標準模型在二十世紀是一個發展完備的模型，透過許多實驗的測試，標準模型都能準確的預測夸克家族成員的存在。但是在二十一世紀有許多超越標準模型的現象學紛紛開始出現，例如微中子質量不為零、暗物質的存在、物質反物質的不對稱等等。這些現象學很直接地告訴物理學家，標準模型有其有效性，其有效性會在某個能量尺度底下試用。至今，我們依然不知道標準模型的有效能量尺度為何。這也就延伸成一個”階層問題”。於是，我們針對”階層問題”去提出假設，假設在兆電子伏特的能量尺度以上會出現新物理，而此新物理的能量尺度可以延緩階層問題存在的嚴重性。
我們使用”最小組合希格斯場模型”當”超越標準模型”的基礎理論，從中選取頂夸克與Z波色子的單一生成頻道去做模擬分析，找尋”頂夥伴”。在我們的分析之中，大強子對撞機的中心能量為14兆電子伏特，積分光度為300飛靶分之一。最後，我們給出來自超越標準模型與標準模型經過分析後剩餘的訊號作為結論。

We all know the Standard Model cannot describe all phenomena emerging from modern experiments. Apparently, it must exists a Beyond Standard Model which can satisfy some or all phenomena. In the beginning, we at- tempt to solve the Hierarchy problem which has disturbed at the physicist so far. In brief, that means we are able to find one new particle at least on TeV energy scale at the Large Hadron Collider (LHC).
Following the Minimal Composite Higgs Model (MCHM), it bases on a large symmetry SO(5)/SO(4) in strong dynamic sector above electroweak scale v. Therefore, it predicts heavy fermionic quarks (top partners) at the TeV energy order. We apply several analysis tools, such as Feynrule, Mad- graph 5, and MadAnalysis 5, doing simulations for those extra fermionic quarks at 14 TeV and luminosity equals to 300fb−1.
For illumination, we use ”Singlet T Model”, which only remains a charge 2/3 top partner mixing with Standard Model by Yukawa interaction. Fur- thermore, we employ a model independent framework, which can apply in any models with extra vector-like quarks, as simplified model approach. For instance, you can use the model independent framework in Little Higgs Model (LHM) with T parity. As we know that the Singlet T Model is the most simplest case in MHCM. However, There are still a number of ways to assign the representation and the interaction between the different charge of vector-like quarks. It is totally beyond this work and others group have done a few researches. As a result, we will represent the probability to discover the new state in T → tZ channel.

[1] Georges Aad, T Abajyan, B Abbott, J Abdallah, S Abdel Khalek, AA Abdelalim, O Abdinov, R Aben, B Abi, M Abolins, et al. Ob- servation of a new particle in the search for the standard model higgs boson with the atlas detector at the lhc. Physics Letters B, 716(1):1–29, 2012.
[2] CMS collaboration et al. Measurement of the differential cross section for isolated prompt photon production in pp collisions at 7 tev. arXiv preprint arXiv:1108.2044, 2011.
[3] Nima Arkani-Hamed, Andrew G Cohen, Emanuel Katz, and Ann E Nelson. The littlest higgs. Journal of High Energy Physics, 2002(07):034, 2002.
[4] Martin Schmaltz and David Tucker-Smith. Little higgs review. arXiv preprint hep-ph/0502182, 2005.
[5] Ignatios Antoniadis, Karim Benakli, and Mariano Quir ́os. Finite higgs mass without supersymmetry. New Journal of Physics, 3(1):20, 2001.

[6] Susumu Fujita. Modular invariance of bosonic string on orbifolds. arXiv
preprint hep-th/0410193, 2004.
[7] Kaustubh Agashe, Roberto Contino, and Alex Pomarol. The minimal
composite higgs model. Nuclear Physics B, 719(1):165–187, 2005.
[8] Shinya Matsuzaki and Koichi Yamawaki. Is 125 gev techni-dilaton found
at lhc? Physics Letters B, 719(4):378–382, 2013.
[9] Roshan Foadi, Mads T Frandsen, and Francesco Sannino. 125 gev higgs boson from a not so light technicolor scalar. Physical Review D, 87(9):095001, 2013.
[10] Jihn E Kim and Hans Peter Nilles. The μ-problem and the strong cp- problem. Physics Letters B, 138(1):150–154, 1984.
[11] Roberto Contino, Leandro Da Rold, and Alex Pomarol. Light custodians in natural composite higgs models. Physical Review D, 75(5):055014, 2007.
[12] Oleksii Matsedonskyi, Giuliano Panico, and Andrea Wulzer. Light top partners for a light composite higgs. Journal of High Energy Physics, 2013(1):1–40, 2013.
[13] Gu ̈nther Dissertori, Elisabetta Furlan, Filip Moortgat, and Pascal Nef. Discovery potential of top-partners in a realistic composite higgs model with early lhc data. Journal of High Energy Physics, 2010(9):1–29, 2010.
[14] Otto Eberhardt, Geoffrey Herbert, Heiko Lacker, Alexander Lenz, An- dreas Menzel, Ulrich Nierste, and Martin Wiebusch. Impact of a higgs
boson at a mass of 126 gev on the standard model with three and four
fermion generations. Physical review letters, 109(24):241802, 2012.
[15] Nicolas Bonne and Gregory Moreau. Reproducing the higgs boson data
with vector-like quarks. Physics Letters B, 717(4):409–419, 2012.
[16] G Moreau. Constraining extra fermion (s) from the higgs boson data.
Physical Review D, 87(1):015027, 2013.
[17] Roberto Contino, Margherita Ghezzi, Mauro Moretti, Giuliano Panico, Fulvio Piccinini, and Andrea Wulzer. Anomalous couplings in double higgs production. Journal of High Energy Physics, 2012(8):1–21, 2012.
[18] Juan Antonio Aguilar-Saavedra. Light higgs boson discovery from fermion mixing. Journal of High Energy Physics, 2006(12):033, 2006.
[19] A Azatov, O Bondu, A Falkowski, M Felcini, S Gascon-Shotkin, DK Ghosh, G Moreau, AY Rodriguez-Marrero, and S Sekmen. Higgs bo- son production via vectorlike top-partner decays: Diphoton or multilep- ton plus multijets channels at the lhc. Physical Review D, 85(11):115022, 2012.
[20] Adrian Carmona, Mikael Chala, and Jose Santiago. New higgs pro- duction mechanism in composite higgs models. Journal of High Energy Physics, 2012(7):1–27, 2012.
[21] Keisuke Harigaya, Shigeki Matsumoto, Mihoko M Nojiri, and Kohsaku Tobioka. Search for the top partner at the lhc using multi-b-jet channels. Physical Review D, 86(1):015005, 2012.
[22] Chien-Yi Chen, S Dawson, and IM Lewis. Top partners and higgs boson
production. Physical Review D, 90(3):035016, 2014.
[23] Kingman Cheung, Jae Sik Lee, and Po-Yan Tseng. Higgs precision (higgcision) era begins. Journal of High Energy Physics, 2013(5):1–37, 2013.
[24] Kingman Cheung, Jae Sik Lee, and Po-Yan Tseng. Higgcision updates 2014. arXiv preprint arXiv:1407.8236, 2014.
[25] Giacomo Cacciapaglia, Aldo Deandrea, Naveen Gaur, Daisuke Harada, Yasuhiro Okada, and Luca Panizzi. Interplay of vector-like top partner multiplets in a realistic mixing set-up. arXiv preprint arXiv:1502.00370, 2015.
[26] Ju ̈rgen Reuter and Marco Tonini. Top partner discovery in the t tz channel at the lhc. Journal of High Energy Physics, 2015(1):1–27, 2014.
[27] Mihailo Backovi ́c, Thomas Flacke, Seung J Lee, and Gilad Perez. Lhc top partner searches beyond the 2 tev mass region. arXiv preprint arXiv:1409.0409, 2014.
[28] JA Aguilar-Saavedra. Pair production of heavy q= 2/3 singlets at lhc. Physics Letters B, 625(3):234–244, 2005.
[29] Juan Antonio Aguilar-Saavedra. Identifying top partners at lhc. Journal of High Energy Physics, 2009(11):030, 2009.
[30] Joshua Berger, Jay Hubisz, and Maxim Perelstein. A fermionic top part- ner: naturalness and the lhc. Journal of High Energy Physics, 2012(7):1– 27, 2012.
[31] G Cynolter and E Lendvai. Electroweak precision constraints on vector- like fermions. The European Physical Journal C, 58(3):463–469, 2008.
[32] Francisco del Aguila, Jos ́e Santiago, and Manolo P ́erez-Victoria. Ob- servable contributions of new exotic quarks to quark mixing. Journal of High Energy Physics, 2000(09):011, 2000.
[33] L Lavoura and Joao P Silva. Oblique corrections from vectorlike singlet and doublet quarks. Physical Review D, 47(5):2046, 1993.
[34] Yasuhiro Okada and Luca Panizzi. Lhc signatures of vector-like quarks. Advances in High Energy Physics, 2013, 2013.
[35] Gino Isidori, Yosef Nir, and Gilad Perez. Flavor physics constraints for physics beyond the standard model. arXiv preprint arXiv:1002.0900, 2010.
[36] Aldo Deandrea. Atomic parity violation in cesium and implications for new physics. Physics Letters B, 409(1):277–282, 1997.
[37] Aleph Collaboration, Delphi Collaboration, L3 Collaboration, Opal Col- laboration, SLD collaboration, LEP Electroweak Working Group, et al. Precision electroweak measurements on the z resonance. arXiv preprint hep-ex/0509008, 2005.
[38] CMS collaboration. Cms b2g twiki page.
[39] ATLAS Collaboration. Atlas exotics twiki page.
[40] Mathieu Buchkremer, Giacomo Cacciapaglia, Aldo Deandrea, and Luca Panizzi. Model Independent Framework for Searches of Top Partners. Nucl.Phys., B876:376–417, 2013.
[41] C ́edric Delaunay, Thomas Flacke, J Gonzalez-Fraile, Seung J Lee, Giu- liano Panico, and Gilad Perez. Light non-degenerate composite partners at the lhc. Journal of High Energy Physics, 2014(2):1–57, 2014.
[42] Andrea De Simone, Oleksii Matsedonskyi, Riccardo Rattazzi, and An- drea Wulzer. A first top partner hunter’s guide. Journal of High Energy Physics, 2013(4):1–50, 2013.
[43] Sidney Coleman, J Wess, and Bruno Zumino. Structure of phenomeno- logical lagrangians. i. Physical Review, 177(5):2239, 1969.
[44] Curtis G Callan Jr, Sidney Coleman, J Wess, and Bruno Zumino. Struc- ture of phenomenological lagrangians. ii. Physical Review, 177(5):2247, 1969.
[45] Marc Gillioz, R Gro ̈ber, Andreas Kapuvari, and M Mu ̈hlleitner. Vector- like bottom quarks in composite higgs models. Journal of High Energy Physics, 2014(3):1–46, 2014.
[46] Mathieu Buchkremer, Giacomo Cacciapaglia, Aldo Deandrea, and Luca Panizzi. Model-independent framework for searches of top partners. Nuclear Physics B, 876(2):376–417, 2013.
[47] Neil D. Christensen and Claude Duhr. FeynRules - Feynman rules made
easy. Comput.Phys.Commun., 180:1614–1641, 2009.
[48] Neil D. Christensen, Claude Duhr, Benjamin Fuks, Jurgen Reuter, and Christian Speckner. Introducing an interface between WHIZARD and FeynRules. Eur.Phys.J., C72:1990, 2012.
[49] Celine Degrande, Claude Duhr, Benjamin Fuks, David Grellscheid, Olivier Mattelaer, et al. UFO - The Universal FeynRules Output. Com- put.Phys.Commun., 183:1201–1214, 2012.
[50] Adam Alloul, Neil D. Christensen, C ́eline Degrande, Claude Duhr, and Benjamin Fuks. FeynRules 2.0 - A complete toolbox for tree-level phe- nomenology. Comput.Phys.Commun., 185:2250–2300, 2014.
[51] Johan Alwall, Michel Herquet, Fabio Maltoni, Olivier Mattelaer, and Tim Stelzer. Madgraph 5: going beyond. Journal of High Energy Physics, 2011(6):1–40, 2011.
[52] Eric Conte, Benjamin Fuks, and Guillaume Serret. MadAnalysis 5, A User-Friendly Framework for Collider Phenomenology. Com- put.Phys.Commun., 184:222–256, 2013.
[53] Jung Chang, Kingman Cheung, Jae Sik Lee, and Chih-Ting Lu. Probing the Top-Yukawa Coupling in Associated Higgs production with a Single Top Quark. JHEP, 1405:062, 2014.
[54] Serguei Chatrchyan et al. Performance of tau-lepton reconstruction and identification in CMS. JINST, 7:P01001, 2012.
[55] Serguei Chatrchyan et al. Identification of b-quark jets with the CMS
experiment. JINST, 8:P04013, 2013.
[56] Serguei Chatrchyan et al. Evidence for the 125 GeV Higgs boson decay-
ing to a pair of τ leptons. JHEP, 1405:104, 2014.
[57] ATLAS Collaboration et al. Expected photon performance in the atlas experiment, apr, 2011. Technical report, ATL-PHYS-PUB-2011-007.