Pseudoscalar versus pseudovector pion-nucleon couplings in the nucleonic axion bremsstrahlung rate of neutron-star matter

Naoki Iwamoto

doi:10.1103/PhysRevD.39.2120

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Pseudoscalar versus pseudovector pion-nucleon couplings in the nucleonic axion bremsstrahlung rate of neutron-star matter

Naoki Iwamoto

Department of Physics and Astronomy, The University of Toledo, Toledo, Ohio 43606

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Phys. Rev. D 39, 2120 – Published 15 April, 1989

DOI: https://doi.org/10.1103/PhysRevD.39.2120

Abstract

The difference between the pseudoscalar and pseudovector πN couplings are examined in the context of the nucleonic axion bremsstrahlung rate. With the pseudovector coupling, eight diagrams contribute to the matrix element for axion bremsstrahlung. A naive use of the pseudoscalar coupling for these eight diagrams, on the other hand, gives a different matrix element and overestimates the energy-loss rate of degenerate neutron-star matter via neutron-neutron axion bremsstrahlung typically by an order of magnitude.

References (25)

For reviews see, e.g., P. Sikivie, in Where are the Elementary Particles?, proceedings of the 14th Summer School on Particle Physics, Gif-sur-Yvette, France, 1982, edited by P. Fayet et al. (National Institute for Nuclear and Particle Physics, Paris, 1983), p. 1; F. Wilczek, in How Far Are We From the Gauge Forces, proceedings of the International School of Subnuclear Physics, Erice, Italy, 1983, edited by A. Zichichi (Plenum, New York, 1985), p. 157.
See also J. E. Kim, Phys. Rep. 150, 1 (1987); H.-Y. Cheng, Phys. Rev. D 36, 1649 (1987); Phys. Rep. 158, 1 (1988).
S. De Panfilis, A. C. Melissinos, B. E. Moskowitz, J. T. Rogers, Y. K. Semertzidis, W. U. Wuensch, H. J. Halama, A. G. Prodell, W. B. Fowler and F. A. Nezrick, Phys. Rev. Lett. 59, 839 (1987).
F. T. Avignone III, R. L. Brodzinski, S. Dimopoulos, G. D. Starkman, A. K. Drukier, D. N. Spergel, G. Gelmini and B. W. Lynn, Phys. Rev. D 35, 2752 (1987).
B. E. Moskowitz, Nucl. Instrum. Methods A 264, 98 (1988).
It was recently pointed out that there is no upper bound on the PQ-symmetry-breaking scale in the cosmological models with inflation: A. D. Linde, Phys. Lett. B 201, 437 (1988); S. Dimopoulos and L. J. Hall, Phys. Rev. Lett. 60, 1899 (1988).
See also T. Kephart and T. Weiler, Phys. Rev. Lett. 58, 171 (1987); M. S. Turner, ibid. 59, 2489 (1988).
M. Dine, W. Fischler and M. Srednicki, Phys. Lett. 104B, 199 (1981).
A. P. Zhitnitskii, Yad. Fiz. 31, 497 (1980) [Sov. J. Nucl. Phys. 31, 260 (1980)].
J. E. Kim, Phys. Rev. Lett. 43, 103 (1979).
M. Shifman, A. Vainshtein and V. Zakharov, Nucl. Phys. B166, 493 (1980).
N. Iwamoto, Phys. Rev. Lett. 53, 1198 (1984).
A. Pantziris and K. Kang, Phys. Rev. D 33, 3509 (1986).
Recently, the results of Refs. 12 and 13 have been applied to the supernova 1987A to constrain the axion parameters. See Refs. 15–17.
G. Raffelt and D. Seckel, Phys. Rev. Lett. 60, 1793 (1988).
M. S. Turner, Phys. Rev. Lett. 60, 1797 (1988); R. P. Brinkmann and M. S. Turner, Phys. Rev. D 38, 2338 (1988); A. Burrows, M. S. Turner and R. P. Brinkmann, ibid. 39, 1020 (1989).
R. Mayle, J. R. Wilson, J. Ellis, K. Olive, D. N. Schramm and G. Steigman, Phys. Lett. B 203, 188 (1988).
M. Srednicki, Nucl. Phys. B260, 689 (1985).
D. Kaplan, Nucl. Phys. B260, 215 (1985).
Equations (2.3) and (2.5), which include this factor, correct and replace Eqs. (4) and (5) of Ref. 12, respectively. A detailed account of Ref. 12 will be published elsewhere.
The same correction as stated in Ref. 20 applies to the energy loss rate (2.27) and (2.29) of Ref. 13. This leads to Eq. (2.8), which has been expressed in units of erg ${cm}^{- 3}$ _ $s^{- 1}$ _.
J. J. Sakurai, Advanced Quantum Mechanics (Addison-Wesley, Reading, MA, 1967), Sec. 4.6. J. D. Bjorken and S. D. Drell, Relativistic Quantum Mechanics (McGraw-Hill, New York, 1964), Chap. 10.
As far as the nucleons are nonrelativistic, the final result is not affected by at which stage the nonrelativistic limit is taken. Therefore, the criticism in Ref. 9 of Ref. 13 seems irrelevant.
After the submission of the original version of the present paper, I received a paper by K. Choi, K. Kang, and J. E. Kim [Phys. Rev. Lett. 62, 849 (1989)], which also discusses and clarifies the importance of the dimension-5 term.
See Ref. 9 in Ref. 13.

[c1] For reviews see, e.g., P. Sikivie, in Where are the Elementary Particles?, proceedings of the 14th Summer School on Particle Physics, Gif-sur-Yvette, France, 1982, edited by P. Fayet et al. (National Institute for Nuclear and Particle Physics, Paris, 1983), p. 1; F. Wilczek, in How Far Are We From the Gauge Forces, proceedings of the International School of Subnuclear Physics, Erice, Italy, 1983, edited by A. Zichichi (Plenum, New York, 1985), p. 157.

[c2] See also J. E. Kim, Phys. Rep. 150, 1 (1987); H.-Y. Cheng, Phys. Rev. D 36, 1649 (1987); Phys. Rep. 158, 1 (1988).

[c3] S. De Panfilis, A. C. Melissinos, B. E. Moskowitz, J. T. Rogers, Y. K. Semertzidis, W. U. Wuensch, H. J. Halama, A. G. Prodell, W. B. Fowler and F. A. Nezrick, Phys. Rev. Lett. 59, 839 (1987).

[c4] F. T. Avignone III, R. L. Brodzinski, S. Dimopoulos, G. D. Starkman, A. K. Drukier, D. N. Spergel, G. Gelmini and B. W. Lynn, Phys. Rev. D 35, 2752 (1987).

[c5] B. E. Moskowitz, Nucl. Instrum. Methods A 264, 98 (1988).

[c6] It was recently pointed out that there is no upper bound on the PQ-symmetry-breaking scale in the cosmological models with inflation: A. D. Linde, Phys. Lett. B 201, 437 (1988); S. Dimopoulos and L. J. Hall, Phys. Rev. Lett. 60, 1899 (1988).

[c7] See also T. Kephart and T. Weiler, Phys. Rev. Lett. 58, 171 (1987); M. S. Turner, ibid. 59, 2489 (1988).

[c8] M. Dine, W. Fischler and M. Srednicki, Phys. Lett. 104B, 199 (1981).

[c9] A. P. Zhitnitskii, Yad. Fiz. 31, 497 (1980) [Sov. J. Nucl. Phys. 31, 260 (1980)].

[c10] J. E. Kim, Phys. Rev. Lett. 43, 103 (1979).

[c11] M. Shifman, A. Vainshtein and V. Zakharov, Nucl. Phys. B166, 493 (1980).

[c12] N. Iwamoto, Phys. Rev. Lett. 53, 1198 (1984).

[c13] A. Pantziris and K. Kang, Phys. Rev. D 33, 3509 (1986).

[c14] Recently, the results of Refs. 12 and 13 have been applied to the supernova 1987A to constrain the axion parameters. See Refs. 15–17.

[c15] G. Raffelt and D. Seckel, Phys. Rev. Lett. 60, 1793 (1988).

[c16] M. S. Turner, Phys. Rev. Lett. 60, 1797 (1988); R. P. Brinkmann and M. S. Turner, Phys. Rev. D 38, 2338 (1988); A. Burrows, M. S. Turner and R. P. Brinkmann, ibid. 39, 1020 (1989).

[c17] R. Mayle, J. R. Wilson, J. Ellis, K. Olive, D. N. Schramm and G. Steigman, Phys. Lett. B 203, 188 (1988).

[c18] M. Srednicki, Nucl. Phys. B260, 689 (1985).

[c19] D. Kaplan, Nucl. Phys. B260, 215 (1985).

[c20] Equations (2.3) and (2.5), which include this factor, correct and replace Eqs. (4) and (5) of Ref. 12, respectively. A detailed account of Ref. 12 will be published elsewhere.

[c21] The same correction as stated in Ref. 20 applies to the energy loss rate (2.27) and (2.29) of Ref. 13. This leads to Eq. (2.8), which has been expressed in units of erg ${cm}^{- 3}$ _ $s^{- 1}$ _.

[c22] J. J. Sakurai, Advanced Quantum Mechanics (Addison-Wesley, Reading, MA, 1967), Sec. 4.6. J. D. Bjorken and S. D. Drell, Relativistic Quantum Mechanics (McGraw-Hill, New York, 1964), Chap. 10.

[c23] As far as the nucleons are nonrelativistic, the final result is not affected by at which stage the nonrelativistic limit is taken. Therefore, the criticism in Ref. 9 of Ref. 13 seems irrelevant.

[c24] After the submission of the original version of the present paper, I received a paper by K. Choi, K. Kang, and J. E. Kim [Phys. Rev. Lett. 62, 849 (1989)], which also discusses and clarifies the importance of the dimension-5 term.

[c25] See Ref. 9 in Ref. 13.

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Pseudoscalar versus pseudovector pion-nucleon couplings in the nucleonic axion bremsstrahlung rate of neutron-star matter

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