暗物質直接探測在具有以下特質的模型，如：違背同位旋的耦合，放熱散射， 和/或輕介體粒子，被探究為了減少 CDMS-Si 實驗的正面信號與其他負面搜索的分歧。我們特別聚焦於能導致予與自旋無關的暗物質-核子散射的非標準有效算符，而這些算符對於動量轉移與暗物質移動速度有不同依賴性。因此， 選擇這樣的有效算符在最後的擬合上比較有平緩的效果。然而，通過LUX， PandaX-II 和 PICO-60 實驗的最新限制，我們發現，在幾乎所有被考慮的模型裡，CDMS-Si 的信號範圍都被 LUX，PandaX-II與PICO-60實驗嚴重限制或完全排除。所以，我們得出的結論是，用現今的暗物質框架來解釋CDMS-Si的信號是非常困難的事。

Dark matter (DM) direct detections are investigated for models with the following properties: isospin-violating couplings, exothermic scatterings, and/or a light mediator, with the aim to reduce the tension between the CDMS-Si positive signals and other negative searches. In particular, we focus on the non-standard effective operators which could lead to the spin-independent DM-nucleus scatterings with non-trivial dependencies on the momentum transfer or DM velocity. As a result, such effective operator choices have the very mild effects on the final fittings. Furthermore, by including the latest constraints from LUX, PandaX-II, and PICO-60, we find that, for almost all the considered models, the predicted CDMS-Si signal regions are either severely constrained or completely excluded by the LUX, PandaX-II and PICO-60 data, including the most promising Xe-phobic exothermic DM models with/without a light mediator. Therefore, we conclude that it is very difficult for the present DM framework to explain the CDMS-Si excess.

[1] J. Michell, Phil. Trans. R. Soc. Lond. 74, 35-57 (1784)
[2] F. W. Bessel, MNRAS 6, 136 (1844)
[3] G. Bertone and D. Hooper, [arXiv:1605.04909 [astro-ph.CO]].
[4] A. Secchi, Memoir (1877)
[5] K. Garrett and G. Duda, Adv. Astron. 2011, 968283 (2011) doi:
10.1155/2011/968283 [arXiv:1006.2483 [hep-ph]].
[6] J. H. Oort, Bull. Astron. Inst. Netherlands 6, 249 (1932)
[7] F. Zwicky, Astrophys. J. 86, 217 (1937). doi:10.1086/143864
[8] J. de Swart, G. Bertone and J. van Dongen, Nature Astron. 1, 0059 (2017) doi:
10.1038/s41550017-0059, 10.1038/s41550-017-0059 [arXiv:1703.00013 [astroph.CO]].
[9] K. C. Freeman, Astrophysical Journal 160, 811 (1970) doi:10.1086/150474
[10] V. C. Rubin and W. K. Ford, Jr., Astrophys. J. 159, 379 (1970). doi:
10.1086/150317
[11] D. Majumdar, CRC Press (2014) ISBN:978-1-4665-7212-6
[12] D. Majumdar, hep-ph/0703310 [HEP-PH].
[13] A. Mazumdar, arXiv:1106.5408 [hep-ph].
[14] F. S. Queiroz, arXiv:1605.08788 [hep-ph].
[15] M. J. Jee et al., Astrophys. J. 661, 728 (2007) doi:10.1086/517498 [arXiv:
0705.2171 [astro-ph]].
[16] K. A. Olive et al. [Particle Data Group Collaboration], Chin. Phys. C 38,
090001 (2014). doi:10.1088/1674-1137/38/9/090001
[17] P. A. R. Ade et al. [Planck Collaboration], arXiv:1502.01589 [astro-ph.CO].
[18] S. Dodelson and L. M. Widrow, Phys. Rev. Lett. 72, 17 (1994) doi:10.1103/
PhysRevLett.72.17 [hep-ph/9303287].
[19] G. Steigman and M. S. Turner, Nucl. Phys. B 253, 375 (1985). doi:
10.1016/0550-3213(85)90537-1
[20] G. Jungman, M. Kamionkowski and K. Griest, Phys. Rept. 267, 195 (1996)
doi:10.1016/0370-1573(95)00058-5 [hep-ph/9506380].
[21] J. L. Feng, Ann. Rev. Astron. Astrophys. 48, 495 (2010) doi:10.1146/annurevastro-082708-101659 [arXiv:1003.0904 [astro-ph.CO]].
[22] M. W. Goodman and E. Witten, Phys. Rev. D 31, 3059 (1985). doi:10.1103/
PhysRevD.31.3059
[23] P. F. Smith and J. D. Lewin, Phys. Rept. 187, 203 (1990). doi:10.1016/0370-1573(90)90081-C J. D. Lewin and P. F. Smith, Astropart. Phys. 6, 87 (1996).
doi:10.1016/S0927-6505(96)00047-3
[24] R. Bernabei et al. [DAMA Collaboration], Eur. Phys. J. C 56, 333 (2008)
doi:10.1140/epjc/s10052-008-0662-y [arXiv:0804.2741 [astro-ph]].
[25] R. Bernabei et al. [DAMA and LIBRA Collaborations], Eur. Phys. J. C 67, 39
(2010) doi:10.1140/epjc/s10052-010-1303-9 [arXiv:1002.1028 [astro-ph.GA]].
[26] C. E. Aalseth et al. [CoGeNT Collaboration], Phys. Rev. Lett. 106, 131301
(2011) doi:10.1103/PhysRevLett.106.131301 [arXiv:1002.4703 [astro-ph.CO]].
[27] C. E. Aalseth et al., Phys. Rev. Lett. 107, 141301 (2011) doi:10.1103/PhysRevLett.107.141301 [arXiv:1106.0650 [astro-ph.CO]].
[28] C. E. Aalseth et al. [CoGeNT Collaboration], Phys. Rev. D 88, 012002 (2013)
doi:10.1103/PhysRevD.88.012002 [arXiv:1208.5737 [astro-ph.CO]].
[29] C. E. Aalseth et al. [CoGeNT Collaboration], arXiv:1401.3295 [astro-ph.CO].
[30] C. E. Aalseth et al., arXiv:1401.6234 [astro-ph.CO].
[31] G. Angloher et al., Eur. Phys. J. C 72, 1971 (2012) doi:10.1140/epjc/s10052-012-1971-8 [arXiv:1109.0702 [astro-ph.CO]].
[32] R. Agnese et al. [CDMS Collaboration], Phys. Rev. Lett. 111, no. 25, 251301
(2013) doi:10.1103/PhysRevLett.111.251301 [arXiv:1304.4279 [hep-ex]].
[33] R. Agnese et al. [SuperCDMS Collaboration], Phys. Rev. Lett. 112, no. 24,
241302 (2014) doi:10.1103/PhysRevLett.112.241302 [arXiv:1402.7137 [hepex]].
[34] R. Agnese et al. [SuperCDMS Collaboration], Phys. Rev. Lett. 112, no.
4, 041302 (2014) doi: 10.1103/ PhysRevLett. 112.041302 [arXiv: 1309.3259
[physics.ins-det]].
[35] R. Agnese et al. [SuperCDMS Collaboration], Phys. Rev. Lett. 116, no. 7,
071301 (2016) doi:10.1103/PhysRevLett.116.071301 [arXiv:1509.02448 [astroph.CO]].
[36] J. Angle et al. [XENON10 Collaboration], Phys. Rev. Lett. 107, 051301
(2011) Erratum: [Phys. Rev. Lett. 110, 249901 (2013)] doi: 10.1103/
PhysRevLett.110.249901, 10.1103/PhysRevLett.107.051301 [arXiv:1104.3088
[astro-ph.CO]].
[37] E. Aprile et al. [XENON100 Collaboration], Phys. Rev. D 84, 052003 (2011)
doi:10.1103/PhysRevD.84.052003 [arXiv:1103.0303 [hep-ex]].
[38] E. Aprile et al. [XENON100 Collaboration], Phys. Rev. Lett. 109, 181301
(2012) doi:10.1103/PhysRevLett.109.181301 [arXiv:1207.5988 [astro-ph.CO]].
[39] E. Aprile et al. [XENON100 Collaboration], Astropart. Phys. 54, 11 (2014)
doi:10.1016/j.astropartphys.2013.10.002 [arXiv:1207.3458 [astro-ph.IM]].
[40] E. Aprile et al. [XENON100 Collaboration], Phys. Rev. D 94, no. 12, 122001
(2016) doi:10.1103/PhysRevD.94.122001 [arXiv:1609.06154 [astro-ph.CO]].
[41] LUX Collaboration, D. McKinsey and R. Gaitskell, First Science Result from
the LUX Dark Matter Experiment, http://luxdarkmatter.org, Oct. 30, 2013.
[42] D. S. Akerib et al. [LUX Collaboration], Phys. Rev. Lett. 112, 091303 (2014)
doi:10.1103/PhysRevLett.112.091303 [arXiv:1310.8214 [astro-ph.CO]].
[43] D. S. Akerib et al. [LUX Collaboration], arXiv:1512.03506 [astro-ph.CO].
[44] D. S. Akerib et al. [LUX Collaboration], Phys. Rev. Lett. 118, no. 2,
021303 (2017) doi:10.1103/PhysRevLett.118.021303 [arXiv:1608.07648 [astroph.CO]].
[45] Q. Yue et al. [CDEX Collaboration], Phys. Rev. D 90, 091701 (2014) doi:
10.1103/PhysRevD.90.091701 [arXiv:1404.4946 [hep-ex]].
[46] W. Zhao et al. [CDEX Collaboration], Phys. Rev. D 93, no. 9, 092003 (2016)
doi:10.1103/PhysRevD.93.092003 [arXiv:1601.04581 [hep-ex]].
[47] M. Xiao et al. [PandaX Collaboration], Sci. China Phys. Mech. Astron. 57,
2024 (2014) doi:10.1007/s11433-014-5598-7 [arXiv:1408.5114 [hep-ex]].
[48] A. Tan et al. [PandaX Collaboration], Phys. Rev. D 93, no. 12, 122009 (2016)
doi:10.1103/PhysRevD.93.122009 [arXiv:1602.06563 [hep-ex]].
[49] A. Tan et al. [PandaX-II Collaboration], Phys. Rev. Lett. 117, no. 12, 121303
(2016) doi:10.1103/PhysRevLett.117.121303 [arXiv:1607.07400 [hep-ex]].
[50] C. Amole et al. [PICO Collaboration], Phys. Rev. Lett. 114, no. 23,
231302 (2015) doi:10.1103/PhysRevLett.114.231302 [arXiv:1503.00008 [astroph.CO]].
[51] C. Amole et al. [PICO Collaboration], arXiv:1702.07666 [astro-ph.CO].
[52] G. Angloher et al. [CRESST Collaboration], Eur. Phys. J. C 76, no. 1, 25
(2016) doi:10.1140/epjc/s10052-016-3877-3 [arXiv:1509.01515 [astro-ph.CO]].
[53] A. Kurylov and M. Kamionkowski, Phys. Rev. D 69, 063503 (2004) doi:
10.1103/PhysRevD.69.063503 [hep-ph/0307185].
[54] F. Giuliani, Phys. Rev. Lett. 95, 101301 (2005) doi:10.1103/PhysRevLett.
95.101301 [hep-ph/0504157].
[55] J. L. Feng, J. Kumar, D. Marfatia and D. Sanford, Phys. Lett. B 703, 124
(2011) [arXiv:1102.4331 [hep-ph]].
[56] V. Cirigliano, M. L. Graesser, G. Ovanesyan and I. M. Shoemaker, Phys.
Lett. B 739, 293 (2014) doi:10.1016/j.physletb.2014.10.058 [arXiv:1311.5886
[hep-ph]].
[57] C. Savage, G. Gelmini, P. Gondolo and K. Freese, JCAP 0904, 010 (2009)
doi:10.1088/1475-7516/2009/04/010 [arXiv:0808.3607 [astro-ph]].
[58] A. L. Fitzpatrick, D. Hooper and K. M. Zurek, Phys. Rev. D 81,
115005 (2010) doi:10.1103/PhysRevD.81.115005 [arXiv:1003.0014 [hep-ph]].
S. Chang, J. Liu, A. Pierce, N. Weiner and I. Yavin, JCAP 1008, 018 (2010)
doi:10.1088/1475-7516/2010/08/018 [arXiv:1004.0697 [hep-ph]]. M. T. Frandsen, F. Kahlhoefer, J. March-Russell, C. McCabe, M. McCullough and
K. Schmidt-Hoberg, Phys. Rev. D 84, 041301 (2011) doi:10.1103/PhysRevD.
84.041301 [arXiv:1105.3734 [hep-ph]]. X. G. He, B. Ren and J. Tandean,
Phys. Rev. D 85, 093019 (2012) doi:10.1103/PhysRevD.85.093019, 10.1103/
PhysRevD.85.119902, 10.1103/PhysRevD.85.119906 [arXiv:1112.6364 [hepph]]. N. Okada and O. Seto, Phys. Rev. D 88, 063506 (2013) doi:10.1103/
PhysRevD.88.063506 [arXiv:1304.6791 [hep-ph]].
[59] M. T. Frandsen, F. Kahlhoefer, S. Sarkar and K. Schmidt-Hoberg, JHEP
1109, 128 (2011) doi:10.1007/JHEP09(2011)128 [arXiv:1107.2118 [hep-ph]].
[60] J. M. Cline and A. R. Frey, Phys. Rev. D 84, 075003 (2011) doi:10.1103/
PhysRevD.84.075003 [arXiv:1108.1391 [hep-ph]].
[61] X. Gao, Z. Kang and T. Li, JCAP 1301, 021 (2013) doi:10.1088/1475-7516/2013/01/021 [arXiv:1107.3529 [hep-ph]].
[62] N. Chen, Y. Zhang, Q. Wang, G. Cacciapaglia, A. Deandrea and L. Panizzi,
JHEP 1405, 088 (2014) doi:10.1007/ JHEP05(2014)088 [arXiv:1403.2918
[hep-ph]].
[63] B. Batell, M. Pospelov and A. Ritz, Phys. Rev. D 79, 115019 (2009) doi:
10.1103/PhysRevD.79.115019 [arXiv:0903.3396 [hep-ph]].
[64] P. W. Graham, R. Harnik, S. Rajendran and P. Saraswat, Phys. Rev. D 82,
063512 (2010) doi:10.1103/PhysRevD.82.063512 [arXiv:1004.0937 [hep-ph]].
[65] P. J. Fox, G. Jung, P. Sorensen and N. Weiner, Phys. Rev. D 89, no. 10,
103526 (2014) doi:10.1103/PhysRevD.89.103526 [arXiv:1401.0216 [hep-ph]].
[66] M. McCullough and L. Randall, JCAP 1310, 058 (2013) doi:10.1088/1475-7516/2013/10/058 [arXiv:1307.4095 [hep-ph]].
[67] M. T. Frandsen and I. M. Shoemaker, Phys. Rev. D 89, no. 5, 051701 (2014)
doi:10.1103/PhysRevD.89.051701 [arXiv:1401.0624 [hep-ph]].
[68] N. Chen, Q. Wang, W. Zhao, S. T. Lin, Q. Yue and J. Li, Phys. Lett. B 743,
205 (2015) doi:10.1016/j.physletb.2015.02.043 [arXiv:1404.6043 [hep-ph]].
[69] G. B. Gelmini, A. Georgescu and J. H. Huh, JCAP 1407, 028 (2014) doi:
10.1088/1475-7516/2014/07/028 [arXiv:1404.7484 [hep-ph]].
[70] T. Li, S. Miao and Y. F. Zhou, JCAP 1503, no. 03, 032 (2015) doi:
10.1088/1475-7516/2015/03/032 [arXiv:1412.6220 [hep-ph]].
[71] K. C. Yang, arXiv:1604.04979 [hep-ph].
[72] E. Del Nobile, G. B. Gelmini, P. Gondolo and J. H. Huh, JCAP 1403, 014
(2014) doi:10.1088/1475-7516/2014/03/014 [arXiv:1311.4247 [hep-ph]].
[73] M. I. Gresham and K. M. Zurek, Phys. Rev. D 89, no. 1, 016017 (2014) doi:
10.1103/PhysRevD.89.016017 [arXiv:1311.2082 [hep-ph]].
[74] S. J. Witte and G. B. Gelmini, arXiv:1703.06892 [hep-ph].
[75] C. Q. Geng, D. Huang, C. H. Lee and Q. Wang, JCAP 1608, no. 08, 009
(2016) doi:10.1088/1475-7516/2016/08/009 [arXiv:1605.05098 [hep-ph]].
[76] C. Q. Geng, D. Huang and C. H. Lee, arXiv:1705.06546 [hep-ph].
[77] S. Chang, A. Pierce and N. Weiner, JCAP 1001, 006 (2010) doi:10.1088/1475-7516/2010/01/006 [arXiv:0908.3192 [hep-ph]].
[78] J. Fan, M. Reece and L. T. Wang, JCAP 1011, 042 (2010) doi:10.1088/1475-7516/2010/11/042 [arXiv:1008.1591 [hep-ph]].
[79] A. L. Fitzpatrick, W. Haxton, E. Katz, N. Lubbers and Y. Xu, JCAP 1302,
004 (2013) doi:10.1088/1475-7516/2013/02/004 [arXiv:1203.3542 [hep-ph]].
[80] A. L. Fitzpatrick, W. Haxton, E. Katz, N. Lubbers and Y. Xu, arXiv:
1211.2818 [hep-ph].
[81] N. Anand, A. L. Fitzpatrick and W. C. Haxton, Phys. Rev. C 89, no. 6,
065501 (2014) doi:10.1103/PhysRevC.89.065501 [arXiv:1308.6288 [hep-ph]].
[82] R. Catena, A. Ibarra and S. Wild, arXiv:1602.04074 [hep-ph].
[83] J. Fan, A. Katz, L. Randall and M. Reece, Phys. Rev. Lett. 110, no. 21,
211302 (2013) doi:10.1103/PhysRevLett.110.211302 [arXiv:1303.3271 [hepph]].
[84] J. Fan, A. Katz, L. Randall and M. Reece, Phys. Dark Univ. 2, 139 (2013)
doi:10.1016/j.dark.2013.07.001 [arXiv:1303.1521 [astro-ph.CO]].
[85] K. Freese, J. A. Frieman and A. Gould, Phys. Rev. D 37, 3388 (1988). doi:
10.1103/PhysRevD.37.3388
[86] M. Szydagis [LUX and LZ Collaborations], “The present and future of searching for dark matter with LUX and LZ”, available at http://lux.brown.edu/
talks/ICHEP2016_Szydagis.pdf.
[87] R. J. Barlow, Nucl. Instrum. Meth. A 297, 496 (1990). doi:10.1016/0168-9002(90)91334-8
[88] CDMS Collaboration, K. McCarthy, “Dark matter search results
from the silicon detectors of the cryogenic dark matter search experiment,” available at http:// cdms.berkeley.edu/ presentations/
APS_CDMS_Si_2013_McCarthy.pdf.
[89] S. Yellin, “Finding an upper limit in the presence of unknown background,”
Phys. Rev. D 66, 032005 (2002) doi:10.1103/PhysRevD.66.032005[physics/
0203002].
[90] J. Lindhard, V. Nielsen, M. Scharff, and P. V. Thomsen, K. Dan. Vidensk.
Selsk. Mat. Fys. Medd. 33, 10 (1963) available at http://www.sdu.dk/Bibliotek/matfys.
[91] P. Sorensen and C. E. Dahl, Phys. Rev. D 83, 063501 (2011) doi:10.1103/
PhysRevD.83.063501 [arXiv:1101.6080 [astro-ph.IM]].
[92] S. T. Lin et al. [TEXONO Collaboration], Phys. Rev. D 79, 061101 (2009)
doi:10.1103/PhysRevD.79.061101 [arXiv:0712.1645 [hep-ex]].
[93] A. M. Green, Phys. Rev. D 65, 023520 (2002) [astro-ph/0106555].