(mZ ;mZ ,m2h)]

cos2(β − α)}, (3.11)

2Note that in this scheme, there will be gauge-dependence in the calculation of the counter

term of β [26]. For convenience, we will adopt this convention and the Feynman-’t-Hooft gauge

is used throughout the calculations. For more sophisticated gauge-independent renormalization

scheme to deal with α and β, see [27–30]. Corresponding implementations have been uploaded to

https://github.com/ycwu1030/THDMNLO FA.

– 7 –

∆T =1

16πm2W s2

W

{[F (m2

H± ,m2A) + F (m2

H± ,m2H)− F (m2

A ,m2H)]

+[F (m2

H± ,m2h)− F (m2

H± ,m2H)− F (m2

A ,m2h) + F (m2

A ,m2H)

+F (m2W ,m2

H)− F (m2W ,m2

h)− F (m2Z ,m

2H) + F (m2

Z ,m2h)

+4m2ZB0(m2

Z ,m2H ,m

2h)− 4m2

WB0(m2W ,m2

H ,m2h)]

cos2(β − α)}, (3.12)

∆U = −∆S +1

πm2W

{[B22(m2

W ,m2A,m

2H±)− 2B22(m2

W ,m2H± ,m2

H±) + B22(m2W ,m

2H ,m

2H±)]

+[B22(m2

W ,m2h,m

2H±)− B22(m2

W ,m2H ,m

2H±) + B22(m2

W ,m2W ,m

2H)− B22(m2

W ,m2W ,m

2h)

−m2WB0(m2

W ,m2W ,m

2H) +m2

WB0(m2W ,m

2W ,m

2h)]

cos2(β − α)}, (3.13)

4 Global Fitting

In our analysis, global fit is performed to get the constraints on the model parameters

by constructing the χ2 with the profile likelihood method

χ2 =∑i

(µBSMi − µobs

i )2

σ2µi

, (4.1)

where µBSMi = (σ×BR)BSM

(σ×BR)SM, and i runs over all available channels, the corresponding

errors σµi for all these channels are listed in Tab. 1.

We also incorporate the Z-pole precision measurements by fitting into the oblique

parameters S, T and U of which the χ2 reads

χ2 =∑ij

(Xi − Xi)(V−1)ij(Xj − Xj), (4.2)

with Xi = (∆S,∆T,∆U)2HDM being the predicted values in 2HDM, while Xi =

(∆S,∆T,∆U) being the best-fit central value (assuming 0 for future measurements). V

is the covariance matrix with Vij = σiρijσj. The corresponding errors σi and the corre-

lation matrix ρij are listed in Tab. 3 for both current measurement and ILC prospects.

At tree level, the Higgs couplings only involve tan β and cos(β − α). Hence, from

Higgs measurement, we can only constraint the parameter space in tan β vs. cos(β −α) plane. The results from ATLAS [12] and CMS [11] are shown in Fig. 3. Beside

the extra arm corresponding to the wrong sign scenario, the current measurement

strongly constrain the range of cos(β − α). This can be further improved by the Higgs

measurement at the ILC which can be seen in Fig. 4. From the fitting results, at tree

level, we can already constrain the cos(β − α) to be at least less than 0.01.

– 8 –

Figure 3. Current constraints from ATLAS (left) and CMS (right) for the Type-II 2HDM

in tanβ vs. cos(β − α) plane. Figures are getting from [11, 12].

-0.015 -0.01 -0.005-0.01 0 0.005 0.01 0.0150.1

0.2

0.5

1

2

5

10

20

30

50

cos(β-α)

tanβ

2HDM TYPE-II

Δμ/μ of FCC 5ab-1

Δμ/μ of ILC Full

κ-fit of ILC

ILC Lumi

Figure 4. The prospected constraints from ILC measurement for the Type-II 2HDM in tanβ

vs. cos(β − α) plane.

– 9 –

Using hZZ coupling as example, at tree level, the couplings is

LhZZ =m2Z

vsβ−αhZµZ

µ ≈(

1− 1

2c2β−α

)m2Z

vhZµZ

µ. (4.3)

Hence, the deviation from the SM value is 12c2β−α

m2Z

v. With the constraints from the

ILC prospect, the coupling deviation is at about O(10−4) level. In this case, the loop

induced correction which is not vanished even in the alignment limit can not be ignored

any more. Further, including loop correction which has heavy scalars running in the

loop also provides the possibility to constrain the mass of heavy scalars as well as

the triple scalar couplings. With this consideration, we will consider three cases in

sequence:

• Tree-level alignment + Mass degenerate:

– cos(β − α) = 0, mΦ ≡ mH = mA = mH± .

• Non-alignment + Mass degenerate:

– cos(β − α) 6= 0, mΦ ≡ mH = mA = mH± .

• Non-alignment + Non-degenerate:

– cos(β − α) 6= 0, ∆mA = mA −mH , ∆mC = mH± −mH .

4.1 Alignment and Mass Degenerate Case

The first case we consider is when cos(β−α) = 0 and all the heavy scalars are degenerate

in mass. In this case, the free parameters are tan β, mΦ and λ. The corresponding

exclusion results are shown in Fig. 5 where lines with different colors represent the

exclusions for different choice of λ in mΦ-tan β plane. The region to the right of the

lines and the upper left region are allowed. From this figure, we can see that when

the triple scalar coupling is not strong, we still have large allowed region as shown by

the red and blue curves. The gaps around 350 GeV come from the top-pair threshold.

When the triple scalar coupling is strong, the exclusion curves provide lower limits on

the heavy scalar mass which is consistent with our prospects. For√λv2 = 300 GeV, a

lower limit of 500 GeV on the mass is expected, while for√λv2 = 500 GeV, the heavy

scalar mass should be larger than 1200 GeV.

– 10 –

125 500 1000 1500 20000.1

0.2

0.5

1

2

5

10

1520

mϕ(mH0=mA=mH± , GeV)

tanβ

ILC, 2HDM one-loop correction,type-II

95%CL, Sqrt(λv2) = 0 GeV95%CL, Sqrt(λv2) = 100 GeV

95%CL, Sqrt(λv2) = 300 GeV

95%CL, Sqrt(λv2) = 500 GeV

Sqrt(λv2) = Sqrt(mϕ2-

m122

sβ cβ

)

Figure 5. The exclusion line from Higgs measurement in the mΦ-tanβ plane for different

choice of λ

4.2 Non-alignment and Mass Degenerate Case

The second case we consider is when we deviate from the alignment limit but still

assume that all heavy scalars are degenerated. In this case, the free parameters are

tan β, cos(β − α), mΦ and λ. We first show the result in Fig. 6 in the mΦ-tan β plane

for different choice of cos(β−α) (represented by lines with different colors) and of√λv2

(left panel:√λv2 = 0 GeV and right panel:

√λv2 = 300 GeV). The constraints on

other parameters are similar to the previous case, while it also shows different exclusion

patterns for negative and positive choice of cos(β−α). Note that, for the tree-level only

results, Fig. 4, the constraints is symmetric for cos(β −α). This shows the importance

of the interference between loop corrections and the tree level couplings.

To make this more clearer, we show the results in the cos(β − α)-tan β plane in

Fig. 7. In the left panel,√λv2 = 300 GeV is fixed. The red region is the global

fitting allowed region, while lines with different colors are the constraints from different

couplings as indicated by the label. We can see that at large tan β region, the constraints

from κτ and κb push the allowed region away from the tree level results. At low tan β

region, the allowed region is cut off by κc and κg. Note that we are still in the degenerate

cases, with this small cos(β − α) we are probing, the constraint from κz is rather weak

as shown by the green line in the upper right corner. The effects of√λv2 is shown in

the right panel of Fig. 7. We can see that the region will deviate from the tree level

cases with increase of√λv2. Note that there is no more allowed region for larger value

of√λv2 which put an upper limit on λ.

– 11 –

125 500 1000 1500 2000m (mH0 = mA = mH ± , GeV)

0.1

0.2

0.5

1

2

5

10

20

50

tan

cos( )=0

cos( )=0.005

cos( )=-0.005

Tree+Loop, v2 = 0 GeV

125 500 1000 1500 2000m (mH0 = mA = mH ± , GeV)

0.1

0.2

0.5

1

2

5

10

20

50

tan

cos( )=0

cos( )=0.005

cos( )=-0.005

Tree+Loop, v2 = 300 GeV

Figure 6. The exclusion lines for different choice of cos(β − α) in mΦ-tanβ plane, the left

panel is for√λv2 = 0 GeV while the right panel is for

√λv2 = 300 GeV.

-0.01 -0.005 0 0.005 0.01cos(β−α)

0.1

0.2

0.5

1

2

5

10

20

50ta

nβ

√λv2

300

200

100 0

mΦ = 600 GeV

Figure 7. The exclusion lines in the cos(β − α)-tanβ plane for mΦ = 600 GeV. In the left

panel,√λv2 = 300 GeV is fixed. The red region is the global fitting allowed region, while

lines with different colors are the constraints from different couplings as indicated by the

label. The black dashed line represents the tree level result. In the right panel, only the

global fitting allowed regions are shown for different choice of√λv2.

4.3 Non-alignment and Non-degenerate Case

The last case we consider is the most general one. We allow both the deviation from the

alignment and also the mass splittings. The new free parameters are the mass splittings

among different scalars: ∆mA = mA −mH , ∆mC = mH± −mH . The constraints on

other parameters are similar to previous case. Hence, we focus on the constraints on

– 12 –

mass differences here. When allowing mass splitting, the Z-pole measurements will

also provide stringent constraints. The constraints from the T parameter is shown

in Fig. 8 in mA-mC plane. From this plot we can see that the Z-pole measurement

has already put a strong constraint on the mass difference. Hence, a natural question

would be whether the Higgs measurement can provide further information on the mass

difference.

-300 -200 -100 0 100 200 300-300

-200

-100

0

100

200

300

ΔmA (GeV)

ΔmC(GeV

)

ΔTΔT = -0.051ΔT = -0.0255

ΔT = 0.051ΔT = 0.0255ΔT = 0

-2σ -1σ

1σ 2σ

Figure 8. The constraints from T-parameter in mA-mC plane. The blue and red lines

represent the 1-σ and 2-σ region respectively.

The results from the Higgs measurement are shown in Fig. 9. In the left column, the

individual constraints from Higgs measurement (solid lines) and Z-pole measurement

(dashed line) are shown. We can see that both Higgs measurement and Z-pole mea-

surement can constrain the mass splitting, while these two constraints are mis-aligned.

Furthermore, the Higgs measurement is quite sensitive to the value of cos(β−α). How-

ever, the T parameter constraints here merely changes for the range of the cos(β − α)

we considered here. When combining these, the allowed region is further shrunk as

shown in the right column of Fig. 9. This result clearly shows the complementarity

between the Higgs measurement and Z-pole measurement. For cos(β − α) = 0 (blue

lines), increasing the mass of the heavy scalar leads to larger allowed region which is

consistent with the decoupling limit. However, when we deviate from cos(β − α) = 0

(±0.007 as shown by red and green lines in the plots), the allowed the region is even

smaller for larger mass. This is due to the fact that when we approach decoupling limit,

the parameter space will also be pushed into alignment limits, otherwise we suffer from

either the unitarity/perturbativity problem or large correction induced by triple scalar

couplings.

– 13 –

-400 -300 -200 -100 0 100 200 300 400∆mA (GeV)

-400

-300

-200

-100

0

100

200

300

400

∆mC (

GeV

)

cos(β−α) = 0.007cos(β−α) = 0. 0cos(β−α) = −0.007

mH = 600, √λv2 = 0 GeV

-400 -300 -200 -100 0 100 200 300 400∆mA (GeV)

-400

-300

-200

-100

0

100

200

300

400

∆mC (

GeV

)

cos(β−α) = 0.007cos(β−α) = 0. 0cos(β−α) = −0.007

mH = 600, √λv2 = 0 GeV

-400 -300 -200 -100 0 100 200 300 400∆mA (GeV)

-400

-300

-200

-100

0

100

200

300

400

∆mC (

GeV

)

cos(β−α) = 0.007cos(β−α) = 0. 0cos(β−α) = −0.007

mH = 2000, √λv2 = 0 GeV

-400 -300 -200 -100 0 100 200 300 400∆mA (GeV)

-400

-300

-200

-100

0

100

200

300

400

∆mC (

GeV

)cos(β−α) = 0.007cos(β−α) = 0. 0cos(β−α) = −0.007

mH = 2000, √λv2 = 0 GeV

Figure 9. The constraints from Higgs measurement (left column) and Higgs measurement

combined with Z-pole measurement (right column) in ∆mA-∆mC plane. The mass are set

by mH = 600 and 2000 GeV for upper two and lower two panels respectively. Lines with

different colors are for different choices of cos(β − α) as indicated in the legend. The dashed

contours in the left column are the Z-pole constraints which barely changes with cos(β − α)

in this range.

5 Summary

In this paper, we examined the impacts of the precision measurements of the SM

parameters at the proposed Higgs factories using Type-II 2HDM as an example. At

tree level, the current measurement has already push the model into the alignment

– 14 –

limit region. The proposed Higgs factories can do even better with clean background.

In this region, for some coupling, the loop corrections can not be ignored any more.

When including loop induced contributions, we can further set bounds on the heavy

scalar masses as well as the mass splitting. The triple scalar couping is constrained as

well. In this sense, the Higgs precision measurement is complementary to the Z-pole

measurement. The combination of these two kinds measurements can certainly provide

more information about the new physics.

Acknowledgments

We would like to thank Han Yuan and Huanian Zhang for collaboration at the early

stage of this project. We would also like to thank Liantao Wang and Manqi Ruan

for valuable discussions. NC is supported by the National Natural Science Foundation

of China (under Grant No. 11575176) and Center for Future High Energy Physics

(CFHEP). TH is supported in part by the U.S. Department of Energy under grant

No. DE-FG02-95ER40896 and by the PITT PACC. SS is supported by the Department

of Energy under Grant No. DE-FG02-13ER41976/DE-SC0009913. WS were supported

in part by the National Natural Science Foundation of China (NNSFC) under grant

No. 11675242. YW is supported by the Natural Sciences and Engineering Research

Council of Canada (NSERC). TH also acknowledges the hospitality of the Aspen Center

for Physics, which is supported by National Science Foundation grant PHY-1607611.

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