Beyond the Standard Model
SimulatedLarge Hadron ColliderCMS particle detector data depicting aHiggs boson produced by colliding protons decaying into hadron jets and electrons
Standard Model
Evidence Hierarchy problem Dark matter Dark energy Quintessence Phantom energy Dark radiation Dark photon Cosmological constant problem Strong CP problem Neutrino oscillation
Theories Brans–Dicke theory Cosmic censorship hypothesis Fifth force F-theory Theory of everything Unified field theory Grand Unified Theory Technicolor Kaluza–Klein theory 6D (2,0) superconformal field theory Noncommutative quantum field theory Quantum cosmology Brane cosmology String theory Superstring theory M-theory Mathematical universe hypothesis Mirror matter Randall–Sundrum model N = 4 supersymmetric Yang–Mills theory Twistor string theory Dark fluid Doubly special relativity de Sitter invariant special relativity Causal fermion systems Black hole thermodynamics Unparticle physics Graviphoton Graviscalar Graviton Gravitino Massive gravity Gauge gravitation theory Gauge theory gravity CPT symmetry
Supersymmetry MSSM NMSSM Superstring theory M-theory Supergravity Supersymmetry breaking Extra dimensions Large extra dimensions
Quantum gravity False vacuum String theory Spin foam Quantum foam Quantum geometry Loop quantum gravity Quantum cosmology Loop quantum cosmology Causal dynamical triangulation Causal fermion systems Causal sets Canonical quantum gravity Semiclassical gravity Superfluid vacuum theory
Experiments ANNIE Gran Sasso INO LHC SNO Super-K Tevatron NOvA
v t e

Thedark photon (alsohidden,heavy,para-, orsecluded photon) is a hypotheticalhidden sectorparticle, proposed as aforce carrier similar to thephoton ofelectromagnetism but potentially connected todark matter.^[1] In a minimal scenario, this new force can be introduced by extending the gauge group of theStandard Model of Particle Physics with a newabelianU(1)gauge symmetry. The corresponding newspin-1gauge 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. The dark photon can also interact with the Standard Model if some of the fermions are charged under the new abelian group.^[3] The possible charging arrangements are restricted by a number of consistency requirements such asanomaly cancellation and constraints coming fromYukawa matrices.

Observations of gravitational effects that cannot be explained byvisible matter alone imply the existence of matter which does not couple or only very weakly couples 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., incosmic 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 calculatedanomalous magnetic moment of the muon,^[7][8][9] although the simplest realisations of this idea are now in conflict with other experimental data.^[10] This discrepancy is usually thought of as a persisting hint forphysics beyond the Standard Model and should be accounted for by generalnew 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 themisalignment mechanism.^[11]

Adding a sector containing dark photons to theLagrangian 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., aDirac 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${\displaystyle A^{\mathrm{\prime }}}$ and theStandard Model hypercharge fields. The operator at play is${\displaystyle F_{\mu \nu }^{\mathrm{\prime }}{B}^{\mu \nu }}$, where${\displaystyle F_{\mu \nu }^{\mathrm{\prime }}}$ is thefield 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. Afterelectroweak symmetry breaking and diagonalising the terms containing the field strength tensors (kinetic terms) by redefining the fields, the relevant terms in the Lagrangian are

$${\displaystyle \mathcal{L}\supset -\frac{1}{4}{F}^{\mathrm{\prime }\mu \nu }{F}_{\mu \nu }^{\mathrm{\prime }}+\frac{1}{2}{m}_{A^{\mathrm{\prime }}}^2{A}^{\mathrm{\prime }\mu }{A}_{\mu }^{\mathrm{\prime }}+ϵe{A}^{\mathrm{\prime }\mu }{J}_{\mu }^{EM}}$$

where${\displaystyle m_{A^{\mathrm{\prime }}}}$ is the mass of the dark photon (in this case it can be thought of as being generated by theHiggs orStueckelberg mechanism),${\displaystyle ϵ}$ is the parameter describing the kinetic mixing strength and${\displaystyle J_{\mu }^{EM}}$ denotes theelectromagnetic 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.^[12][13] The incorporation of new Dirac fermions as dark matter particles in this theory is uncomplicated and can be achieved by simply adding theDirac terms to the Lagrangian.^[14] A massless dark photon, however, will be fully decoupled from the Standard Model and will not have any experimental consequence by itself.^[15] If there is an additional particle in the model which was originally interacting with the dark photon, it will become amillicharged particle which could be directly searched for.^[16][17]

A massive dark photon candidate with kinetic mixing strength${\displaystyle ϵ}$ could spontaneously convert to a Standard Modelphoton^[18]. A cavity, with resonant frequency tuned to match the mass of a dark photon candidate${\displaystyle hf=m_{A^{\mathrm{\prime }}}{c}^2}$, 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 foraxion dark matter. With linear amplification, however, is difficult to overcome the effective noise imposed by thestandard 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 atthe University of Chicago in collaboration withFermilab.^[19]The experiment has excluded dark photon candidates with mass centered around 24.86 μeV and${\displaystyle ϵ\ge 1.68\times {10}^{-15}}$ by using asuperconducting 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.

For a dark photon mass above theMeV, current limits are dominated by experiments based inparticle accelerators. Assuming that dark photons produced in the collisions would then decay mainly into positron-electronpairs, the experiments search for an excess ofelectron-positron pairs that would originate from the dark photondecay. On average, experimental results now indicate that this hypothetical particle must interact withelectrons 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 aGeV), the best limits would arise fromcollider experiments. While several experimental apparatus have been leveraged in the search for this particle,^[20] some notable examples are theBaBar experiment,^[10] or theLHCb^[21] andCMS experiments at theLHC. For dark photon of intermediary masses (roughly between theelectron andproton masses), the best constraints arise fromfixed target experiments. As an example, the Heavy Photon Search (HPS) experiment^[22] atJefferson Lab collides multi-GeV electrons with a tungsten target foil in searching for this particle.

• Dark radiation – Postulated type of radiation that mediates interactions of dark matter
• Dual photon – Hypothetical particle dual to the photon
• Fifth force – Speculative physics theory
• Millicharged particles
• Light dark matter
• Photino – Hypothetical superpartner of the photon

• Bosons
• Dark matter
• Hypothetical elementary particles
• Physics beyond the Standard Model
• Dark concepts in astrophysics
• Force carriers

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