本文利用最近的數據研究對於在2HDMs理論中mH±以及tanβ這兩種自由參數之間的關係。藉由在B物理中B→Xsγ、B0−B0 mixing、Z→bb 和 Bs→µ+µ−這四個反應過程，來對mH±及tanβ分別在2HDMs的四種模型 (Type I、Type II、Lepton Specific 和 Flipped) 中給出限制。在 95%C.L.下，mH±在Type II和Flipped中會大於500GeV ，但是Type I和Lepton Specific在tanβ>2的區域並沒對於mH±給出限制。相反 的，若不希望mH±>1000GeV，在tanβ<2的區域是不被允許的。第二部分定義了一個參數:R≡VBF/ggh，這個參數跟衰變到哪種狀態的資訊無關，統計誤差和系統誤差也會因為相除的關係而下降。所以期望用這個參數來對2HDMs中的自由參數做限制會比用一般的signal strength 來做限制會有比較好的表現。利用ALTAS文章中的數據，在
Lepton Specific 這個模型中，R 的方法有比較強的限制結果。

We studied the relation between the mass of charged scalar boson and vacuum expectation value ratio(tan β) in the four types 2HDM. According to the constraints on flavor physics B→Xsγ,B0−B0 mixing, Z→bb and Bs→µ+µ−, H± mass in the Type II and Flipped is larger than 500GeV. But there are no constraints on H± mass in the Type I and Lepton Specific when tanβ is larger than 2. On the contrary, in small tanβ region, H± mass becomes larger than 700GeV with the decreasing tanβ. Because mass is so heavy at low tanβ region, we choose that tanβ is larger than 1 in the next step, which is the analysis of the ATLAS Higgs physics data according to the ATLAS paper. Next, we can test new model via signal strength analysis. However, there are information of production and final state both in signal strength. If we want to look into different production µhZZ∗ cross sections, we can define the ratio R≡ VBF/ggh. It is independent to theoretical predictions on partial decay width and branch ratio. Moreover, many experimental
systemic uncertainties can be cancelled in this ratio. We choose gg→H→WW∗ for our reference because it has smallest statistical and overall uncertainties. As results of this method, we find that the constraint on the Lepton Specific is better than using ordinary
signal strength method.

[1] F. Englert and R. Brout, Broken Symmetry and the Mass of Gauge Vector Mesons. Phys. Rev. Lett. 13 (1964) 321.
[2] P. W. Higgs, Broken symmetries, massless particles and gauge fields. Phys. Lett. 12 (1964) 132.
[3] S. Weinberg, A model of leptons. Phys. Rev. Lett. 19 (1967) 1264.
[4] A. Salam, Weak and electromagnetic interactions, in Elementary particle physics:relativistic groups and analyticity. N. Svartholm, ed. p.367 Almqvist & Wiskell, 1968.
[5] ATLAS Collaboration, Observation of a new particle in the search for the Standard Model
Higgs boson with the ATLAS detector at the LHC. Phys. Lett. B 716 (2012) 1, arXiv:1207.7214[hep-ex].
[6] CMS Collaboration, Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC. Phys. Lett. B 716 (2012) 30, arXiv:1207.7235[hep-ex].
[7] John F. Gunion, Howard E. Haber, Gordon L. Kane and Sally Dawson, The Higgs Hunter’s Guide. Front.Phys. 80 (2000)
[8] G. C. Branco, P. M. Ferreira, L. Lavoura, M. N. Rebelo, Marc Sher and Joaaaaa˜o P.Silva, Theory and phenomenology of two-Higgs-doublet models. (2011) arXiv:1106.0034v3 [hep-ph]
[9] Konstantin Chetyrkin, Mikolaj Misiak, Manfred Münz, Weak Radiative B- Meson Decay Beyond Leading Logarithms. (1998), arXiv:hep-ph/9612313v3[hep-ph]
[10] M. Ciuchini, G. Degrassi, P. Gambino, G.F. Giudice, Next-to-Leading QCD Corrections to B→Xs+γ:Standard Model and Two-Higgs Doublet Model.(1998), arXiv:hep-ph/9710335v3 [hep-ph]
[11] O.Deschamps, S. Descotes-Genon, S.Monteil, VNiess, S.T’Jampens and V.Tisserand, The Two Higgs Doublet Model of Type II facing flavour physics data. (2010) arXiv:0907.5135v2 [hep-ph]
[12] Xiao-Dong Cheng, Ya-Dong Yang and Xing-Bo Yuan, Phenomenological discriminations of the Yukawa interactions in two-Higgs doublet models with Z2 symmetry. (2014) arXiv:1401.6657v3 [hep-ph]
[13] T. Inami and C.S. Lim, Effects of Superheavy Quarks and Leptons in Low- Energy Weak Processes KL→µµ, K+→πνν¯ and K0 ↔K¯0. Prog. Theor. Phys. 65,297(1981)
[14] Abdul Wahab El Kaffas and Osland, Constraining the Two-Higgs-Doublet-Model parameter space. (2007) arXiv:0706.2997v1 [hep-ph]
[15] Patricia Ball, Robert Fleischer, Probing New Physics through B Mixing: Status, Benchmarks and Prospects. arXiv:hep-ph/0604249
[16] Howard E. Haber and Heather E. Logan, Radiative Corrections to the Zbb Vertex and Constraints on Extended Higgs Sectors. (1999) arXiv:hep-ph/9909335v1
[17] G.Degrassi and P.Slavich, QCD Corrections in two-Higgs-doublet exten- sions of the Standard Model with Minimal Flavor Violations. (2010) arXiv:1002.1071v2 [hep-ph]
[18] Xiao-Dong Cheng, Ya-Dong Yang and Xing-Bo Yuan, Revisiting Bs→µ+µ− in the two-Higgs doublet models with Z2 symmetry. (2016) arXiv:1511.01829v2 [hep-ph]
[19] Eung Jin Chun, Muon g-2 in two-Higgs-doublet models.(2015)arXiv:1511.05225v1 [hep-ph]
[20] Felix Kling, Jose Miguel No, Shufang Sua, Anatomy of Exotic Higgs Decaysin 2HDM. (2016) arXiv:1604.01406v1 [hep-ph]
[21] Xin-Qiang Li, Jie Lu and Antonio Pich, B0→l+l− Decays in the Aligned Two-Higgs-Doublet Model. (2014) arXiv:1404.5865v2 [hep-ph]
[22] The ATLAS Collaboration, Measurements of the Higgs boson production and decay rates and coupling strengths using pp col lision data at √s = 7 and 8 TeV in the ATLAS experiment. (2016) arXiv:1507.04548v2 [hep-ex]
[23] A. Arhrib, R. Benbrik, Chuan-Hung Chen, Melina Gomez-Bock and Souad Semlali, Two-Higgs-Doublet type-II and-III models and t→ch at the LHC. (2016) arXiv:1508.06490v4
[24] Xin-Qiang Li, Jie Lu and Antonio Pich, B0→ℓ+ℓ− Aligned Two-Higgs-Doublet Model.(2014) arXiv:1404.5865v2 [hep-ph]
[25] C. Patrignani et al.(Particle Data Group), Review of Particle Physics. Chin.Phys. C40 (2016) no.10, 100001