Dark Photons

It’s humbling to think that ordinary matter, including all of the elementary particles we’ve ever detected in laboratory experiments, only makes up about 5% of the energy density of the universe. The rest, of course, comes in the form of a dark sector: some form of energy density that can be reliably inferred through the gravitational fields it creates, but which we haven’t been able to make or touch directly ourselves.

It’s irresistible to imagine that the dark sector might be interesting. In other words, thinking like a physicist, it’s natural to wonder whether the dark sector might be complicated, with a rich phenomenology all its own. And in fact there is something interesting going on: over the last 15 years we’ve established that the dark sector comes in at least two different pieces! There is dark matter, 25% of the universe, which we know is like “matter” because it behaves that way — in particular, it clumps together under the force of gravity, and its energy density dilutes away as the universe expands. And then there is dark energy, 70% of the universe, which seems to be eerily uniform — smoothly distributed through space, and persistent (non-diluting) through time. So, there is at least that much structure in the dark sector.

But so far, there’s no evidence of anything interesting beyond that. Indeed, the individual components of dark matter and dark energy seem relatively vanilla and featureless; more precisely, taking them to be “minimal” provides an extremely good fit to the data. For dark matter, “minimal” means that the particles are cold (slowly moving) and basically non-interacting with each other. For dark energy, “minimal” means that it is perfectly constant throughout space and time — a pure vacuum energy, rather than something more lively.

Still — all we have are upper limits, not firm conclusions. It’s certainly possible that there is a bushel of interesting physics going on in the dark sector, but it’s just too subtle for us to have noticed yet. So it’s important for we theorists to propose specific, testable models of non-minimal dark sectors, so that observers have targets to shoot for when we try to constrain just how interesting the darkness really is.

Along those lines, Lotty Ackerman, Matt Buckley, Marc Kamionkowski and I have just submitted a paper that explores what I think is a particularly provocative possibility: that, just like ordinary matter couples to a long-range force known as “electromagnetism” mediated by particles called “photons,” dark matter couples to a new long-range force known (henceforth) as “dark electromagnetism,” mediated by particles known (from now on) as “dark photons.”

Dark Matter and Dark Radiation
Authors: Lotty Ackerman, Matthew R. Buckley, Sean M. Carroll, Marc Kamionkowski

We explore the feasibility and astrophysical consequences of a new long-range U(1) gauge field (“dark electromagnetism”) that couples only to dark matter, not to the Standard Model. The dark matter consists of an equal number of positive and negative charges under the new force, but annihilations are suppressed if the dark matter mass is sufficiently high and the dark fine-structure constant $hatalpha$ is sufficiently small. The correct relic abundance can be obtained if the dark matter also couples to the conventional weak interactions, and we verify that this is consistent with particle-physics constraints. The primary limit on $hatalpha$ comes from the demand that the dark matter be effectively collisionless in galactic dynamics, which implies $hatalpha$ < 10-3 for TeV-scale dark matter. These values are easily compatible with constraints from structure formation and primordial nucleosynthesis. We raise the prospect of interesting new plasma effects in dark matter dynamics, which remain to be explored.

Just to translate that a bit, here is the idea. We’re imagining there is a completely new kind of photon, which couples to dark matter but not to ordinary matter. So there can be dark electric fields, dark magnetic fields, dark radiation, etc. The dark matter itself consists half of particles with dark charge +1, and half with antiparticles with dark charge -1. Now you might say to yourself, “Why don’t the particles and antiparticles all just annihilate into dark photons?” That kind of thinking is probably why ideas like this weren’t explored twenty years ago (as far as we know). But if you think about it, there is clearly a range of possibilities for which the dark matter doesn’t annihilate very efficiently; for example, if the mass of the individual dark matter particles was sufficiently large, their density would be very low, and they just wouldn’t ever bump into each other. Alternatively, if the strength of the new force was extremely weak, it just wouldn’t be that effective in bringing particles and antiparticles together.

None of that is surprising; the interesting bit is that when you run the numbers, they turn out to be pretty darn reasonable, as far as particle physics is concerned. For DM particles weighing several hundred times the mass of the proton, there should be about one DM particle per coffee-cup-sized volume of space. The strength of the dark electromagnetic force is characterized, naturally, by the dark fine-structure constant; remember that ordinary electromagnetism is characterized by the ordinary fine-structure constant α = 1/137. It turns out that the upper limit on the dark fine-structure constant required to stop the dark matter particles from annihilating away is — about the same! I was expecting it to be 10-15 or something like that, and it was remarkable that such large values were allowed.

However, we know a little more about the dark matter than “it doesn’t annhilate.” We also know that it is close to collisionless — dark matter particles don’t bump into each other very often. If they did, all sorts of things would happen to the shape of galaxies and clusters that we don’t actually observe. So there is another limit on the strength of dark electromagnetism: interactions should be sufficiently weak that dark matter particles don’t “cool off” by interacting with each other in galaxies and clusters. That turns into a more stringent bound on the dark fine-structure constant: about an order of magnitude smaller, at $hatalpha$ < 10-3. Still, not so bad.

More interestingly, we can’t say with perfect confidence that the dark matter really is effectively non-interacting. If a model like ours is right, and the strength of dark electromagnetism is near the upper bound of its allowed value, there might be very important consequences for the evolution of large-scale structure. At the moment, it’s a little bit hard to figure out what those consequences actually are, for mundane calculational reasons. What we are proposing is that the dark matter is really a plasma, and to understand how structure forms, one needs to consider dark magnetohydrodynamics. That’s a non-trivial task, but we’re hoping it will keep a generation of graduate students cheerfully occupied.

The idea of new forces acting on dark matter is by no means new; I’ve worked on it recently myself, and so have certain co-bloggers. (Strong, silent types who are too proud to blog about their own papers.) What’s exciting about dark photons is that they are much more natural from a particle-physics perspective. Typical models of quintessence and long-range fifth forces invoke scalar fields, which are easy and fun to work with, but which by all rights should have huge masses, and therefore not be very long-range at all. The dark photon comes from a gauge symmetry, just like the ordinary photon, and its masslessness is therefore completely natural.

Even the dark photon is not new. In a recent paper, Feng, Tu, and Yu proposed not just dark photons, but a barrelful of new dark fields and interactions:

Thermal Relics in Hidden Sectors
Authors: Jonathan L. Feng, Huitzu Tu, Hai-Bo Yu

Dark matter may be hidden, with no standard model gauge interactions. At the same time, in WIMPless models with hidden matter masses proportional to hidden gauge couplings squared, the hidden dark matter’s thermal relic density may naturally be in the right range, preserving the key quantitative virtue of WIMPs. We consider this possibility in detail. We first determine model-independent constraints on hidden sectors from Big Bang nucleosynthesis and the cosmic microwave background. Contrary to conventional wisdom, large hidden sectors are easily accommodated…

They show that these models manage to evade all sorts of limits you might be worried about, from getting the right relic abundance to fitting in with constraints from primordial nucleosynthesis and the cosmic microwave background.

Our model is actually simpler, because we have a different flavor of fish to fry: the possible impacts of this new long-range force in the dark sector on observable cosmological dynamics. We’re not sure yet what all of those impacts are, but they are fun to contemplate. And of course, another difference between dark electromagnetism and a boring scalar force is that electromagnetism has both positive and negative charges — thus, both attractive and repulsive forces. (Scalar forces tend to be simply attractive, and get all mixed up with gravity.) So we can imagine much more than a single species of dark matter; what if you had two different types of stable particles that carried dark charge? Then we’d be able to make dark atoms, and could start writing papers on dark chemistry.

You know that dark biology is not far behind. Someday perhaps we’ll be exchanging signals with the dark internet.

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74 Responses to Dark Photons

  1. Sean says:

    Thanks for the references, everyone, we will look them over. I wouldn’t be surprised if we missed some very referenceable stuff, but we did ask around to see if this particular idea had been examined before, and as far as we can tell it hasn’t. Again, the idea of interactions (even long-range U(1) interactions) in the dark sector is not new, but I think we are the first to take seriously the astrophysical consequences of such a force.

    TimG– Sure, the dark matter density is much higher in the center of a galaxy or cluster than it is in an average spot in the universe. But once you check the numbers, it’s still not nearly high enough for interactions to be significant — that’s one of things we checked.

    Lab Lemming– Jason is right, this is “cold” dark matter, but I was thinking of cooling in the context of galactic dynamics. Baryons cool off through dissipation and settle to the bottom of gravitational potential wells very efficiently; you don’t want the DM to do that, or it’s incompatible with observations.

    Arun, the DM can be either fermionic or bosonic.

    Count Iblis– That’s a good question, and we examined the possibility of dark E&M mixing with ordinary E&M. If they don’t mix at very high energies, we verified that there is no mixing induced at low energies; that’s just how the Feynman diagrams work out. So why don’t know why they don’t mix at high energies, but at least the setup is stable under quantum corrections.

    Shantanu– We checked against various limits on the DM interaction cross-section, including the bullet cluster.

  2. Lawrence B. Crowell says:

    I have not read this paper yet. I must confess that I wonder where the additional U(1) comes from. I suppose maybe it is from a mechanism similar to some U(n) breaking into n copies of U(1).

    If dark matter is some SUSY partner, or composite such as the neutralino, then is this U(1) gauge boson also a vector boson which is paired up with a fermion? Further, I wonder about the charge. There must be a charge which defines the source for this field. If the currents associated with this field, some form of divE = rho or int B*da = oint J*dx, are associated with SUSY partners, then this charge should be present in ordinary matter. SUSY transformations don’t wipe away charges.

    Lawrence B. Crowell

  3. Sean says:

    Yes, I forgot to mention: our DM candidate is certainly not some superpartner of any of the particles in the Standard Model, since we don’t want any of them to carry dark charge.

  4. ObsessiveMathsFreak says:

    Jason Dick

    See http://arxiv.org/abs/0803.0556.

    A few minutes googling turned up this resource on Dark Matter. The authors claims that existing results justifying dark matter are based on the assumption that classical models predict Keplerian dynamics for galactic disks, i.e. that the orbits of stars in the galactic disk should behave like planetary orbits in a solar system with increasing distance. This talk by V. Rubin from 2000 also seems to confirm that this is the general assumption among astronomers, and that failure of galactic rotations to fit this Keplerian model is taken as evidence for dark matter.

    As Feng and Gallo point out in their paper above, this assumption that Keplerian dynamics should apply to galactic disk is really not justified. Quite a brief investigation of the integrals involved will show that the Shell theorem does not apply to 2 dimensional discs, which Galaxies more or less are, we should not expect at all that velocities will obey a Keplerian profile, and should not really be surprised when they don’t.

    It seems that this assumption may be due to the fact that calculating the gravitational forces of 2D discs involves evaluating elliptic integrals which have singularities at their boundaries, a task which only really became open to general investigation in the last ten years or so with the advent of personal computers and computer algebraic and numerical programs. Prior to this, evaluations of such integrals would have required a not insubstantial budget, so it would not be surprising to find that the Keplerian assumption was never subjected to much scrutiny.

    The forumulae in the Feng and Gallo paper are (integrations excepted) quite elementary. In the paper in fact, they attempt to solve the inverse problem of determining the galactic mass density from the observed velocity profile.

    Given the seemingly mistaken assumptions of astronomers that Keplerians dynamics should apply to disks, one must also wonder about the assumptions made of Galactic clusters, composed as they are of these two dimensional discs which do not behave as spherical attractors.

    Anyway, as I mentioned before, astronomically speaking, I am a lay person, so I will stop there, and remind the reader that my assessment is not a fully informed one. Still, I think that it would be worth reviewing some of the “settled” concepts in astrophysics using the tools and methods which have become available over the last 80 or so years. We have the technology.

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  6. Sili says:

    I’m onto you. Next you’ll team up with Phil Plait and discover away for this new and improved dark stuff to destroy Earth and, hey presto!, you’ll be wanting to be made professors of Defence Against the Dark Arts.

    there should be about one DM particle per coffee-cup-sized volume of space.

    Espresso or cappouchino?

  7. Lawrence B. Crowell says:

    Sean: Yes, I forgot to mention: our DM candidate is certainly not some superpartner … .

    This reminds me of an idea I had some years ago where quantum field theory was fundamentally octonionic, where there are 7 copies of quaternions. Each of these copies “defined” a “standard model,” but they only transformed between each other by very weak interactions that are nonassociative. I gave up on the idea, but I played with the idea that there exist 6 other “gauge worlds” which collectively composed what we call dark matter.

    What ever this dark matter is it clearly does not dissipate energy much, such as EM radiation emitted by hot plasmas and the rest. In order for gravity to clump matter into small volumes you need this sort of mechanism. Dark matter particles then appear to largely orbit around without giving up their energy and so DM clouds are diffuse and extensive.

    For your model to hold, what do you propose as the charge sources, or the dark matter fermions analogous to electrons etc which carry this additional U(1) charge?

    Lawrence B. Crowell

  8. Aiya-Oba says:

    Congratulations Sean, I think you have discovered a whole new world is Astrophysics.-Aiya-Oba(Poet/Philosopher).

  9. Jason Dick says:


    You could have actually read the link before typing such a long post. It had precious little to do with galaxy rotation curves. Galaxy rotation curves are only one small piece of evidence for dark matter, and if that’s the only evidence we had, we wouldn’t be nearly so confident that it’s out there.

    That aside, however, the reason why astronomers believe that galaxy rotation curves should at least approximately follow Keplerian dynamics is because the majority of the stars in most galaxies is near the core. The density of stars falls off dramatically with distance from the center, so the fact that spiral galaxies are disk-like is actually a pretty small effect. Furthermore, the galaxy rotation curves have been also shown to be inconsistent with Newtonian physics in elliptical galaxies.

  10. milkshake says:

    What if there was a DM/anti-DM asymmetry and all massive DM particles happened to have the same “dark charge” sign so that the “dark electromagnetism” effectively acted as a repulsive interaction? Would this fit the observed DM distribution in the galaxies?

  11. Lawrence B. Crowell says:


    This is a very good point. If there are dark charges q_d then there have to be an equal number of opposite charges -q_d. Why? Imagine there is a space with only one charge on it. Suppose the space is a sphere. Then in a classical picture the lines of force leave all these charges and have “nowhere to go.” These lines of charges would wind around the space densely and some thought should indicate this is a divergence! If the space is flat the problem still remains, for you end up with a divergent field density “at infinity.” So from a topological vector field perspective lines of force which leave some source must terminate at an opposite charge.

    So there have to be opposite dark charges in this model. The question is whether the dark matter particles are particle-antiparticle pairs or not. The data is not entirely clear as yet. The article by Cirelli et. al http://arxiv.org/abs/0809.2409 reports on PAMELA data which suggest ~1 TeV DM-antiDM annihilations. Of course this does not lend weight one way or the other for this dark U(1) theory, but if this theory is right it might lend support for anti-DM particles with opposite dark charges. On the other hand, we might find the oppositely charged DM have to be at least in part due to some some other species. If this is the case this would suggest that dark matter corresponds to some alternate particle-gauge “world” coupled to our world largey by gravitation and very weakly by maybe some other processes. Will the LHC resolve some of these questions?

    Lawrence B. Crowell

  12. sleep says:

    Is it possible to test these ideas using the LHC? Why not?

  13. Lawrence B. Crowell says:

    We might be able to produce dark matter in the LHC. The Pamela results give a possible hint that we might be able to get dark matter at the TeV range. Of course if we produce dark matter particle we might have a devil of a time detecting them. It took 40 years to get the neutrino more or less figured out and figuring out the nature of dark matter particles could turn out to be much the same story.

    Lawrence B. Crowell

  14. Lab Lemming says:

    Assuming that a dark matter observer couldn’t interact with our EM, strong, and weak forces, could they see the gravitational signal of light matter? Or would they have to be unlucky enough to wander past a star in order to notice it?

  15. Sean says:

    In principle, dark astronomers doing very high-precision cosmology could certainly observe the existence of “ordinary” matter via its gravitational field. In practice, there aren’t going to be any dark observers, as the dark matter has to interact pretty weakly to be consistent with our observations, and that makes it very difficult to make an observer.

    Unfortunately there don’t seem to be any particle-physics signatures of this model. Again, the coupling to dark photons is pretty small, so dark matter particles will behave pretty much like ordinary WIMPs in the LHC or elsewhere. It might be possible to detect the dark matter, but it would be extremely hard to tell that there were such things as dark photons.

  16. Zenshadow says:

    I’m a layman to physics. Just Joe the Layman here. I was wondering if there had been any studies done to see if there is a link between when Inflation began (immediately following the big bang) and the ‘disappearance’ of anti-matter. Could they be aspects of the same event? The conversion of all that anti-matter to energy would power the inflation is my hypothesis. You can include me in any paper that gets published on this concept, lol.

  17. Quasar9 says:

    oops I just realised this post is two days old.
    Happy Halloween!

  18. S Halayka says:

    This is very interesting work…

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  20. tyler says:

    a golden age for Cosmic Variance! so many interesting posts and so little comments trolling!

    I have been working for 6 months just to formulate this idea as a question intelligent enough to ask here – and now here is the answer! Fascinating and very much appreciated!

    regarding the last paragraph in your initial post, sean, any dark biology would soon imply dark sex, which would of course provide 98% of the content in the dark internet.

  21. tyler says:

    too many exclamation points! too much strong Portland coffee!

    sorry about that

  22. Marshall says:

    Interesting paper.

    You should also consider solar system bounds on dark matter. This can be done in a number of ways – by comparing the mass of Earth as seen from the Moon and as from Lageos (Adler, S.A., J. Phys. A: Math. Theor. 41 (2008) 412002, or http://arxiv.org/pdf/0808.0899) or the disturbance in solar system celestial dynamics (http://arxiv.org/pdf/0806.3767, http://arxiv.org/pdf/0810.2827), or on its effects on the internal dynamics of the planets (http://arxiv.org/pdf/0808.2823).

    Remember that dark matter will clump gravitationally, which could have been important in the early universe and those clumps may have survived (Nature, VOL 433, 27 Jan 2005, 389). Such clumps will interact with normal matter gravitationally (if no other way), and that says that some fraction will be bound in structures with normal matter. If a dark matter clump comes through the solar system, and it gravitationally interacts with one of the planets, there is a chance that some of the clumps, or some portion of the clumps, will become gravitationally bound to the solar system, and thus detectable. (The same 3 body interactions will apply to individual dark matter particles if there is no clumping of dark matter.) Even if the rms velocity of the clumps is too high to make this very probable, 4.5 billion years is a long time and there will be a dark matter halo around the Sun, and maybe individual planets as well; this should be considered tests of dark matter.

  23. Alsee says:

    Is it a reasonable hypothesis to suggest that there are N independent sets of matter of equal mass? Given the current estimated ratio of dark matter to normal matter that would set N equal to 7 or 8. That would mean our dark matter problem would actually be composed of 6 or 7 sets of dark matter, with each of them dark to each of the others. The only cross-interaction would be via gravity.

    If our dark matter is composed of 6 or 7 independent sets then the density within each set is far lower, and the viable strength of interaction would be much higher within each set of dark matter. It would be neat if the self-interactions within each were exactly mirrors of the forces and strengths within our “light matter”, but as I understand it I think that would cause way too much clumping in violation of observations.

  24. Andrew P says:

    This idea of a second electromagnetism is not new. It actually dates from the 1950s which speculated on a mirror sector that would restore the global symmetries that are violated by neutrinos. A guy named Foot has publised a lot of papers on arxiv.org about mirror matter. I will point out that if the particle (atomic) masses are much larger than in the normal sector, mirror electromagentism could have a strength similar to our own, and still match observations. There is also no need for much mirror antimatter as mirror matter could have lost all antimatter by a mechanism similar to our own sector. If mirror atoms have a different mass, nuclear fusion, and thus stars made of mirror matter, might not exist. But even if there are no mirror stars, there should still be accretion phenomena, and they should emit dark sector light. A telescope that could see in mirror light might see nothing but quasars and glowing jets.

    How about something even wierder. Suppose that tachyons exist. Would a bound state of 2 tachyons itself be a tachyon? Or would it be a subluminal particle that is spread out over a large spatial volume. My gut tells me that it is the latter, but I do not know how to calculate this. If something like this exists, it could make for a very hard to detect form of dark matter.

  25. Lawrence B. Crowell says:

    Dark matter might indeed be due to a range of different fields, from braney LambdaCDM, to SUSY pairs and maybe alternate gauge fields and particles. It could be a complex world of sorts. Since dark matter is weakly interacting I agree with Sean that it is not likely to lead to complex configurations requred for “dark observers.”

    Lawrence B. Crowell