Abstract
It has been recently shown that a chiral molecule accelerates linearly along a spatially uniform magnetic field, as a result of the parity-time symmetry breaking induced in its QED self-interaction. In this work we extend that result to fundamental particles which present EW self-interaction, in which case parity is violated by the EW interaction itself. In particular, we demonstrate that, in a spatially uniform and adiabatically time-varying magnetic field, an unpolarized proton coupled to the leptonic vacuum acquires a kinetic momentum antiparallel to the magnetic field, whereas virtual leptons gain an equivalent Casimir momentum in the opposite direction. That momentum is proportional to the magnetic field and to the square of Fermi's constant. We prove that the kinetic energy of the proton is a magnetic energy which constitutes a Doppler-shift correction to its EW self-energy.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
K.A. Milton, The Casimir Effect: Physical Manifestations of Zero-point Energy, World Scientific, Singapore (2001).
P.W. Milonni, The Quantum Vacuum, Academic Press, San Diego U.S.A. (1994).
S. Weinberg, The Cosmological Constant Problem, Rev. Mod. Phys.61 (1989) 1 [INSPIRE].
R.L. Jaffe, The Casimir effect and the quantum vacuum, Phys. Rev.D 72 (2005) 021301 [hep-th/0503158] [INSPIRE].
H.B.G. Casimir, On the attraction between two perfectly conducting plates, Proc. Kon. Ned. Akad. Wet.51 (1948) 793.
E.M. Lifschitz, The theory of molecular attractive forces between solids, Sov. Phys.2 (1956) 73.
S.K. Lamoreaux, Demonstration of the Casimir force in the 0.6 to 6 micrometers range, Phys. Rev. Lett.78 (1997) 5 [Erratum ibid.81 (1998) 5475] [INSPIRE].
F. London, Zur Theorie und Systematik der Molekularkräfte, Z. Phys.63 (1930) 245.
H.B.G. Casimir and D. Polder, The Inuence of retardation on the London-van der Waals forces, Phys. Rev.73 (1948) 360 [INSPIRE].
W.E. Lamb and R.C. Retherford, Fine Structure of the Hydrogen Atom by a Microwave Method, Phys. Rev.72 (1947) 241 [INSPIRE].
H.A. Bethe, The Electromagnetic shift of energy levels, Phys. Rev.72 (1947) 339 [INSPIRE].
A. Chodos, R.L. Jaffe, K. Johnson, C.B. Thorn and V.F. Weisskopf, A New Extended Model of Hadrons, Phys. Rev.D 9 (1974) 3471 [INSPIRE].
P. Hasenfratz and J. Kuti, The quark bag model, Phys. Rept.40 (1978) 75 [INSPIRE].
M.N. Chernodub, V.A. Goy, A.V. Molochkov and H.H. Nguyen, Casimir Effect in Yang-Mills Theory in D = 2 + 1, Phys. Rev. Lett.121 (2018) 191601 [arXiv:1805.11887] [INSPIRE].
R. Durrer and M. Ruser, The Dynamical Casimir effect in braneworlds, Phys. Rev. Lett.99 (2007) 071601 [arXiv:0704.0756] [INSPIRE].
A. Feigel, Quantum Vacuum Contribution to the Momentum of Dielectric Media, Phys. Rev. Lett.92 (2004) 020404 [physics/0304100] [INSPIRE].
B.A. van Tiggelen, G.L. J.A. Rikken and V. Krstic, Momentum Transfer from Quantum Vacuum to Magnetoelectric Matter, Phys. Rev. Lett.96 (2006) 130402 [INSPIRE].
B.A. van Tiggelen, Zero-point momentum in complex media, Eur. Phys. J.D 47 (2008) 261 [arXiv:0706.3302].
B.A. van Tiggelen, S. Kawka and G.L. J.A. Rikken, QED corrections to the electromagnetic Abraham force: Casimir momentum of the hydrogen atom?, Eur. Phys. J.D 66 (2012) 272 [arXiv:1202.5278] [INSPIRE].
O.A. Croze, Alternative derivation of the Feigel effect and call for its experimental verification, Proc. Roy. Soc.A 468 (2012) 429.
M. Donaire, B. van Tiggelen and G.L. J.A. Rikken, Casimir Momentum of a Chiral Molecule in a Magnetic Field, Phys. Rev. Lett.111 (2013) 143602 [arXiv:1304.6767] [INSPIRE].
M. Donaire, B.A. van Tiggelen and G.L.J.A. Rikken, Transfer of linear momentum from the quantum vacuum to a magnetochiral molecule, J. Phys. Cond. Matt.27 (2015) 214002.
C.S. Wu, E. Ambler, R.W. Hayward, D.D. Hoppes and R.P. Hudson, Experimental Test of Parity Conservation in Beta Decay, Phys. Rev.105 (1957) 1413 [INSPIRE].
M. Karliner and H.J. Lipkin, New Quark Relations for Hadron Masses and Magnetic Moments: A Challenge for Explanation from QCD, Phys. Lett.B 650 (2007) 185 [hep-ph/0608004] [INSPIRE].
M.D. Scadron, R. Delbourgo, and G. Rupp, Constituent Quark Masses and the Electroweak Standard Model, J. Phys.G 32 (2006) 736 [hep-ph/0603196].
G.J. Mao, A. Iwamoto and Z.X. Li, A Study of Neutron Star Structure in Strong Magnetic Fields that includes Anomalous Magnetic Moments, Chin. J. Astron. Astrophys.3 (2003) 359.
H. Wen, L.S. Kisslinger, W. Greiner and G. Mao, Neutron spin polarization in strong magnetic fields, Int. J. Mod. Phys.E 14 (2005) 1197 [astro-ph/0408299] [INSPIRE].
M.E. Peskin and D.V. Schroeder, An Introduction to Quantum Field Theory, Westview Press, Chicago U.S.A. (1995).
C. Itzykson and J.B. Zuber, Quantum Field Theory, McGraw-Hill Inc., New York U.S.A. (1980).
J.J. Sakurai, Advanced Quantum Mechanics, Addison-Wesley, Boston U.S.A. (1994).
K. Bhattacharya and P.B. Pal, Inverse beta decay of arbitrarily polarized neutrons in a magnetic field, Pramana J. Phys.62 (2004) 1041.
K. Bhattacharya, Solution of the Dirac equation in presence of an uniform magnetic field, arXiv:0705.4275 [INSPIRE].
M. Bander and H.R. Rubinstein, Proton Beta decay in large magnetic fields, Phys. Lett.B 311 (1993) 187 [hep-ph/9204224] [INSPIRE].
A. Broderick, M. Prakash and J.M. Lattimer, The Equation of state of neutron star matter in strong magnetic fields, Astrophys. J.537 (2000) 351 [astro-ph/0001537] [INSPIRE].
L. Conci and M. Traini, Quark Momentum Distribution in Nucleons, Few-Body Syst.8 (1990) 123.
N. Isgur and G. Karl, P-wave baryons in the quark model, Phys. Rev.D 18 (1978) 4187 [INSPIRE].
N. Isgur and G. Karl, Positive Parity Excited Baryons in a Quark Model with Hyperfine Interactions, Phys. Rev.D 19 (1979) 2653 [Erratum ibid.D 23 (1981) 817] [INSPIRE].
A. De Rújula, H. Georgi and S.L. Glashow, Hadron Masses in a Gauge Theory, Phys. Rev.D 12 (1975) 147 [INSPIRE].
N. Isgur, Meson-like baryons and the spin orbit puzzle, Phys. Rev.D 62 (2000) 014025 [hep-ph/9910272] [INSPIRE].
R.P. Feynman and M. Gell-Mann, Theory of Fermi interaction, Phys. Rev.109 (1958) 193 [INSPIRE].
E.C.G. Sudarshan and R.e. Marshak, Chirality invariance and the universal Fermi interaction, Phys. Rev.109 (1958) 1860 [INSPIRE].
J.D. Jackson, S.B. Treiman and H.W. Wyld, Possible tests of time reversal invariance in Beta decay, Phys. Rev.106 (1957) 517 [INSPIRE].
J.S. Nico, Neutron beta decay, J. Phys.G 36 (2009) 104001 [INSPIRE].
M.S. Sozzi, Discrete Symmetries and CP Violation. From Experiment to Theory, Oxford University Press Inc., New York U.S.A. (2008).
D. Flamm and F. Schoberl, Introduction to the Quark Model of Elementary Particles, Gordon & Breach Science Publishers, London U.K. (1983).
R.F. Álvarez-Estrada, F. Fernández, J.L. Sánchez-Gómez and V. Vento, Models of Hadron Structure Based on Quantum Chromodynamics, Springer-Verlag, Berlin Germany (1986).
A.J.G. Hey and R.L. Kelly, Baryon spectroscopy, Phys. Rept.96 (1983) 71 [INSPIRE].
A. Chodos, R.L. Jaffe, K. Johnson and C.B. Thorn, Baryon Structure in the Bag Theory, Phys. Rev.D 10 (1974) 2599 [INSPIRE].
S.G. Shulga and T.P. Ilicheva, Quasi-potential approach to the three-quark nucleon wave function, Russ. Phys. J.47 (2004) 1242 [INSPIRE].
V.R. Khalilov, Electroweak nucleon decays in a superstrong magnetic field, Theor. Math. Phys. 145 (2005) 1462 [INSPIRE].
D.B. Melrose and V.V. Zheleznyakov, Quantum Theory of Cyclotron Emission and the X-ray Line in Her X-1, Astron. Astrophys.95 (1981) 86.
A.Y. Potekhin and D. Lai, Statistical equilibrium and ion cyclotron absorption/emission in strongly magnetized plasmas, Mon. Not. Roy. Astron. Soc.376 (2007) 793 [astro-ph/0701285] [INSPIRE].
C.P. Slichter, Principles of Magnetic Resonance, Springer, Berlin Germany (1990).
BASE collaboration, Observation of Spin Flips with a Single Trapped Proton, Phys. Rev. Lett.106 (2011) 253001 [arXiv:1104.1206] [INSPIRE].
D. Pines and P. Nozieres, The Theory of Quantum Liquids, Benjamin, New York U.S.A. (1966), pg. 295.
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1907.13518
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Donaire, M. Acceleration of an unpolarized proton along a uniform magnetic field: Casimir momentum of leptons. J. High Energ. Phys. 2019, 41 (2019). https://doi.org/10.1007/JHEP10(2019)041
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP10(2019)041