IPMU13-0140UCB-PTH-13/06

A Natural Higgs Mass in Supersymmetry from Non-Decoupling Effects

Xiaochuan Lu,1, ∗ Hitoshi Murayama,1, 2, 3, † Joshua T. Ruderman,1, 2, ‡ and Kohsaku Tobioka3, 4, §

1Department of Physics, University of California, Berkeley, California 94720, USA2Theoretical Physics Group, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA

3Kavli Institute for the Physics and Mathematics of the Universe (WPI),Todai Institutes for Advanced Study, University of Tokyo, Kashiwa 277-8583, Japan

4Department of Physics, University of Tokyo, Hongo, Tokyo 113-0033, Japan

The Higgs mass implies fine-tuning for minimal theories of weak scale supersymmetry (SUSY).Non-decoupling effects can boost the Higgs mass when new states interact with the Higgs, but newsources of SUSY breaking that accompany such extensions threaten naturalness. We show that asinglet with a Dirac mass can increase the Higgs mass while maintaining naturalness in the presenceof large SUSY breaking in the singlet sector. We explore the modified Higgs phenomenology of thisscenario, which we call the “Dirac NMSSM.”

Introduction: The discovery of a new resonance at125 GeV [1], that appears to be the long-sought Higgsboson, marks a great triumph of experimental and the-oretical physics. On the other hand, the presence ofthis light scalar forces us to face the naturalness prob-lem of its mass. Arguably, the best known mechanismto ease the naturalness problem is weak-scale supersym-metry (SUSY), but the lack of experimental signaturesis pushing SUSY into a tight corner. In addition, theobserved mass of the Higgs boson is higher than whatwas expected in the Minimal Supersymmetric StandardModel (MSSM), requiring fine-tuning of parameters atthe 1% level or worse [2].

If SUSY is realized in nature, one possibility is to giveup on naturalness [3]. Alternatively, theories that retainnaturalness must address two problems, (I) the missingsuperpartners and (II) the Higgs mass. The collider lim-its on superpartners are highly model-dependent and canbe relaxed when superpartners unnecessary for natural-ness are taken to be heavy [4], when less missing energyis produced due to a compressed mass spectrum [5] ordue to decays to new states [6], and when R-parity is vi-olated [7]. Even if superpartners have evaded detectionfor one of these reasons, we must address the surprisinglyheavy Higgs mass.

There have been many attempts to extend the MSSMto accommodate the Higgs mass. In such extensions,new states interact with the Higgs, raising its mass byincreasing the strength of the quartic interaction of thescalar potential. If the new states are integrated outsupersymmetrically, their effects decouple and the Higgsmass is not increased. On the other hand, SUSY breakingcan lead to non-decoupling effects that increase the Higgsmass. One possibility is a non-decoupling F -term, asin the NMSSM (MSSM plus a singlet) [8, 9] or λSUSY(allowing for a Landau pole) [10]. A second possibilityis a non-decoupling D-term that results if the Higgs ischarged under a new gauge group [11]. In general, theseextensions require new states at the few hundred GeVscale, so that the new sources of SUSY breaking do not

spoil naturalness.For example, consider the NMSSM, where a singlet

superfield, S, interacts with the MSSM Higgses, Hu,d,through the superpotential,

W ⊃ λSHuHd +M

2S2 + µHuHd. (1)

The Higgs mass is increased by,

∆m2h = λ2v2 sin2 2β

(m2S

M2 +m2S

), (2)

where m2S is the SUSY breaking soft mass m2

S |S|2,tanβ = vu/vd is the ratio of the VEVs of the up anddown-type Higgses, and v =

√v2u + v2

d = 174 GeV. No-tice that this term decouples in the supersymmetric limit,M � mS , which means mS should not be too small.On the other hand, mS feeds into the Higgs soft masses,m2Hu,d

at one-loop, requiring fine-tuning if mS � mh.Therefore, there is tension between raising the Higgsmass, which requires large mS , and naturalness, whichdemands small mS .

In this letter, we point out that, contrary to the aboveexample, a lack of light scalars can help raise the Higgsmass without a cost to naturalness, if the singlet has aDirac mass. We begin by introducing the model anddiscussing the Higgs mass and naturalness properties.

M

mh

mass

mS

MSSM

S

S, S , S

FIG. 1. A typical spectrum of the Dirac NMSSM, whichallows for large mS without spoiling naturalness.

2

Then, we discuss the phenomenology of the Higgs sec-tor, which can be discovered or constrained with futurecollider data. We finish with our conclusions.

The Model: To illustrate this possibility, we considera modification of Eq. 1 where S receives a Dirac masswith another singlet, S,

W = λSHuHd +MSS + µHuHd. (3)

We call this model the Dirac NMSSM. The absenceof various dangerous operators (such as large tadpolesfor the singlets) follows from a U(1)PQ × U(1)S Peccei-Quinn-like symmetry,

Hu Hd S S µ M

U(1)PQ 1 1 −2 −2 −2 4

U(1)S 0 0 0 1 0 −1

Here, U(1)S has the effect of differentiating S and S andforbidding the operator SHuHd. Because µ and M ex-plicitly break the U(1)PQ × U(1)S symmetry, we regardthem to be spurions originating from chiral superfields(“flavons” [12]) so that the superpotential should not de-pend on their complex conjugates to avoid certain un-wanted terms (“SUSY zeros” [13]). By classifying allpossible operators induced by these spurions, we see thata tadpole for S is suppressed until the weak scale,

W ⊃ cSµMS , (4)

where cS is a O(1) coefficient. Other terms involving onlysinglets are forbidden by the symmetries or suppressed bythe cutoff.

The following soft supersymmetry breaking terms areallowed by the symmetries,

∆Vsoft = m2Hu|Hu|2 +m2

Hd|Hd|2 +m2

S |S|2 +m2S |S|

2

+λAλSHuHd +MBSSS + µBHuHd + c.c.

+tSS + tSS + c.c. (5)

The last tadpole arises from a non-holomorphic termµ†S. Both soft tadpoles naturally have weak-scale sizesdue the symmetry and spurion structure.

We would like to understand whether the new quarticterm, |λHuHd|2, can naturally raise the Higgs mass. In-tegrating out S and S we find the following potential forthe doublet-like Higgses,

Veff = |λHuHd|2(

1− M2

M2 +m2S

)(6)

− λ2

M2 +m2S

∣∣AλHuHd + µ∗(|Hu|2 + |Hu|2)∣∣2 .

where we keep leading (M2 +m2S,S

)−1 terms and neglect

the tadpole terms for simplicity. The new contributionto the Higgs quartic does not decouple when m2

Sis large.

The SM-like Higgs mass becomes,

m2h = m2

h,MSSM(mt) + λ2v2 sin2 2β

(m2S

M2 +m2S

)− λ2v2

M2 +m2S

|Aλ sin 2β − 2µ∗|2 , (7)

in the limit where the VEVs and mass-eigenstates arealigned.

The Higgs sector is natural when there are no large ra-diative corrections to m2

Hu,d. The renormalization group

(RG) of the up-type Higgs contains the terms,

µd

dµm2Hu

=1

8π23y2t

(m2Q3

+m2tR

+m2S

)+ . . . (8)

While heavy stops or mS lead to fine-tuning, we findthat mS does not appear. In fact, the RGs for m2

Hu,d

are independent of mS to all orders in mass-independentschemes, because S couples to the MSSM+S sector onlythrough the dimensionful coupling M . There is logarith-mic sensitivity to mS from the one-loop finite thresholdcorrection,

δm2H ≡ δm2

Hu,d=

(λM)2

(4π)2log

M2 +m2S

M2. (9)

which still allows for very heavy mS without fine-tuning.One may wonder if there are dangerous finite threshold

corrections to m2Hu

at higher order, after integrating outS. In fact, there is no quadratic sensitivity to m2

Sto all

orders. This follows because any dependence on m2S

mustbe proportional to |M |2 (since S decouples when M → 0and by conservation of U(1)S), but |M |2m2

Shas too high

mass dimension. The mass dimension cannot be reducedfrom other mass parameters appearing in the denomi-nator because threshold corrections are always analyticfunctions of IR mass parameters [14].

It may seem contradictory that naturalness is main-tained in the limit of very heavy mS , since removing theS scalar from the spectrum constitutes a hard breakingof SUSY. The reason is that the effective theory, withthe S fermion but no scalar present at low energies isactually equivalent to a theory with only softly brokensupersymmetry, where the MSSM is augmented by theKahler operators,

Keff = S†S

− θ2θ2(M DαS DαS + c.c.+M2|S + cSµ|2

)(10)

and where the scalar and F -term of S are reintroducedat low-energy but completely decoupled from the otherstates. We call this mechanism semi-soft supersymmetrybreaking. It is crucial that S couples to the other fieldsonly through dimensionful couplings. Note that Diracgauginos are a different example where adding new fieldscan lead to improved naturalness properties [15].

The most natural region of parameter space, sum-marized in Fig. 1, has mS and M at the hundreds of

3

20

30

50

102 103 104 105102

103

104

105

M @GeVD

mS

@GeV

D

Dirac NMSSML=30

102

D=103Λ=0.74, tanΒ=2

Μeff=150 GeV

mS=800 GeV

20

50

50

102 103 104 105102

103

104

105

M @GeVD

mS

@GeV

D

NMSSML=30

102

103

104

D=105

Λ=0.74, tanΒ=2

Μeff=150 GeV

FIG. 2. The tuning ∆, defined in Eq. 11, for the Dirac NMSSM is shown on the left as a function of M and mS . Forcomparison, the tuning of the NMSSM is shown on the right , as a function of M and mS . The red region has high fine-tuning,∆ > 100, and the purple region requires mt > 2 TeV, signaling severe fine-tuning & O(103).

GeV scale, to avoid large corrections to mHu, and large

mS & 10 TeV, to maximize the second term of Eq. (7).The tree-level contribution to the Higgs mass can be largeenough such that mt takes a natural value at the hun-dreds of GeV scale.

We have performed a quantitative study of the fine-tuning in the Dirac NMSSM, shown to the left of Fig. 2as a function of (M,mS). We computed the radiativecorrections from the top sector to the Higgs mass atRG-improved Leading-Log order, analogous to [16]. Wehave confirmed that our results match the FeynHiggssoftware [17], for the MSSM, within ∆mh ' 1 GeV inthe parameter regime of interest. We fix At = 0 forsimplicity, and other parameters are fixed according tothe table, shown below. Here, we adopt a parameterµeff ≡ µ+λ 〈S〉 for convenience. We have chosen λ to sat-urate the upper-limit such that it does not reach a Lan-dau pole below the unification scale [18]. For each valueof (M,mS), the stop soft masses, mt = mtR

= mQ3, are

chosen to maintain the lightest scalar mass at 125 GeV.The degree of fine-tuning is estimated by

∆ =2

m2h

max

(m2Hu,m2

Hd,dm2

Hu

d lnµL,dm2

Hd

d lnµL, δm2

H , beff

),

(11)where beff = µB + λ(Aλ 〈S〉 + M

⟨S⟩) and we take

L ≡ log(Λ/mt) = 30, corresponding to high-scale SUSYbreaking.

For comparison, the right of Fig. 2 shows the tuningin the NMSSM, which corresponds to the Dirac NMSSMreplacing S → S (which removes the U(1)S symmetry).The superpotential of the NMSSM corresponds to Eq.(1)plus the tadpole cSµMS. We treat mS as a free param-eter instead of mS and use the same fine-tuning measure

of Eq.(11), except the threshold correction δm2H is absent

and beff = µB + λ 〈S〉 (Aλ +M).We see that the least-tuned region of the Dirac

NMSSM corresponds to M ∼ 2 TeV and mS & 10 TeV,where the tree-level correction to the Higgs mass is maxi-mized. The fine-tuning is dominated by δm2

H in the largeM region, and by the contribution of mt to mHu in therest of the plane. On the other-hand, the NMSSM be-comes highly tuned when mS is large (since it radiativelycorrects mHu,d

), and then mS . 1 TeV is favored. Notethat region of low-tuning in the NMSSM extends to thesupersymmetric limit, mS → 0. In this region the Higgsmass is increased by a new contribution to the quar-tic coupling proportional to λ2(Mµ sin 2β−µ2)/M2 (seeRef.[9] for more details).Higgs Phenomenology: We now discuss the ex-

perimental signatures of the Dirac NMSSM. The phe-nomenology of the NMSSM is well-studied [2, 19]. Thenatural region of the Dirac NMSSM differs from theNMSSM in that the singlet states are too heavy to be pro-duced at the LHC. The low-energy Higgs phenomenol-ogy is that of a two Higgs doublet model, and we fo-cus here on the nature of the SM-like Higgs, h, and theheavier doublet-like Higgs, H [20]. The properties of thetwo doublets differ from the MSSM due to the presenceof the non-decoupling quartic coupling |λHuHd|2, whichraises the Higgs mass by the semi-soft SUSY breaking,described above.

benchmark parameters

λ = 0.74 tanβ = 2 µeff = 150 GeV

beff =(190 GeV)2 Aλ = 0 Bs = 100 GeV

M = 1 TeV mS = 10 TeV mS = 800 GeV

4

200 300 400 500 600 7000.8

0.9

1.0

1.1

1.2

1.3

mH @GeVD

Σ�Σ

SM,B

R�B

RSM

SM-like Higgs

Σ�ΣSMggFVBF�VHttH

BR�BRSMΓΓ

WW�ZZbb�ΤΤ

200 300 400 500 600 70010-3

10-2

10-1

1

mH @GeVD

BR

Heavy Doublet Higgs

WW

ZZ

ΤΤ

bb

gg

tthh

C� +

C� - ΧΧ

M1=1 TeVM2=2 TeV

Μeff=150 GeV

FIG. 3. The branching ratios and production cross sections of the SM-like Higgs are shown, normalized to the SM values [21, 22],on the left as a function of the heavy doublet-like Higgs mass, mH . On the right, we show several branching ratios of the heavydoublet-like Higgs as a function of its mass. Note that the location of the chargino/neutralino thresholds depend on the -inospectrum. Here we take heavy gauginos and µeff = 150 GeV.

200 250 300 350 4000.0

0.5

1.0

1.5

2.0

0

1

2

3

4

5

mH @GeVD

Σ×B

R�Σ

×BR

Lim

it

Current LimitsD

Χ2

ATLAS ZZ

CMS ZZ

CMS WW

ATLAS WW

L=5fb-1H7TeVL +20fb-1H8TeVLDΧ2

2Σ

200 300 400 500 600 7000

5

10

15

20

25

mH @GeVD

DΧ2

Future Reach from Coupling Measurements

ILC500+LHCILC250+LHC

LHC, 3000fb-1at 14TeVLHC, 300fb-1at 14TeVATLAS Expectation

5fb-1H7TeVL +20fb-1H8TeVL

5Σ

3Σ

2Σ

H®

ZZ

*®4l

Higgs

CouplingsHC

MS+

AT

LA

SL

FIG. 4. The left plot shows current constraints on our model. The right axis corresponds to ∆χ2 for the SM-like Higgscouplings with the 7 and 8 TeV datasets [23–26] neglecting correlations between the measurements of different couplings. Theleft axis shows σ/σlim for direct searches, H → ZZ,WW [24, 26]. The right plot shows the expected ∆χ2 from combinedmeasurements of the Higgs-like couplings at the high-luminosity LHC at

√s = 14 TeV [27] and the ILC at

√s = 250, 500 GeV.

The optimistic [28] (conservative [29]) ILC reach curves are solid (dashed) and neglect (include) theoretical uncertainties inthe Higgs branching ratios. The ILC analyses include the expected LHC measurements. For comparison we show the presentlimits and also the expected limit of the current ATLAS measurements (solid, black).

We consider the tree-level scalar mass matrix, and wefind that the couplings of the SM-like Higgs to leptonsand down-type quarks are lowered, while couplings tothe up-type quarks are slightly increased compared tothose in the SM, which results in the deviations to thecross sections and decay patterns shown to the left ofFig. 3. These effects decouple in limit mH � mh, whichcorresponds to large beff . We also show, to the rightof Fig. 3, the decay branching ratios of H. Due to thenon-decoupling term, di-Higgs decay, H → 2h, becomesthe dominant decay once its threshold is opened, mH &250 GeV.

There are now two relevant constraints on the Higgssector of the Dirac NMSSM. The first comes from mea-surements of the couplings of the SM-like Higgs fromATLAS [23, 24] and CMS [25, 26]. The second comesfrom direct searches for the heavier state decaying to di-bosons, H → ZZ,WW [24, 26]. The former excludesmH . 220 GeV at 95%, while the latter extends thislimit to mH ∼ 250 GeV (except for a small gap nearmH ≈ 235 GeV) as can be seen to the left of Fig. 4. Wealso estimate the future reach to probe mH with futureHiggs coupling measurements [27–29], shown to the rightof Fig. 4. The 2σ exclusion reach is mH ' 280 GeV

5

at the high-luminosity LHC, and mH ' 400(580) GeVwith(without) theoretical uncertainty at ILC500. Theincreased sensitivity at the ILC is dominated by the im-proved measurements projected for the bb and τ+τ− cou-plings [28].

Discussion: The LHC has discovered a new parti-cle, consistent with the Higgs boson, with a mass near125 GeV. Weak-scale SUSY must be reevaluated in lightof this discovery. Naturalness demands new dynamicsbeyond the minimal theory, such as a non-decoupling F -term, but this implies new sources of SUSY breaking thatthemselves threaten naturalness. In this paper, we haveidentified a new model where the Higgs couples to a sin-glet field with a Dirac mass. The non-decoupling F -termis naturally realized through semi-soft SUSY breaking,because large mS helps raise the Higgs mass but doesnot threaten naturalness. The first collider signaturesof the Dirac NMSSM are expected to be those of theMSSM fields, with the singlet sector naturally heavierthan 1 TeV.

The key feature of semi-soft SUSY breaking in theDirac NMSSM is that S couples to the MSSM onlythrough the dimensionful Dirac mass, M . We note thatinteractions between S and other new states are not con-strained by naturalness, even if these states experienceSUSY breaking. Therefore, the Dirac NMSSM representsa new type of portal, whereby our sector can interact withnew sectors, with large SUSY breaking, without spoilingnaturalness in our sector.

Acknowledgments: We thank Lawrence Hall,Matthew McCullough, Satyanarayan Mukhopadhyay,Tilman Plehn, Satoshi Shirai, and Neal Weiner for help-ful discussions. We especially thank Yasunori Nomurafor discussions and for pointing out that the Dirac masscan be thought of as a new type of portal. The work ofHM was supported in part by the U.S. DOE under Con-tract No. DEAC03-76SF00098, by the NSF under GrantNo. PHY-1002399, by the JSPS Grant (C) No. 23540289,by the FIRST program Subaru Measurements of Imagesand Redshifts (SuMIRe), CSTP, and by WPI, MEXT,Japan. JTR is supported by a fellowship from the MillerInstitute for Basic Research in Science. The work of KTis supported in part by the Grant-in-Aid for JSPS Fel-lows.

∗ luxiaochuan123456@gmail.com† hitoshi@berkeley.edu, hitoshi.murayama@ipmu.jp‡ ruderman@berkeley.edu§ kohsaku.tobioka@ipmu.jp

[1] G. Aad et al. [ATLAS Collaboration], Phys. Lett. B 716,1 (2012), 1207.7214; S. Chatrchyan et al. (CMS Collab-oration), Phys. Lett. B 716, 30 (2012), 1207.7235.

[2] L. J. Hall, D. Pinner and J. T. Ruderman, JHEP 1204,131 (2012), 1112.2703.

[3] J. D. Wells, hep-ph/0306127; N. Arkani-Hamedand S. Dimopoulos, JHEP 0506, 073 (2005) [hep-th/0405159].

[4] S. Dimopoulos and G. F. Giudice, Phys. Lett. B 357,573 (1995) [hep-ph/9507282]; A. G. Cohen, D. B. Ka-plan and A. E. Nelson, Phys. Lett. B 388, 588 (1996)[hep-ph/9607394]; M. Papucci, J. T. Ruderman andA. Weiler, JHEP 1209, 035 (2012) [arXiv:1110.6926[hep-ph]]; C. Brust, A. Katz, S. Lawrence and R. Sun-drum, JHEP 1203, 103 (2012) [arXiv:1110.6670 [hep-ph]].

[5] T. J. LeCompte and S. P. Martin, Phys. Rev. D 85,035023 (2012) [arXiv:1111.6897 [hep-ph]]; H. Murayama,Y. Nomura, S. Shirai and K. Tobioka, Phys. Rev. D 86,115014 (2012) [arXiv:1206.4993 [hep-ph]].

[6] J. Fan, M. Reece and J. T. Ruderman, JHEP1111, 012 (2011) [arXiv:1105.5135 [hep-ph]]; J. Fan,M. Reece and J. T. Ruderman, JHEP 1207, 196(2012) [arXiv:1201.4875 [hep-ph]]; M. Baryakhtar,N. Craig and K. Van Tilburg, JHEP 1207, 164 (2012)[arXiv:1206.0751 [hep-ph]].

[7] For a review, R. Barbier, C. Berat, M. Besan-con, M. Chemtob, A. Deandrea, E. Dudas, P. Fayetand S. Lavignac et al., Phys. Rept. 420, 1 (2005)[hep-ph/0406039]. For recent studies, see for example,C. Csaki, Y. Grossman and B. Heidenreich, Phys. Rev. D85, 095009 (2012) [arXiv:1111.1239 [hep-ph]]. P. W. Gra-ham, D. E. Kaplan, S. Rajendran and P. Saraswat, JHEP1207, 149 (2012) [arXiv:1204.6038 [hep-ph]]. J. T. Ru-derman, T. R. Slatyer and N. Weiner, arXiv:1207.5787[hep-ph].

[8] J. R. Espinosa and M. Quiros, Phys. Lett. B 279, 92(1992); U. Ellwanger, C. Hugonie and A. M. Teixeira,Phys. Rept. 496, 1 (2010) [arXiv:0910.1785 [hep-ph]];

[9] Y. Nomura, D. Poland and B. Tweedie, Phys. Lett. B633, 573 (2006) [hep-ph/0509244].

[10] R. Harnik, G. D. Kribs, D. T. Larson and H. Murayama,Phys. Rev. D 70, 015002 (2004) [hep-ph/0311349];R. Barbieri, L. J. Hall, Y. Nomura and V. S. Rychkov,Phys. Rev. D 75, 035007 (2007) [hep-ph/0607332];M. Dine, N. Seiberg and S. Thomas, Phys. Rev. D 76,095004 (2007) [arXiv:0707.0005 [hep-ph]].

[11] P. Batra, A. Delgado, D. E. Kaplan and T. M. P. Tait,JHEP 0402, 043 (2004) [hep-ph/0309149]; A. Mal-oney, A. Pierce and J. G. Wacker, JHEP 0606, 034(2006) [hep-ph/0409127]; C. Cheung and H. L. Roberts,arXiv:1207.0234 [hep-ph].

[12] N. Arkani-Hamed, C. D. Carone, L. J. Hall and H. Mu-rayama, Phys. Rev. D 54, 7032 (1996) [hep-ph/9607298].

[13] M. Leurer, Y. Nir and N. Seiberg, Nucl. Phys. B 420,468 (1994) [hep-ph/9310320].

[14] H. Georgi, Ann. Rev. Nucl. Part. Sci. 43, 209 (1993).[15] P. J. Fox, A. E. Nelson and N. Weiner, JHEP 0208, 035

(2002) [hep-ph/0206096].[16] H. E. Haber and R. Hempfling, Phys. Rev. D 48, 4280

(1993) [hep-ph/9307201]. M. S. Carena, J. R. Espinosa,M. Quiros and C. E. M. Wagner, Phys. Lett. B 355,209 (1995) [hep-ph/9504316], H. E. Haber, R. Hempflingand A. H. Hoang, Z. Phys. C 75, 539 (1997) [hep-ph/9609331]. M. S. Carena, J. R. Ellis, A. Pilaftsis andC. E. M. Wagner, Nucl. Phys. B 586, 92 (2000) [hep-ph/0003180].

[17] M. Frank, T. Hahn, S. Heinemeyer, W. Hollik, H. Rze-hak and G. Weiglein, JHEP 0702, 047 (2007) [hep-

6

ph/0611326].[18] R. Barbieri, L. J. Hall, A. Y. Papaioannou, D. Pap-

padopulo and V. S. Rychkov, JHEP 0803, 005 (2008)[arXiv:0712.2903 [hep-ph]].

[19] For recent studies, see for example, U. Ellwanger,JHEP 1203, 044 (2012) [arXiv:1112.3548 [hep-ph]];K. Agashe, Y. Cui and R. Franceschini, JHEP 1302,031 (2013) [arXiv:1209.2115 [hep-ph]]; R. T. D’Agnolo,E. Kuflik and M. Zanetti, JHEP 1303, 043 (2013)[arXiv:1212.1165 [hep-ph]]; T. Gherghetta, B. von Har-ling, A. D. Medina and M. A. Schmidt, JHEP 1302, 032(2013) [JHEP 1302, 032 (2013)] [arXiv:1212.5243 [hep-ph]]; C. Cheung, S. D. McDermott and K. M. Zurek,JHEP 1304, 074 (2013) [arXiv:1302.0314 [hep-ph]];R. Barbieri, D. Buttazzo, K. Kannike, F. Sala andA. Tesi, arXiv:1304.3670 [hep-ph].

[20] For recent studies, see for example, N. Craig, J. A. Evans,R. Gray, C. Kilic, M. Park, S. Somalwar and S. Thomas,JHEP 1302, 033 (2013) [arXiv:1210.0559 [hep-ph]];N. Craig, J. Galloway and S. Thomas, arXiv:1305.2424[hep-ph].

[21] S. Dittmaier et al. [LHC Higgs Cross Section WorkingGroup Collaboration], arXiv:1101.0593 [hep-ph].

[22] S. Dittmaier, S. Dittmaier, C. Mariotti, G. Passarino,R. Tanaka, S. Alekhin, J. Alwall and E. A. Bagnaschi etal., arXiv:1201.3084 [hep-ph].

[23] [ATLAS Collaboration], ATLAS-CONF-2013-034,ATLAS-CONF-2013-012, ATLAS-CONF-2013-030,ATLAS-CONF-2012-160.

[24] [ATLAS Collaboration], ATLAS-CONF-2013-013,ATLAS-CONF-2013-067.

[25] [CMS Collaboration], CMS-PAS-HIG-13-001,CMS-PAS-HIG-13-004,CMS-PAS-HIG-12-044.

[26] [CMS Collaboration], CMS-PAS-HIG-13-002, CMS-PAS-HIG-13-003.

[27] ATLAS-collaboration, ATL-PHYS-PUB-2012-004.[28] M. E. Peskin, arXiv:1207.2516 [hep-ph].[29] M. Klute, R. Lafaye, T. Plehn, M. Rauch and D. Zer-

was, Europhys. Lett. 101, 51001 (2013) [arXiv:1301.1322[hep-ph]].