# Dark photon

The dark photon (also hidden, heavy, para- or secluded photon) is a hypothetical hidden sector particle, proposed as a force carrier similar to the photon of electromagnetism but potentially connected to dark matter.[1] In a minimal scenario, this new force can be introduced by extending the gauge group of the Standard Model of Particle Physics with a new abelian U(1) gauge symmetry. The corresponding new spin-1 gauge boson (i.e. the dark photon) can then couple very weakly to electrically charged particles through kinetic mixing with the ordinary photon[2] and could thus be detected. Other types of couplings beyond kinetic mixing are also possible.[3]

## Motivation

Observations of gravitational effects, that cannot be explained by visible matter alone, imply the existence of matter which does not or does only very weakly couple to the known forces of Nature. This dark matter dominates the matter density of the Universe, but its particles (if there are any) have eluded direct and indirect detection so far. Given the rich interaction structure of the well-known Standard Model particles, which make up only the subdominant component of the Universe, it is natural to think about a similarly interactive behaviour of dark sector particles. Dark photons could be part of these interactions among dark matter particles and provide a non-gravitational window (a so-called vector portal) into their existence by kinematically mixing with the Standard Model photon.[1][4] Further motivation for the search for dark photons comes from several observed anomalies in astrophysics (e.g. in cosmic rays) that could be related to dark matter interacting with a dark photon.[5][6] Arguably the most interesting application of dark photons arises in the explanation of the discrepancy between the measured and the calculated anomalous magnetic moment of the muon.[7][8][9] This discrepancy is usually thought of as a persisting hint for physics beyond the Standard Model and should be accounted for by general new physics models. Beside the effect on electromagnetism via kinetic mixing and possible interactions with dark matter particles, dark photons (if massive) can also play the role of a dark matter candidate themselves. This is theoretically possible through the misalignment mechanism.[10]

## Theory

Adding a sector containing dark photons to the Lagrangian of the Standard Model can be done in a straightforward and minimal way by introducing a new U(1) gauge field.[2] The specifics of the interaction between this new field, potential new particle content (e.g. a Dirac fermion for dark matter) and the Standard Model particles are virtually only limited by the creativity of the theorist and the constraints that have already been put on certain kinds of couplings. The arguably most popular basic model involves a single new broken U(1) gauge symmetry and kinetic mixing between the corresponding dark photon field ${\displaystyle A^{\prime }}$ and the Standard Model hypercharge fields. The operator at play is ${\displaystyle F_{\mu \nu }^{\prime }B^{\mu \nu }}$, where ${\displaystyle F_{\mu \nu }^{\prime }}$ is the field strength tensor of the dark photon field and ${\displaystyle B^{\mu \nu }}$denotes the field strength tensor of the Standard Model weak hypercharge fields. This term arises naturally by writing down all terms allowed by the gauge symmetry. After electroweak symmetry breaking and diagonalising the terms containing the field strength tensors (kinetic terms) by redefining the fields, the relevant terms in the Lagrangian are

${\displaystyle {\mathcal {L}}\supset -{\frac {1}{4}}F^{\prime \mu \nu }F_{\mu \nu }^{\prime }+{\frac {1}{2}}m_{A^{\prime }}^{2}A^{\prime \mu }A_{\mu }^{\prime }+\epsilon eA^{\prime \mu }J_{\mu }^{EM}}$

where ${\displaystyle m_{A^{\prime }}}$is the mass of the dark photon (in this case it can be thought of as being generated by the Higgs or Stueckelberg mechansim), ${\displaystyle \epsilon }$ is the parameter describing the kinetic mixing strength and ${\displaystyle J_{\mu }^{EM}}$denotes the electromagnetic current with its coupling ${\displaystyle e}$. The fundamental parameters of this model are thus the mass of the dark photon and the strength of the kinetic mixing. Other models leave the new U(1) gauge symmetry unbroken, resulting in a massless dark photon carrying a long-range interaction.[11] A massless dark photon, however, will experimentally be hard to distinguish from the Standard Model photon. The incorporation of new Dirac fermions as dark matter particles in this theory is uncomplicated and can be achieved by simply adding the Dirac terms to the Lagrangian.[12]

## References

1. ^ a b Essig, R.; Jaros, J. A.; Wester, W.; Adrian, P. Hansson; Andreas, S.; Averett, T.; Baker, O.; Batell, B.; Battaglieri, M. (2013-10-31). "Dark Sectors and New, Light, Weakly-Coupled Particles". arXiv: [hep-ph].
2. ^ a b Holdom, Bob (1986-01-09). "Two U(1)'s and ϵ charge shifts". Physics Letters B. 166 (2): 196–198. Bibcode:1986PhLB..166..196H. doi:10.1016/0370-2693(86)91377-8. ISSN 0370-2693.
3. ^ Galison, Peter; Manohar, Aneesh (1984-03-08). "Two Z's or not two Z's?". Physics Letters B. 136 (4): 279–283. Bibcode:1984PhLB..136..279G. doi:10.1016/0370-2693(84)91161-4. ISSN 0370-2693.
4. ^ Battaglieri, Marco; Belloni, Alberto; Chou, Aaron; Cushman, Priscilla; Echenard, Bertrand; Essig, Rouven; Estrada, Juan; Feng, Jonathan L.; Flaugher, Brenna (2017-07-14). "US Cosmic Visions: New Ideas in Dark Matter 2017: Community Report". arXiv: [hep-ph].
5. ^ Pospelov, Maxim; Ritz, Adam (January 2009). "Astrophysical Signatures of Secluded Dark Matter". Physics Letters B. 671 (3): 391–397. arXiv:. Bibcode:2009PhLB..671..391P. doi:10.1016/j.physletb.2008.12.012.
6. ^ Arkani-Hamed, Nima; Finkbeiner, Douglas P.; Slatyer, Tracy R.; Weiner, Neal (2009-01-27). "A Theory of Dark Matter". Physical Review D. 79 (1). arXiv:. Bibcode:2009PhRvD..79a5014A. doi:10.1103/PhysRevD.79.015014. ISSN 1550-7998.
7. ^ Pospelov, Maxim (2009-11-02). "Secluded U(1) below the weak scale". Physical Review D. 80 (9). arXiv:. Bibcode:2009PhRvD..80i5002P. doi:10.1103/PhysRevD.80.095002. ISSN 1550-7998.
8. ^ Endo, Motoi; Hamaguchi, Koichi; Mishima, Go (2012-11-27). "Constraints on Hidden Photon Models from Electron g-2 and Hydrogen Spectroscopy". Physical Review D. 86 (9). arXiv:. Bibcode:2012PhRvD..86i5029E. doi:10.1103/PhysRevD.86.095029. ISSN 1550-7998.
9. ^ Giusti, D.; Lubicz, V.; Martinelli, G.; Sanfilippo, F.; Simula, S. (October 2017). "Strange and charm HVP contributions to the muon ($g - 2)$ including QED corrections with twisted-mass fermions". Journal of High Energy Physics. 2017 (10). arXiv:. Bibcode:2017JHEP...10..157G. doi:10.1007/JHEP10(2017)157. ISSN 1029-8479.
10. ^ Arias, Paola; Cadamuro, Davide; Goodsell, Mark; Jaeckel, Joerg; Redondo, Javier; Ringwald, Andreas (2012-06-08). "WISPy Cold Dark Matter". Journal of Cosmology and Astroparticle Physics. 2012 (6): 013–013. arXiv:. Bibcode:2012JCAP...06..013A. doi:10.1088/1475-7516/2012/06/013. ISSN 1475-7516.
11. ^ Ackerman, Lotty; Buckley, Matthew R.; Carroll, Sean M.; Kamionkowski, Marc (2009-01-23). "Dark Matter and Dark Radiation". Physical Review D. 79 (2). arXiv:. Bibcode:2009PhRvD..79b3519A. doi:10.1103/PhysRevD.79.023519. ISSN 1550-7998.
12. ^ Ilten, Philip; Soreq, Yotam; Williams, Mike; Xue, Wei (2018-01-15). "Serendipity in dark photon searches". arXiv: [hep-ph].