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{{short description|Hypothetical force carrier particle connected to dark matter}}{{Beyond the Standard Model}}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.ARXIV, 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, 1311.0029, hep-ph, 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 photonJOURNAL, 1986-01-09, Two U(1)'s and ϵ charge shifts, Physics Letters B, en, 166, 2, 196–198, 10.1016/0370-2693(86)91377-8, 0370-2693, Holdom, Bob, 1986PhLB..166..196H, and could thus be detected. The dark photon can also interact with the Standard Model if some of the fermions are charged under the new abelian group.JOURNAL, 1984-03-08, Two Z's or not two Z's?, Physics Letters B, en, 136, 4, 279–283, 10.1016/0370-2693(84)91161-4, 0370-2693, Galison, Peter, Manohar, Aneesh, 1984PhLB..136..279G, The possible charging arrangements are restricted by a number of consistency requirements such as anomaly cancellation and constraints coming from Yukawa matrices.

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.ARXIV, Battaglieri, Marco, Belloni, Alberto, Chou, Aaron, Cushman, Priscilla, Echenard, Bertrand, Essig, Rouven, Estrada, Juan, Feng, Jonathan L., Flaugher, Brenna, Brenna Flaugher, 2017-07-14, US Cosmic Visions: New Ideas in Dark Matter 2017: Community Report, 1707.04591, hep-ph, 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.JOURNAL, Pospelov, Maxim, Ritz, Adam, January 2009, Astrophysical Signatures of Secluded Dark Matter, Physics Letters B, 671, 3, 391–397, 10.1016/j.physletb.2008.12.012, 0810.1502, 2009PhLB..671..391P, 14611829, JOURNAL, Arkani-Hamed, Nima, Finkbeiner, Douglas P., Slatyer, Tracy R., Weiner, Neal, 2009-01-27, A Theory of Dark Matter, Physical Review D, 79, 1, 015014, 10.1103/PhysRevD.79.015014, 1550-7998, 0810.0713, 2009PhRvD..79a5014A, 17059718, 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,JOURNAL, Pospelov, Maxim, 2009-11-02, Secluded U(1) below the weak scale, Physical Review D, 80, 9, 095002, 0811.1030, 2009PhRvD..80i5002P, 10.1103/PhysRevD.80.095002, 1550-7998, 202294, JOURNAL, 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, 095029, 1209.2558, 2012PhRvD..86i5029E, 10.1103/PhysRevD.86.095029, 1550-7998, 118418557, JOURNAL, 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, 157, 1707.03019, 2017JHEP...10..157G, 10.1007/JHEP10(2017)157, 1029-8479, 119060801, although the simplest realisations of this idea are now in conflict with other experimental data.JOURNAL, Lees, J. P., Poireau, V., Tisserand, V., Grauges, E., Palano, A., Eigen, G., Stugu, B., Brown, D. N., Feng, M., Kerth, L. T., Kolomensky, Yu. G., Lee, M. J., Lynch, G., Koch, H., Schroeder, T., 2014-11-10, Search for a Dark Photon in e + e − Collisions at BaBar,weblink Physical Review Letters, en, 113, 20, 10.1103/PhysRevLett.113.201801, 0031-9007, free, 2445/133066, free, 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.JOURNAL, 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, 10.1088/1475-7516/2012/06/013, 1475-7516, 1201.5902, 2012JCAP...06..013A, 55566455,

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. 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 A^{prime} and the Standard Model hypercharge fields. The operator at play is F_{munu}^prime B^{munu}, where F_{munu}^{prime} is the field strength tensor of the dark photon field and B^{munu}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 aremathcal{L}supset-frac{1}{4}F^{primemunu}F^{prime}_{munu}+frac{1}{2}m_{A^prime}^{2}A^{primemu}A^{prime}_mu+epsilon e A^{primemu}J_{mu}^{EM}where 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 mechanism), epsilon is the parameter describing the kinetic mixing strength and J_{mu}^{EM}denotes the electromagnetic current with its coupling 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.JOURNAL, Ackerman, Lotty, Buckley, Matthew R., Carroll, Sean M., Kamionkowski, Marc, 2009-01-23, Dark Matter and Dark Radiation, Physical Review D, 79, 2, 023519, 0810.5126, 2009PhRvD..79b3519A, 10.1103/PhysRevD.79.023519, 1550-7998, 10056950, JOURNAL, Foot, Robert, Vagnozzi, Sunny, 2015, Dissipative hidden sector dark matter, Physical Review D, 91, 2, 023512, 1409.7174, 2015PhRvD..91b3512F, 10.1103/PhysRevD.91.023512, 119288106, 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.JOURNAL, Ilten, Philip, Soreq, Yotam, Williams, Mike, Xue, Wei, 2018-01-15, Serendipity in dark photon searches, Journal of High Energy Physics, 2018, 6, 4, 1801.04847, 2018JHEP...06..004I, 10.1007/JHEP06(2018)004, 59408241, A massless dark photon, however, will be fully decoupled from the Standard Model and will not have any experimental consequence by itself.JOURNAL, Holdom, Bob, January 1986, Two U(1)'s and ϵ charge shifts,weblink Physics Letters B, en, 166, 2, 196–198, 10.1016/0370-2693(86)91377-8, If there is an additional particle in the model which was originally interacting with the dark photon, it will become a millicharge particle which could be directly searched for.JOURNAL, Antel, C., Battaglieri, M., Beacham, J., Boehm, C., Buchmüller, O., Calore, F., Carenza, P., Chauhan, B., Cladè, P., Coloma, P., Crivelli, P., Dandoy, V., Darmé, L., Dey, B., Deppisch, F. F., 2023-12-11, Feebly-interacting particles: FIPs 2022 Workshop Report,weblink The European Physical Journal C, en, 83, 12, 10.1140/epjc/s10052-023-12168-5, 1434-6052, free, 20.500.11850/648117, free, JOURNAL, Ilten, Philip, Soreq, Yotam, Williams, Mike, Xue, Wei, 2018-01-15, Serendipity in dark photon searches, Journal of High Energy Physics, 2018, 6, 4, 1801.04847, 10.1007/JHEP06(2018)004, 2018JHEP...06..004I, 59408241,

Experiments

Direct conversion

(File:DarkPhoton.pdf|thumb|491x491px|Constraints on the dark photon's kinetic mixing parameter)A massive dark photon candidate with kinetic mixing strength epsilon could spontaneously convert to a Standard Model photon. A cavity, with resonant frequency tuned to match the mass of a dark photon candidate hf = m_{A^prime}c^2, can be used to capture the resulting photon.One technique to detect the presence of signal photon in the cavity is to amplify the cavity field with a quantum limited amplifier. This method is prevalent in the search for axion dark matter. With linear amplification, however, is difficult to overcome the effective noise imposed by the standard quantum limit and search for dark photon candidates that would produce a mean cavity population much less than 1 photon.By counting the number of photons in the cavity, it is possible to subvert the quantum limit. This technique has been demonstrated by researchers at the University of Chicago in collaboration with Fermilab.JOURNAL The experiment has excluded dark photon candidates with mass centered around 24.86 μeV and epsilon geq 1.68 times 10^{-15} by using a superconducting qubit to repeatedly measure the same photon. This has enabled a search speed up of over 1,000 as compared to the conventional linear amplification technique.

Accelerator searches

For a dark photon mass above the MeV, current limits are dominated by experiments based in particle accelerators. Assuming that dark photons produced in the collisions would then decay mainly into positron-electron pairs, the experiments search for an excess of electron-positron pairs that would originate from the dark photon decay. On average, experimental results now indicate that this hypothetical particle must interact with electrons at least a thousand times more feebly than the standard photon.In more details, for a dark photon which would be more massive than a proton (thus with mass larger than a GeV), the best limits would arise from collider experiments. While several experimental apparatus have been leveraged in the search for this particle,JOURNAL, Antel, C., Battaglieri, M., Beacham, J., Boehm, C., Buchmüller, O., Calore, F., Carenza, P., Chauhan, B., Cladè, P., Coloma, P., Crivelli, P., Dandoy, V., Darmé, L., Dey, B., Deppisch, F. F., 2023-12-11, Feebly-interacting particles: FIPs 2022 Workshop Report,weblink The European Physical Journal C, en, 83, 12, 10.1140/epjc/s10052-023-12168-5, 1434-6052, free, 20.500.11850/648117, free, some notable examples are the BaBar experiment, or the LHCbJOURNAL, Aaij, R., Abellán Beteta, C., Ackernley, T., Adeva, B., Adinolfi, M., Afsharnia, H., Aidala, C. A., Aiola, S., Ajaltouni, Z., Akar, S., Albicocco, P., Albrecht, J., Alessio, F., Alexander, M., Alfonso Albero, A., 2020-01-29, Search for A ′ → μ + μ − Decays,weblink Physical Review Letters, en, 124, 4, 10.1103/PhysRevLett.124.041801, 0031-9007, free, 2445/174990, free, and CMS experiments at the LHC. For dark photon of intermediary masses (roughly between the electron and proton masses), the best constraints arise from fixed target experiments. As an example, the Heavy Photon Search (HPS) experimentWEB, 11 March 2016, SLAC Elementary Particle Physics page, Heavy Photon Search,weblink 23 February 2023, 31 May 2023,weblink dead, at Jefferson Lab collides multi-GeV electrons with a tungsten target foil in searching for this particle.

See also

• {{annotated link|Dark radiation}}
• {{annotated link|Dual photon}}
• {{annotated link|Fifth force}}
• Millicharge particles
• Light dark matter
• {{annotated link|Photino}}

References

{{reflist|25em}}{{Dark matter}}