Photon Masses in the Landscape and the Swampland

TL;DR

The work argues that while tiny photon masses are technically natural in EFT, quantum gravity disfavors arbitrarily small Stückelberg masses because the $m_A\to0$ limit lies at infinite field-space distance and triggers a light tower of states per the Swampland Distance Conjecture, yielding a UV cutoff $\Lambda_{UV}$ that scales as $\min\big((m_A M_{Pl}/e)^{1/2}, e^{1/3} M_{Pl}\big)$. By formulating conjectures for axions and Stückelberg masses through BF theory and applying the Weak Gravity Theorem, the paper derives concrete constraints: $\Lambda_{UV} \lesssim \min(\sqrt{m_A M_{Pl}/e}, e^{1/3} M_{Pl})$ and, in the axion/B-field picture, $\Lambda_{UV} \lesssim \sqrt{f M_{Pl}}$. These bounds imply the Standard Model photon must be exactly massless and severely limit light dark-photon scenarios unless their mass arises via the Higgs mechanism. The results, supported by string-theoretic evidence and BF-theory reasoning, have significant implications for experimental searches and cosmology of dark photons, while also highlighting caveats and potential loopholes that could guide future model-building and proofs of the underlying conjectures.

Abstract

In effective quantum field theory, a spin-1 vector boson can have a technically natural small mass that does not originate from the Higgs mechanism. For such theories, which may be written in Stückelberg form, there is no point in field space at which the mass is exactly zero. I argue that quantum gravity differs from, and constrains, effective field theory: arbitrarily small Stückelberg masses are forbidden. In particular, the limit in which the mass goes to zero lies at infinite distance in field space, and this distance is correlated with a tower of modes becoming light according to the Swampland Distance Conjecture. Application of Tower or Sublattice variants of the Weak Gravity Conjecture makes this statement more precise: for a spin-1 vector boson with coupling constant $e$ and Stückelberg mass $m$, local quantum field theory breaks down at energies at or below $Λ_{\rm UV} = \min((m M_{\rm Pl}/e)^{1/2}, e^{1/3} M_{\rm Pl})$. Combined with phenomenological constraints, this argument implies that the Standard Model photon must be exactly massless. It also implies that much of the parameter space for light dark photons, which are the target of many experimental searches, is compatible only with Higgs and not Stückelberg mass terms. This significantly affects the experimental limits and cosmological histories of such theories. I explain various caveats and weak points of the arguments, including loopholes that could be targets for model-building.

Figures (2)

• Figure 1: Contours of the maximum possible UV cutoff on a theory of a Stückelberg photon, as a function of the photon mass $m_\gamma$ and the gauge coupling $e$. Unless $e$ is exceptionally tiny, the bound is set by $\sqrt{m_\gamma M_{\rm Pl}/e}$. Vertical orange dashed lines depict upper bounds on the Standard Model photon mass: $6 \times 10^{-16}~{\rm eV}$ from Jupiter's magnetic field Davis:1975mn; $2 \times 10^{-14}~{\rm eV}$ from FRBs Wu:2016brqBonetti:2016cpoBonetti:2017pym. The vertical green dashed line marks the approximate smallest mass for which generation of dark photon dark matter from inflationary fluctuations is efficient Graham:2015rva.
• Figure 2: Illustrating the distinction between field-theoretic axion (or abelian Higgs model) strings and fundamental (or Stückelberg) strings. The string at long distances is very similar in the two cases. The difference is that a fundamental string---including those appeaing in the Stückelberg theory---has a singular core, as the would-be symmetry-restoring point lies an infinite distance away in field space. In the latter case, but not the former, we interpret the square root of the string tension as an upper bound on the energy at which local effective field theory is valid.