Weinberg operator contribution to the CP-odd nuclear force in the quark model

[1] G. Aad et al. (ATLAS Collaboration), Phys. Lett. B 716,1 (2012).

[2] S. Chatrchyan et al. (CMS Collaboration), Phys. Lett. B 716, 30 (2012).

[3] A. D. Sakharov, Pis’ma Zh. Eksp. Teor. Fiz. 5, 32 (1967) [JETP Lett. 5, 24 (1967)].

[4] M. Kobayashi and T. Maskawa, Prog. Theor. Phys. 49, 652 (1973).

[5] G. R. Farrar and M. E. Shaposhnikov, Phys. Rev. D 50, 774 (1994).

[6] P. Huet and E. Sather, Phys. Rev. D 51, 379 (1995).

[7] X. G. He, B. H. J. McKellar, and S. Pakvasa, Int. J. Mod. Phys. A 04, 5011 (1989); 06, 1063(E) (1991).

[8] W. Bernreuther and M. Suzuki, Rev. Mod. Phys. 63, 313 (1991); 64, 633(E) (1992).

[9] I. B. Khriplovich and S. K. Lamoreaux, CP Violation Without Strangeness (Springer, Berlin, Germany, 1997).

[10] M. Pospelov and A. Ritz, Ann. Phys. (Amsterdam) 318, 119 (2005).

[11] T. Fukuyama, Int. J. Mod. Phys. A 27, 1230015 (2012).

[12] J. L. Hewett, H. Weerts, R. Brock, J. N. Butler, B. C. K. Casey, J. Collar, A. de Gouvea, R. Essig, Y. Grossman, W. Haxton et al., arXiv:1205.2671.

[13] J. Engel, M. J. Ramsey-Musolf, and U. van Kolck, Prog. Part. Nucl. Phys. 71, 21 (2013).

[14] N. Yamanaka, Analysis of the Electric Dipole Moment in the R-parity Violating Supersymmetric Standard Model (Springer, Berlin, Germany, 2014).

[15] J. S. M. Ginges and V. V. Flambaum, Phys. Rep. 397, 63 (2004).

[16] N. Yamanaka, B. K. Sahoo, N. Yoshinaga, T. Sato, K. Asahi, and B. P. Das, Eur. Phys. J. A 53, 54 (2017).

[17] T. Chupp, P. Fierlinger, M. Ramsey-Musolf, and J. Singh, Rev. Mod. Phys. 91, 015001 (2019).

[18] R. Alarcon, J. Alexander, V. Anastassopoulos, T. Aoki, R. Baartman, S. Baeßler, L. Bartoszek, D. H. Beck, F. Bedeschi, R. Berger et al., arXiv:2203.08103.

[19] C. Y. Seng, Phys. Rev. C 91, 025502 (2015).

[20] N. Yamanaka and E. Hiyama, J. High Energy Phys. 02 (2016) 067.

[21] N. Yamanaka, Nucl. Phys. A963, 33 (2017).

[22] J. Lee, N. Yamanaka, and E. Hiyama, Phys. Rev. C 99, 055503 (2019).

[23] Y. Yamaguchi and N. Yamanaka, Phys. Rev. Lett. 125, 241802 (2020).

[24] Y. Ema, T. Gao, and M. Pospelov, arXiv:2202.10524.

[25] G. W. Bennett et al. (Muon (g-2) Collaboration), Phys. Rev. D 80, 052008 (2009).

[26] B. Graner, Y. Chen, E. G. Lindahl, and B. R. Heckel, Phys. Rev. Lett. 116, 161601 (2016); 119, 119901(E) (2017).

[27] M. Bishof, R. H. Parker, K. G. Bailey, J. P. Greene, R. J. Holt, M. R. Kalita, W. Korsch, N. D. Lemke, Z. T. Lu, P. Mueller et al., Phys. Rev. C 94, 025501 (2016).

[28] V. Andreev et al. (ACME Collaboration), Nature (London) 562, 355 (2018).

[29] F. Allmendinger, I. Engin, W. Heil, S. Karpuk, H.-J. Krause, B. Niederländer, A. Offenhäusser, M. Repetto, U. Schmidt, and S. Zimmer, Phys. Rev. A 100, 022505 (2019).

[30] C. Abel et al. (nEDM Collaboration), Phys. Rev. Lett. 124, 081803 (2020).

[31] F. J. M. Farley, K. Jungmann, J. P. Miller, W. M. Morse, Y. F. Orlov, B. L. Roberts, Y. K. Semertzidis, A. Silenko, and E. J. Stephenson, Phys. Rev. Lett. 93, 052001 (2004).

[32] Y. Sakemi et al., J. Phys. Conf. Ser. 302, 012051 (2011).

[33] V. Anastassopoulos, S. Andrianov, R. Baartman, M. Bai, S. Baessler, J. Benante, M. Berz, M. Blaskiewicz, T. Bowcock, K. Brown et al., Rev. Sci. Instrum. 87, 115116 (2016).

[34] A. C. Vutha, M. Horbatsch, and E. A. Hessels, Atoms 6, 3 (2018), Special Issue on High Precision Measurements of Fundamental Constants.

[35] V. V. Flambaum, Phys. Rev. C 99, 035501 (2019).

[36] V. V. Flambaum and I. B. Samsonov, Phys. Rev. Res. 2, 023042 (2020).

[37] Z. Omarov, H. Davoudiasl, S. Haciomeroglu, V. Lebedev, W. M. Morse, Y. K. Semertzidis, A. J. Silenko, E. J. Stephenson, and R. Suleiman, Phys. Rev. D 105, 032001 (2022).

[38] A. Zakharova and A. Petrov, Phys. Rev. A 103, 032819 (2021).

[39] P. I. Porshnev, Phys. Scr. 96, 035303 (2021).

[40] R. A. Ready, G. Arrowsmith-Kron, K. G. Bailey, D. Battaglia, M. Bishof, D. Coulter, M. R. Dietrich, R. Fang, B. Hanley, J. Huneau et al., Nucl. Instrum. Methods Phys. Res., Sect. A 1014, 165738 (2021).

[41] M. Köksal, Nucl. Phys. B971, 115520 (2021).

[42] W. A. Terrano and M. V. Romalis, Quantum Sci. Technol. 7, 014001 (2022).

[43] V. V. Flambaum and A. J. Mansour, Phys. Rev. C 105, 065503 (2022).

[44] Storage Ring EDM Collaboration, http://www.bnl.gov/ edm/.

[45] Q. Bonnefoy, E. Gendy, C. Grojean, and J. T. Ruderman, J. High Energy Phys. 08 (2022) 032.

[46] S. Weinberg, Phys. Rev. Lett. 63, 2333 (1989).

[47] D. A. Dicus, Phys. Rev. D 41, 999 (1990).

[48] G. Boyd, A. K. Gupta, S. P. Trivedi, and M. B. Wise, Phys. Lett. B 241, 584 (1990).

[49] H. Y. Cheng, Phys. Rev. D 42, 2329 (1990).

[50] I. I. Y. Bigi and N. G. Uraltsev, Zh. Eksp. Teor. Fiz. 100, 363 (1991) [Sov. Phys. JETP 73, 198 (1991)].

[51] I. I. Y. Bigi and N. G. Uraltsev, Nucl. Phys. B353, 321 (1991).

[52] T. Hayashi, Y. Koide, M. Matsuda, and M. Tanimoto, Prog. Theor. Phys. 91, 915 (1994).

[53] T. Hayashi, Y. Koide, M. Matsuda, M. Tanimoto, and S. Wakaizumi, Phys. Lett. B 348, 489 (1995).

[54] Y. L. Wu, arXiv:hep-ph/9404241.

[55] M. Jung and A. Pich, J. High Energy Phys. 04 (2014) 076.

[56] J. Brod, U. Haisch, and J. Zupan, J. High Energy Phys. 11 (2013) 180.

[57] W. Dekens, J. de Vries, J. Bsaisou, W. Bernreuther, C. Hanhart, U. G. Meißner, A. Nogga, and A. Wirzba, J. High Energy Phys. 07 (2014) 069.

[58] V. Cirigliano, W. Dekens, J. de Vries, and E. Mereghetti, Phys. Rev. D 94, 016002 (2016).

[59] V. Cirigliano, W. Dekens, J. de Vries, and E. Mereghetti, Phys. Rev. D 94, 034031 (2016).

[60] G. Panico, M. Riembau, and T. Vantalon, J. High Energy Phys. 06 (2018) 056.

[61] V. Cirigliano, A. Crivellin, W. Dekens, J. de Vries, M. Hoferichter, and E. Mereghetti, Phys. Rev. Lett. 123, 051801 (2019).

[62] U. Haisch and A. Hala, J. High Energy Phys. 11 (2019)

[63] K. Cheung, A. Jueid, Y. N. Mao, and S. Moretti, Phys. Rev. D 102, 075029 (2020).

[64] M. Dine and W. Fischler, Phys. Lett. B 242, 239 (1990).

[65] J. Dai, H. Dykstra, R. G. Leigh, S. Paban, and D. Dicus, Phys. Lett. B 237, 216 (1990); 242, 547(E) (1990).

[66] R. L. Arnowitt, M. J. Duff, and K. S. Stelle, Phys. Rev. D 43, 3085 (1991).

[67] S. Abel, S. Khalil, and O. Lebedev, Nucl. Phys. B606, 151

[68] D. A. Demir, M. Pospelov, and A. Ritz, Phys. Rev. D 67, 015007 (2003).

[69] D. A. Demir, O. Lebedev, K. A. Olive, M. Pospelov, and A. Ritz, Nucl. Phys. B680, 339 (2004).

[70] G. Degrassi, E. Franco, S. Marchetti, and L. Silvestrini, J. High Energy Phys. 11 (2005) 044.

[71] S. Abel and O. Lebedev, J. High Energy Phys. 01 (2006)

[72] J. R. Ellis, J. S. Lee, and A. Pilaftsis, J. High Energy Phys. 10 (2008) 049.

[73] Y. Li, S. Profumo, and M. Ramsey-Musolf, J. High Energy Phys. 08 (2010) 062.

[74] S. M. Zhao, T. F. Feng, B. Yan, H. B. Zhang, Y. J. Zhang, B. Chen, and X. Q. Li, J. High Energy Phys. 10 (2013) 020.

[75] F. Sala, J. High Energy Phys. 03 (2014) 061.

[76] J. Hisano, D. Kobayashi, W. Kuramoto, and T. Kuwahara, J. High Energy Phys. 11 (2015) 085.

[77] Y. Nakai and M. Reece, J. High Energy Phys. 08 (2017)

[78] B. Yan, S.M. Zhao, and T. F. Feng, Nucl. Phys. B975, 115671 (2022).

[79] D. Chang, C. S. Li, and T. C. Yuan, Phys. Rev. D 42, 867

[80] I. Z. Rothstein, Phys. Lett. B 249, 467 (1990).

[81] F. Xu, H. An, and X. Ji, J. High Energy Phys. 03 (2010)

[82] K. Choi, S. H. Im, H. Kim, and D. Y. Mo, Phys. Lett. B 760, 666 (2016).

[83] T. Abe, J. Hisano, and R. Nagai, J. High Energy Phys. 03 (2018) 175; 09 (2018) 20.

[84] W. Dekens, J. de Vries, M. Jung, and K. K. Vos, J. High Energy Phys. 01 (2019) 069.

[85] L. Di Luzio, R. Grbber, and P. Paradisi, Phys. Rev. D 104, 095027 (2021).

[86] W. Dekens, L. Andreoli, J. de Vries, E. Mereghetti, and F. Oosterhof, J. High Energy Phys. 11 (2021) 127.

[87] H. Gisbert, V. Miralles, and J. Ruiz-Vidal, J. High Energy Phys. 04 (2022) 077.

[88] A. Faessler, T. Gutsche, S. Kovalenko, and V. E. Lyubovitskij, Phys. Rev. D 73 (2006), 114023.

[89] A. Faessler, T. Gutsche, S. Kovalenko, and V. E. Lyubovitskij, Phys. Rev. D 74 (2006), 074013.

[90] M. J. Booth, Phys. Rev. D 48, 1248 (1993).

[91] ML E. Pospelov, Phys. Lett. B 328, 441 (1994).

[92] Y. Yamaguchi and N. Yamanaka, Phys. Rev. D 103, 013001 (2021).

[93] V. G. Baryshevsky and PI. Porshnev, arXiv:2012.11751.

[94] V. G. Baryshevsky and P. I. Porshnev, Phys. Scr. 97, 035302 (2022).

[95] U. Haisch and A. Hala, J. High Energy Phys. 11 (2019) 154.

[96] N. Yamanaka and E. Hiyama, Phys. Rev. D 103, 035023 (2021).

[97] ML Chemtob, Phys. Rev. D 45, 1649 (1992).

[98] C. Dib, A. Faessler, T. Gutsche, S. Kovalenko, J. Kuckei, V. E. Lyubovitskij, and K. Pumsa-ard, J. Phys. G 32, 547 (2006).

[99] Y. Hatta, Phys. Rev. D 102, 094004 (2020).

[100] Y. Hatta, Phys. Lett. B 814, 136126 (2021).

[101] C. Weiss, Phys. Lett. B 819, 136447 (2021).

[102] M. Abramczyk, S. Aoki, T. Blum, T. Izubuchi, H. Ohki, and S. Syritsyn, Phys. Rev. D 96, 014501 (2017).

[103] J. Dragos, T. Luu, A. Shindler, J. de Vries, and A. Yousif, Phys. Rev. C 103, 015202 (2021).

[104] V. Cirigliano, E. Mereghetti, and P. Stoffer, J. High Energy Phys. 09 (2020) 094.

[105] M. D. Rizik, C. J. Monahan, and A. Shindler (SymLat Collaboration), Phys. Rev. D 102, 034509 (2020).

[106] V. G. Baryshevsky, arXiv:2004.01900.

[107] S. Aiola, L. Bandiera, G. Cavoto, F. De Benedetti, J. Fu, V. Guidi, L. Henry, D. Marangotto, F. M. Vidal, V. Mascagna et al., Phys. Rev. D 103, 072003 (2021).

[108] V. M. Biryukov and J. Ruiz Vidal, Eur. Phys. J. C 82, 149 (2022).

[109] Y. Unai, D. Severt, J. de Vries, C. Hanhart, and U.G. MeiBner, Phys. Rev. D 105, 055026 (2022).

[110] V. V. Flambaum, LB. Samsonov, and H. B. Tran Tan, Phys. Rev. D 102, 115036 (2020).

[Ill] J. de Vries, R. Higa, C.P. Liu, E. Mereghetti, I. Stetcu, R. G. E. Timmermans, and U. van Kolck, Phys. Rev. C 84, 065501 (2011).

[112] J. Bsaisou, J. de Vries, C. Hanhart, S. Liebig, U.G. Meissner, D. Minossi, A. Nogga, and A. Wirzba, J. High Energy Phys. 03 (2015) 104; 05 (2015) 83.

[113] J. Bsaisou, U. G. MeiBner, A. Nogga, and A. Wirzba, Ann. Phys. (Amsterdam) 359, 317 (2015).

[114] N. Yamanaka, Int. J. Mod. Phys. E 26, 1730002 (2017).

[115] N. Osamura, P. Gubler, and N. Yamanaka, J. High Energy Phys. 06 (2022) 072.

[116] E. Epelbaum, H.W. Hammer, and U.G. Meissner, Rev. Mod. Phys. 81, 1773 (2009).

[117] Y. H. Song, R. Lazauskas, and V. Gudkov, Phys. Rev. C 87, 015501 (2013).

[118] N. Yamanaka and E. Hiyama, Phys. Rev. C 91, 054005 (2015).

[119] P. Froese and P. Navratil, Phys. Rev. C 104, 025502 (2021).

[120] N. Yamanaka, arXiv:2112.06478.

[121] R. B. Wiringa, V. G. J. Stoks, and R. Schiavilla, Phys. Rev. C 51, 38 (1995).

[122] M. Gell-Mann, Phys. Lett. 8, 214 (1964).

[123] B. Sakita, Phys. Rev. 136, B1756 (1964).

[124] N. Isgur and G. Karl, Phys. Rev. D 20, 1191 (1979).

[125] S. Capstick and W. Roberts, Prog. Part. Nucl. Phys. 45, S241 (2000).

[126] N. Isgur and G. Karl, Phys. Rev. D 18, 4187 (1978).

[127] N. Isgur and G. Karl, Phys. Rev. D 19, 2653 (1979); 23, 817(E) (1981).

[128] S. Godfrey and N. Isgur, Phys. Rev. D 32, 189 (1985).

[129] S. Capstick and N. Isgur, Phys. Rev. D 34, 2809 (1986).

[130] W. Roberts and M. Pervin, Int. J. Mod. Phys. A 23, 2817

[131] M. Karliner, B. Keren-Zur, H. J. Lipkin, and J. L. Rosner, Ann. Phys. (Amsterdam) 324, 2 (2009).

[132] T. Yoshida, E. Hiyama, A. Hosaka, M. Oka, and K. Sadato, Phys. Rev. D 92, 114029 (2015).

[133] E. Hiyama, A. Hosaka, M. Oka, and J. M. Richard, Phys. Rev. C 98, 045208 (2018).

[134] R. Aaij et al. (LHCb Collaboration), Phys. Rev. Lett. 115, 072001 (2015).

[135] M. Oka and K. Yazaki, Phys. Lett. 90B, 41 (1980).

[136] M. Oka and K. Yazaki, Prog. Thcor. Phys. 66, 556 (1981).

[137] M. Oka and K. Yazaki, Prog. Thcor. Phys. 66, 572 (1981).

[138] M. Oka and K. Yazaki, Nucl. Phys. A402, 477 (1983); A458, 773(E) (1986).

[139] M. Oka, K. Shimizu, and K. Yazaki, Phys. Lett. 130B, 365 (1983).

[140] O. Morimatsu, S. Ohta, K. Shimizu, and K. Yazaki, Nucl. Phys. A420, 573 (1984).

[141] O. Morimatsu, K. Yazaki, and M. Oka, Nucl. Phys. A424, 412 (1984).

[142] M. Oka, K. Shimizu, and K. Yazaki, Nucl. Phys. A464, 700 (1987).

[143] S. Takeuchi, K. Shimizu, and K. Yazaki, Nucl. Phys. A504, 777 (1989).

[144] M. Oka and S. Takeuchi, Phys. Rev. Lett. 63, 1780 (1989).

[145] S. Takeuchi and M. Oka, Phys. Rev. Lett. 66, 1271 (1991).

[146] M. Oka and S. Takeuchi, Nucl. Phys. A524, 649 (1991).

[147] T. Inoue, S. Takeuchi, and M. Oka, Nucl. Phys. A597, 563

[148] K. Sasaki, T. Inoue, and M. Oka, Nucl. Phys. A669, 331 (2000); A678, 455(E) (2000).

[149] M. Oka, K. Shimizu, and K. Yazaki, Prog. Theor. Phys. Suppl. 137, 1 (2000).

[150] Y. Fujiwara, Y. Suzuki, and C. Nakamoto, Prog. Part. Nucl. Phys. 58, 439 (2007).

[151] A. Park, S. H. Lee, T. Inoue, and T. Hatsuda, Eur. Phys. J. A 56, 93 (2020).

[152] N. Ishii, S. Aoki, and T. Hatsuda, Phys. Rev. Lett. 99, 022001 (2007).

[153] S. Aoki, T. Hatsuda, and N. Ishii, Prog. Theor. Phys. 123, 89 (2010).

[154] T. Inoue, N. Ishii, S. Aoki, T. Doi, T. Hatsuda, Y. Ikeda, K. Murano, H. Nemura, and K. Sasaki (HAL QCD Collabo­ ration), Phys. Rev. Lett. 106, 162002 (2011).

[155] S. Gongyo, K. Sasaki, S. Aoki, T. Doi, T. Hatsuda, Y. Ikeda, T. Inoue, T. Iritani, N. Ishii, T. Miyamoto et al., Phys. Rev. Lett. 120, 212001 (2018).

[156] A. E Falcao, O. Oliveira, and P. J. Silva, Phys. Rev. D 102, 114518 (2020).

[157] E. Braaten, C. S. Li, and T. C. Yuan, Phys. Rev. Lett. 64, 1709 (1990).

[158] E. Braaten, C. S. Li, and T. C. Yuan, Phys. Rev. D 42, 276 (1990).

[159] J. Hisano, K. Tsumura, and M. J. S. Yang, Phys. Lett. B 713, 473 (2012).

[160] W. Dekens and J. de Vries, J. High Energy Phys. 05 (2013) 149.

[161] J. de Vries, G. Falcioni, F. Herzog, and B. Ruijl, Phys. Rev. D 102, 016010 (2020).

[162] J. Kley, T. Theil, E. Venturini, and A. Weiler, arXiv:2109.15085.

[163] C. Degrande and J. Toucheque, J. High Energy Phys. 04 (2022) 032.

[164] E. Hiyama, Y. Kino, and M. Kamimura, Prog. Part. Nucl. Phys. 51, 223 (2003).

[165] LA. Wheeler, Phys. Rev. 52, 1083 (1937).

[166] LA. Wheeler, Phys. Rev. 52, 1107 (1937).

[167] K. Wildermuth and Th. Kanellopoulos, Nucl. Phys. 7, 150 (1958); 9, 449 (1958).

[168] I. Shimodaya, R. Tamagaki, and H. Tanaka, Prog. Theor. Phys. 27, 793 (1962).

[169] S. Takeuchi, K. Shimizu, and K. Yazaki, Nucl. Phys. A481, 693 (1988).

[170] N. Yamanaka, T. Yamada, E. Hiyama, and Y. Funaki, Phys. Rev. C 95, 065503 (2017).

[171] N. Yamanaka, T. Yamada, and Y. Funaki, Phys. Rev. C 100, 055501 (2019).

[172] K. Yanase and N. Shimizu, Phys. Rev. C 102, 065502 (2020).

[173] K. Yanase, Phys. Rev. C 103, 035501 (2021).

[174] N. Yamanaka, S. Hashimoto, T. Kaneko, and H. Ohki (JLQCD Collaboration), Phys. Rev. D 98, 054516 (2018).

[175] R. Gupta, S. Park, M. Hoferichter, E. Mereghetti, B. Yoon, and T. Bhattacharya, Phys. Rev. Lett. 127, 242002 (2021).

[176] A. Courtoy, A. S. Miramontes, H. Avakian, M. Mirazita, and S. Pisano, Phys. Rev. D 106, 014027 (2022).