# What gives mass to dark matter particles?

Assuming that dark matter is not made of WIMPs (weakly interacting massive particles), but interacts only gravitationally, what would be the possible mechanism giving mass to dark matter particles? If they don't interact weakly, they couldn't get mass from interacting with the Higgs field. The energy of gravitational interactions alone does not seem to be sufficient to account for a large particle mass. Would this imply that dark matter consists of a very large number of particles with a very small mass, perhaps much smaller than of neutrinos? Or do we need quantum gravity to explain the origin of mass of dark matter?

• have you read this en.wikipedia.org/wiki/Dark_matter . There are various proposals , it is an open research question on many levels. – anna v May 30 '18 at 18:16
• Not all mass comes from the Higgs interaction - the Higgs isn't an explanation for mass in general, it's just an explanation for the mass of the electron (and some other particles). Every interaction can give rise to mass (or decrease it), and fundamental particles can be massive too. And the interaction involved (if any) could consistently with the standard model be completely unobservable to us, except through gravity, if there's no chain of interactions between the particles and "our" matter. And that's not the weirdest possibility (though already extremely speculative). – Luaan May 31 '18 at 10:33
• @Luaan All massive particles in SM interact with the Higgs field. (Except for neutrinos, which are not massive in SM.) The Higgs field is not responsible for all mass, this is not the point. The point is that the Higgs field is responsible for a particle being massive, having a rest mass. Energy is responsible for all mass. The Higgs interaction defines whether this energy is localized (belongs to a massive particle that can rest) or not (belongs to a massless particle moving with the speed of light like glouns). Thanks for your comments, but they don't seem to help with the question I asked. – safesphere May 31 '18 at 15:10
• The neutrino oscillations show that the neutrinos have mass. the SM is extended to that. There have been calculations on whether the neutrinos could be the dark mass candidates, and their masses are too small for a viable model of creating enough of them after the inflation period. (thats why the neutralinos are candidates) A new model has to be based on existing ones. Just saying many particles is not enough. – anna v May 31 '18 at 16:01
• But that's exactly the thing - the way the Higgs field gives an electron mass is exactly the same as e.g. the way the proton gets (most of) its mass from the strong nuclear force (though that's just one model). The only real difference is that only the Higgs field has a non-zero average value in our universe (e.g. the strong field is non-zero on average "inside" a proton, but not in the universe as a whole) - if it didn't, Higgs bosons would be the only massive "fundamental" particles (and electrons etc. wouldn't be mass-less - they just wouldn't exist at all). – Luaan Jun 1 '18 at 8:15

I think this question contains a misconception unfortunately caused by popular science descriptions of the Standard Model.

The question seems to assume there needs to be some concrete source that particles "get" mass from, as if mass is a resource like money and the Higgs field is giving it out. But that's not right. In a generic field theory there is no issue adding a new field $\psi$ whose particles have mass. The only thing you have to do is make sure the Lagrangian has a term proportional to $\psi^2$.

You might protest that this violates the conservation of energy because the mass has to "come from" somewhere, but that's not right. Mass is the energy price for creating a particle. I don't create money by changing the pricetag of an item in a store.

The reason science popularizers say that mass must come from the Higgs mechanism is because of a peculiarity of the Standard Model (SM). The symmetries of the SM forbid a term such as $\psi^2$ for any field $\psi$ in the SM, so we need a trick to get a mass term. In brief, the Higgs field $\phi$ allows us to write terms like $\phi \psi^2$ which do respect the symmetry. This is an interaction term, but we can set up the Lagrangian so the Higgs field $\phi$ acquires a constant part, yielding the $\psi^2$ mass term we wanted.

However, once you start speculating about dark matter models, especially dark matter that does not interact with the electroweak force at all, these constraints don't apply and generically there is nothing forbidding a $\psi^2$ term. There's no need for any special mechanism for "giving" mass. You just treat mass exactly like you did in high school, intro mechanics and quantum mechanics: write it down, call it $m$ and call it a day.

• I think this answer contains a misconception unfortunately caused by a popular confusion between physics and math. Physics is based on math, but is more than that. Physics is life, it has meaning. It takes intuition. All known massive particles (let's set mysterious neutrinos aside for now) acquire mass (not the amount, but the fact of having it) from the Higgs field. Apparently, any known particle can move in time, only if it interacts with a scalar field permeating the universe. Sounds like a fundamental reason, a law of nature perhaps? So can we just add mass by hand? Sure, on paper we can. – safesphere May 31 '18 at 17:38
• @safesphere Indeed, intuition is extremely important for doing physics. But it's important to have the intuition rooted in something, like real mathematics, so you can check it and fix it. For example, we get about a question a day here from people who reject special relativity and refuse to read the arguments supporting it, because it conflicts with their physical intuition. – knzhou May 31 '18 at 18:01
• @safesphere If you try to make a general principle just from one example, without knowing how the example works in full, you may be misled. Recall the cargo cultists who thought that building a runway on their island would make planes magically appear. It is kind of like seeing one Java program and thinking that every program in the world must contain "public static void main(String[] args)". – knzhou May 31 '18 at 18:03
• @safesphere I mean, I don't disagree that the Higgs mechanism is a very common and important way to end up with particles with mass. But I can think of several dark matter candidates that don't get mass from the Higgs off the top of my head. And even for the ones that do get mass from a Higgs mechanism, it's often a different Higgs field from the one in the SM. – knzhou May 31 '18 at 18:06

There are various ways dark matter could acquire mass that have nothing to do with the standard model weak force. For example, there are theories involving a hidden sector- particles that do not interact with the standard model gauge bosons at all, but have their own interactions.

Note that the Higgs mechanism is not required for all mass generation in the standard model. The massive gauge bosons acquire their mass through the Higgs mechanism, but there are models where the fermionic masses are acquired through different mechanisms. The source of mass for neutrinos in particular is unknown.

Without knowing what dark matter is, it is of course impossible to determine how it acquires mass.

If it has no interactions at all, there's no need for a mechanism to acquire mass. Explicit mass terms in the standard model Lagrangian are only a problem because they break gauge symmetry. If a field doesn't couple to the gauge fields, its mass terms don't break gauge symmetry, and the mass can just be added to the Lagrangian by hand.

• My question is specifically about the dark matter that interacts only gravitationally. Thus the hidden sector and all other interactions are excluded. Sorry, but you seem to be answering a more generic question than mine. There are no known ways in the Standard Model that I am aware of for only gravitationally interacting dark matter to acquire mass. – safesphere May 30 '18 at 18:30
• @safesphere If it has no interactions at all, there's no contradictions to just give it a mass "by hand" in the Lagrangian, since it doesn't interact with any gauge fields and so a mass term does not break gauge symmetry. – Chris May 30 '18 at 19:06
• @safesphere The Standard Model isn't a complete description of the universe. It just describes all the (non-gravitational) interactions between the quantum fields/particles you see around you. If dark matter doesn't interact with those fields/particles, it has nothing to do with the Standard Model. The reason the electron requires (something like) the Higgs field within SM is that it interacts weakly - and weak interaction breaks some pretty important symmetries. If you "take away" the Higgs, you get two "electron" fields - one of which is weakly interacting, and the other isn't. – Luaan May 31 '18 at 10:42
• @safesphere If you want a quick picture of what the interactions and particles would look like if the average value of the Higgs field were zero (it is thought that happens at extremely high energies, possibly during the very earliest time of our unvierse), profmattstrassler.com/articles-and-posts/… is a great summary. The site also has lots of deeper (though still very simple) explanations about the Standard Model and quantum physics in general. – Luaan May 31 '18 at 10:47
• @safesphere A particle with no interactions at all is at least as unnatural, and if you posit a particle has no interactions, putting the mass in by hand is the only way for it to have mass. As for quantum gravity, the only honest answer is "nobody knows." Also, as an aside, I wouldn't say QFT works out easier for massless particles. Particles naturally acquire mass in a QFT. You can only have massless particles if there is some unbroken symmetry that protects the masslessness of the particle. – Chris May 31 '18 at 19:21

From: "A White Paper on keV Sterile Neutrino Dark Matter" (9 Feb 2017), by over 130 authors:

"Executive Summary

Despite decades of searching, the nature and origin of Dark Matter (DM) remains one of the biggest mysteries in modern physics. Astrophysical observations over a vast range of physical scales and epochs clearly show that the movement of celestial bodies, the gravitational distortion of light and the formation of structures in the Universe cannot be explained by the known laws of gravity and observed matter distribution $^{[1–7]}$.

They can, however, be brought into very good agreement if one postulates the presence of large amounts of non-luminous DM in and between the galaxies, a substance which is much more abundant in the Universe than ordinary matter $^{[1]}$. Generic ideas for what could be behind DM, such as Massive Compact Halo Objects (MACHOs) $^{[8–11]}$ are largely ruled out $^{[12, 13]}$ or at least disfavored $^{[14, 15]}$. Alternative explanations based on a modification of the law of gravity $^{[16]}$ have not been able to match the observations on various different scales. Thus, the existence of one or several new elementary particles appears to be the most attractive explanation.

As a first step, the suitability of known particles within the well-tested Standard Model (SM) has been examined. Indeed, the neutral, weakly interacting, massive neutrino could in principle be a DM candidate. However, neutrinos are so light that even with the upper limit for their mass $^{[17, 18]}$ they could not make up all of the DM energy density $^{[19]}$. Moreover, neutrinos are produced with such large (relativistic) velocities that they would act as hot DM (HDM), preventing the formation of structures such as galaxies or galaxy clusters $^{[20]}$.

Consequently, explaining DM in terms of a new elementary particle clearly requires physics beyond the SM. There are multiple suggested extensions to the SM, providing a variety of suitable DM candidates, but to date there is no clear evidence telling us which of these is correct."

...

References:

1. Planck collaboration, P. A. R. Ade et al., Planck 2015 results. XIII. Cosmological parameters, Astron. Astrophys. 594 (2016) A13, [1502.01589].
2. M. Persic, P. Salucci and F. Stel, The Universal rotation curve of spiral galaxies: 1. The Dark matter connection, Mon. Not. Roy. Astron. Soc. 281 (1996) 27, [astro-ph/9506004].
3. S. M. Faber and R. E. Jackson, Velocity dispersions and mass to light ratios for elliptical galaxies, Astrophys. J. 204 (1976) 668.
4. N. Kaiser and G. Squires, Mapping the dark matter with weak gravitational lensing, Astrophys. J. 404 (1993) 441–450.
5. D. Clowe, A. Gonzalez and M. Markevitch, Weak lensing mass reconstruction of the interacting cluster 1E0657-558: Direct evidence for the existence of dark matter, Astrophys. J. 604 (2004) 596–603, [astro-ph/0312273].
6. W. J. Percival, S. Cole, D. J. Eisenstein, R. C. Nichol, J. A. Peacock, A. C. Pope et al., Measuring the Baryon Acoustic Oscillation scale using the SDSS and 2dFGRS, Mon. Not. Roy. Astron. Soc. 381 (2007) 1053–1066, [0705.3323].
7. R. Dave, L. Hernquist, N. Katz and D. H. Weinberg, The Low redshift Lyman alpha forest in cold dark matter cosmologies, Astrophys. J. 511 (1999) 521–545, [astro-ph/9807177].
8. B. Paczynski, Gravitational microlensing by the galactic halo, Astrophys. J. 304 (1986) 1–5.
9. K. Griest, Galactic Microlensing as a Method of Detecting Massive Compact Halo Objects, Astrophys. J. 366 (1991) 412–421.
10. EROS collaboration, T. Lasserre, Not enough stellar mass machos in the galactic halo, Astron. Astrophys. 355 (2000) L39–L42, [astro-ph/0002253].
11. D. P. Bennett, Large Magellanic Cloud microlensing optical depth with imperfect event selection, Astrophys. J. 633 (2005) 906–913, [astro-ph/0502354].

...

1. K. Griest, A. M. Cieplak and M. J. Lehner, New Limits on Primordial Black Hole Dark Matter from an Analysis of Kepler Source Microlensing Data, Phys. Rev. Lett. 111 (2013) 181302.
2. P. Pani and A. Loeb, Tidal capture of a primordial black hole by a neutron star: implications for constraints on dark matter, JCAP 1406 (2014) 026, [1401.3025].
3. M. Milgrom, A Modification of the Newtonian dynamics as a possible alternative to the hidden mass hypothesis, Astrophys. J. 270 (1983) 365–370.
4. C. Kraus et al., Final results from phase II of the Mainz neutrino mass search in tritium beta decay, Eur. Phys. J. C40 (2005) 447–468, [hep-ex/0412056].
5. V. M. Lobashev et al., Direct search for mass of neutrino and anomaly in the tritium beta spectrum, Phys. Lett. B460 (1999) 227–235.
6. E. W. Kolb and M. S. Turner, The Early Universe, Front. Phys. 69 (1990) 1–547.
7. S. D. M. White, C. S. Frenk and M. Davis, Clustering in a Neutrino Dominated Universe, Astrophys. J. 274 (1983) L1–L5.

Also see: "The mass of the dark matter particle from theory and observations" (10 Apr 2012), by de Vega, Salucci, and Sanchez, on page 12:

"9. Conclusions

Dark matter is characterized by two basic quantities: the DM particle mass $m$ and the number of ultrarelativistic degrees of freedom at decoupling $g_d$ (or, alternatively the decoupling temperature $T_d$). We obtain the density profiles and theoretical relations between $m$ and $g_d$ involving the observable densities ...

From the observed values of the surface density we present here clear evidence that the mass of the DM particle is about one or two keV.".

• Only 130 authors? That's a shame. The photon-photon interaction paper had a lot more ;) - nature.com/nphys/journal/v13/n9/full/nphys4208.html#group-1 – safesphere May 31 '18 at 15:28
• @safesphere - I presume that they agree with the "executive summary", I would be in no position to disagree with their findings. I like to put the date and the authors after the link but in that case the number of authors (counted it only once) will have to do. The link you provided clearly has more authors, I wouldn't want to count them all. 🤯 - I hope the answer provides you with what is currently though to be the answer to your question, and the mass of the DM particle(s?). There are plenty of linked papers, checking the 'cited by' will find the newest info. Thanks for reading. – Rob May 31 '18 at 16:39

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