# Extended Grimus–Stockinger theorem and inverse-square law violation in quantum field theory

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## Abstract

We study corrections to the Grimus–Stockinger theorem dealing with the large-distance asymptotic behavior of the external wave-packet modified neutrino propagator within the framework of a field-theoretical description of the neutrino-oscillation phenomenon. The possibility is discussed that these corrections, responsible for breakdown of the classical inverse-square law (ISL), can lead to measurable effects at small but macroscopic distances accessible in the SBL (anti)neutrino experiments and in particular can provide an explanation of the well-known reactor antineutrino anomaly.

## Keywords

Sterile Neutrino Neutrino Energy Detector Vertex GALLEX Momentum Spread## Notes

### Acknowledgements

This work was supported by the Federal Target Program “Scientific and Scientific-Pedagogical Personnel of the Innovative Russia” under Contract No. 14.U02.21.0913 The authors would like to thank Z.G. Berezhiani, S.E. Korenblit, and especially D.V. Naumov (who was the active partner in the early stages of this research) for very useful suggestions, comments and criticisms.

## References

- 1.C. Giunti, C.W. Kim,
*Fundamentals of Neutrino Physics and Astrophysics*(Oxford University Press, London, 2007) CrossRefGoogle Scholar - 2.C. Giunti, C.W. Kim, J.A. Lee, U.W. Lee, Phys. Rev. D
**48**, 4310 (1993). arXiv:hep-ph/9305276 [hep-ph] ADSCrossRefGoogle Scholar - 3.W. Grimus, P. Stockinger, Phys. Rev. D
**54**, 3414 (1996). arXiv:hep-ph/9603430 ADSCrossRefGoogle Scholar - 4.S. Mohanty, arXiv:hep-ph/9706328 (1997)
- 5.C. Giunti, C.W. Kim, U.W. Lee, Phys. Lett. B
**421**, 237 (1998). arXiv:hep-ph/9709494 ADSCrossRefGoogle Scholar - 6.J.E. Campagne, Phys. Lett. B
**400**, 135 (1997) ADSCrossRefGoogle Scholar - 7.
- 8.
- 9.A. Ioannisian, A. Pilaftsis, Phys. Rev. D
**59**, 053003 (1999). arXiv:hep-ph/9809503 ADSCrossRefGoogle Scholar - 10.W. Grimus, P. Stockinger, S. Mohanty, Phys. Rev. D
**59**, 013011 (1999). arXiv:hep-ph/9807442 ADSCrossRefGoogle Scholar - 11.W. Grimus, S. Mohanty, P. Stockinger, arXiv:hep-ph/9909341 (1999)
- 12.W. Grimus, S. Mohanty, P. Stockinger, Phys. Rev. D
**61**, 033001 (2000). arXiv:hep-ph/9904285 ADSCrossRefGoogle Scholar - 13.C.Y. Cardall, D.J.H. Chung, Phys. Rev. D
**60**, 073012 (1999). arXiv:hep-ph/9904291 ADSCrossRefGoogle Scholar - 14.
- 15.M. Beuthe, arXiv:hep-ph/0010054 (2000)
- 16.
- 17.
- 18.
- 19.M. Garbutt, B.H.J. McKellar, arXiv:hep-ph/0308111 (2003)
- 20.A. Asahara, K. Ishikawa, T. Shimomura, T. Yabuki, Prog. Theor. Phys.
**113**, 385 (2005). arXiv:hep-ph/0406141 ADSCrossRefGoogle Scholar - 21.A.D. Dolgov, O.V. Lychkovskiy, A.A. Mamonov, L.B. Okun, M.V. Rotaev, M.G. Schepkin, Nucl. Phys. B
**729**, 79 (2005). arXiv:hep-ph/0505251 ADSCrossRefGoogle Scholar - 22.
- 23.E. Akhmedov, J. Kopp, M. Lindner, J. High Energy Phys.
**05**, 005 (2008). arXiv:0802.2513 [hep-ph] ADSCrossRefGoogle Scholar - 24.V.A. Naumov, D.V. Naumov, Russ. Phys. J.
**53**, 549 (2010) CrossRefMATHGoogle Scholar - 25.
- 26.
- 27.B.D. Keister, W.N. Polyzou, Phys. Scr.
**81**, 055102 (2010). arXiv:0908.1404 [hep-ph] ADSCrossRefGoogle Scholar - 28.A.E. Bernardini, M.M. Guzzo, C.C. Nishi, Fortschr. Phys.
**59**, 372 (2011). arXiv:1004.0734 [hep-ph] MathSciNetCrossRefMATHGoogle Scholar - 29.C. Anastopoulos, N. Savvidou, arXiv:1005.4307 [quant-ph] (2010)
- 30.D.V. Naumov, V.A. Naumov, J. Phys. G
**37**, 105014 (2010). arXiv:1008.0306v2 [hep-ph] ADSCrossRefGoogle Scholar - 31.E. Akhmedov, A. Smirnov, Found. Phys.
**41**, 1279 (2011). arXiv:1008.2077 [hep-ph] ADSCrossRefMATHGoogle Scholar - 32.E. Akhmedov, J. Kopp, J. High Energy Phys.
**04**, 008 (2010). arXiv:1001.4815 [hep-ph] ADSCrossRefGoogle Scholar - 33.
- 34.E. Akhmedov, D. Hernandez, A. Smirnov, J. High Energy Phys.
**04**, 052 (2012). arXiv:1201.4128 [hep-ph] ADSCrossRefGoogle Scholar - 35.E. Akhmedov, A. Wilhelm, J. High Energy Phys.
**01**, 165 (2013). arXiv:1205.6231 [hep-ph] MathSciNetADSCrossRefGoogle Scholar - 36.S.E. Korenblit, D.V. Taychenachev, arXiv:1304.5192 [hep-th] (2013)
- 37.C. Giunti, M. Laveder, Phys. Rev. C
**83**, 065504 (2011). arXiv:1006.3244 [hep-ph] ADSCrossRefGoogle Scholar - 38.G. Mention, M. Fechner, Th. Lasserre, Th.A. Mueller, D. Lhuillier et al., Phys. Rev. D
**83**, 073006 (2011). arXiv:1101.2755 [hep-ex] ADSCrossRefGoogle Scholar - 39.Th.A. Mueller, D. Lhuillier, M. Fallot, A. Letourneau, S. Cormon et al., Phys. Rev. C
**83**, 054615 (2011). arXiv:1101.2663 [hep-ex] ADSCrossRefGoogle Scholar - 40.
- 41.M.V. Fedoryuk,
*Metod Perevala*(Nauka, Moscow, 1977) MATHGoogle Scholar - 42.P. Anselmann et al. (GALLEX Collaboration), Phys. Lett. B
**342**, 440 (1995) ADSCrossRefGoogle Scholar - 43.W. Hampel et al. (GALLEX Collaboration), Phys. Lett. B
**420**, 114 (1998) ADSCrossRefGoogle Scholar - 44.F. Kaether, W. Hampel, G. Heusser, J. Kiko, T. Kirsten, Phys. Lett. B
**685**, 47 (2010). arXiv:1001.2731 [hep-ex] ADSCrossRefGoogle Scholar - 45.J.N. Abdurashitov, V.N. Gavrin, S.V. Girin, V.V. Gorbachev, T.V. Ibragimova et al., Phys. Rev. Lett.
**77**, 4708 (1996) ADSCrossRefGoogle Scholar - 46.J.N. Abdurashitov et al. (SAGE Collaboration), Phys. Rev. C
**59**, 2246 (1999). arXiv:hep-ph/9803418 ADSCrossRefGoogle Scholar - 47.J.N. Abdurashitov, V.N. Gavrin, S.V. Girin, V.V. Gorbachev, P.P. Gurkina et al., Phys. Rev. C
**73**, 045805 (2006). arXiv:nucl-ex/0512041 ADSCrossRefGoogle Scholar - 48.Th. Lasserre, J. Phys. Conf. Ser.
**375**, 042042 (2012) ADSCrossRefGoogle Scholar - 49.Th. Lasserre, in
*PoS (EPS-HEP2011)*(2011), p. 100 Google Scholar - 50.G. Mention, J. Phys. Conf. Ser.
**408**, 012025 (2013) ADSCrossRefGoogle Scholar - 51.C. Zhang, X. Qian, P. Vogel, Phys. Rev. D
**87**, 073018 (2013). arXiv:1303.0900 [nucl-ex] ADSCrossRefGoogle Scholar - 52.J.M. Conrad, C.M. Ignarra, G. Karagiorgi, M.H. Shaevitz, J. Spitz, Adv. High Energy Phys.
**2013**, 163897 (2013). arXiv:1207.4765 [hep-ex] Google Scholar - 53.C. Giunti, M. Laveder, Y.F. Li, Q.Y. Liu, H.W. Long, Phys. Rev. D
**86**, 113014 (2012). arXiv:1210.5715 [hep-ph] ADSCrossRefGoogle Scholar - 54.S.K. Kang, Y.D. Kim, Y. Ko, K. Siyeon, arXiv:1303.6173 [hep-ph] (2013)
- 55.J. Kopp, P.A.N. Machado, M. Maltoni, T. Schwetz, J. High Energy Phys.
**05**, 050 (2013). arXiv:1303.3011v2 [hep-ph] ADSCrossRefGoogle Scholar - 56.C. Giunti, Acta Phys. Pol. B, Proc. Suppl.
**6**, 667 (2013) CrossRefGoogle Scholar - 57.K.N. Abazajian, M.A. Acero, S.K. Agarwalla, A.A. Aguilar-Arevalo, C.H. Albright et al., arXiv:1204.5379 [hep-ph] (2012)
- 58.J. Hamann, S. Hannestad, G.G. Raffelt, Y.Y.Y. Wong, J. Cosmol. Astropart. Phys.
**09**, 034 (2011). arXiv:1108.4136 [astro-ph.CO] ADSCrossRefGoogle Scholar - 59.A. Mirizzi, G. Mangano, N. Saviano, E. Borriello, C. Giunti et al., arXiv:1303.5368 [astro-ph.CO] (2013)
- 60.F.P. An et al. (Daya Bay Collaboration), Phys. Rev. Lett.
**108**, 171803 (2012). arXiv:1203.1669 [hep-ex] ADSCrossRefGoogle Scholar - 61.F.P. An et al. (Daya Bay Collaboration), Chin. Phys. C
**37**, 011001 (2013). arXiv:1210.6327 [hep-ex] CrossRefGoogle Scholar - 62.J.K. Ahn et al. (RENO Collaboration), Phys. Rev. Lett.
**108**, 191802 (2012). arXiv:1204.0626 [hep-ex] ADSCrossRefGoogle Scholar - 63.A. Palazzo, arXiv:1308.5880 [hep-ph] (2013)
- 64.C. Giunti, M. Laveder, Y.F. Li, H.W. Long, arXiv:1308.5288 [hep-ph] (2013)
- 65.A. Esmaili, E. Kemp, O.L.G. Peres, Z. Tabrizi, arXiv:1308.6218 [hep-ph] (2013)
- 66.H. Furuta, Y. Fukuda, T. Hara, T. Haruna, N. Ishihara et al., Nucl. Instrum. Methods Phys. Res., Sect. A, Accel. Spectrom. Detect. Assoc. Equip.
**662**, 90 (2012). arXiv:1108.2910 [hep-ex] ADSCrossRefGoogle Scholar - 67.D.A. Dwyer, K.M. Heeger, B.R. Littlejohn, P. Vogel, arXiv:1109.6036 [hep-ex] (2011)
- 68.
- 69.A.S. Cucoanes (Nucifer Collaboration), J. Phys. Conf. Ser.
**375**, 042063 (2012) ADSCrossRefMATHGoogle Scholar - 70.A.V. Derbin, A.S. Kayunov, V.N. Muratova, arXiv:1204.2449 [hep-ph] (2012)
- 71.A.P. Serebrov, V.G. Zinoviev, A.K. Fomin, U.E. Loginov, M.S. Onegin et al., arXiv:1205.2955 [hep-ph] (2012)
- 72.V. Belov, V. Brudanin, M. Danilov, V. Egorov, M. Fomina et al., J. Instrum.
**08**, P05018 (2013). arXiv:1304.3696 [physics.ins-det] CrossRefGoogle Scholar - 73.M. Elnimr, I. Stancu, M. Yeh, R. Svoboda, M.J. Wetstein, F.G. Garcia, B. Osmanov, H. Ray, R. Tayloe, J. Boissevain et al., arXiv:1307.7097 [physics.ins-det] (2013)
- 74.
- 75.J. Gaffiot, Nucl. Phys. B, Proc. Suppl.
**237–238**, 326 (2013) CrossRefGoogle Scholar