Mixing of the photon with low-mass particles

Georg Raffelt; Leo Stodolsky

doi:10.1103/PhysRevD.37.1237

Access by Xinjiang University

Mixing of the photon with low-mass particles

Georg Raffelt

Leo Stodolsky

Astronomy Department, University of California, Berkeley, California 94720
Institute for Geophysics and Planetary Physics, Lawrence Livermore National Laboratory, Livermore, California 94550

Max-Planck-Institut fur Physik und Astrophysik, Postfach 401212, 8000 Munchen 40, Federal Republic of Germany

PDF

Phys. Rev. D 37, 1237 – Published 1 March, 1988

DOI: https://doi.org/10.1103/PhysRevD.37.1237

Abstract

Photons can mix with low-mass bosons in the presence of external electromagnetic fields if these particles—not necessarily of spin 1—couple by a two-photon vertex. Important examples are the hypothetical axion (spin 0) and graviton (spin 2). We develop a formalism which is adapted to study the evolution of a photon (axion, graviton) beam in the presence of external fields. We apply our results to discuss the possibility of detecting axions by a measurement of the magnetically induced birefringence of the vacuum. We also discuss photon-axion (graviton) transitions in pulsar magnetic fields. The QED-induced nonlinearity of Maxwell’s equations causes magnetic birefringence effects which are much stronger than the axion-induced effects in the range of axion parameters allowed by astrophysical constraints. Also, this QED effect induces an index of refraction for photons in vacuum which is so large near pulsars that photon-axion (graviton) transitions are strongly suppressed. However, this QED effect can be canceled by plasma refractive effects, leading to degeneracy between photons and axions so that resonant transitions can occur in analogy with the Mikheyev-Smirnov-Wolfenstein effect. The adiabatic condition can be met only in spatially extended systems, possibly in the magnetosphere of magnetic white dwarfs. Our conclusions differ substantially from several recent discussions of various aspects of these mixing phenomena.

References (36)

See, e.g., J. J. Sakurai, Invariance Principles and Elementary Particles (Princeton University Press, Princeton, NJ, 1964).
S. M. Bilenky and B. Pontecorvo, Phys. Rep. 41, 225 (1978).
R. D. Peccei and H. Quinn, Phys. Rev. Lett. 38, 1440 (1977); S. Weinberg, ibid. 40, 223 (1978); F. Wilczek, ibid. 40, 279 (1978).
For general properties of invisible-axion models, see D. B. Kaplan, Nucl. Phys. B260, 215 (1985); M. Srednicki, ibid. B260, 689 (1985). For a recent review of axion properties and the CP problem see H.-Y. Cheng, Report No. IUHET-125, 1986 (unpublished).
See Ref. 23, and references therein.
See the most recent articles and references therein: M. S. Turner, Phys. Rev. D 32, 843 (1985); ibid. 33, 889 (1986); W. G. Unruh, ibid. 32, 831 (1985); R. L. Davis, Phys. Lett. B 180, 225 (1986); T. DeGrand, T. W. Kephart and T. J. Weiler, Phys. Rev. D 33, 910 (1986).
L. D. Landau, Dokl. Akad. Nauk. SSSR 60, 207 (1948); C. N. Yang, Phys. Rev. 77, 242 (1950).
T. Erber, [Nature (London) 190, 25 (1961)] was the first author to suggest the use of the change in the polarization state of a light beam to measure the QED magnetically induced birefringence of vacuum. However, his claim that the different refractive indices for polarization parallel and perpendicular to the field lead to a rotation of the plane of polarization is incorrect. It leads to elliptical polarization.
W.-Y. Tsai and T. Erber, Phys. Rev. D 12, 1132 (1975); R. Novick, M. C. Weisskopf, J. R. P. Angel and P. G. Sutherland, Astrophys. J. 215, L117 (1977).
S. L. Adler, Ann. Phys. (N.Y.) 67, 599 (1971). This author uses the indices || and ppd in the exact opposite way from our discussion.
D. E. Morris, Phys. Rev. D 34, 843 (1986).
M. Yoshimura, Report No. KEK-87-43, 1987 (unpublished).
W. Heisenberg and H. Euler, Z. Phys. 98, 714 (1936). For a modern description see C. Itzykson and J.-B. Zuber, Quantum Field Theory (McGraw-Hill, New York, 1980).
Note that the expression $B_{crit}$ = $m_{e}^{2}$ /e is independent of whether one uses rationalized ( α = $e^{2}$ / 4 π ) or unrationalized ( α = $e^{2}$ ) natural units. However, since always α approx case 1 over 137, the actual value for the dimensionless number e is accordingly different.
K. van Bibber et al., Phys. Rev. Lett. 59, 759 (1987).
M. Gasperini, Phys. Rev. Lett. 59, 396 (1987).
L. Maiani, R. Petronzio and E. Zavattini, Phys. Lett. B 175, 359 (1986).
A. C. Melissinos . et al., experimental proposal, University of Rochester, 1987 (unpublished).
P. Sikivie, Phys. Rev. Lett. 51, 1415 (1983); ibid. 52, 695(E) (1984).
P. Sikivie, Phys. Rev. D 32, 2988 (1985); L. M. Krauss, J. E. Moody, F. Wilczek and D. E. Morris, Phys. Rev. Lett. 55, 1797 (1985).
S. DePanfilis et al., Phys. Rev. Lett. 59, 839 (1987).
D. E. Morris (unpublished).
G. G. Raffelt and D. S. P. Dearborn, Phys. Rev. D 36, 2211 (1987).
Note that in natural Lorentz-Heaviside units ( α = $e^{2}$ / 4 pi approx case 1 over 137 ), consistently used in this paper, the amount of magnetic induction B that would be specified as 1 G in unrationalized cgs units can be expressed as 1.95 times $10^{- 2}$ eV $^{2}$ .
E. Iacopini and E. Zavattini, Phys. Lett. 85B, 151 (1979).
L. Landolt and H. Börnstein, Zahlenwerte und Funktionen, 6th ed. (Springer, Berlin, 1962), Vol. II. 8. The Cotton-Mouton constant at a pressure of 100 kg/cm $^{2}$ is C = - 4.05 times $10^{- 14}$ G ${}^{- 2}{cm}^{- 1}$ for O $_{2}$ and - 0.33 times $10^{- 14}$ for N $_{2}$ . For water at 16.6 ° C it is - 0.39 times $10^{- 14}$ .
C. W. Misner, K. S. Thorne, and J. A. Wheeler, Gravitation (Freeman, San Francisco, 1973).
An early experiment to measure the QED-induced magnetic birefringence of the vacuum was performed by V. Knapp, Nature 197, 659 (1963). It appears to us, however, that the polarization was chosen as 0 degr and 90 degr with respect to B ${vec}_{e}$ so that the (vacuum) Cotton-Mouton effect could not have been measured.
A. A. Ansel'm, Yad. Fiz. 42, 1480 (1985) [Sov. J. Nucl. Phys. 42, 936 (1985)].
L. Wolfenstein, Phys. Rev. D 17, 2369 (1978); ibid. 20, 2634 (1979); S. P. Mikheyev and A. Yu. Smirnov, Yad. Fiz. 42, 1441 (1985) [Sov. J. Nucl. Phys. 42, 913 (1985)]; Nuovo Cimento 9C, 17 (1986) Zh. Eksp. Teor. Fiz. 91, 7 (1986) [Sov. Phys. JETP 64, 4 (1986)]; H. A. Bethe, Phys. Rev. Lett. 56, 1305 (1986).
The authors of Ref. 17 agree that, for a multiple beam path, their original result is incorrect due to the nonlinear dependence of $φ_{a}$ on z [R. Petronzio (private communication)].
N. Iwamoto, Phys. Rev. Lett. 53, 1198 (1984).
S. Tsuruta and K. Nomoto, in Observational Cosmology, IAU-Symposium No. 124, Beijing, China, 1986 (unpublished).
S. L. Shapiro and S. A. Teukolsky, Black Holes, White Dwarfs, and Neutron Stars (Wiley, New York, 1983).
P. Goldreich and W. H. Julian, Astrophys. J. 157, 869 (1969).
Morris agrees that, in view of our discussion, the axion-photon conversion in the magnetosphere of a neutron star (Ref. 11) would be negligible (private communication).

[c1] See, e.g., J. J. Sakurai, Invariance Principles and Elementary Particles (Princeton University Press, Princeton, NJ, 1964).

[c2] S. M. Bilenky and B. Pontecorvo, Phys. Rep. 41, 225 (1978).

[c3] R. D. Peccei and H. Quinn, Phys. Rev. Lett. 38, 1440 (1977); S. Weinberg, ibid. 40, 223 (1978); F. Wilczek, ibid. 40, 279 (1978).

[c4] For general properties of invisible-axion models, see D. B. Kaplan, Nucl. Phys. B260, 215 (1985); M. Srednicki, ibid. B260, 689 (1985). For a recent review of axion properties and the CP problem see H.-Y. Cheng, Report No. IUHET-125, 1986 (unpublished).

[c5] See Ref. 23, and references therein.

[c6] See the most recent articles and references therein: M. S. Turner, Phys. Rev. D 32, 843 (1985); ibid. 33, 889 (1986); W. G. Unruh, ibid. 32, 831 (1985); R. L. Davis, Phys. Lett. B 180, 225 (1986); T. DeGrand, T. W. Kephart and T. J. Weiler, Phys. Rev. D 33, 910 (1986).

[c7] L. D. Landau, Dokl. Akad. Nauk. SSSR 60, 207 (1948); C. N. Yang, Phys. Rev. 77, 242 (1950).

[c8] T. Erber, [Nature (London) 190, 25 (1961)] was the first author to suggest the use of the change in the polarization state of a light beam to measure the QED magnetically induced birefringence of vacuum. However, his claim that the different refractive indices for polarization parallel and perpendicular to the field lead to a rotation of the plane of polarization is incorrect. It leads to elliptical polarization.

[c9] W.-Y. Tsai and T. Erber, Phys. Rev. D 12, 1132 (1975); R. Novick, M. C. Weisskopf, J. R. P. Angel and P. G. Sutherland, Astrophys. J. 215, L117 (1977).

[c10] S. L. Adler, Ann. Phys. (N.Y.) 67, 599 (1971). This author uses the indices || and ppd in the exact opposite way from our discussion.

[c11] D. E. Morris, Phys. Rev. D 34, 843 (1986).

[c12] M. Yoshimura, Report No. KEK-87-43, 1987 (unpublished).

[c13] W. Heisenberg and H. Euler, Z. Phys. 98, 714 (1936). For a modern description see C. Itzykson and J.-B. Zuber, Quantum Field Theory (McGraw-Hill, New York, 1980).

[c14] Note that the expression $B_{crit}$ = $m_{e}^{2}$ /e is independent of whether one uses rationalized ( α = $e^{2}$ / 4 π ) or unrationalized ( α = $e^{2}$ ) natural units. However, since always α approx case 1 over 137, the actual value for the dimensionless number e is accordingly different.

[c15] K. van Bibber et al., Phys. Rev. Lett. 59, 759 (1987).

[c16] M. Gasperini, Phys. Rev. Lett. 59, 396 (1987).

[c17] L. Maiani, R. Petronzio and E. Zavattini, Phys. Lett. B 175, 359 (1986).

[c18] A. C. Melissinos . et al., experimental proposal, University of Rochester, 1987 (unpublished).

[c19] P. Sikivie, Phys. Rev. Lett. 51, 1415 (1983); ibid. 52, 695(E) (1984).

[c20] P. Sikivie, Phys. Rev. D 32, 2988 (1985); L. M. Krauss, J. E. Moody, F. Wilczek and D. E. Morris, Phys. Rev. Lett. 55, 1797 (1985).

[c21] S. DePanfilis et al., Phys. Rev. Lett. 59, 839 (1987).

[c22] D. E. Morris (unpublished).

[c23] G. G. Raffelt and D. S. P. Dearborn, Phys. Rev. D 36, 2211 (1987).

[c24] Note that in natural Lorentz-Heaviside units ( α = $e^{2}$ / 4 pi approx case 1 over 137 ), consistently used in this paper, the amount of magnetic induction B that would be specified as 1 G in unrationalized cgs units can be expressed as 1.95 times $10^{- 2}$ eV $^{2}$ .

[c25] E. Iacopini and E. Zavattini, Phys. Lett. 85B, 151 (1979).

[c26] L. Landolt and H. Börnstein, Zahlenwerte und Funktionen, 6th ed. (Springer, Berlin, 1962), Vol. II. 8. The Cotton-Mouton constant at a pressure of 100 kg/cm $^{2}$ is C = - 4.05 times $10^{- 14}$ G ${}^{- 2}{cm}^{- 1}$ for O $_{2}$ and - 0.33 times $10^{- 14}$ for N $_{2}$ . For water at 16.6 ° C it is - 0.39 times $10^{- 14}$ .

[c27] C. W. Misner, K. S. Thorne, and J. A. Wheeler, Gravitation (Freeman, San Francisco, 1973).

[c28] An early experiment to measure the QED-induced magnetic birefringence of the vacuum was performed by V. Knapp, Nature 197, 659 (1963). It appears to us, however, that the polarization was chosen as 0 degr and 90 degr with respect to B ${vec}_{e}$ so that the (vacuum) Cotton-Mouton effect could not have been measured.

[c29] A. A. Ansel'm, Yad. Fiz. 42, 1480 (1985) [Sov. J. Nucl. Phys. 42, 936 (1985)].

[c30] L. Wolfenstein, Phys. Rev. D 17, 2369 (1978); ibid. 20, 2634 (1979); S. P. Mikheyev and A. Yu. Smirnov, Yad. Fiz. 42, 1441 (1985) [Sov. J. Nucl. Phys. 42, 913 (1985)]; Nuovo Cimento 9C, 17 (1986) Zh. Eksp. Teor. Fiz. 91, 7 (1986) [Sov. Phys. JETP 64, 4 (1986)]; H. A. Bethe, Phys. Rev. Lett. 56, 1305 (1986).

[c31] The authors of Ref. 17 agree that, for a multiple beam path, their original result is incorrect due to the nonlinear dependence of $φ_{a}$ on z [R. Petronzio (private communication)].

[c32] N. Iwamoto, Phys. Rev. Lett. 53, 1198 (1984).

[c33] S. Tsuruta and K. Nomoto, in Observational Cosmology, IAU-Symposium No. 124, Beijing, China, 1986 (unpublished).

[c34] S. L. Shapiro and S. A. Teukolsky, Black Holes, White Dwarfs, and Neutron Stars (Wiley, New York, 1983).

[c35] P. Goldreich and W. H. Julian, Astrophys. J. 157, 869 (1969).

[c36] Morris agrees that, in view of our discussion, the axion-photon conversion in the magnetosphere of a neutron star (Ref. 11) would be negligible (private communication).

Physical Review D

Export citation

Export citation

Mixing of the photon with low-mass particles

Abstract

References (36)

Outline

Information

Filter

Filter

Article Lookup

Enter a citation