Universe’s Worth of Electrons to Probe Long-Range Interactions of High-Energy Astrophysical Neutrinos

Astrophysical searches for new long-range interactions complement collider searches for new short-range interactions. Conveniently, neutrino flavor oscillations are keenly sensitive to the existence of long-ranged flavored interactions between neutrinos and electrons, motivated by lepton-number symmetries of the standard model. For the first time, we probe them using TeV-PeV astrophysical neutrinos and accounting for all large electron repositories in the local and distant Universe. The high energies and colossal number of electrons grant us unprecedented sensitivity to the new interaction, even if it is extraordinarily feeble. Based on IceCube results for the flavor composition of astrophysical neutrinos, we set the ultimate bounds on long-range neutrino flavored interactions.

Figure 1

Constraints on the $Z_{e\mu }^{\prime }$ boson mediating long-range neutrino-electron interactions. Our limits come from the flavor composition of high-energy astrophysical neutrinos at $1\sigma$, using current IceCube results and projections for IceCube and IceCube-Gen2, assuming normal neutrino mass ordering and a spectrum $\propto E_{\nu }^{-2.5}$. Existing direct limits are from atmospheric [25] and solar and reactor neutrinos [26]. Indirect limits from searches for nonstandard neutrino interactions [27, 28, 29] (90% C.L.), tests of the equivalence principle [30] (95% C.L.), and black-hole superradiance [31] (90% C.L.). The weak gravity conjecture [32] suggests that gravity is the weakest force and so $g_{e\mu }^{\prime 2}\ge G_N{m}_{\nu }^2$; we adopt a neutrino mass $m_{\nu }=0.01\mathrm{eV}$.

Figure 2

Electron repositories in the local and distant Universe used to set limits on long-range neutrino-electron interactions.

Figure 3

Long-range potential $V_{e\beta }$ induced by the $L_e-L_{\beta }$ symmetry ($\beta =\mu$, $\tau$) sourced by electrons in Earth, the Moon, Sun, Milky Way, and by cosmological electrons. The $Z_{e\beta }^{\prime }$ boson that mediates the potential has mass $m_{e\beta }^{\prime }$ and coupling $g_{e\beta }^{\prime }$. The curve is the isocontour of the potential at a value the vacuum oscillation Hamiltonian—concretely, its element $H_{\mathrm{vac},ee}$—evaluated at $E_{\nu }=100\mathrm{TeV}$, plus the potential $V_{\mathrm{mat}}^{\oplus }$ due to standard matter effects inside Earth. Because of the $\sim 1/E_{\nu }$ dependence of ${\mathbf{H}}_{\mathrm{vac}}$ and the $\sim g_{e\beta }^{\prime 2}$ dependence of $V_{e\beta }$, the isocontour would shift to lower couplings at higher $E_{\nu }$.

Figure 4

Flavor ratios at Earth $f_{\alpha ,\oplus }$ as functions of the long-range potential $V_{e\mu }$ associated to the $L_e-L_{\mu }$ symmetry for three illustrative choices of flavor ratios at the sources $(f_{e,S}:f_{\mu ,S}:f_{\tau ,S})=(\frac{1}{3}:\frac{2}{3}:0)$ (nominal case), $(0:1:0)$ (shown in the Supplemental Material [40]) and $(1:0:0)$ (pure ${\nu }_e$ from neutron decay shown only for illustration). We assume equal fluxes of $\nu$ and $\overline{\nu }$. In this plot, neutrino energy is fixed at $E_{\nu }=100\mathrm{TeV}$ for illustration, but our limits are obtained using energy-averaged flavor ratios $⟨f_{\alpha ,\oplus }⟩$ (see main text), which behave similarly to $V_{e\beta }$. For every value of $V_{e\mu }$, we scan over values of the standard-mixing parameters within their $1\sigma$ ranges [54] under normal ordering (NO). We include the IceCube $1\sigma$ flavor contours that we use to set limits on the new interaction: the current one [16] (“IceCube 2015”) and projections for IceCube [55] (“IceCube 2017”) and IceCube-Gen2 [56, 57]. For comparison, we show the regions of $f_{\alpha ,\oplus }$ allowed by standard mixing at $1\sigma$.