5.3 Thermal Field Theory
77
Q = −
d
3 k
(2π) 3
Im L (ω, k) + Im T (ω, k)
ω(e ω/T − 1)
,
(5.27)
from which the luminosity in Eq. (5.18) can be computed and compared with the
astrophysical limit of interest. The expression for Im L ,T (ω, k) for the massive
dark photon can be found in [30–32] where plasma effects are also included.
References
1. P. Fayet, Effects of the Spin 1 partner of the Goldstino (Gravitino) on neutral current phenomenology. Phys. Lett. B 95, 285–289 (1980)
2. P. Fayet, On the search for a new Spin 1 Boson. Nucl. Phys. B 187, 184–204 (1981)
3. L.B. Okun, Limits of electrodynamics: paraphotons? Sov. Phys. JETP 56, 502 (1982). [Zh.
Eksp. Teor. Fiz.83,892(1982)]
4. H. Georgi, P.H. Ginsparg, S.L. Glashow, Photon oscillations and the cosmic background radiation. Nature 306, 765–766 (1983)
5. R. Peccei, H.R. Quinn, CP conservation in the presence of instantons. Phys. Rev. Lett. 38,
1440–1443 (1977)
6. J.R. Ellis, J. Gunion, H.E. Haber, L. Roszkowski, F. Zwirner, Higgs bosons in a nonminimal
supersymmetric model. Phys. Rev. D 39, 844 (1989)
7. J. Derendinger, C.A. Savoy, Quantum effects and SU(2) x U(1) breaking in supergravity gauge
theories. Nucl. Phys. B 237, 307–328 (1984)
8. J. Frere, D. Jones, S. Raby, Fermion masses and induction of the weak scale by supergravity.
Nucl. Phys. B 222, 11–19 (1983)
9. V. Silveira, A. Zee, Scalar phantoms. Phys. Lett. B 161, 136–140 (1985)
10. T. Binoth, J. van der Bij, Influence of strongly coupled, hidden scalars on Higgs signals. Z.
Phys. C 75, 17–25 (1997). arXiv:hep-ph/9608245
11. B. Patt, F. Wilczek, Higgs-field portal into hidden sectors. arXiv:hep-ph/0605188
12. P. Minkowski, μ → eγ at a Rate of One Out of 10 9 Muon Decays? Phys. Lett. B 67, 421–428
(1977)
13. T. Yanagida, Horizontal symmetry and masses of neutrinos. Prog. Theor. Phys. 64, 1103 (1980)
14. M. Gell-Mann, P. Ramond, R. Slansky, Complex spinors and unified theories. Conf. Proc. C
790927, 315–321 (1979). arXiv:1306.4669 [hep-th]
15. R.N. Mohapatra, G. Senjanovic, Neutrino masses and mixings in gauge models with spontaneous parity violation. Phys. Rev. D 23, 165 (1981)
16. J.C. Pati, A. Salam, Lepton number as the fourth color. Phys. Rev. D 10, 275–289 (1974).
[Erratum: Phys.Rev.D 11, 703–703 (1975)]
17. R. Mohapatra, J.C. Pati, A natural left-right symmetry. Phys. Rev. D 11, 2558 (1975)
18. R.N. Mohapatra, J.C. Pati, Left-Right gauge symmetry and an Isoconjugate model of CP
violation. Phys. Rev. D 11, 566–571 (1975)
19. G. Senjanovic, R.N. Mohapatra, Exact left-right symmetry and spontaneous violation of parity.
Phys. Rev. D 12, 1502 (1975)
20. J.L. Hewett et al., Fundamental Physics at the Intensity Frontier (2012). arXiv:1205.2671
[hep-ex]. http://lss.fnal.gov/archive/preprint/fermilab-conf-12-879-ppd.shtml
21. R. Essig et al., Working group report: new light weakly coupled particles, in Proceedings, 2013
Community Summer Study on the Future of U.S. Particle Physics: Snowmass on the Mississippi
(CSS2013): Minneapolis, MN, USA, July 29–Aug 6, 2013. arXiv:1311.0029 [hep-ph]. http://
www.slac.stanford.edu/econf/C1307292/docs/IntensityFrontier/NewLight-17.pdf
22. M. Raggi, V. Kozhuharov, Results and perspectives in dark photon physics. Riv. Nuovo Cim.
38(10), 449–505 (2015)
77
Q = −
d
3 k
(2π) 3
Im L (ω, k) + Im T (ω, k)
ω(e ω/T − 1)
,
(5.27)
from which the luminosity in Eq. (5.18) can be computed and compared with the
astrophysical limit of interest. The expression for Im L ,T (ω, k) for the massive
dark photon can be found in [30–32] where plasma effects are also included.
References
1. P. Fayet, Effects of the Spin 1 partner of the Goldstino (Gravitino) on neutral current phenomenology. Phys. Lett. B 95, 285–289 (1980)
2. P. Fayet, On the search for a new Spin 1 Boson. Nucl. Phys. B 187, 184–204 (1981)
3. L.B. Okun, Limits of electrodynamics: paraphotons? Sov. Phys. JETP 56, 502 (1982). [Zh.
Eksp. Teor. Fiz.83,892(1982)]
4. H. Georgi, P.H. Ginsparg, S.L. Glashow, Photon oscillations and the cosmic background radiation. Nature 306, 765–766 (1983)
5. R. Peccei, H.R. Quinn, CP conservation in the presence of instantons. Phys. Rev. Lett. 38,
1440–1443 (1977)
6. J.R. Ellis, J. Gunion, H.E. Haber, L. Roszkowski, F. Zwirner, Higgs bosons in a nonminimal
supersymmetric model. Phys. Rev. D 39, 844 (1989)
7. J. Derendinger, C.A. Savoy, Quantum effects and SU(2) x U(1) breaking in supergravity gauge
theories. Nucl. Phys. B 237, 307–328 (1984)
8. J. Frere, D. Jones, S. Raby, Fermion masses and induction of the weak scale by supergravity.
Nucl. Phys. B 222, 11–19 (1983)
9. V. Silveira, A. Zee, Scalar phantoms. Phys. Lett. B 161, 136–140 (1985)
10. T. Binoth, J. van der Bij, Influence of strongly coupled, hidden scalars on Higgs signals. Z.
Phys. C 75, 17–25 (1997). arXiv:hep-ph/9608245
11. B. Patt, F. Wilczek, Higgs-field portal into hidden sectors. arXiv:hep-ph/0605188
12. P. Minkowski, μ → eγ at a Rate of One Out of 10 9 Muon Decays? Phys. Lett. B 67, 421–428
(1977)
13. T. Yanagida, Horizontal symmetry and masses of neutrinos. Prog. Theor. Phys. 64, 1103 (1980)
14. M. Gell-Mann, P. Ramond, R. Slansky, Complex spinors and unified theories. Conf. Proc. C
790927, 315–321 (1979). arXiv:1306.4669 [hep-th]
15. R.N. Mohapatra, G. Senjanovic, Neutrino masses and mixings in gauge models with spontaneous parity violation. Phys. Rev. D 23, 165 (1981)
16. J.C. Pati, A. Salam, Lepton number as the fourth color. Phys. Rev. D 10, 275–289 (1974).
[Erratum: Phys.Rev.D 11, 703–703 (1975)]
17. R. Mohapatra, J.C. Pati, A natural left-right symmetry. Phys. Rev. D 11, 2558 (1975)
18. R.N. Mohapatra, J.C. Pati, Left-Right gauge symmetry and an Isoconjugate model of CP
violation. Phys. Rev. D 11, 566–571 (1975)
19. G. Senjanovic, R.N. Mohapatra, Exact left-right symmetry and spontaneous violation of parity.
Phys. Rev. D 12, 1502 (1975)
20. J.L. Hewett et al., Fundamental Physics at the Intensity Frontier (2012). arXiv:1205.2671
[hep-ex]. http://lss.fnal.gov/archive/preprint/fermilab-conf-12-879-ppd.shtml
21. R. Essig et al., Working group report: new light weakly coupled particles, in Proceedings, 2013
Community Summer Study on the Future of U.S. Particle Physics: Snowmass on the Mississippi
(CSS2013): Minneapolis, MN, USA, July 29–Aug 6, 2013. arXiv:1311.0029 [hep-ph]. http://
www.slac.stanford.edu/econf/C1307292/docs/IntensityFrontier/NewLight-17.pdf
22. M. Raggi, V. Kozhuharov, Results and perspectives in dark photon physics. Riv. Nuovo Cim.
38(10), 449–505 (2015)