臺灣博碩士論文加值系統

微中子的電磁特性或各類暗物質（例：惰性微中子）造成探測器原子電離的過程對於目前很多使用純原子構成的探測器的直接探測實驗來說相當重要。尤其目前的微中子與暗物質的實驗已經將探測器偵測的能量範圍降低到千電子伏特以下，使用精確的原子多體方法才足以提供可靠的原子電離計算來和實驗對照。在有光游離數據和可解析的氫原子計算驗證的前提下，我們使用第一原理多體理論在5~10%的精確度內來表現原子多體效應如何影響微中子與暗物質對於鍺元素或氙元素中的電子的散射截面。本論文的主要目標是用第一原理多體理論來研究：(1) 微中子的電磁特性，(2) 暗物質基於有效場論的交互作用強度，(3) 太陽微中子在噸級液態氙探測器中造成的低能量電子反衝，它不僅是直接探測弱作用大質量粒子實驗中的一種不可約化的重要背景，也可以在標準太陽模型預測的精度水平下用來量測太陽微中子的通量。

The processes of atomic ionization of detectors by scattering with neutrinos in a search of their electromagnetic properties and with light dark matter candidates (e.g. sterile neutrino) are interested for many experimental groups, because those studies on neutrinos and dark matters rely on the direct detection with detectors composed by pure atom or crystal. As current experimental searches for neutrinos and dark matters have lowered the detector threshold down to the sub-keV regime, accurate many-body calculations for atomic ionization are warranted for giving reliable results of experimental comparisons. With the benchmark of photoionization and analytic hydrogen calculations, we perform ab initio many-body methods to show how atomic effects modify the cross sections of neutrino or dark matter scattering with electrons in Ge, Xe and other targets within 5~10% accuracy. The main goal is applying these methods to study (1) neutrino electromagnetic properties, (2) dark matter interactions within effective field theory framework, and (3) low-energy electronic recoil caused by solar neutrinos in multi-ton xenon detectors, which is an important subject not only because it is a source of the irreducible background for direct searches of weakly interacting massive particles (WIMPs), but also because it provides a viable way to measure the solar pp and 7Be neutrinos at the precision level of current standard solar model predictions.

1 Introduction 1
2 Formulation of Neutrinos and Dark Matter Direct Detection 5
2.1 Neutrinos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.2 Dark Matters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.3 Sterile Neutrinos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3 Analytic Hydrogen Studies of Atomic Response and Approximations for Atomic Ionization 24
3.1 Toy Model - Hydrogen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.2 Some Approximations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.2.1 Free electron approximation . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.2.2 Equivalent photon approximation . . . . . . . . . . . . . . . . . . . . . . 28
3.2.3 Longitudinal photon approximation . . . . . . . . . . . . . . . . . . . . . 29
4 Ab initio Many-Body Methods for Atomic Transition 31
4.1 The MCRRPA Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
4.2 From MCRRPA to Scattering Amplitudes . . . . . . . . . . . . . . . . . . . . . . 37
4.3 Atomic Structure of Detectors by MCDF . . . . . . . . . . . . . . . . . . . . . . . 39
4.4 Photoabsorption of Ge and Xe by MCRRPA . . . . . . . . . . . . . . . . . . . . . 43
5 Results and Discussions 47
5.1 Constraints on Neutrino Electromagnetic Properties . . . . . . . . . . . . . . . . . 47
5.2 Electronic and Nuclear Contributions in Sub-GeV Dark Matter Scattering . . . . . 49
5.2.1 Leading-Order Interactions of c1, d1, c4, and d4 . . . . . . . . . . . . . . . 49
5.2.2 Next-to-Leading-Order Interactions of c11, d11, c10, and d10 . . . . . . . . . 54
5.3 Direct Constraints on Dark Matter Sterile Neutrinos . . . . . . . . . . . . . . . . . 56
5.3.1 Hydrogen case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
5.3.2 Germanium case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
5.4 Solar Neutrino Backgrounds in Liguid-Xe Detectors . . . . . . . . . . . . . . . . 67
6 Conclusions and Future Works 73
6.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
6.2 Future works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
Bibliography 76

[1] C. Giunti and A. Studenikin, arXiv:1403.6344; C. Broggini, C. Giunti, and A. Studenikin, Adv. High Energy Phys. 2012, 459526 (2012); H. T. Wong and H. B. Li, Mod. Phys. Lett. A 20, 1103 (2005).
[2] A. Tan et al. (PandaX-II), Phys. Rev. Lett. 117, 121303 (2016), arXiv:1607.07400 [hep-ex].
[3] D. S. Akerib et al., (2016), arXiv:1608.07648 [astro-ph.CO].
[4] R. Essig, J. A. Jaros, W. Wester, P. H. Adrian, S. Andreas et al., arXiv:1311.0029.
[5] J. L. Feng and J. Kumar, Phys. Rev. Lett. 101, 231301 (2008).
[6] J. L. Feng, M. Kaplinghat, H. Tu, and H.-B. Yu, J. Cosmol. Astropart. Phys. 07 (2009) 004.
[7] C. Boehm and P. Fayet, Nucl. Phys. B 683, 219 (2004).
[8] C. Boehm, P. Fayet, and J. Silk, Phys. Rev. D 69, 101302 (2004).
[9] N. Borodatchenkova, D. Choudhury, and M. Drees, Phys. Rev. Lett. 96, 141802 (2006).
[10] M. Pospelov, A. Ritz, and M. B. Voloshin, Phys. Lett. B 662, 53 (2008).
[11] P. Fayet, Phys. Rev. D 75, 115017 (2007). 76
[12] D. Hooper and K. M. Zurek, Phys. Rev. D 77, 087302 (2008).
[13] M. Pospelov, A. Ritz, and M. B. Voloshin, Phys. Rev. D 78, 115012 (2008).
[14] K. Rajagopal, M. S. Turner, and F. Wilczek, Nucl. Phys. B 358, 447 (1991).
[15] L. Covi, J. E. Kim, and L. Roszkowski, Phys. Rev. Lett. 82, 4180 (1999).
[16] K.-Y. Choi, L. Covi, J. E. Kim, and L. Roszkowski, J. High Energy Phys. 04 (2012) 106.
[17] S. Dodelson and L. M. Widrow, Phys. Rev. Lett. 72, 17 (1994).
[18] X.-D. Shi and G. M. Fuller, Phys. Rev. Lett. 82, 2832 (1999).
[19] A. D. Dolgov and S. H. Hansen, Astropart. Phys. 16, 339 (2002).
[20] A. Boyarsky, J. Lesgourgues, O. Ruchayskiy, and M. Viel, Phys. Rev. Lett. 102, 201304 (2009).
[21] K. N. Abazajian, Phys. Rev. Lett. 112, 161303 (2014).
[22] K. Abazajian, G. M. Fuller, and W. H. Tucker, Astrophys. J. 562, 593 (2001).
[23] A. Boyarsky, A. Neronov, O. Ruchayskiy, M. Shaposhnikov, and I. Tkachev, Phys. Rev. Lett. 97, 261302 (2006).
[24] E. Bulbul, M. Markevitch, A. Foster, R. K. Smith, M. Loewenstein and S.W. Randall, Astrophys. J. 789, 13 (2014).
[25] A. Boyarsky, O. Ruchayskiy, D. Iakubovskyi, and J. Franse, Phys. Rev. Lett. 113, 251301 (2014).
[26] R. Essig, J. Mardon, and T. Volansky, Phys. Rev. D 85, 076007 (2012).
[27] R. Essig, A. Manalaysay, J. Mardon, P. Sorensen, and T. Volansky, Phys. Rev. Lett. 109, 021301 (2012).
[28] H. An, M. Pospelov, J. Pradler, and A. Ritz, Phys. Lett. B 747, 331 (2015).
[29] K.-N. Huang and W. R. Johnson, Phys. Rev. A 25, 634 (1982).
[30] J. P. Desclaux, Comput. Phys. Commun. 9, 31 (1975).
[31] J.-W. Chen, H.-C. Chi, K.-N. Huang, C.-P. Liu, H.-T. Shiao, L. Singh, H. T.Wong, C.-L.Wu, and C.-P.Wu, Phys. Lett. B 731, 159 (2014).
[32] J.-W. Chen, H.-C. Chi, H.-B. Li, C.-P. Liu, L. Singh, H. T. Wong, C.-L.Wu, and C.-P.Wu, Phys. Rev. D 90, 011301(R) (2014).
[33] J.-W. Chen, H.-C. Chi, K.-N. Huang, H.-B. Li, C.-P. Liu, L. Singh, H. T. Wong, C.-L. Wu,
and C.-P. Wu, Phys. Rev. D 91, 013005 (2015).
[34] J.-W. Chen, H.-C. Chi, C.-P. Liu, C.-L. Wu, and C.-P. Wu, Phys. Rev. D 92, 096013 (2015).
[35] J.-W. Chen, H.-C. Chi, S.-T. Lin, C.-P. Liu, L. Singh, H. T. Wong, C.-L. Wu, and C.-P. Wu, Phys. Rev. D 93, 093012 (2016).
[36] J.-W. Chen, H.-C. Chi, C.-P. Liu, and C.-P. Wu, arXiv:1610.04177.
[37] W. Marciano, A. Sanda, Phys. Lett. B 67, 303 (1977).
[38] B. W. Lee, R. E. Shrock, Phys. Rev. D 16, 1444 (1977).
[39] K. Fujikawa, R. Shrock, Phys. Rev. Lett. 45, 963 (1980).
[40] M. Fukugita, T. Yanagida, Physics of Neutrinos, Springer, Berlin, 2003.
[41] N. F. Bell, V. Cirigliano, M. J. Ramsey-Musolf, P. Vogel, M. B. Wise, Phys. Rev. Lett. 95, 151802 (2005).
[42] N. F. Bell, M. Gorchtein, M. J. Ramsey-Musolf, P. Vogel, P. Wang, Phys. Lett. B 642, 377 (2006).
[43] G. C. Joshi, H. Lew, and R. R. Volkas, Mod. Phys. Lett. A 05, 2721 (1990); R. Foot, H. Lew, and R. R. Volkas, J. Phys. G 19, 361 (1993).
[44] K. S. Babu and R. N. Mohapatra, Phys. Rev. Lett. 63, 938 (1989); Phys. Rev. D 41, 271 (1990).
[45] B. Holdom, Phys. Lett. B 166, 196 (1986); R. Foot, H. Lew, and R. R. Volkas, Phys. Lett. B 272, 67 (1991); I. Antoniadis and K. Benakli, Phys. Lett. B 295, 219 (1992); A. Yu. Ignatiev
and G. C. Joshi, Phys. Lett. B 381, 216 (1996).
[46] J. Fan, M. Reece, and L.-T. Wang, J. Cosmol. Astropart. Phys. 11 (2010) 042.
[47] A. L. Fitzpatrick, W. Haxton, E. Katz, N. Lubbers, and Y. Xu, J. Cosmol. Astropart. Phys. 02 (2013) 004.
[48] J.-W. Chen, C.-P. Liu, C.-F. Liu, and C.-L.Wu, Phys. Rev. D 88, 033006 (2013).
[49] P. B. Pal and L. Wolfenstein, Phys. Rev. D 25, 766 (1982).
[50] A. Nordsieck, Phys. Rev. 93, 785 (1954).
[51] A. R. Holt, J. Phys. B 2, 1209 (1969).
[52] D. Belki, J. Phys. B 14, 1907 (1981).
[53] M. S. Gravielle and J. E. Miraglia, Comput. Phys. Commun. 69, 53 (1992).
[54] J. Frenkel, Wave Mechanics (Clarendon, Oxford, 1934).
[55] P. Langho , S. Epstein, and M. Karplus, Rev. Mod. Phys. 44, 602 (1972).
[56] W. R. Johnson and K.-N. Huang, Phys. Rev. Lett. 48, 315 (1982).
[57] B. L. Henke, E. M. Gullikson, and J. C. Davis, Atom. Data Nucl. Data Tables 54, 181 (1993).
[58] J. Samson and W. Stolte, J. Electron Spectrosc. Relat. Phenom. 123, 265 (2002).
[59] I. H. Suzuki and N. Saito, J. Electron Spectrosc. Relat. Phenom. 129, 71 (2003).
[60] L. Zheng, M. Cui, Y. Zhao, J. Zhao, and K. Chen, J. Electron Spectrosc. Relat. Phenom. 152, 143 (2006).
[61] M. Band, Y. I. Kharitonov, and M. B. Trzhask-Ovskaya, At. Data Nucl. Data Tables 23, 443 (1979).
[62] J. J. Yeh and I. Lindau, At. Data Nucl. Data Tables 32, 1 (1985).
[63] H. B. Li et al., Phys. Rev. Lett. 90, 131802 (2003).
[64] H. T. Wong et al., Phys. Rev. D 75, 012001 (2007).
[65] A. G. Beda, V. B. Brudanin, V. G. Egorov, D. V. Medvedev, V. S. Pogosov, M. V. Shirchenko, and A. S. Starostin, Adv. High Energy Phys. 2012, 350150 (2012).
[66] A. G. Beda, V. B. Brudanin, V. G. Egorov, D. V. Medvedev, V. S. Pogosov, E. A. Shevchik, M. V. Shirchenko, A. S. Starostin, and I. V. Zhitnikov, Phys. Part. Nucl. Lett. 10, 139 (2013).
[67] H. T. Wong, H.-B. Li, and S.-T. Lin, Phys. Rev. Lett. 105, 061801 (2010).
[68] M. Deniz et al. (TEXONO Collaboration), Phys. Rev. D 81, 072001 (2010); 82, 033004 (2010).
[69] A. K. Soma et al. (TEXONO Collaboration), arXiv:1411.4802.
[70] R. Catena and P. Ullio, J. Cosmol. Astropart. Phys. 08 (2010) 004.
[71] T. Piffl et al., Astron. Astrophys. 562, A91 (2014).
[72] A. M. Serenelli, W. C. Haxton, and C. Pena-Garay, Astrophys. J. 743, 24 (2011).
[73] E. G. Adelberger et al., Rev. Mod. Phys. 83, 195 (2011).
[74] J. N. Bahcall and C. Pena-Garay, New J. Phys. 6, 63 (2004).
[75] K. A. Olive et al. (Particle Data Group), Chin. Phys. C 38, 090001 (2014).
[76] L. Baudis, A. Ferella, A. Kish, A. Manalaysay, T. Marrodan Undagoitia, et al., JCAP 1401, 044 (2014).
[77] J. Aalbers et al. (DARWIN), arXiv:1606.07001 [astro-ph.IM].
[78] D. S. Akerib et al. (LUX), Phys. Rev. Lett. 112, 091303 (2014).
[79] D. Yu. Akimov et al., Phys. Lett. B 709, 14 (2012).
[80] M. Schumann, L. Baudis, L. Butikofer, A. Kish, and M. Selvi, JCAP 1510, 016 (2015).