Isaac Scientific Publishing

Journal of Particle Physics

Quantum Mechanics of ‘Two Path’ Experiments: Comparison of Neutrino Oscillations and the Young Double Slit

Download PDF (477 KB) PP. 1 - 12 Pub. Date: July 19, 2017

DOI: 10.22606/jpp.2017.11001

Author(s)

  • J.H.Field*
    Département de Physique Nucléaire et Corpusculaire, Université de Genève 24, quai Ernest-Ansermet CH-1211Genève 4.

Abstract

Feynman path integral analyses of a two-neutrino-flavour electron appearence experiment and the Young double slit are compared. The comparison reveals a conceptual flaw in previous work of the present author that led to a false claim of the incorrectness of standard formulas for the oscillation phase. In both calculations, path amplitudes add coherently, but no putative ‘neutrino flavour eigenstates’ are invoked in the former case. It is shown that the coherent production of these eigenstates is incompatible with the measured values of Γ(π → eν)/Γ(π → µν) and the PMNS matrix elements. Applications of the path integral approach to other two-path quantum interference experiments are compared with neutrino oscillations, and other treatments of the latter in the literature are critically discussed.

Keywords

Quantum mechanics, neutrino oscillations

References

[1] R.P.Feynman., Rev. Mod. Phys. 20 367; R.P.Feynman and A.R.Hibbs, Quantum mechanics and Path Integrals, McGraw Hill, New York, 1965.

[2] J.H.Field, Ann. Phys. (NY) 321 (2006) 627.

[3] J.H.Field, Eur. J. Phys. 34 (2013) 1507.

[4] R.P.Feynman, QED, The Strange Theory of Light and Matter, Princeton University Press, New Jersey, 1985. Chapter 3 p.103

[5] F.Halzen and A.D.Martin, Quarks & Leptons, John Wiley,New York, 1984. Section 13.4.

[6] B.Pontecorvo, Zh. Eksp. Teor. Fiz. 53 (1967 1717) [ Sov. Phys. JETP 26 (1968) 984].

[7] Z.Maki, M.Nakagawa and S.Sakata, Prog. Theor. Phys. 28 (1962) 870.

[8] K.Nakamura et al., Review of Particle Properties, Journal of Physics G37 (2010) 075021.

[9] G.L.Fogli et al., Phys. Rev. D84 (2011) 053007.

[10] F.P.An et al., (The Daya Bay Collaboration) Phys. Rev. Lett. 108 (2012) 171803.

[11] J.H.Field, Eur. Phys. J. C30 (2003) 305.

[12] J.H.Field, Eur. Phys. J. C37 (2004) 359.

[13] J.H.Field, On some erroneous comments on the literature of neutrino oscillations in the website ‘Neutrino Unbound’ of C.Giunti, http://arxiv.org/abs/hep-ph/0306300

[14] J.H.Field, Remarks on: ‘Theory of Neutrino Oscillations’ (hep-ph/0311241) by C.Giunti, the comments by L.B.Okun et al in hep-ph/0312151, and Giunti’s reply in hep-ph/0312180, http://arxiv.org/abs/hepph/0401051

[15] P.A.M.Dirac, The Principles of Quantum Mechanics (4th Edition), OUP, London 1958 Section 28, Eq. (20.

[16] J.H.Field, The Meaning of Coherence in Weak Decay Processes: ‘Neutrino Oscillations’ Reconsidered, http://arxiv.org/abs/hep-ph/0503034v2.

[17] K.Eguchi et al., Phys. Rev. Lett. 90 (2003) 021802..

[18] V.Gribov and B.Pontecorvo, Phys. Lett. B28 (1969) 493.

[19] B.Kayser, Neutrino mass mixing and flavour change, in Review of Particle Properties, Phys. Lett. B667 (2008) 163.

[20] N.Cabibbo, Phys. Rev. Lett. 10 (1963) 531; M.Kobayashi and T.Maskawa, Prog. Theor. Phys. 49 (1973) 652.

[21] Ref. [5] Section 12.6.

[22] W.Marciano and A.Sirlin, Phys. Rev. Lett. 36 (1976) 1425.

[23] T.Goldman and W.Wilson, Phys. Rev. D15 (1977) 709.

[24] C.Giunti, “Coherence in Neutrino Oscillations,” http://arxiv.org/abs/hep-ph/0302045.

[25] T.Kajita and Y.Totsuka, Rev. Mod. Phys. 73 (2001) 85.

[26] M.H.Ahn et al., Phys. Rev. Lett. 90 (2003) 041801.

[27] E.Shrock, Phys. Lett. B96 (1980) 159.

[28] R.E.Shrock, Phys. Rev. D24 (1981) 1232; D24 (1981) 1275.

[29] C.Giunti, C.W.Kim and U.W.Lee, Phys. Rev. D45 (1992) 2414.

[30] B.Kayser, Phys. Rev. D24 (1981) 110.

[31] C.Giunti, C.W.Kim and U.W.Lee, Phys. Rev. D44 (1991) 3635.

[32] H.G.Berry and J.L.Subtil, Phys. Rev. Lett. 27 (1971) 1103.

[33] C.Blondel, C.Delsart and F.Dulieu, Phys. Rev. Lett. 77 (1996 3755).

[34] C.Bracher et al., Am J. Phys. 66 (1998) 38.

[35] C.Blondel, S.Berge and C.Delsart, Am J. Phys. 69 (2001) 810.

[36] M.Blasone, P.P.Pachêco and H.W.C.Tseung, Phys. Rev. D67 (2003) 073011.

[37] See, for example, J.J.Sakurai, Advanced Quantum Mechanics, Addison Wesley, Redwood City Calif, 1976 Section 2-3 p.29.

[38] Ref [37] p.32.

[39] P.Ramond, Field Theory, a Modern Primer, Benjamin/Cummings, Reading Massachusetts, 1981.

[40] S.Weinberg, The Quantum Theory of Fields Vol I, CUP, Cambridge, 1995 Ch 9 p.376.

[41] P.A.M.Dirac, Physikalische Zeitschrift der Sowjetunion Band 3, Heft 1 (1933). Reprinted in: Selected Papers on Quantum Electrodynamics, Ed. J.Schwinger, Dover, New York, (1958) P312; See also Ref. [15], Chapter V, Section 32.

[42] The first paper in Ref. [1], Section 7.