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Higgs-strahlung production of the lightest CP-even Higgs boson at ILC in natural NMSSM
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Higgs-strahlung production of the lightest CP-even Higgs boson at ILC in natural NMSSM Zhaoxia Heng, Wenlong Wang, Haijing Zhou∗ College of Physics and Materials Science, Henan Normal University, Xinxiang 453007, China
a r t i c l e
i n f o
Article history: Received 6 January 2017 Revised 16 April 2017 Accepted 17 April 2017 Available online xxx
a b s t r a c t Considering various experimental constraints, we scan over the parameter space of the NMSSM by requiring the fine tuning measures Z and h are less than 50. Then in the allowed parameter space we investigate the Higgs-strahlung production of the lightest CPeven Higgs boson h1 at ILC assuming the next-to-lightest CP-even Higgs boson acts as SMlike. we calculate the cross section of the process e+ e− → Zh1 at ILC with center-of-mass energy of 250 GeV, and also discuss the decay patterns of h1 . We find that the cross section of the process e+ e− → Zh1 can reach about 84 fb. Moreover, the cross section increases with the mass of h1 and strongly depends on the Higgs doublet-component of h1 . For most of the surviving samples, h1 mainly decays to bb¯ . However, for certain regions of the surviving samples, the branching ratio of h1 → γ γ can maximally reach 2%, which can be used to discriminate the NMSSM from MSSM. © 2017 The Physical Society of the Republic of China (Taiwan). Published by Elsevier B.V. All rights reserved.
1. Introduction The discovery of a Higgs boson in July 2012 by the ATLAS and CMS collaborations at the CERN Large Hadron Collider (LHC) [1] has marked a great success in the history of particle physics. The properties of this new boson is largely consistent with the predictions in the Standard Model (SM). And there aslo exist various new physics models that can accommodate this new Higgs boson. For example, the Minimal Supersymmetric Standard Model (MSSM) can accommodate a Higgs boson with mass near 125 GeV [2], but it requires higher order corrections mainly from the third generation squark sector, which will lead to some degrees of fine-tuning. Nevertheless, this fine-tuning problem can be alleviated in the next-to-minimal supersymmetric standard model (NMSSM) [3], which extends the MSSM with an additional Higgs singlet. In the NMSSM, due to the coupling between the Higgs doublets and singlet in the superpotential, the mass of the SM-like Higgs boson gets additional contribution at tree-level. Moreover, whenever the next-to-lightest CP-even Higgs boson acts as the SM-like Higgs boson, the mixing between the Higgs doublet and singlet fields can also push up the Higgs boson mass [4,5]. So it does not require large radiative corrections from the third generation squark loops to accommodate a Higgs boson near 125 GeV. Therefore, the NMSSM is more natural in predicting Higgs boson mass. And it can also predict rather low fine tunings in getting the Z boson and Higgs boson mass [6]. Based on the current LHC data, various Higgs couplings to SM fermions and vector bosons still have large uncertainties, so the precision measurements of the Higgs boson are rather challenging at the LHC. To precisely investigate the properties ∗
Corresponding author. E-mail address: [email protected] (H. Zhou).
http://dx.doi.org/10.1016/j.cjph.2017.04.007 0577-9073/© 2017 The Physical Society of the Republic of China (Taiwan). Published by Elsevier B.V. All rights reserved.
Please cite this article as: Z. Heng et al., Higgs-strahlung production of the lightest CP-even Higgs boson at ILC in natural NMSSM, Chinese Journal of Physics (2017), http://dx.doi.org/10.1016/j.cjph.2017.04.007
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of Higgs boson, some high energy e+ e− collider with clean environment, such as the International Linear Collider (ILC) [7], are proposed. At e+ e− collider for a center-of-mass energy of 250 GeV, the Higgs-strahlung process e+ e− → Zh is the main production channel for the Higgs boson, which has been extensively studied in the SM [8] and some new physics models, such as the Minimal Dilaton Model [9] and the Manohar–Wise model [10]. Furthermore, the production of some exotic Higgs boson is also possible at the ILC for center-of-mass energy at 250 GeV. For example, in the NMSSM, considering various experimental and theoretical constraints, the lightest CP-even Higgs h1 can be singlet-dominant and much lighter than the SM-like Higgs h, and the exotic Higgs production channel e+ e− → Zh1 may occur. In this work we investigate the Higgs-strahlung production of the lightest CP-even Higgs boson e+ e− → Zh1 at ILC in Natural NMSSM assuming the next-to-lightest CP-even Higgs boson is SM-like. We scan the NMSSM parameters by considering various experimental constraints and requiring the fine tuning measures Z and h are less than 50, then for the surviving √ samples we calculate the cross section of the process e+ e− → Zh1 at the ILC with s = 250 GeV. Since the discovery potential of Higgs boson depends on the production cross section along with its subsequent decay spectrum, we also discuss the decay patterns of the lightest CP-even Higgs boson h1 . This work is organized as follows. In Section 2 we briefly review the Higgs sector of the NMSSM and also discuss the naturalness in NMSSM. In Section 3 we scan the parameter space by considering various experimental constraints, then we calculate the cross section of the exotic Higgs production e+ e− → Zh1 in natural NMSSM and also discuss the branching ratio of h1 with h1 decaying to bb¯ , τ + τ − and γ γ . Finally, we summarize our results in Section 4. 2. Natural NMSSM In addition to the two Higgs doublet Hˆ u and Hˆ d as in MSSM, NMSSM contains one more gauge singlet superfield Sˆ. The superpotential and the corresponding soft breaking terms for the Higgs sector in NMSSM can be given by [11],
WNMSSM = WF + λHˆu · Hˆd Sˆ +
1 ˆ3 κS , 3
(1)
NMSSM ˜ 2u |Hu |2 + m ˜ 2d |Hd |2 + m ˜ 2S |S|2 + Vsoft =m
Aλ λSHu · Hd +
Aκ 3 κ S + h.c. . 3
(2)
˜ u, m ˜ d, m ˜ S , Aλ where WF denotes the superpotential in MSSM without the μ term, λ, κ are dimensionless couplings, and m and Aκ are the soft-breaking parameters. Recall that the main motivation for constructing the NMSSM is to generate the effective μ term through μ = λvs with vs is the vacuum expectation value (VEV) of the singlet field, thus the μ problem in MSSM can be naturally solved. The VEVs of the other Higgs fields Hu and Hd (i.e. vu and vd ) are related by the mass of W boson, which makes one of them as a free parameter and can be parametrized as tan β = vu /vd . ˜ u, m ˜ d, m ˜ S can be traded for mZ , tan β After the electroweak symmetry breaking, the three soft breaking parameters m and μ by the minimization conditions of the scalar potential. Therefore, the Higgs sector of NMSSM at the tree level can be described by the following six independent parameters,
λ, κ , tan β , μ, MA , Aκ , with MA2 =
(3)
2μ(Aλ +κvs ) . sin 2β
The scalar field Hu , Hd and S in the NMSSM can be described as
⎛
Hu = ⎝
⎞
⎛ ⎞ φ + iϕ vd + d √ d 1 ⎠ ⎝ 2 ⎠, S = vs + √ (σ + iξ ), φu + iϕu , Hd = Hu+
vu +
√
Hd−
2
2
(4)
and the diagonalization of their mass matrices provides the physical Higgs bosons,
⎛ ⎞ ⎛ ⎞ ⎛ ⎞ + + a1 φu ϕu H ⎝h2 ⎠ = U S ⎝φd ⎠, ⎝ a2 ⎠ = U P ⎝ϕd ⎠, H = U C u+ , + Hd G h3 σ ξ G0 ⎛ ⎞ h1
(5)
where h1 , h2 , h3 denote the physical CP-even Higgs boson with mh1 < mh2 < mh3 , a1 , a2 are the physical CP-odd Higgs boson with ma1 < ma2 , H + is the physical charged Higgs boson, and G0 and G+ are Goldstone bosons eaten by Z and W bosons respectively. Note that the physical Higgs boson states are the admixtures of Higgs doublet and singlet states, and the elements of the orthogonal matrices US (UP ) affect the couplings of CP-even (CP-odd) Higgs bosons with fermions and vector bosons. For example, the couplings of CP-even Higgs bosons hi (i= 1, 2, 3) with b quark, τ lepton and Z boson are given by
mb mτ S S gh bb¯ = √ UiS2 , ghi τ + τ − = √ UiS2 , ghi ZZ = gSM hi ZZ × (cos β Ui2 + sin β Ui1 ) i 2v cos β 2v cos β
(6)
where v2 = v2u + v2d and gSM is the corresponding coupling of Higgs boson with Z bosons in the SM. Hereafter we call the h ZZ i
Higgs boson with the largest coupling to Z boson as SM-like Higgs boson (denoted by h). Please cite this article as: Z. Heng et al., Higgs-strahlung production of the lightest CP-even Higgs boson at ILC in natural NMSSM, Chinese Journal of Physics (2017), http://dx.doi.org/10.1016/j.cjph.2017.04.007
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3
Fig. 1. The Feynman diagram of e+ e− → Zh1 in natural NMSSM.
Due to the coupling λHˆu · Hˆd Sˆ in the superpotential, the tree level mass of the SM-like Higgs boson is increased to
m2h,tree = m2Z cos2 2β + λ2 v2 sin 2β 2
(7)
Clearly, large value of λ or/and small value of tan β is preferred to enhance the SM-like Higgs boson mass at the tree level. Moreover, the mixing between the Higgs doublet and singlet fields can also significantly alter the Higgs boson mass. Specially, if h1 acts as h, the mixing will pull down the mass, while if h2 acts as h, the mixing will push up the mass. Consequently, mh2 125 GeV does not require large radiative correction from top squark loops [4,12]. So in this paper, we consider the scenario that h2 acts as the SM-like Higgs boson h, and here h1 is a singlet-dominant scalar. Referring to the naturalness in NMSSM, two following fine tuning quantities are usually considered [13],
∂ log m2Z ∂ log m2h , Z = max , h = max ∂ log pi ∂ log pi i i
(8)
and the formulae of calculating them can be found in [3,14]. Here pi includes the parameters in Eq. (3) and top quark Yukawa coupling Yt , which are all defined at the weak scale. Note that Yt is used to estimate the sensitivity of mZ and mh to top squark masses. Clearly, Z (h ) measures the sensitivity of mZ (mh ) to SUSY parameters at weak scale, and the larger value for any of them indicates more tuning to get the corresponding mass. 3. Calculations and numerical results In this work, we scan the parameters of NMSSM by considering various experimental constraints: (1) The constraints from fine-tuning requiring Z ≤ 50 and h ≤ 50. (2) All the constraints implemented in the package NMSSMTools-4.9.0 [15], such as limits from the LEP and the Tevatron on various sparticle masses as well as on the neutralino/chargino pair production rates, constraints from B-physics observables and the muon anomalous magnetic moment at 2σ level, dark matter constraints from relic density at 2σ level and LUX limits on the Spin-Independent scattering rate. (3) The constraints from the direct searches for Higgs bosons at LEP, Tevatron and LHC. To implement these constraints, we adopt the package HiggsSignals for 125 GeV Higgs data fit [16], and use the package HiggsBounds for non-standard Higgs boson search at colliders [17]. (4) The constraints from searches for sparticles at the LHC Run-I. We adopt the package FastLim [18] and SModelS [19] as well as the detailed Monte–Carlo simulations to implement these constraints. In our scan, we fix the soft parameters in the first two generation squark sector and gluino mass at 2 TeV. For the soft breaking parameters in the slepton sector, we assume them a common value ml˜ and treat it as a free parameter. We also assume the parameters mU3 = mD3 and At = Ab . Then we use the package NMSSMTools-4.9.0 to perform an extensive random scan over the following parameter regions:
0 < λ, κ ≤ 0.75,
2 ≤ tan β ≤ 60,
100 GeV ≤ μ ≤ 1 TeV, |Aκ | ≤ 2TeV, 100 GeV ≤ ml˜ ≤ 1 TeV, 100 GeV ≤ MQ3 , MU3 ≤ 2 TeV, |At | ≤ min(3 MQ2 3 + MU23 , 5TeV ), 50 GeV ≤ MA ≤ 2 TeV,
20GeV ≤ M1 ≤ 50 0GeV,
10 0GeV ≤ M2 ≤ 1TeV,
(9)
In the scan, we only pick up the samples satisfying the next-to-lightest CP-even Higgs boson (h2 ) being the SM-like Higgs h, and require 122 GeV ≤ mh ≤ 128 GeV. We find that, for the survived samples, the lightest CP-even Higgs boson h1 is singlet dominant, and the two fine tuning quantities Z and h may be as low as about 2 [6]. For these survived samples, we use HiggsSignals to perform fit with the experimental Higgs data from the Tevatron and LHC, which are provided by the program HiggsSignals. We calculate χ 2 for each Higgs search channel, and eventually the p-values are evaluated. Again, we pick up samples satisfying p-values larger than 0.05. √ For the International Linear Collider (ILC) operating at s = 250 GeV, the main production mechanism of neutral Higgs bosons in natural NMSSM is Higgs-stuahlung process e+ e− → Zhi . In this paper, we consider the production of lightest CP√ even Higgs boson h1 at ILC with s = 250 GeV, i.e. e+ e− → Zh1 . The corresponding Feynman diagram at tree level is shown in Fig. 1, and the amplitude can be written as
M=
S S + sin β U11 ie2 mZ cos β U12 2 v¯ ( p2 )(1 − 4sW + γ5 )γμ u( p1 )ε μ ( p3 ) 2 2 2 2 4sW cW ( p1 + p2 ) − mZ
(10)
Please cite this article as: Z. Heng et al., Higgs-strahlung production of the lightest CP-even Higgs boson at ILC in natural NMSSM, Chinese Journal of Physics (2017), http://dx.doi.org/10.1016/j.cjph.2017.04.007
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Fig. 2. The scatter plots of the surviving samples in natural NMSSM, showing the cross section of e+ e− → Zh1 for lightest CP-even Higgs boson h1 .
√ s = 250 GeV versus the mass of the
In above equation, sW = sin θW , cW = cos θW with θ W denoting the Weiberg angle, v¯ ( p2 ) and u(p1 ) represent the spinors of the positron and electron fields respectively, and ε μ (p3 ) is the polarization vector of Z field. Clearly, we can see that the modified coupling of h1 ZZ can significantly affect the cross section of the process. √ In Figs. 2 and 3 we show the cross section of e+ e− → Zh1 in Natural NMSSM for s = 250 GeV. From the figures we can clearly see that the cross section can reach to about 84 fb. And the cross section increases with the mass of the S |. This is because the cross section of e+ e− → Zh mainly depends lightest CP-even Higgs boson h1 and the values of |U11 1 on h1 ZZ coupling. Eq. (6) manifests that, for moderate or large tan β , h1 ZZ coupling largely depends on the matrix element S . For larger values of |U S |, the mixing between the Higgs doublet and singlet is larger, which leads to the mass of Higgs U11 11 S . So the cross section boson h1 more close to the mass of SM-like Higgs boson h and smaller values of matrix element U13 S , which is exactly shown on the right panel of Fig. 3. of e+ e− → Zh1 decreases with the value of matrix element U13 Since the discovery potential of Higgs boson depends on the production cross section along with its subsequent decay spectrum and the resulting rate, we now discuss the decay patterns of the lightest CP-even Higgs boson h1 . In Fig. 4 we show the branching ratio of the lightest CP-even Higgs boson h1 with h1 decaying to bb¯ , τ + τ − and γ γ . The figure clearly shows that, for most of the surviving samples, h1 dominantly decays to bb¯ with branching ratio close to 90%, and the rest to τ + τ − S ) leads to a sizable with branching ratio close to 10%. This is because the finite fraction of Higgs doublet component (i.e. U12 + − + − ¯ ¯ coupling of h1 with bb and τ τ (see Eq. (6)). Therefore, the partial widths of h1 → bb, τ τ would be dominant, which results in the enhancements of branching ratios of h1 → bb¯ , τ + τ − . However, for certain regions of the surviving samples, the branching ratio of h1 → γ γ can be greatly enhanced, and its branching ratio can maximally reach to 2%. This is mainly due to the strong suppression of partial widths of h1 → bb¯ , τ + τ − , which comes from the suppression of the mixing between the Higgs singlet and doublet states. In this case, we find that h1 is highly singlet-dominant. Actually, for all the survived samples, h1 is singlet-dominant, which leads to the production cross section of h1 at the LHC is very small, and subsequently Please cite this article as: Z. Heng et al., Higgs-strahlung production of the lightest CP-even Higgs boson at ILC in natural NMSSM, Chinese Journal of Physics (2017), http://dx.doi.org/10.1016/j.cjph.2017.04.007
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Fig. 3. Same as Fig. 2, but showing the cross section of e+ e− → Zh1 for
√
5
S S s = 250 GeV versus the elements of the rotation matrices U11 and U13 , respectively.
S Fig. 4. Same as Fig. 2, but showing the branching ratio of the lightest CP-even Higgs boson h1 versus mh1 and the elements of the rotation matrices U12 ,
respectively. The dots ‘•’ (black) denote the decay channel h1 → bb¯ , the circles ‘◦’ (blue) denote h1 → τ + τ − , and the plus ‘+’ (red) denote h1 → γ γ .
the signal rate of h1 at the LHC is quite small and it cannot be observed. We check the sample with the largest cross section of e+ e− → Zh1 , and find that the diphoton signal rate of h1 at 8TeV LHC is about 1.39fb, which is smaller than the ATLAS bounds on the rate with the same mass of h1 [20]. We also note that, for little regions of the surviving samples, whenever the decay h1 → a1 a1 is kinematically allowed, it will be the dominant one with the branching ratio reach to 90% or more. 4. Conclusion Compared with the MSSM, NMSSM can naturally predict a Higgs boson with mass near 125 GeV. And NMSSM can also predict rather low fine tunings in getting Higgs boson and Z boson mass. When the next-to-lightest CP-even Higgs boson Please cite this article as: Z. Heng et al., Higgs-strahlung production of the lightest CP-even Higgs boson at ILC in natural NMSSM, Chinese Journal of Physics (2017), http://dx.doi.org/10.1016/j.cjph.2017.04.007
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in NMSSM is SM-like, the lightest CP-even Higgs boson h1 is singlet-dominant and may be much lighter than the SM-like Higgs h. In this work we investigate the Higgs-strahlung production process e+ e− → Zh1 in natural NMSSM. Considering various experimental constraints, we scan over the parameter space of the NMSSM. Then in the allowed parameter space we calculate the cross section of the process e+ e− → Zh1 at ILC with center-of-mass energy of 250 GeV, and we also discuss the decay patterns of the lightest CP-even Higgs boson h1 . We find that the cross section of the process e+ e− → Zh1 can reach about 84 fb. Moreover, the cross section increases with the mass of h1 and strongly depends on the Higgs doubletcomponent of h1 . For most of the surviving samples, h1 mainly decays to bb¯ . However, for certain regions of the surviving samples, the branching ratio of h1 → γ γ can maximally reach 2%, which can be used to discriminate the NMSSM from MSSM. Acknowledgement This work was supported in part by the National Natural Science Foundation of China (NNSFC) under grant No. 11305050. References [1] G. Aad, ATLAS Collaboration, et al., Phys. Lett. B 716 (2012) 1; S. Chatrchyan, CMS Collaboration, et al., Phys. Lett. B 716 (2012) 30. [2] M. Carena, S. Gori, N.R. Shah, C.E.M. Wagner, JHEP 1203 (2012) 014, doi:10.1007/JHEP03(2012)014; S. Heinemeyer, O. Stal, G. Weiglein, Phys. Lett. B 710 (2012) 201, doi:10.1016/j.physletb.2012.02.084; J. Cao, Z. Heng, D. Li, J.M. Yang, Phys. Lett. B 710 (2012) 665, doi:10.1016/j.physletb.2012.03.052; J. Cao, Z. Heng, T. Liu, J.M. Yang, Phys. Lett. B 703 (2011) 462, doi:10.1016/j.physletb.2011.08.024; Z. Heng, Adv. High Energy Phys. 2012 (2012) 312719, doi:10.1155/2012/312719; J. Cao, Z. Heng, J.M. Yang, J. Zhu, JHEP 1210 (2012) 079, doi:10.1007/JHEP10(2012)079; Z. Kang, T. Li, T. Liu, C. Tong, J.M. Yang, Phys. Rev. D 86 (2012) 095020, doi:10.1103/PhysRevD.86.095020. [arXiv: 1203.2336[hep-ph]]. [3] U. Ellwanger, G. Espitalier-Noel, C. Hugonie, JHEP 1109 (2011) 105. [arXiv: 1107.2472[hep-ph]]. [4] J.J. Cao, Z.X. Heng, J.M. Yang, Y.M. Zhang, J.Y. Zhu, JHEP 1203 (2012) 086, doi:10.1007/JHEP03(2012)086. [arXiv: 1202.5821[hep-ph]]. [5] Z. Kang, J. Li, T. Li, JHEP 1211 (2012) 024, doi:10.1007/JHEP11(2012)024. [arXiv: 1201.5305[hep-ph]]. [6] J. Cao, Y. He, L. Shang, W. Su, Y. Zhang, JHEP 1608 (2016) 037, doi:10.1007/JHEP08(2016)037. [arXiv: 1606.04416[hep-ph]], J. Cao, Y. He, L. Shang, W. Su, P. Wu and Y. Zhang, arXiv: 1609.00204[hep-ph]. [7] G. Aarons, ILC Collaboration, et al., [arXiv:0709.1893 [hep-ph]]. [8] A. Denner, J. Kublbeck, R. Mertig, M. Bohm, Z. Phys. C 56 (1992) 261; C. Englert, M. McCullough, JHEP 1307 (2013) 168, doi:10.1007/JHEP07(2013)168; M. McCullough, Phys. Rev. D 90 (1) (2014) 015001; N. Liu, J. Ren, L. Wu, P. Wu, J.M. Yang, JHEP 1404 (2014) 189, doi:10.1007/JHEP04(2014)189. [arXiv: 1311.6971[hep-ph]]. [9] J. Cao, Z. Heng, D. Li, L. Shang, P. Wu, JHEP 1408 (2014) 138, doi:10.1007/JHEP08(2014)138; Z.X. Heng, D.W. Li, H.J. Zhou, Commun. Theor. Phys. 63 (2) (2015) 188. [arXiv: 1405.4489[hep-ph]]. [10] Z.X. Heng, H.J. Zhou, Chin. J. Phys. 54 (2016) 308–313. [11] U. Ellwanger, C. Hugonie, A.M. Teixeira, Phys. Rept. 496 (2010) 1, doi:10.1016/j.physrep.2010.07.001; M. Maniatis, Int. J. Mod. Phys. A 25 (2010) 3505, doi:10.1142/S0217751X10049827. [arXiv: 0906.0777[hep-ph]]. [12] U. Ellwanger, JHEP 1203 (2012) 044, doi:10.1007/JHEP03(2012)044. [arXiv: 1112.3548[hep-ph]]. [13] H. Baer, V. Barger, D. Mickelson, Phys. Rev. D 88 (9) (2013) 095013, doi:10.1103/PhysRevD.88.095013. [arXiv: 1309.2984[hep-ph]]. [14] M. Farina, M. Perelstein, B. Shakya, JHEP 1404 (2014) 108, doi:10.1007/JHEP04(2014)108. [arXiv: 1310.0459[hep-ph]]. [15] U. Ellwanger, J.F. Gunion, C. Hugonie, JHEP 0502 (2005) 066, doi:10.1088/1126-6708/2005/02/066; U. Ellwanger, C. Hugonie, Comput. Phys. Commun. 175 (2006) 290, doi:10.1016/j.cpc.2006.04.004. [hep-ph/0508022]. [16] P. Bechtle, S. Heinemeyer, O. Stal, T. Stefaniak, G. Weiglein, Eur. Phys. J. C 74 (2) (2014) 2711, doi:10.1140/epjc/s10052- 013- 2711- 4; O. Stal, T. Stefaniak, PoS EPS -HEP2013 (2013) 314. [arXiv: 1310.0459[hep-ph]]. [17] P. Bechtle, O. Brein, S. Heinemeyer, G. Weiglein, K.E. Williams, Comput. Phys. Commun. 181 (2010) 138, doi:10.1016/j.cpc.20 09.09.0 03. [arXiv: 0811. 4169[hep-ph]]; Comput. Phys. Commun. 182, 2605 (2011) doi:10.1016/j.cpc.2011.07.015 [arXiv: 1102.1898[hep-ph]]. [18] M. Papucci, K. Sakurai, A. Weiler, L. Zeune, Eur. Phys. J. C 74 (11) (2014) 3163, doi:10.1140/epjc/s10052- 014- 3163- 1. [arXiv: 1402.0492[hep-ph]]. [19] S. Kraml, S. Kulkarni, U. Laa, A. Lessa, W. Magerl, D. Proschofsky-Spindler, W. Waltenberger, Eur. Phys. J. C 74 (2014) 2868, doi:10.1140/epjc/ s10052- 014- 2868- 5. [arXiv: 1312.4175[hep-ph]]. [20] G. Aad, ATLAS Collaboration, et al., Phys. Rev. Lett. 113 (17) (2014) 171801, doi:10.1103/PhysRevLett.113.171801. [arXiv: 1407.6583[hep-ex]].
Please cite this article as: Z. Heng et al., Higgs-strahlung production of the lightest CP-even Higgs boson at ILC in natural NMSSM, Chinese Journal of Physics (2017), http://dx.doi.org/10.1016/j.cjph.2017.04.007
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Chinese Journal of Physics 0 0 0 (2017) 1–6
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Higgs-strahlung production of the lightest CP-even Higgs boson at ILC in natural NMSSM Zhaoxia Heng, Wenlong Wang, Haijing Zhou∗ College of Physics and Materials Science, Henan Normal University, Xinxiang 453007, China
a r t i c l e
i n f o
Article history: Received 6 January 2017 Revised 16 April 2017 Accepted 17 April 2017 Available online xxx
a b s t r a c t Considering various experimental constraints, we scan over the parameter space of the NMSSM by requiring the fine tuning measures Z and h are less than 50. Then in the allowed parameter space we investigate the Higgs-strahlung production of the lightest CPeven Higgs boson h1 at ILC assuming the next-to-lightest CP-even Higgs boson acts as SMlike. we calculate the cross section of the process e+ e− → Zh1 at ILC with center-of-mass energy of 250 GeV, and also discuss the decay patterns of h1 . We find that the cross section of the process e+ e− → Zh1 can reach about 84 fb. Moreover, the cross section increases with the mass of h1 and strongly depends on the Higgs doublet-component of h1 . For most of the surviving samples, h1 mainly decays to bb¯ . However, for certain regions of the surviving samples, the branching ratio of h1 → γ γ can maximally reach 2%, which can be used to discriminate the NMSSM from MSSM. © 2017 The Physical Society of the Republic of China (Taiwan). Published by Elsevier B.V. All rights reserved.
1. Introduction The discovery of a Higgs boson in July 2012 by the ATLAS and CMS collaborations at the CERN Large Hadron Collider (LHC) [1] has marked a great success in the history of particle physics. The properties of this new boson is largely consistent with the predictions in the Standard Model (SM). And there aslo exist various new physics models that can accommodate this new Higgs boson. For example, the Minimal Supersymmetric Standard Model (MSSM) can accommodate a Higgs boson with mass near 125 GeV [2], but it requires higher order corrections mainly from the third generation squark sector, which will lead to some degrees of fine-tuning. Nevertheless, this fine-tuning problem can be alleviated in the next-to-minimal supersymmetric standard model (NMSSM) [3], which extends the MSSM with an additional Higgs singlet. In the NMSSM, due to the coupling between the Higgs doublets and singlet in the superpotential, the mass of the SM-like Higgs boson gets additional contribution at tree-level. Moreover, whenever the next-to-lightest CP-even Higgs boson acts as the SM-like Higgs boson, the mixing between the Higgs doublet and singlet fields can also push up the Higgs boson mass [4,5]. So it does not require large radiative corrections from the third generation squark loops to accommodate a Higgs boson near 125 GeV. Therefore, the NMSSM is more natural in predicting Higgs boson mass. And it can also predict rather low fine tunings in getting the Z boson and Higgs boson mass [6]. Based on the current LHC data, various Higgs couplings to SM fermions and vector bosons still have large uncertainties, so the precision measurements of the Higgs boson are rather challenging at the LHC. To precisely investigate the properties ∗
Corresponding author. E-mail address: [email protected] (H. Zhou).
http://dx.doi.org/10.1016/j.cjph.2017.04.007 0577-9073/© 2017 The Physical Society of the Republic of China (Taiwan). Published by Elsevier B.V. All rights reserved.
Please cite this article as: Z. Heng et al., Higgs-strahlung production of the lightest CP-even Higgs boson at ILC in natural NMSSM, Chinese Journal of Physics (2017), http://dx.doi.org/10.1016/j.cjph.2017.04.007
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of Higgs boson, some high energy e+ e− collider with clean environment, such as the International Linear Collider (ILC) [7], are proposed. At e+ e− collider for a center-of-mass energy of 250 GeV, the Higgs-strahlung process e+ e− → Zh is the main production channel for the Higgs boson, which has been extensively studied in the SM [8] and some new physics models, such as the Minimal Dilaton Model [9] and the Manohar–Wise model [10]. Furthermore, the production of some exotic Higgs boson is also possible at the ILC for center-of-mass energy at 250 GeV. For example, in the NMSSM, considering various experimental and theoretical constraints, the lightest CP-even Higgs h1 can be singlet-dominant and much lighter than the SM-like Higgs h, and the exotic Higgs production channel e+ e− → Zh1 may occur. In this work we investigate the Higgs-strahlung production of the lightest CP-even Higgs boson e+ e− → Zh1 at ILC in Natural NMSSM assuming the next-to-lightest CP-even Higgs boson is SM-like. We scan the NMSSM parameters by considering various experimental constraints and requiring the fine tuning measures Z and h are less than 50, then for the surviving √ samples we calculate the cross section of the process e+ e− → Zh1 at the ILC with s = 250 GeV. Since the discovery potential of Higgs boson depends on the production cross section along with its subsequent decay spectrum, we also discuss the decay patterns of the lightest CP-even Higgs boson h1 . This work is organized as follows. In Section 2 we briefly review the Higgs sector of the NMSSM and also discuss the naturalness in NMSSM. In Section 3 we scan the parameter space by considering various experimental constraints, then we calculate the cross section of the exotic Higgs production e+ e− → Zh1 in natural NMSSM and also discuss the branching ratio of h1 with h1 decaying to bb¯ , τ + τ − and γ γ . Finally, we summarize our results in Section 4. 2. Natural NMSSM In addition to the two Higgs doublet Hˆ u and Hˆ d as in MSSM, NMSSM contains one more gauge singlet superfield Sˆ. The superpotential and the corresponding soft breaking terms for the Higgs sector in NMSSM can be given by [11],
WNMSSM = WF + λHˆu · Hˆd Sˆ +
1 ˆ3 κS , 3
(1)
NMSSM ˜ 2u |Hu |2 + m ˜ 2d |Hd |2 + m ˜ 2S |S|2 + Vsoft =m
Aλ λSHu · Hd +
Aκ 3 κ S + h.c. . 3
(2)
˜ u, m ˜ d, m ˜ S , Aλ where WF denotes the superpotential in MSSM without the μ term, λ, κ are dimensionless couplings, and m and Aκ are the soft-breaking parameters. Recall that the main motivation for constructing the NMSSM is to generate the effective μ term through μ = λvs with vs is the vacuum expectation value (VEV) of the singlet field, thus the μ problem in MSSM can be naturally solved. The VEVs of the other Higgs fields Hu and Hd (i.e. vu and vd ) are related by the mass of W boson, which makes one of them as a free parameter and can be parametrized as tan β = vu /vd . ˜ u, m ˜ d, m ˜ S can be traded for mZ , tan β After the electroweak symmetry breaking, the three soft breaking parameters m and μ by the minimization conditions of the scalar potential. Therefore, the Higgs sector of NMSSM at the tree level can be described by the following six independent parameters,
λ, κ , tan β , μ, MA , Aκ , with MA2 =
(3)
2μ(Aλ +κvs ) . sin 2β
The scalar field Hu , Hd and S in the NMSSM can be described as
⎛
Hu = ⎝
⎞
⎛ ⎞ φ + iϕ vd + d √ d 1 ⎠ ⎝ 2 ⎠, S = vs + √ (σ + iξ ), φu + iϕu , Hd = Hu+
vu +
√
Hd−
2
2
(4)
and the diagonalization of their mass matrices provides the physical Higgs bosons,
⎛ ⎞ ⎛ ⎞ ⎛ ⎞ + + a1 φu ϕu H ⎝h2 ⎠ = U S ⎝φd ⎠, ⎝ a2 ⎠ = U P ⎝ϕd ⎠, H = U C u+ , + Hd G h3 σ ξ G0 ⎛ ⎞ h1
(5)
where h1 , h2 , h3 denote the physical CP-even Higgs boson with mh1 < mh2 < mh3 , a1 , a2 are the physical CP-odd Higgs boson with ma1 < ma2 , H + is the physical charged Higgs boson, and G0 and G+ are Goldstone bosons eaten by Z and W bosons respectively. Note that the physical Higgs boson states are the admixtures of Higgs doublet and singlet states, and the elements of the orthogonal matrices US (UP ) affect the couplings of CP-even (CP-odd) Higgs bosons with fermions and vector bosons. For example, the couplings of CP-even Higgs bosons hi (i= 1, 2, 3) with b quark, τ lepton and Z boson are given by
mb mτ S S gh bb¯ = √ UiS2 , ghi τ + τ − = √ UiS2 , ghi ZZ = gSM hi ZZ × (cos β Ui2 + sin β Ui1 ) i 2v cos β 2v cos β
(6)
where v2 = v2u + v2d and gSM is the corresponding coupling of Higgs boson with Z bosons in the SM. Hereafter we call the h ZZ i
Higgs boson with the largest coupling to Z boson as SM-like Higgs boson (denoted by h). Please cite this article as: Z. Heng et al., Higgs-strahlung production of the lightest CP-even Higgs boson at ILC in natural NMSSM, Chinese Journal of Physics (2017), http://dx.doi.org/10.1016/j.cjph.2017.04.007
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3
Fig. 1. The Feynman diagram of e+ e− → Zh1 in natural NMSSM.
Due to the coupling λHˆu · Hˆd Sˆ in the superpotential, the tree level mass of the SM-like Higgs boson is increased to
m2h,tree = m2Z cos2 2β + λ2 v2 sin 2β 2
(7)
Clearly, large value of λ or/and small value of tan β is preferred to enhance the SM-like Higgs boson mass at the tree level. Moreover, the mixing between the Higgs doublet and singlet fields can also significantly alter the Higgs boson mass. Specially, if h1 acts as h, the mixing will pull down the mass, while if h2 acts as h, the mixing will push up the mass. Consequently, mh2 125 GeV does not require large radiative correction from top squark loops [4,12]. So in this paper, we consider the scenario that h2 acts as the SM-like Higgs boson h, and here h1 is a singlet-dominant scalar. Referring to the naturalness in NMSSM, two following fine tuning quantities are usually considered [13],
∂ log m2Z ∂ log m2h , Z = max , h = max ∂ log pi ∂ log pi i i
(8)
and the formulae of calculating them can be found in [3,14]. Here pi includes the parameters in Eq. (3) and top quark Yukawa coupling Yt , which are all defined at the weak scale. Note that Yt is used to estimate the sensitivity of mZ and mh to top squark masses. Clearly, Z (h ) measures the sensitivity of mZ (mh ) to SUSY parameters at weak scale, and the larger value for any of them indicates more tuning to get the corresponding mass. 3. Calculations and numerical results In this work, we scan the parameters of NMSSM by considering various experimental constraints: (1) The constraints from fine-tuning requiring Z ≤ 50 and h ≤ 50. (2) All the constraints implemented in the package NMSSMTools-4.9.0 [15], such as limits from the LEP and the Tevatron on various sparticle masses as well as on the neutralino/chargino pair production rates, constraints from B-physics observables and the muon anomalous magnetic moment at 2σ level, dark matter constraints from relic density at 2σ level and LUX limits on the Spin-Independent scattering rate. (3) The constraints from the direct searches for Higgs bosons at LEP, Tevatron and LHC. To implement these constraints, we adopt the package HiggsSignals for 125 GeV Higgs data fit [16], and use the package HiggsBounds for non-standard Higgs boson search at colliders [17]. (4) The constraints from searches for sparticles at the LHC Run-I. We adopt the package FastLim [18] and SModelS [19] as well as the detailed Monte–Carlo simulations to implement these constraints. In our scan, we fix the soft parameters in the first two generation squark sector and gluino mass at 2 TeV. For the soft breaking parameters in the slepton sector, we assume them a common value ml˜ and treat it as a free parameter. We also assume the parameters mU3 = mD3 and At = Ab . Then we use the package NMSSMTools-4.9.0 to perform an extensive random scan over the following parameter regions:
0 < λ, κ ≤ 0.75,
2 ≤ tan β ≤ 60,
100 GeV ≤ μ ≤ 1 TeV, |Aκ | ≤ 2TeV, 100 GeV ≤ ml˜ ≤ 1 TeV, 100 GeV ≤ MQ3 , MU3 ≤ 2 TeV, |At | ≤ min(3 MQ2 3 + MU23 , 5TeV ), 50 GeV ≤ MA ≤ 2 TeV,
20GeV ≤ M1 ≤ 50 0GeV,
10 0GeV ≤ M2 ≤ 1TeV,
(9)
In the scan, we only pick up the samples satisfying the next-to-lightest CP-even Higgs boson (h2 ) being the SM-like Higgs h, and require 122 GeV ≤ mh ≤ 128 GeV. We find that, for the survived samples, the lightest CP-even Higgs boson h1 is singlet dominant, and the two fine tuning quantities Z and h may be as low as about 2 [6]. For these survived samples, we use HiggsSignals to perform fit with the experimental Higgs data from the Tevatron and LHC, which are provided by the program HiggsSignals. We calculate χ 2 for each Higgs search channel, and eventually the p-values are evaluated. Again, we pick up samples satisfying p-values larger than 0.05. √ For the International Linear Collider (ILC) operating at s = 250 GeV, the main production mechanism of neutral Higgs bosons in natural NMSSM is Higgs-stuahlung process e+ e− → Zhi . In this paper, we consider the production of lightest CP√ even Higgs boson h1 at ILC with s = 250 GeV, i.e. e+ e− → Zh1 . The corresponding Feynman diagram at tree level is shown in Fig. 1, and the amplitude can be written as
M=
S S + sin β U11 ie2 mZ cos β U12 2 v¯ ( p2 )(1 − 4sW + γ5 )γμ u( p1 )ε μ ( p3 ) 2 2 2 2 4sW cW ( p1 + p2 ) − mZ
(10)
Please cite this article as: Z. Heng et al., Higgs-strahlung production of the lightest CP-even Higgs boson at ILC in natural NMSSM, Chinese Journal of Physics (2017), http://dx.doi.org/10.1016/j.cjph.2017.04.007
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Fig. 2. The scatter plots of the surviving samples in natural NMSSM, showing the cross section of e+ e− → Zh1 for lightest CP-even Higgs boson h1 .
√ s = 250 GeV versus the mass of the
In above equation, sW = sin θW , cW = cos θW with θ W denoting the Weiberg angle, v¯ ( p2 ) and u(p1 ) represent the spinors of the positron and electron fields respectively, and ε μ (p3 ) is the polarization vector of Z field. Clearly, we can see that the modified coupling of h1 ZZ can significantly affect the cross section of the process. √ In Figs. 2 and 3 we show the cross section of e+ e− → Zh1 in Natural NMSSM for s = 250 GeV. From the figures we can clearly see that the cross section can reach to about 84 fb. And the cross section increases with the mass of the S |. This is because the cross section of e+ e− → Zh mainly depends lightest CP-even Higgs boson h1 and the values of |U11 1 on h1 ZZ coupling. Eq. (6) manifests that, for moderate or large tan β , h1 ZZ coupling largely depends on the matrix element S . For larger values of |U S |, the mixing between the Higgs doublet and singlet is larger, which leads to the mass of Higgs U11 11 S . So the cross section boson h1 more close to the mass of SM-like Higgs boson h and smaller values of matrix element U13 S , which is exactly shown on the right panel of Fig. 3. of e+ e− → Zh1 decreases with the value of matrix element U13 Since the discovery potential of Higgs boson depends on the production cross section along with its subsequent decay spectrum and the resulting rate, we now discuss the decay patterns of the lightest CP-even Higgs boson h1 . In Fig. 4 we show the branching ratio of the lightest CP-even Higgs boson h1 with h1 decaying to bb¯ , τ + τ − and γ γ . The figure clearly shows that, for most of the surviving samples, h1 dominantly decays to bb¯ with branching ratio close to 90%, and the rest to τ + τ − S ) leads to a sizable with branching ratio close to 10%. This is because the finite fraction of Higgs doublet component (i.e. U12 + − + − ¯ ¯ coupling of h1 with bb and τ τ (see Eq. (6)). Therefore, the partial widths of h1 → bb, τ τ would be dominant, which results in the enhancements of branching ratios of h1 → bb¯ , τ + τ − . However, for certain regions of the surviving samples, the branching ratio of h1 → γ γ can be greatly enhanced, and its branching ratio can maximally reach to 2%. This is mainly due to the strong suppression of partial widths of h1 → bb¯ , τ + τ − , which comes from the suppression of the mixing between the Higgs singlet and doublet states. In this case, we find that h1 is highly singlet-dominant. Actually, for all the survived samples, h1 is singlet-dominant, which leads to the production cross section of h1 at the LHC is very small, and subsequently Please cite this article as: Z. Heng et al., Higgs-strahlung production of the lightest CP-even Higgs boson at ILC in natural NMSSM, Chinese Journal of Physics (2017), http://dx.doi.org/10.1016/j.cjph.2017.04.007
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Fig. 3. Same as Fig. 2, but showing the cross section of e+ e− → Zh1 for
√
5
S S s = 250 GeV versus the elements of the rotation matrices U11 and U13 , respectively.
S Fig. 4. Same as Fig. 2, but showing the branching ratio of the lightest CP-even Higgs boson h1 versus mh1 and the elements of the rotation matrices U12 ,
respectively. The dots ‘•’ (black) denote the decay channel h1 → bb¯ , the circles ‘◦’ (blue) denote h1 → τ + τ − , and the plus ‘+’ (red) denote h1 → γ γ .
the signal rate of h1 at the LHC is quite small and it cannot be observed. We check the sample with the largest cross section of e+ e− → Zh1 , and find that the diphoton signal rate of h1 at 8TeV LHC is about 1.39fb, which is smaller than the ATLAS bounds on the rate with the same mass of h1 [20]. We also note that, for little regions of the surviving samples, whenever the decay h1 → a1 a1 is kinematically allowed, it will be the dominant one with the branching ratio reach to 90% or more. 4. Conclusion Compared with the MSSM, NMSSM can naturally predict a Higgs boson with mass near 125 GeV. And NMSSM can also predict rather low fine tunings in getting Higgs boson and Z boson mass. When the next-to-lightest CP-even Higgs boson Please cite this article as: Z. Heng et al., Higgs-strahlung production of the lightest CP-even Higgs boson at ILC in natural NMSSM, Chinese Journal of Physics (2017), http://dx.doi.org/10.1016/j.cjph.2017.04.007
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in NMSSM is SM-like, the lightest CP-even Higgs boson h1 is singlet-dominant and may be much lighter than the SM-like Higgs h. In this work we investigate the Higgs-strahlung production process e+ e− → Zh1 in natural NMSSM. Considering various experimental constraints, we scan over the parameter space of the NMSSM. Then in the allowed parameter space we calculate the cross section of the process e+ e− → Zh1 at ILC with center-of-mass energy of 250 GeV, and we also discuss the decay patterns of the lightest CP-even Higgs boson h1 . We find that the cross section of the process e+ e− → Zh1 can reach about 84 fb. Moreover, the cross section increases with the mass of h1 and strongly depends on the Higgs doubletcomponent of h1 . For most of the surviving samples, h1 mainly decays to bb¯ . However, for certain regions of the surviving samples, the branching ratio of h1 → γ γ can maximally reach 2%, which can be used to discriminate the NMSSM from MSSM. Acknowledgement This work was supported in part by the National Natural Science Foundation of China (NNSFC) under grant No. 11305050. References [1] G. Aad, ATLAS Collaboration, et al., Phys. Lett. B 716 (2012) 1; S. Chatrchyan, CMS Collaboration, et al., Phys. Lett. B 716 (2012) 30. [2] M. Carena, S. Gori, N.R. Shah, C.E.M. Wagner, JHEP 1203 (2012) 014, doi:10.1007/JHEP03(2012)014; S. Heinemeyer, O. Stal, G. Weiglein, Phys. Lett. B 710 (2012) 201, doi:10.1016/j.physletb.2012.02.084; J. Cao, Z. Heng, D. Li, J.M. Yang, Phys. Lett. B 710 (2012) 665, doi:10.1016/j.physletb.2012.03.052; J. Cao, Z. Heng, T. Liu, J.M. Yang, Phys. Lett. B 703 (2011) 462, doi:10.1016/j.physletb.2011.08.024; Z. Heng, Adv. High Energy Phys. 2012 (2012) 312719, doi:10.1155/2012/312719; J. Cao, Z. Heng, J.M. Yang, J. Zhu, JHEP 1210 (2012) 079, doi:10.1007/JHEP10(2012)079; Z. Kang, T. Li, T. Liu, C. Tong, J.M. Yang, Phys. Rev. D 86 (2012) 095020, doi:10.1103/PhysRevD.86.095020. [arXiv: 1203.2336[hep-ph]]. [3] U. Ellwanger, G. Espitalier-Noel, C. Hugonie, JHEP 1109 (2011) 105. [arXiv: 1107.2472[hep-ph]]. [4] J.J. Cao, Z.X. Heng, J.M. Yang, Y.M. Zhang, J.Y. Zhu, JHEP 1203 (2012) 086, doi:10.1007/JHEP03(2012)086. [arXiv: 1202.5821[hep-ph]]. [5] Z. Kang, J. Li, T. Li, JHEP 1211 (2012) 024, doi:10.1007/JHEP11(2012)024. [arXiv: 1201.5305[hep-ph]]. [6] J. Cao, Y. He, L. Shang, W. Su, Y. Zhang, JHEP 1608 (2016) 037, doi:10.1007/JHEP08(2016)037. [arXiv: 1606.04416[hep-ph]], J. Cao, Y. He, L. Shang, W. Su, P. Wu and Y. Zhang, arXiv: 1609.00204[hep-ph]. [7] G. Aarons, ILC Collaboration, et al., [arXiv:0709.1893 [hep-ph]]. [8] A. Denner, J. Kublbeck, R. Mertig, M. Bohm, Z. Phys. C 56 (1992) 261; C. Englert, M. McCullough, JHEP 1307 (2013) 168, doi:10.1007/JHEP07(2013)168; M. McCullough, Phys. Rev. D 90 (1) (2014) 015001; N. Liu, J. Ren, L. Wu, P. Wu, J.M. Yang, JHEP 1404 (2014) 189, doi:10.1007/JHEP04(2014)189. [arXiv: 1311.6971[hep-ph]]. [9] J. Cao, Z. Heng, D. Li, L. Shang, P. Wu, JHEP 1408 (2014) 138, doi:10.1007/JHEP08(2014)138; Z.X. Heng, D.W. Li, H.J. Zhou, Commun. Theor. Phys. 63 (2) (2015) 188. [arXiv: 1405.4489[hep-ph]]. [10] Z.X. Heng, H.J. Zhou, Chin. J. Phys. 54 (2016) 308–313. [11] U. Ellwanger, C. Hugonie, A.M. Teixeira, Phys. Rept. 496 (2010) 1, doi:10.1016/j.physrep.2010.07.001; M. Maniatis, Int. J. Mod. Phys. A 25 (2010) 3505, doi:10.1142/S0217751X10049827. [arXiv: 0906.0777[hep-ph]]. [12] U. Ellwanger, JHEP 1203 (2012) 044, doi:10.1007/JHEP03(2012)044. [arXiv: 1112.3548[hep-ph]]. [13] H. Baer, V. Barger, D. Mickelson, Phys. Rev. D 88 (9) (2013) 095013, doi:10.1103/PhysRevD.88.095013. [arXiv: 1309.2984[hep-ph]]. [14] M. Farina, M. Perelstein, B. Shakya, JHEP 1404 (2014) 108, doi:10.1007/JHEP04(2014)108. [arXiv: 1310.0459[hep-ph]]. [15] U. Ellwanger, J.F. Gunion, C. Hugonie, JHEP 0502 (2005) 066, doi:10.1088/1126-6708/2005/02/066; U. Ellwanger, C. Hugonie, Comput. Phys. Commun. 175 (2006) 290, doi:10.1016/j.cpc.2006.04.004. [hep-ph/0508022]. [16] P. Bechtle, S. Heinemeyer, O. Stal, T. Stefaniak, G. Weiglein, Eur. Phys. J. C 74 (2) (2014) 2711, doi:10.1140/epjc/s10052- 013- 2711- 4; O. Stal, T. Stefaniak, PoS EPS -HEP2013 (2013) 314. [arXiv: 1310.0459[hep-ph]]. [17] P. Bechtle, O. Brein, S. Heinemeyer, G. Weiglein, K.E. Williams, Comput. Phys. Commun. 181 (2010) 138, doi:10.1016/j.cpc.20 09.09.0 03. [arXiv: 0811. 4169[hep-ph]]; Comput. Phys. Commun. 182, 2605 (2011) doi:10.1016/j.cpc.2011.07.015 [arXiv: 1102.1898[hep-ph]]. [18] M. Papucci, K. Sakurai, A. Weiler, L. Zeune, Eur. Phys. J. C 74 (11) (2014) 3163, doi:10.1140/epjc/s10052- 014- 3163- 1. [arXiv: 1402.0492[hep-ph]]. [19] S. Kraml, S. Kulkarni, U. Laa, A. Lessa, W. Magerl, D. Proschofsky-Spindler, W. Waltenberger, Eur. Phys. J. C 74 (2014) 2868, doi:10.1140/epjc/ s10052- 014- 2868- 5. [arXiv: 1312.4175[hep-ph]]. [20] G. Aad, ATLAS Collaboration, et al., Phys. Rev. Lett. 113 (17) (2014) 171801, doi:10.1103/PhysRevLett.113.171801. [arXiv: 1407.6583[hep-ex]].
Please cite this article as: Z. Heng et al., Higgs-strahlung production of the lightest CP-even Higgs boson at ILC in natural NMSSM, Chinese Journal of Physics (2017), http://dx.doi.org/10.1016/j.cjph.2017.04.007