For example, according to the gauge theory a massless, spin 1, Abelian field must be electromagnetic field, but could there be another field which obeys the very same Maxwell’s equation, except that the charge term is not regular charges, but an entirely different type of charges known as “dark charges”? Consequently, the quanta of the fields (dark photons) don’t interact with regular matters just like dark matters. Besides the coupling constant may not be 1/137. Do our theories prohibit the existence of such fields? It’s likely that gravity is the only spin 2 field because energy and momentum are universal, but there can be different types of charges like electric and color charges.
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- $\begingroup$ Judging by a cursory scan of the literature, $\mathrm{U}(1)$ and $\mathrm{SU}(N)$ groups, the latter typically taking $N=2$, are often considered in models of dark radiation. $\endgroup$J.G.– J.G.2025-10-19 16:11:06 +00:00Commented Oct 19 at 16:11
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2 Answers
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2 Of course. Mathematically it's the same. The only thing that connects a physical theory to reality is an observation. You can postulate millions of fields that are mathematically equivalent, but with no interaction, who's to say they exist.
- $\begingroup$ Is this how multi Higgs model works? $\endgroup$哲煜黄– 哲煜黄2025-10-20 03:10:08 +00:00Commented Oct 20 at 3:10
- $\begingroup$ This answer could be improved by actually engaging with the field of physics beyond the Standard Model. We certainly have more guidance into BSM physics than just 'any new physics is equally likely'. $\endgroup$SethK– SethK2025-10-20 22:06:02 +00:00Commented Oct 20 at 22:06
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Great question! Yes, there are many good reasons to think there may be additional $U(1)$ gauge symmetries.
For a dark $U(1)$ gauge theory, you could for example find microphysical motivation in 'mirror' or 'twin' models which postulate another full copy of the Standard Model fields all interacting with their own copy of the gauge fields. These models have dark fermions interacting with dark photons, and also dark gluons and dark W,Z,H bosons. In early days this was just an obvious possibility for a dark sector (a lot of early work is in Russian journals that have not been digitized, but here's an early reference), later gaining some motivation from string theory (see e.g. here), and more recently much activity based on motivation from Higgs physics (starting from here).
More generally an enormous amount of work has been done from a bottom-up perspective, studying the possibility that the dark photon may be dark matter (see e.g. this review), or that dark matter interacts with a dark photon (e.g. this work. There can be intriguing, non-trivial phenomenology there because such a dark photon can subtly interact with the Standard Model photon due to a phenomenon called 'kinetic mixing' which arises naturally (see e.g. here). For an up-to-date overview of the constraints on dark photons can a huge variety of experiments/observations, see here.
It's not an exaggeration to say that over the past decade, one of the most popular directions in particle physics research has been understanding the phenomenology of dark photons and the many possible ways to probe them.
Furthermore, additional photons which are not totally 'dark' but which can link us to dark matter are extremely well-motivated in many of our best theories for what the universe looks like at small distances. In particular, theories of grand unification enlarge the gauge group of the Standard Model. This often results in additional $U(1)$ factors under which the familiar particles are charged, as well as possibly other particles. These additional $U(1)$ factors must be 'Higgsed' (spontaneously broken) so that this photon gets a mass and we do not have an additional force at long distances (of course this is not surprising, you have to spontaneously break whatever grand unified gauge group you introduce).
Perhaps the most familiar example is 'baryon minus lepton number' $U(1)_{B-L}$, which in the Standard Model is a 'global' symmetry. In many theories of grand unification, $U(1)_{B-L}$ starts off as part of the gauge group (e.g. in Pati-Salam or in $SO(10)$, two of the simplest and most well-motivated). There can easily be additional matter which is charged under this gauge group, and which only communicates with us through this broken force, so is 'dark'. Another well-motivated choice is a lepton flavor symmetry e.g. $U(1)_{L_e- L_\mu}$ or $U(1)_{L_\mu - L_\tau}$, first studied here. See here for a review of the constraints on these 'hidden' photons.
Overall, postulating additional gauge symmetries and studying their phenomenology has been a huge endeavor for decades now. There is a lot of microphysical motivation to do so, and there is lots of very interesting cosmological and astrophysical phenomenology that can result from their presence.
