簡易檢索 / 詳目顯示

研究生: 張嘉峰
Chia-Feng Chang
論文名稱: 暗作用力現象學
Light Dark Force Phenomenology
指導教授: 阮自強
Yuan, Tzu-Chiang
張嘉泓
Chang, Chia-Hung
施華強
Sze, Wah-Keunc
學位類別: 碩士
Master
系所名稱: 物理學系
Department of Physics
論文出版年: 2014
畢業學年度: 102
語文別: 英文
論文頁數: 106
中文關鍵詞: 粒子物理現象學量子場論
英文關鍵詞: Quantum Field Theory, particle physics, phenomenology
論文種類: 學術論文
相關次數: 點閱:115下載:28
分享至:
查詢本校圖書館目錄 查詢臺灣博碩士論文知識加值系統 勘誤回報
  • 探討暗作用力U(1)_D 的現象學,包括異常耦合量子場論以及與粒子物理實驗之比較。

    The U(1)D gauge sector containing one dark Higgs boson hD and one dark photon gammaD may be explored through the decays of the 126 GeV particle discovered at the Large Hadron Collider (LHC), assumed here as the heavier mass eigenstate h1 in the mixing of the standard model h with hD. The various decays of h1 to gammaD gammaD, h2 h2, h2 gammaD gammaD and h2 h2 h2 would yield multilepton final states through the mixing of gammaD with the photon and the decay h2 to gammaD gammaD, where h2 is the lighter dark Higgs. Future searches for signals of multilepton jets at the LHC may reveal the existence of this possible dark sector governed simply by the original Abelian Higgs model.

    Non-Standard Model(SM) massive fermions are also introduced to induce the kinetic mixing between the dark U(1)D and the standard model hypercharge U(1)Y at one loop order. We also compute various three point functions induced by the non-SM fermions at one loop for the neutral gauge and Higgs bosons in the external legs. Experimental constraints on the induced mixing parameter and three point vertices are studied in detail and their implications for future experimental search for a dark U(1)D sector are discussed.

    Abstract 2 Acknowledgment 5 I. Introduction 6 II. The Standard Model of Elementary Particles Physics A. The historic motivation of spontaneous symmetry breaking 8 8 B. Gauge Bosons 10 C. Scalar Bosons 10 D. Yukawa Coupling and Fermion Masses 16 III. Higgs Production and Decays at the LHC 20 A. Higgs Production and Decays in Standard Model 21 B. Higgs Production and Decays with LHC result 30 IV. Brief Introduction of Anomaly 33 A. Ward–Takahashi Identities 34 B. Anomaly Cancellation 41 V. Multilepton Higgs Decays through the Dark Portal 44 A. SU (2) L × U (1) Y × U (1) D Model 44 B. Mixing Effects 46 1. Higgs Mass Eigenstates and Their Self Interactions 46 2. Kinetic and Mass Mixing of the neutral gauge bosons 47 C. Non-standard Decays of h 1 49 D. Branching Ratios 52 E. MultiLepton-Jets At LHC 55 F. Conclusions for Multilepton Higgs Decays 60 3VI. Implications of a Dark U (1) D Sector with non-SM Heavy Fermions 62 A. Kinetic Mixing 62 B. Experiment Data 63 1. Fixed Target and Beam Dump Experiments 63 2. ATLAS and CMS Results 64 3. Higgs and Z boson Decay to Invisible 65 C. The Model 66 1. Scalar and Vector Bosons 67 2. Kinetic Mixing and Fermions 68 3. Mass Eigenstate 72 Scalar Mixing 72 Vector Boson Mixing 73 D. Phenomenology 75 1. Standard Higgs h 1 decay modes 75 h 1 → γγ 75 h 1 → ZZ ∗ 77 h 1 → Invisible 79 2. Standard Z boson decay modes 80 Z → γh 2 80 Z → γγ D 83 Z → Invisible 84 E. Discussion 85 F. Conclusions for Dark U (1) D with non-SM Fermions 90 Appendix 92 G. Shift of integration variable for linearly divergent integrals 92 H. One-Loop 3 point function 93 References 100

    [1] P. W. Higgs, Phys. Rev. Lett. 13, 508 (1964); F. Englert and R. Brout, Phys. Rev. Lett.
    13, 321 (1964); G. S. Guralnik, C. R. Hagen and T. W. B. Kibble, Phys. Rev. Lett. 13, 585
    (1964).
    [2] Steven Weinberg, The Quantum Theory of Fields, Vol.I, Cambridge University Press, 1995,
    P.156.
    [3] [zh.wikipedia.org/wiki/File:Mexican hat potential polar with details.svg]]
    [4] [cern.ch or cms.web.cern.ch] and [1012.0530, 1101.0593 and 1201.3084]
    [5] B. Holdom, Phys. Lett. B 166, 196 (1986); Phys. Lett. B 178, 65 (1986).
    [6] M. Cicoli, M. Goodsell, J. Jaeckel and A. Ringwald, arXiv:1103.3705 [hep-th]; M. Goodsell,
    J. Jaeckel, J. Redondo and A. Ringwald, JHEP 0911 (2009) 027 [arXiv:0909.0515 [hep-ph]];
    S. A. Abel, M. D. Goodsell, J. Jaeckel, V. V. Khoze and A. Ringwald, JHEP 0807 (2008) 124
    [arXiv:0803.1449 [hep-ph]]; S. Cassel, D. M. Ghilencea and G. G. Ross, Nucl. Phys. B 827
    (2010) 256 [arXiv:0903.1118 [hep-ph]]; M. E. Krauss, W. Porod and F. Staub, Phys. Rev. D
    88 (2013) 015014 [arXiv:1304.0769 [hep-ph]]; M. Hirsch, W. Porod, L. Reichert and F. Staub,
    Phys. Rev. D 86 (2012) 093018 [arXiv:1206.3516 [hep-ph]]; S. Andreas, M. D. Goodsell and
    A. Ringwald, Phys. Rev. D 87 (2013) 025007 [arXiv:1109.2869 [hep-ph]].
    [7] A. Falkowski, J. T. Ruderman, T. Volansky and J. Zupan, Phys. Rev. Lett. 105, 241801
    (2010) [arXiv:1007.3496 [hep-ph]].
    [8] A. Falkowski, J. T. Ruderman, T. Volansky and J. Zupan, JHEP 1005, 077 (2010)
    [arXiv:1002.2952 [hep-ph]].
    [9] K. Cheung, J. S. Lee and P. -Y. Tseng, JHEP 1305, 134 (2013) [arXiv:1302.3794 [hep-ph]].
    [10] P. P. Giardino, K. Kannike, I. Masina, M. Raidal and A. Strumia, CERN-PH-TH-2013-052
    [arXiv:1303.3570 [hep-ph]].
    [11] J. Ellis and T. You, JHEP 1306, 103 (2013) [arXiv:1303.3879 [hep-ph]].
    [12] G. Belanger, B. Dumont, U. Ellwanger, J. F. Gunion and S. Kraml, LAPTH-032-13,
    LPSC1319, LPT-ORSAY-13-40, UCD-2013-3 [arXiv:1306.2941 [hep-ph]].
    [13] E. C. G. Stueckelberg, Helv. Phys. Acta 11 (1938) 225; V. I. Ogievetskii and I. V. Polubarinov,
    Sov. Phys. JETP 14 (1962) 179.
    [14] S. Chatrchyan et al. [CMS Collaboration], JHEP 1206, 169 (2012) [arXiv:1204.5341 [hep-ex]].
    [15] Searches for Invisible Higgs bosons: Preliminary combined results using LEP data collected
    at energies up to 209 GeV ALEPH Collaboration, DELPHI Collaboration, L3 Collaboration,OPAL Collaboration, the LEP Higgs Working Group, [arXiv:hep-ex/0107032].
    [16] J. Alwall, M. Herquet, F. Maltoni, O. Mattelaer, T. Stelzer, [arXiv:1106.0522v1 [hep-ph]].
    [17] N. D. Christensen, C. Duhr, [arXiv:0806.4194v1 [hep-ph]].
    [18] A.Alloul, B.Fuks, V.Sanz, [arXiv:1310.5150 [hep-ph]]
    [19] F. Maltoni and T. Stelzer, JHEP. 02 (2003) 027.
    [20] J. Pumplin, A Belyaev, J. Huston, D. Stump, and W.K.Tung, JHEP. 02 (2006) 032.
    [21] R. Foot, [arXiv:1401.3965 [astro-ph.CO]]
    [22] S. Weinberg, Phys. Rev. Lett. 19, 1264 (1967).
    [23] Kalliopi Petraki, Lauren Pearce and Alexander Kusenko, [arXiv:1403.1077 [hep-ph]]
    [24] Asher Berlin, Dan Hooper and Samuel D. McDermott, FERMILAB-PUB-14-060-A,
    MCTP-14-07 [arXiv:1404.0022 [hep-ph]]; Kin-Wang Ng, Huitzu Tu, Tzu-Chiang Yuan
    [arXiv:1406.1993v1 [hep-ph]].
    [25] Dan Hooper, Neal Weiner and Wei Xue, Phys.Rev. D86 (2012) 056009 [arXiv:1206.2929
    [hep-ph]]
    [26] R. Essig, et al., [arXiv:1311.0029 [hep-ph]].
    [27] David E. Morrissey and Andrew Paul Spray, [arXiv:1402.4817 [hep-ph]]; Prateek Agrawal,
    Zackaria Chacko and Christopher B. Verhaaren, [arXiv:1402.7369 [hep-ph]].
    [28] Chia-Feng Chang, Ernest Ma and Tzu-Chiang Yuan, JHEP 1403 (2014) 054 [arXiv:1308.6071
    [hep-ph]].
    [29] V. Ar, O. akr, S. Kuday, [arXiv:1403.7960 [hep-ph]]; Bogdan A. Dobrescu and Claudia
    Frugiuele, Phys. Rev. D 89, 035007 (2014) [arXiv:1404.3947 [hep-ph]]; A. Alves, S. Pro-
    fumo and F. S. Queiroz, [arXiv:1312.5281 [hep-ph]]; Ian Anderson, et al., Phys. Rev. D 89,
    035007 (2014) [arXiv:1309.4819]; A. Falkowski, J. T. Ruderman, T. Volansky and J. Zupan,
    Phys. Rev. Lett. 105, 241801 (2010) [arXiv:1007.3496 [hep-ph]]; A. Falkowski, J. T. Ruder-
    man, T. Volansky and J. Zupan, JHEP 1005, 077 (2010) [arXiv:1002.2952 [hep-ph]]; Rouven
    Essig, et al., JHEP11(2013)167 [arXiv:1309.5084].
    [30] Kingman Cheung, Chih-Ting Lu and Tzu-Chiang Yuan, Phys.Rev. D87 (2013) 075001
    [arXiv:1212.1288 [hep-ph]]; Chun-Fu Chang, Kingman Cheung and Tzu-Chiang Yuan, JHEP
    09 (2011) 058 [arXiv:1107.1133 [hep-ph]].
    [31] Michael A. Fedderke,
    Jing-Yuan Chen,
    Edward W. Kolb and Lian-Tao Wang,
    [arXiv:1404.2283 [hep-ph]].
    [32] Ki-Young Choi and Osamu Seto, [arXiv:1305.4322 [hep-ph]].
    [33] S. Gopalakrishna, S. Jung and J. D. Wells, Phys. Rev. D 78, 055002 (2008) [arXiv:0801.3456
    [hep-ph]].
    [34] H. Davoudiasl, H. -S. Lee, I. Lewis and W. J. Marciano, Phys. Rev. D 88, 015022 (2013)
    [arXiv:1304.4935 [hep-ph]], M. Pospelov, Phys. Rev. D 80 (2009) 095002 [arXiv:0811.1030
    [hep-ph]]; H. Davoudiasl, H. -S. Lee and W. J. Marciano, Phys. Rev. D 85, 115019 (2012)
    [arXiv:1203.2947 [hep-ph]]. Pierre Fayet, Phys.Rev.D75:115017,2007 [arXiv:hep-ph/0702176].
    [35] G. Aad et al. [ATLAS Collaboration], Phys. Lett. B 716, 1 (2012) [arXiv:1207.7214 [hep-ex]];
    G. Aad et al. [ATLAS Collaboration], Phys. Lett. B 719, (2012) 299-317 [arXiv:1212.5409
    [hep-ex]]; G. Aad, et al. [ATLAS Collaboration], [arXiv:1302.4403 [hep-ex]]; Georges Aad
    et al. CERN-PH-EP-2014-047 [arXiv:1403.5657 [hep-ex]]; ATLAS-CONF-2013-012, ATLAS-
    CONF-2012-170, ATLAS-CONF-2013-013, ATLAS-CONF-2013-030.
    [36] S. Chatrchyan et al. [CMS Collaboration], Phys. Lett. B 716, 30 (2012) [arXiv:1207.7235
    [hep-ex]]; CMS-PAS-HIG-13-001(γγ), CMS-PAS-HIG-13-002(ZZ ∗ ), CMS-PAS-HIG-13-003,
    CMS-PAS-HIG-13-004, CMS-PAS-HIG-13-005 .
    [37] CMS [Collaboration] CMS-HIG-13-006 Phys. Lett. B 726 (2013) 587 [arXiv:1307.5515v2 [hep-
    ex]].
    [38] G. Abbiendi et al. [OPAL Collaboration], Phys. Lett. B 682, 381 (2010) [arXiv:0707.0373
    [hep-ex]].
    [39] J. P. Lees et al. [BaBar Collaboration], Phys. Rev. Lett. 108, 211801 (2012) [arXiv:1202.1313
    [hep-ex]].
    [40] A. A. Abdo, et al. [Fermi LAT Collaboration], Phys. Rev. Lett. 102, 181101, (2009)
    [arXiv:0905.0025 [astro-ph]].
    [41] O. Adriani, et al. [PAMELA Collaboration] Nature , 458:607-609, 2009, [arXiv:0810.4995
    [astro-ph]].
    [42] S. Schael et al. [ALEPH and DELPHI and L3 and OPAL and SLD and LEP Electroweak
    Working Group and SLD Electroweak Group and SLD Heavy Flavour Group Collaborations],
    Phys. Rept. 427 257 (2006), [arXiv:hep-ex/0412015], and original papers: L3 Collaboration,
    M. Acciarri et al., Phys. Lett. B 412, 201 (1997); L3 Collaboration, O. Adriano et al., Phys.
    Lett. B 297, 469 (1992); OPAL Collaboration, R. Akers et al., Z. Phys.C 65, 47 (1995);
    DELPHI Collaboration, P. Abreu et al., Z. Phys. C 74, 577 (1997).
    [43] M. Reece and L. -T. Wang, JHEP 0907, 051 (2009) [arXiv:0904.1743 [hep-ph]].
    [44] S. Andreas, C. Niebuhr and A. Ringwald, Phys. Rev. D 86, 095019 (2012) [arXiv:1209.6083
    [hep-ph]].
    [45] F. Bossi, arXiv:0904.3815 [hep-ex]; P. -f. Yin, J. Liu and S. -h. Zhu, Phys. Lett. B 679, 362
    (2009) [arXiv:0904.4644 [hep-ph]].
    [46] H. Merkel et al. [A1 Collaboration], Phys. Rev. Lett. 106, 251802 (2011) [arXiv:1101.4091
    [nucl-ex]].
    [47] S. Abrahamyan et al. [APEX Collaboration], Phys. Rev. Lett. 107, 191804 (2011)
    [arXiv:1108.2750 [hep-ex]].
    [48] S. N. Gninenko, Phys. Lett. B 713, 244 (2012) [arXiv:1204.3583 [hep-ph]]; arXiv:1308.6521
    [hep-ph].
    [49] R. Essig, P. Schuster and N. Toro, Phys. Rev. D 80, 015003 (2009) [arXiv:0903.3941 [hep-
    ph]]; B. Batell, M. Pospelov and A. Ritz, Phys. Rev. D 79, 115008 (2009) [arXiv:0903.0363
    [hep-ph]];
    [50] Hooman Davoudiasl, Ian M. Lewis, Phys. Rev. D89 (2014) 055026 [arXiv:1309.6640 [hep-ph]].
    [51] D. Babusci et al. [KLOE-2 Collaboration], Phys. Lett. B 720, 111 (2013) [arXiv:1210.3927
    [hep-ex]].
    [52] J. D. Bjorken, R. Essig, P. Schuster and N. Toro, Phys. Rev. D 80, 075018 (2009)
    [arXiv:0906.0580 [hep-ph]].
    [53] M. Freytsis, G. Ovanesyan and J. Thaler, JHEP 1001 (2010) 111 [arXiv:0909.2862 [hep-ph]].
    [54] The Heavy Photon Search Collaboration (HPS), https://confluence.slac.stanford.edu/display/hpsg/
    [55] B. Wojtsekhowski, AIP Conf. Proc. 1160 (2009) 149 [arXiv:0906.5265 [hep-ex]]; B. Wojt-
    sekhowski, D. Nikolenko and I. Rachek, [arXiv:1207.5089 [hep-ex]].
    [56] A. Denner et al., Eur.Phys.J. C72, 1992 (2012), arXiv.1111.6395; M. S. Chanowitz, M. Fur-
    man and I. Hinchliffe, Phys.Lett. B78, 285 (1978); ibid, Nucl.Phys. B153, 402 (1979).
    [57] Adel
    Bilal,
    Lectures
    on
    Anomalies
    [arXiv:0802.0634];
    P.Anastasopoulos
    et
    al.
    Phys.Rev.D78:085014,2008 [arXiv:0804.1156].
    [58] C. -W. Chiang and K. Yagyu, JHEP 1307, 160 (2013).
    [59] E. Dudas, L. Heurtier, Y. Mambrini, B. Zaldivar, [arXiv:1307.0005 [hep-ph]]; G. Arcadi,
    Y. Mambrini, M. H.G. Tytgat and B. Zaldivar, [arXiv:1401.0221 [hep-ph]].
    [60] P. P. Giardino, K. Kannike, I. Masina, M. Raidal and A. Strumia, CERN-PH-TH-2013-052
    [arXiv:1303.3570 [hep-ph]]; J. Ellis and T. You, JHEP 1306, 103 (2013) [arXiv:1303.3879
    [hep-ph]]; G. Belanger, B. Dumont, U. Ellwanger, J. F. Gunion and S. Kraml, LAPTH-
    032-13, LPSC1319, LPT-ORSAY-13-40, UCD-2013-3 [arXiv:1306.2941 [hep-ph]]; K. Cheung,
    J. S. Lee and P. -Y. Tseng, JHEP 1305, 134 (2013) [arXiv:1302.3794 [hep-ph]].
    [61] J. Beringer et al., (Particle Data Group) Phys. Rev. D86, 010001 (2012)
    [62] V.A.Novikov, L.B.Okun, A.N.Rozanov and M.I.Vysotsky, Rept.Prog.Phys. 62 (1999) 1275-
    1332 [hep-ph/9906465].
    [63] Sarah Andreas, Mark D. Goodsell and Andreas Ringwald, AIP Conf. Proc. 1563, 114 (2013)
    [arXiv:1306.1168 [hep-ph]].
    [64] Kingman Cheung, Kuo-Hsing Tsao and Tzu-Chiang Yuan, [arXiv:1107.1133 [hep-ph]].
    [65] Timothy Cohen, Daniel J. Phalen, Aaron Pierce and Kathryn M. Zurek, [arXiv:1005.1655
    [hep-ph]].
    [66] David J. Gross and R. Jackiw Phys. Rev. D 6, 477 (1972)
    [67] Jackiw, R. (1972). In Lectures on current algebra and it’s applications. Princeton University
    Press, Princeton, New Jersey.
    [68] S. Cassel, D. M. Ghilencea and G. G. Ross, Nucl. Phys. B827:256-280, 2010 [arXiv:0903.1118
    [hep-ph]]; Matthew J. Strassler and Kathryn M. Zurek Phys. Lett. B661:263-267, 2008
    [arXiv:hep-ph/0605193]; Matthew J. Strassler and Kathryn M. Zurek Phys. Lett. B651:374-
    379, 2007 [arXiv:hep-ph/0604261].
    [69] Kingman Cheung and Tzu-Chiang Yuan, JHEP 0703 (2007) 120 [hep-ph/0701107].
    [70] Jackson D. Clarke, Robert Foot and Raymond R. Volkas, [arXiv:1310.8042 [astro-ph]].
    [71] P. Q. Hung Phys. Lett. B649 (2007) 275-279 [hep-ph/0612004] and Phys.Lett.B659:585-
    592,2008 [arXiv:0711.0733 [hep-ph]]. H. Georgi, M. Machacek, Nuclear Physics B262 (1985
    463-477)
    [72] J. D. Bjorken, R. Essig, P. Schuster and N. Toro, Phys. Rev. D 80, 075018 (2009)
    [arXiv:0906.0580 [hep-ph]]; J. B. Dent, F. Ferrer and L. M. Krauss, [arXiv:1201.2683 [astro-
    ph.CO]]. H. K. Dreiner, J.-F. Fortin, C. Hanhart and L. Ubaldi, [arXiv:1310.3826 [hep-ph]].
    [73] Yue Zhang, [arXiv:1404.7172 [hep-ph]]
    [74] F. del Aguila and J. A. Aguilar-Saavedra, Phys. Lett. B672:158-165, 2009 [arXiv:0809.2096].
    [75] Pavel Fileviez Perez, Tao Han and Tong Li, Phys. Rev. D80:073015, 2009 [arXiv:0907.4186].
    [76] D. Feldman, Z. Liu and P. Nath, Phys. Rev D. 75, 115001 [arXiv:0702123v1 [hep-ph]]; Daniel
    Feldman, Pavel Fileviez Perez and Pran Nath, JHEP 1201 (2012) 038 [arXiv:1109.2901 [hep-
    ph]].
    [77] T. Hahn, Generating Feynman diagrams and amplitudes with FeynArts 3, Comput. Phys.
    Commun. 140, 418 (2001) [hep-ph/0012260].
    [78] Jorge C. Romao, Advanced Quantum Field Theory; Jorge C. Romao, S. D. Rindani and
    J. W. F. Valle, Nucl.Phys.B493:56-72,1997 [hep-ph/9612277]; G. Tavares-Velasco and J. J.
    Toscano, J. Phys. G30 (2004) 1299 [hep-ph/0405008]; M. A. Perez, G. Tavares-Velasco and J.
    J. Toscano, Phys. Rev. D69:115004 (2004) [hep-ph/0402156]; Athanasios Dedes and Kristaq
    Suxho, Phys. Rev D.85.095024 [arXiv:1202.4940].
    [79] Jorge C. Romao and Sofia Andringa, Eur. Phys. J. C7:631-642, (1999) [hep-ph/9807536].
    [80] Ettore Remiddi and Lorenzo Tancredi, [arXiv:1311.3342v2]; M. Dubois-Violette and P.W. Mi-
    chor, Indagationes, Math. N. S., 6 (1995), 51–66 [alg-geom/9401006].
    [81] SCHOONSCHIP is a program, made by M. Veltman. See H. Strubbe, Comput. Phys. Com-
    mun.8(1974)1.
    [82] Wai-Yee Keung, Ian Low and Jing Shu, Phys. Rev. Lett.101:091802 (2008) [arXiv:0806.2864
    [hep-ph]]; L. D. Landau, Dokl. Akad. Nawk., USSR 60, 207 (1948); C. N. Yang, Phys. Rev.
    77, 242 (1950).
    [83] Parton distributions for high-energy collisions,M. Gluck, E. Reya, A. Vogt,Z.Phys. C53 (1992)
    127-134.
    [84] [http://durpdg.dur.ac.uk/hepdata/pdf.html]
    [85] Ranjan Laha, Basudeb Dasgupta, John F. Beacom Phys. Rev. D 89, 093025 (2014)
    [arXiv:1304.3460 [hep-ph]]; .
    [86] S. Weinberg, ”The quantum theory of fields. Vol. 2: Modern applications,” Cambridge, UK:
    Univ. Pr. (1996) 489p.
    [87] John F. Gunion, Howard Haber, Gordon Kane, Sally Dawson, Howard E. Haber, The Higgs
    Hunters Guide, ISBN-13: 978-0738203058, ISBN-10: 073820305X P.30
    [88] Abdelhak Djouadi Phys.Rept. 457 (2008) 1-216, [hep-ph/0503172].
    [89] A. Djouadi, V. Driesen, W. Hollik, A. Kraft, Eur.Phys.J.C1:163-175,1998, [arXiv:hep-
    ph/9701342].
    [90] Kingman
    Cheung,
    Thomas
    W.
    Kephart,
    Wai-Yee
    Keung,
    Tzu-Chiang
    Yuan,
    Phys.Lett.B662:436-440,2008, [arXiv:0801.1762 [hep-ph]]. D. Chang, Wai-Yee Keung,
    S.C. Lee, Phys.Rev. D38 (1988) 850-853.
    [91] G. Passarino and M. Veltman, Nucl. Phys. B160 (1979) 151.
    [92] Rouven Essig, Philip Schuster, Natalia Toro, Phys.Rev. D80 (2009) 015003 [arXiv:0903.3941
    [hep-ph]].
    [93] S.N. Gninenko Phys.Rev. D87 (2013) 035030, [arXiv:1301.7555 [hep-ph]] and Phys. Lett. B
    713 (2012) 244-248, [arXiv:1204.3583 [hep-ph]]
    [94] S.N. Gninenko Phys.Rev. D85 (2012) 055027, [arXiv:1112.5438v3 [hep-ph]]
    [95] C. Amsler et al., Phys. Lett. B 333 (1994) 271. C. Amsler et al., Z. Phys. C 70 (1996) 219.
    [96] B. Batell, M. Pospelov, and A. Ritz, Phys. Rev. D 80, 095024 (2009).
    [97] Javier Rasero Daparte, Jos ́e Juan Fern ́andez Melgarejo Lecture note January 16, 2009; Dr.
    Vadim Kaplunovsky’s Lecture Notes; Bertlmann R. A., Anomalies in Quantum Field Theory;
    Bardeen W. A., Gauge Anomalies, Gravitational Anomalies and Superstrings, Tokyo INS
    Sympos.1985:336
    [98] Peskin M. E., Schroeder D. V., An introduction to Quantum Field Theory
    [99] Ta-Pei Cheng, Ling-Fong Li Gauge Theory of elementary particle physics (1988) ISBN-13:
    978-0198519614
    [100] Gianfranco Bertone, Dan Hooper and Joseph Silk, Particle dark matter: Evidence, candidates
    and constraints Phys. Rept. 405 (2005) 279-390 [arXiv:hep-ph/0404175]; Raul Horvatet al.,
    [arXiv:1109.3085]; Ernest Ma, Ivica Picek and Branimir Radovcic, Phys. Lett. B726 (2013)
    744-746 [arXiv:1308.5313 [hep-ph]]; Ernest Ma, [arXiv:1311.3213 [hep-ph]].
    [101] S. Adler (1969). ”Axial-Vector Vertex in Spinor Electrodynamics”. Physical Review 177 (5):
    2426. doi:10.1103/PhysRev.177.2426. J.S. Bell and R. Jackiw (1969). ”A PCAC puzzle: π 0 →
    γγ in the σ-model”. Il Nuovo Cimento A 60: 47
    [102] K. Fujikawa and H. Suzuki (May 2004). Path Integrals and Quantum Anomalies. Clarendon
    Press. ISBN 0-19-852913-9.

    下載圖示
    QR CODE