Spin-1 particle and

the ATLAS Diboson excess!

Tomohiro Abe (KEK) !

based on the works 1507.01185: TA, Ryo Nagai, Shohei Okawa, Masaharu Tanabashi 1507.01681: TA, Teppei Kitahara, Mihoko Nojiri

!基研研究会 PPP2015 　 2015.9.15

今日話したいこと

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Figure 5: Background-only fits to the dijet mass (mj j) distributions in data (a) after tagging with the WZ selection,(b) after tagging with the WW selection and (c) after tagging with the ZZ selection. The significance shown inthe inset for each bin is the di↵erence between the data and the fit in units of the uncertainty on this di↵erence.The significance with respect to the maximum-likelihood expectation is displayed in red, and the significance whentaking the uncertainties on the fit parameters into account is shown in blue. The spectra are compared to the signalsexpected for an EGM W 0 with mW0 = 1.5, 2.0, or 2.5 TeV or to an RS graviton with mGRS = 1.5 or 2.0 TeV.

to the shape of the signal, and N is a log-normal distribution for the nuisance parameters, ✓, modellingthe systematic uncertainty on the signal normalisation. The expected number of events is the bin-wisesum of the events expected for the signal and background: nexp

= nsig

+ nbg

. The number of expectedbackground events in dijet mass bin i, ni

bg, is obtained by integrating dn/dx obtained from eqn. (1) overthat bin. Thus nbg

is a function of the dijet background parameters p1, p2, p3. The number of expectedsignal events, nsig

, is evaluated based on MC simulation assuming the cross section of the model undertest multiplied by the signal strength and including the e↵ects of the systematic uncertainties described in

16

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Figure 5: Background-only fits to the dijet mass (mj j) distributions in data (a) after tagging with the WZ selection,(b) after tagging with the WW selection and (c) after tagging with the ZZ selection. The significance shown inthe inset for each bin is the di↵erence between the data and the fit in units of the uncertainty on this di↵erence.The significance with respect to the maximum-likelihood expectation is displayed in red, and the significance whentaking the uncertainties on the fit parameters into account is shown in blue. The spectra are compared to the signalsexpected for an EGM W 0 with mW0 = 1.5, 2.0, or 2.5 TeV or to an RS graviton with mGRS = 1.5 or 2.0 TeV.

to the shape of the signal, and N is a log-normal distribution for the nuisance parameters, ✓, modellingthe systematic uncertainty on the signal normalisation. The expected number of events is the bin-wisesum of the events expected for the signal and background: nexp

= nsig

+ nbg

. The number of expectedbackground events in dijet mass bin i, ni

bg, is obtained by integrating dn/dx obtained from eqn. (1) overthat bin. Thus nbg

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16

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= nsig

+ nbg

. The number of expectedbackground events in dijet mass bin i, ni

bg, is obtained by integrating dn/dx obtained from eqn. (1) overthat bin. Thus nbg

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16

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It is convenient to use a di↵erent set of the parameters instead of these parameters. Weuse the following 13 parameters to fix the parameters in the electroweak sector,

r, v3, v, ↵, mZ , mZ0 , mh, mH0 , mH , mA, F , Z , gWW 0H0 . (34)

Here, we use r, v3, v instead of three µ parameters. is fixed by the charged Higgs massor the CP-odd Higgs mass. The six �’s have the same information as three CP-evenHiggs masses and their mixing angles (mh, mH , mH0 , ✓1, ✓2, ✓3). We can use mZ , mZ0 ,and ↵(= e2/4⇡) instead of the gauge couplings. In addition, we can exchange (✓1, ✓2,✓3) with (F , Z , gWW 0H0). Since the values of four parameters, v, mZ , ↵, and mh arealready known, the remaining nine parameters are free parameters of this model. In ouranalyses, we take mh = 125 GeV.

We find F is severely constrained close to 1 in mA � mh regime. When the heavyHiggs masses are universal, mA = mH0 = mH , the expression of a quartic coupling �3

by our parameter choice (Eq. (34)) becomes very simple,

�3(µ = mZ0) =2F

2

m2h

v2+

1� 2F

2

m2A

v2. (35)

Theoretical conditions (see subsection 3.2 for more detail) demand 0 < �3 < 4⇡, namely

F >

pm2

A � 8⇡v2pm2

A �m2h

' 1� 8⇡v2 �m2h

2m2A

= 1� 0.2

✓2TeV

mA

◆2

, (36)

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F <mAp

m2A �m2

h

' 1 +m2

h

2m2A

= 1 + 0.002

✓2TeV

mA

◆2

. (37)

Here we assumed mA � mh to obtain the last expressions.Similarly, we find that the coupling ratio Z is also severely constrained close to its

maximized value in mA � mh regime. Typically, the allowed regime is Z = 1�O(1)%.The detailed description is given in Appendix A.

In the following discussion, we take F ' 1, mA = mH = mH0 = O(1) TeV,gWW 0H0 = 0, and we always choose Z to be its maximal value. For the most part ofour numerical analysis, Z is set to 0.95 - 1.00.

3 Phenomenology of Spin-1 Resonances

In this section, we discuss the properties of the W 0 and Z 0 such as production cross sec-tion and decay branching ratios, and also discuss both the theoretical and experimentalconstraints. In the following, we show some formulae with approximation, which helpto understand the parameter dependence. However, we use the exact formulae in ournumerical calculations.

8

It is convenient to use a di↵erent set of the parameters instead of these parameters. Weuse the following 13 parameters to fix the parameters in the electroweak sector,

r, v3, v, ↵, mZ , mZ0 , mh, mH0 , mH , mA, F , Z , gWW 0H0 . (34)

Here, we use r, v3, v instead of three µ parameters. is fixed by the charged Higgs massor the CP-odd Higgs mass. The six �’s have the same information as three CP-evenHiggs masses and their mixing angles (mh, mH , mH0 , ✓1, ✓2, ✓3). We can use mZ , mZ0 ,and ↵(= e2/4⇡) instead of the gauge couplings. In addition, we can exchange (✓1, ✓2,✓3) with (F , Z , gWW 0H0). Since the values of four parameters, v, mZ , ↵, and mh arealready known, the remaining nine parameters are free parameters of this model. In ouranalyses, we take mh = 125 GeV.

We find F is severely constrained close to 1 in mA � mh regime. When the heavyHiggs masses are universal, mA = mH0 = mH , the expression of a quartic coupling �3

by our parameter choice (Eq. (34)) becomes very simple,

�3(µ = mZ0) =2F

2

m2h

v2+

1� 2F

2

m2A

v2. (35)

Theoretical conditions (see subsection 3.2 for more detail) demand 0 < �3 < 4⇡, namely

F >

pm2

A � 8⇡v2pm2

A �m2h

' 1� 8⇡v2 �m2h

2m2A

= 1� 0.2

✓2TeV

mA

◆2

, (36)

and

F <mAp

m2A �m2

h

' 1 +m2

h

2m2A

= 1 + 0.002

✓2TeV

mA

◆2

. (37)

Here we assumed mA � mh to obtain the last expressions.Similarly, we find that the coupling ratio Z is also severely constrained close to its

maximized value in mA � mh regime. Typically, the allowed regime is Z = 1�O(1)%.The detailed description is given in Appendix A.

In the following discussion, we take F ' 1, mA = mH = mH0 = O(1) TeV,gWW 0H0 = 0, and we always choose Z to be its maximal value. For the most part ofour numerical analysis, Z is set to 0.95 - 1.00.

3 Phenomenology of Spin-1 Resonances

In this section, we discuss the properties of the W 0 and Z 0 such as production cross sec-tion and decay branching ratios, and also discuss both the theoretical and experimentalconstraints. In the following, we show some formulae with approximation, which helpto understand the parameter dependence. However, we use the exact formulae in ournumerical calculations.

8

It is convenient to use a di↵erent set of the parameters instead of these parameters. Weuse the following 13 parameters to fix the parameters in the electroweak sector,

r, v3, v, ↵, mZ , mZ0 , mh, mH0 , mH , mA, F , Z , gWW 0H0 . (34)

Here, we use r, v3, v instead of three µ parameters. is fixed by the charged Higgs massor the CP-odd Higgs mass. The six �’s have the same information as three CP-evenHiggs masses and their mixing angles (mh, mH , mH0 , ✓1, ✓2, ✓3). We can use mZ , mZ0 ,and ↵(= e2/4⇡) instead of the gauge couplings. In addition, we can exchange (✓1, ✓2,✓3) with (F , Z , gWW 0H0). Since the values of four parameters, v, mZ , ↵, and mh arealready known, the remaining nine parameters are free parameters of this model. In ouranalyses, we take mh = 125 GeV.

We find F is severely constrained close to 1 in mA � mh regime. When the heavyHiggs masses are universal, mA = mH0 = mH , the expression of a quartic coupling �3

by our parameter choice (Eq. (34)) becomes very simple,

�3(µ = mZ0) =2F

2

m2h

v2+

1� 2F

2

m2A

v2. (35)

Theoretical conditions (see subsection 3.2 for more detail) demand 0 < �3 < 4⇡, namely

F >

pm2

A � 8⇡v2pm2

A �m2h

' 1� 8⇡v2 �m2h

2m2A

= 1� 0.2

✓2TeV

mA

◆2

, (36)

and

F <mAp

m2A �m2

h

' 1 +m2

h

2m2A

= 1 + 0.002

✓2TeV

mA

◆2

. (37)

Here we assumed mA � mh to obtain the last expressions.Similarly, we find that the coupling ratio Z is also severely constrained close to its

maximized value in mA � mh regime. Typically, the allowed regime is Z = 1�O(1)%.The detailed description is given in Appendix A.

In the following discussion, we take F ' 1, mA = mH = mH0 = O(1) TeV,gWW 0H0 = 0, and we always choose Z to be its maximal value. For the most part ofour numerical analysis, Z is set to 0.95 - 1.00.

3 Phenomenology of Spin-1 Resonances

In this section, we discuss the properties of the W 0 and Z 0 such as production cross sec-tion and decay branching ratios, and also discuss both the theoretical and experimentalconstraints. In the following, we show some formulae with approximation, which helpto understand the parameter dependence. However, we use the exact formulae in ournumerical calculations.

8

It is convenient to use a di↵erent set of the parameters instead of these parameters. Weuse the following 13 parameters to fix the parameters in the electroweak sector,

r, v3, v, ↵, mZ , mZ0 , mh, mH0 , mH , mA, F , Z , gWW 0H0 . (34)

Here, we use r, v3, v instead of three µ parameters. is fixed by the charged Higgs massor the CP-odd Higgs mass. The six �’s have the same information as three CP-evenHiggs masses and their mixing angles (mh, mH , mH0 , ✓1, ✓2, ✓3). We can use mZ , mZ0 ,and ↵(= e2/4⇡) instead of the gauge couplings. In addition, we can exchange (✓1, ✓2,✓3) with (F , Z , gWW 0H0). Since the values of four parameters, v, mZ , ↵, and mh arealready known, the remaining nine parameters are free parameters of this model. In ouranalyses, we take mh = 125 GeV.

We find F is severely constrained close to 1 in mA � mh regime. When the heavyHiggs masses are universal, mA = mH0 = mH , the expression of a quartic coupling �3

by our parameter choice (Eq. (34)) becomes very simple,

�3(µ = mZ0) =2F

2

m2h

v2+

1� 2F

2

m2A

v2. (35)

Theoretical conditions (see subsection 3.2 for more detail) demand 0 < �3 < 4⇡, namely

F >

pm2

A � 8⇡v2pm2

A �m2h

' 1� 8⇡v2 �m2h

2m2A

= 1� 0.2

✓2TeV

mA

◆2

, (36)

and

F <mAp

m2A �m2

h

' 1 +m2

h

2m2A

= 1 + 0.002

✓2TeV

mA

◆2

. (37)

Here we assumed mA � mh to obtain the last expressions.Similarly, we find that the coupling ratio Z is also severely constrained close to its

maximized value in mA � mh regime. Typically, the allowed regime is Z = 1�O(1)%.The detailed description is given in Appendix A.

In the following discussion, we take F ' 1, mA = mH = mH0 = O(1) TeV,gWW 0H0 = 0, and we always choose Z to be its maximal value. For the most part ofour numerical analysis, Z is set to 0.95 - 1.00.

3 Phenomenology of Spin-1 Resonances

In this section, we discuss the properties of the W 0 and Z 0 such as production cross sec-tion and decay branching ratios, and also discuss both the theoretical and experimentalconstraints. In the following, we show some formulae with approximation, which helpto understand the parameter dependence. However, we use the exact formulae in ournumerical calculations.

8

It is convenient to use a di↵erent set of the parameters instead of these parameters. Weuse the following 13 parameters to fix the parameters in the electroweak sector,

r, v3, v, ↵, mZ , mZ0 , mh, mH0 , mH , mA, F , Z , gWW 0H0 . (34)

Here, we use r, v3, v instead of three µ parameters. is fixed by the charged Higgs massor the CP-odd Higgs mass. The six �’s have the same information as three CP-evenHiggs masses and their mixing angles (mh, mH , mH0 , ✓1, ✓2, ✓3). We can use mZ , mZ0 ,and ↵(= e2/4⇡) instead of the gauge couplings. In addition, we can exchange (✓1, ✓2,✓3) with (F , Z , gWW 0H0). Since the values of four parameters, v, mZ , ↵, and mh arealready known, the remaining nine parameters are free parameters of this model. In ouranalyses, we take mh = 125 GeV.

We find F is severely constrained close to 1 in mA � mh regime. When the heavyHiggs masses are universal, mA = mH0 = mH , the expression of a quartic coupling �3

by our parameter choice (Eq. (34)) becomes very simple,

�3(µ = mZ0) =2F

2

m2h

v2+

1� 2F

2

m2A

v2. (35)

Theoretical conditions (see subsection 3.2 for more detail) demand 0 < �3 < 4⇡, namely

F >

pm2

A � 8⇡v2pm2

A �m2h

' 1� 8⇡v2 �m2h

2m2A

= 1� 0.2

✓2TeV

mA

◆2

, (36)

and

F <mAp

m2A �m2

h

' 1 +m2

h

2m2A

= 1 + 0.002

✓2TeV

mA

◆2

. (37)

Here we assumed mA � mh to obtain the last expressions.Similarly, we find that the coupling ratio Z is also severely constrained close to its

maximized value in mA � mh regime. Typically, the allowed regime is Z = 1�O(1)%.The detailed description is given in Appendix A.

In the following discussion, we take F ' 1, mA = mH = mH0 = O(1) TeV,gWW 0H0 = 0, and we always choose Z to be its maximal value. For the most part ofour numerical analysis, Z is set to 0.95 - 1.00.

3 Phenomenology of Spin-1 Resonances

In this section, we discuss the properties of the W 0 and Z 0 such as production cross sec-tion and decay branching ratios, and also discuss both the theoretical and experimentalconstraints. In the following, we show some formulae with approximation, which helpto understand the parameter dependence. However, we use the exact formulae in ournumerical calculations.

8

It is convenient to use a di↵erent set of the parameters instead of these parameters. Weuse the following 13 parameters to fix the parameters in the electroweak sector,

r, v3, v, ↵, mZ , mZ0 , mh, mH0 , mH , mA, F , Z , gWW 0H0 . (34)

Here, we use r, v3, v instead of three µ parameters. is fixed by the charged Higgs massor the CP-odd Higgs mass. The six �’s have the same information as three CP-evenHiggs masses and their mixing angles (mh, mH , mH0 , ✓1, ✓2, ✓3). We can use mZ , mZ0 ,and ↵(= e2/4⇡) instead of the gauge couplings. In addition, we can exchange (✓1, ✓2,✓3) with (F , Z , gWW 0H0). Since the values of four parameters, v, mZ , ↵, and mh arealready known, the remaining nine parameters are free parameters of this model. In ouranalyses, we take mh = 125 GeV.

We find F is severely constrained close to 1 in mA � mh regime. When the heavyHiggs masses are universal, mA = mH0 = mH , the expression of a quartic coupling �3

by our parameter choice (Eq. (34)) becomes very simple,

�3(µ = mZ0) =2F

2

m2h

v2+

1� 2F

2

m2A

v2. (35)

Theoretical conditions (see subsection 3.2 for more detail) demand 0 < �3 < 4⇡, namely

F >

pm2

A � 8⇡v2pm2

A �m2h

' 1� 8⇡v2 �m2h

2m2A

= 1� 0.2

✓2TeV

mA

◆2

, (36)

and

F <mAp

m2A �m2

h

' 1 +m2

h

2m2A

= 1 + 0.002

✓2TeV

mA

◆2

. (37)

Here we assumed mA � mh to obtain the last expressions.Similarly, we find that the coupling ratio Z is also severely constrained close to its

maximized value in mA � mh regime. Typically, the allowed regime is Z = 1�O(1)%.The detailed description is given in Appendix A.

In the following discussion, we take F ' 1, mA = mH = mH0 = O(1) TeV,gWW 0H0 = 0, and we always choose Z to be its maximal value. For the most part ofour numerical analysis, Z is set to 0.95 - 1.00.

3 Phenomenology of Spin-1 Resonances

In this section, we discuss the properties of the W 0 and Z 0 such as production cross sec-tion and decay branching ratios, and also discuss both the theoretical and experimentalconstraints. In the following, we show some formulae with approximation, which helpto understand the parameter dependence. However, we use the exact formulae in ournumerical calculations.

8

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Figure 3. The total widths and the branching ratios of the extra vector bosons, W 0 and Z 0. Wetake v3 = 200GeV, r = 0.13, F = 1.00, and mA = mH0 = mH = 2 TeV. Here, 2jets meansBr(W 0 ! ud)+Br(W 0 ! sc) or Br(Z 0 ! uu)+Br(Z 0 ! dd)+Br(Z 0 ! ss)+Br(Z 0 ! cc),`⌫ means Br(W 0 ! e⌫e) ( =Br(W 0 ! µ⌫µ) =Br(W 0 ! ⌧⌫⌧ )), `` means Br(Z 0 ! ee) (=Br(Z 0 ! µµ) =Br(Z 0 ! ⌧⌧)), ⌫⌫ means Br(Z 0 ! ⌫e⌫e)+Br(Z 0 ! ⌫µ⌫µ)+Br(Z 0 ! ⌫⌧⌫⌧ ),and W±H⌥ means Br(W 0 ! W+H�) =Br(W 0 ! W�H+).

11

1000 1500 2000 2500 3000 3500 40000.001

0.01

0.1

1

mW ' @GeVDG totHW'Lêm W

'1000 1500 2000 2500 3000 3500 4000

0.001

0.01

0.1

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mZ' @GeVD

G totHZ'Lê

mZ'

WZWh

2 jets

tb

lȞhH+

ZH+ , WA, WH

1000 1500 2000 2500 3000 3500 40000.001

0.01

0.1

1

mW ' [GeV]

Br(W'ĺ2X

)

ZhWW2 jets

W±H

±

, ZH

hA

ll

tt bbȞȞ

1000 1500 2000 2500 3000 3500 40000.001

0.01

0.1

1

mZ' [GeV]Br

(Z'ĺ2X

)

Figure 3. The total widths and the branching ratios of the extra vector bosons, W 0 and Z 0. Wetake v3 = 200GeV, r = 0.13, F = 1.00, and mA = mH0 = mH = 2 TeV. Here, 2jets meansBr(W 0 ! ud)+Br(W 0 ! sc) or Br(Z 0 ! uu)+Br(Z 0 ! dd)+Br(Z 0 ! ss)+Br(Z 0 ! cc),`⌫ means Br(W 0 ! e⌫e) ( =Br(W 0 ! µ⌫µ) =Br(W 0 ! ⌧⌫⌧ )), `` means Br(Z 0 ! ee) (=Br(Z 0 ! µµ) =Br(Z 0 ! ⌧⌧)), ⌫⌫ means Br(Z 0 ! ⌫e⌫e)+Br(Z 0 ! ⌫µ⌫µ)+Br(Z 0 ! ⌫⌧⌫⌧ ),and W±H⌥ means Br(W 0 ! W+H�) =Br(W 0 ! W�H+).

11

e C!���C!Q���C���� -;/�e M?:J>�?I�D7HHEM�� �� ;/�<EH�C0Q��� -;/�

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results

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e \����<8�?I�;N9BK:;�8O�/Q�f�/>�!

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0.51

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0.05 0.10 0.15 0.20 0.25

160

180

200

220

240

r

v 3@Ge

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sHpp ÆW'ÆWZL+sHpp Æ Z'ÆWWL@fbD

0.5

1

3

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0.05 0.10 0.15 0.20 0.25

160

180

200

220

240

r

v 3@Ge

VD

sHpp ÆW'ÆWZL+sHpp Æ Z'ÆWWL@fbD

Figure 8. The cross sections of W 0 and Z 0 with two gauge bosons in their final states. Wetake mZ0 = 1.9 TeV (left panel), 2.0 TeV (middle panel), and 2.1 TeV (right panel). The colorfilled regions are excluded or constrained. The blue regions are excluded by the experimentalbounds. The regions of g1(µ = mZ0) > 4⇡ are represented by yellow. The cyan regionsare excluded by the bounded below condition. The green regions are constrained from theperturbativity and stability conditions where their cut o↵ scale is 100 (10) TeV in the lightergreen (darker green) region. Below the thick orange lines, the cross section �(pp ! V 0 ! V V )is enough to explain the diboson excess at ATLAS. After taking account of the K-factor, theboundaries of the regions change to the dashed orange lines, and the regions below the dashedblue lines are excluded by the LHC bounds.

Below the thick orange line the cross section �(pp ! V 0 ! V V ) is enough toexplain the total number of the diboson excess events at ATLAS. Here we apply theevent selection e�ciencies for extended gauge model (cf. 10 - 16 % at mJJ = 2 TeV) [1]. We find that these regions are still allowed from the experimental and theoreticalconstraints. Note that a part of these regions are constrained from the stability conditionat ⇤̄ = 100 TeV filled with light green. However, once we take into account the higherorder correction, these constraint would be weaker as we discussed in Sec. 3.2.1. In theparameter regions shown in the figure, �(pp ! W 0 ! WZ)/�(pp ! Z 0 ! WW ) ' 2.This is because the custodial symmetry is enhanced for small r regime.

In the figure we show the leading order (LO) production cross sections. Next-to-leading order and next-to-leading logarithmic (NLO+NLL) corrections to the productionof W 0 and Z 0 are evaluated in Ref [45, 46], and K-factor (�/�LO) is about 1.3. Thismeans that once we consider the QCD correction, the production cross sections in thefigures should be scaled by about 30 %, and the LHC bounds become severer, whilethe theoretical constraints do not change. After taking account of the K-factor, theLHC diboson excess can be explained for the regions below dashed orange lines, and theregions below the dashed blue lines are excluded by the LHC bounds.

Figure 9 shows �(pp ! W 0 ! Wh). The parameter choices and the color notations

20

JH?L?7B?JO�8EKD:

8EKD:;:�8;BEM

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������

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prospect for LHC run-2

95% exclusion limit at LHC run-2

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1600 1800 2000 2200 2400 2600 2800 3000 3200 3400

even

ts/10

0GeV

5

10

15

20

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[GeV]jjm [GeV]jjm1600 1800 2000 2200 2400 2600 2800 3000 3200 3400

fract

ion

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

distribution at 13TeVjjreconstructed m

mW ’ = 2 TeV2.4 TeV2.8 TeV3.2 TeV

Figure 14. mjj distributions for background (left panel) and signal (right panel) atp

s = 13TeV. The background distribution is for 10 fb�1 and signal distributions are normalized to be1 for various input W 0 mass.

1800 2000 2200 2400 2600 2800 3000 32000

10

20

30

40

mW ' [GeV]

ı(ppĺ

W'ĺ

WZ

)[fb

]

Expected limit at 13 TeV

5 fb-1

10 fb-1

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Figure 15. Expected limit on �(pp ! W 0 ! WZ) atp

s = 13 TeV. We take �tot(W 0) =25 GeV.

26

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Summary

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Backup slides

Monte Carlo part

What we did in MC part

A �65:,��(836�e *���:?@;J�7I�� ��������6��T��<8������&����-;/��F-���� ;/��IGHJ4I5����-;/��8O�)2-!"�� ���

e I?=D7B��FF�f�0Q�f�03��C0Q�����-;/�JE�� �-;/��M?:J>�� � ;/�e -KD;����<EH�<H7=C;DJ7J?ED�7D:�>7:HED?P7J?ED�e :;J;9JEH�I?CKB7JEH��;%)!�,��?I�CE:?U;:�KI?D=��7IJ#;J��e 9KJI��I7C;�7I�J>;�9KJI�KI;:�8O��-%�,�

A �;8����8,9;3:�e M;�9>;9A;:�I?=D7B�:?IJH?8KJ?EDI�7=H;;�M?J>�J>;��-%�,�H;IKBJ����-;/��e M;�<EKD:���E<�879A�=HEKD:�?I�JM?9;�E<�J>;��-%�,�H;IKBJ���-;/��e M;�I97B;�EKH�� �� �<EH���-;/�7D7BOI?I

More on our model

constraint on (r, v3)-plane

0.1 0.5 1.0 5.0 10.0 50.050

100

150

200

r

v 3[G

eV]

0.05

mZ’ = mheavy Higgs = 2 TeV, F = 1.00

(a)

0.1 0.5 1.0 5.0 10.0 50.050

100

150

200

r

v 3[G

eV]

0.05

mZ’ = mheavy Higgs = 2 TeV, F = 0.99

(b)

0.1 0.5 1.0 5.0 10.0 50.050

100

150

200

r

v 3[G

eV]

0.05

mZ’ = 2 TeV, mheavy Higgs = 1 TeV, F = 1.00

(c)

Figure 5. The theoretical and experimental constraints in r - v3 plane. We take three di↵erentparameter choice for (mZ0 , mA, F ). The white regions are allowed from all constraints. Thecolored regions are constrained. Gray: the perturbativity conditions for the Higgs quarticcouplings. Yellow: the perturbativity conditions for g1. Cyan: the bounded below condition.Green: the global minimum vacuum condition. Magenta: the stability condition. Blue:the LHC bounds. Red: constraints from the electroweak precision measurements. Black: nophysical solutions. The detail explanation is in the text.

17

g1 > 4π

8EKD:;:�8;BEM8EKD:;:�8;BEM

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0.1

0.5

0.5

1

1

5

10

0.1 0.5 1.0 5.0 10.0 50.050

100

150

200

r

v 3[G

eV]

0.05

mZ’ = mheavy Higgs = 2 TeV, F = 1.00

Figure 7. Contours of the cross section �(pp ! W 0)Br(W 0 ! WZ) + �(pp ! Z 0)Br(Z 0 !WW ) at

ps = 8TeV in a unit of [fb]. We take mZ0 = mA = mH0 = mH = 2 TeV,

F = 1.00. The blue regions are excluded by the current experimental bounds, and theregions of g1(µ = mZ0) > 4⇡ are filled with yellow.

Since the separation of WW , WZ, and ZZ channels are not good and there are sig-nificant overlap among them, we investigate the total cross section �(pp ! W 0)Br(W 0 !WZ)+�(pp ! Z 0)Br(Z 0 ! WW ) at

ps = 8TeV in Fig. 7. In this figure, mZ0 = mA =

mH0 = mH = 2 TeV, F = 1.00 are taken. The blue regions are excluded by the currentexperimental bounds discussed in Sec. 3.2, and the regions of g1(µ = mZ0) > 4⇡ is filledwith yellow. Here we do not show the constraints from the Higgs sector. The crosssection of about 6 fb can be extracted from the number of excess events and the signalselection e�ciency quoted in Ref. [1]. This cross section can be achieved in the regionswhere r is much smaller than 1. This is because the production cross section is enhancedby r�2. Hence, we focus on r ⌧ 1 regions in the remains of the paper.

Note that the strongest LHC constraint to the parameter where the ATLAS dibosonexcess can be explained comes from full hadronic channel of �(pp ! V 0 ! V h) [40],e.g. �(pp ! V 0 ! V h) . 7 fb for mZ0 = 2 TeV. This implies �(pp ! V 0 ! V V ) < 7 fbas we discussed in Sec. 3.1. If the coupling ratio Z deviates from 1, this LHC boundbecomes weaker, because this relation can be modified. However, in this model Z isseverely constrained close to 1 in mA � mh regime (see Appendix A).

We show �(pp ! V 0 ! V V ) in Fig. 8, for mZ0 = 1.9, 2.0, and 2.1 TeV. We takeF = 1.00, and all heavy scalar mass to be the same as mZ0 , mZ0 = mA = mH0 = mH .The color filled regions are excluded or constrained. The color notation is given in thecaption. We find that the cross section is sensitive to the mass. For example, by a changeof mZ0 from 1.9 to 2 TeV (5 % mass di↵erence), the cross section is decreased by about40 %. This is because the PDF rapidly changes in the heavier mass regions (see Fig. 2).

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