Relic neutrinos at accelerator experiments

We present a new technique for observing low energy neutrinos with the aim of detecting the cosmic neutrino background using ion storage rings. Utilizing high energy targets exploits the quadratic increase in the neutrino capture cross section with beam energy, and with sufficient beam energy, enables neutrino capture through inverse-beta decay processes from a stable initial state. We also show that there exist ion systems admitting resonant neutrino capture, capable of achieving larger capture cross sections at lower beam energies than their nonresonant counterparts. We calculate the neutrino capture rate and the optimal experimental runtime for a range of different resonant processes and target ions and we demonstrate that the resonant capture experiment can be performed with beam energies as low as $\mathcal{O}(10\mathrm{TeV})$ per target nucleon. Unfortunately, none of the ion systems discussed here can provide sufficient statistics to discover the cosmic neutrino background with current technology. We address the challenges associated with realizing this experiment in the future, taking into account the uncertainty in the beam and neutrino momentum distributions, synchrotron radiation, as well as the beam stability.

Figure 1

Lab frame fluxes of low-energy electron neutrinos with mass $m_{\nu }=0.1\mathrm{eV}$, alongside the thresholds for Borexino and radiochemical detection experiments. The dashed lines have units ${\mathrm{cm}}^{-2}{\mathrm{s}}^{-1}$ and correspond to (from left to right): ${}^7\mathrm{Be}$ decay to ${}^7{\mathrm{Li}}^{*}$ and ${}^7\mathrm{Li}$, and $pep$ neutrinos. A full discussion of the solar fluxes is given in Appendix pp2, and a comprehensive review of neutrino fluxes at all energy scales can be found in [15].

Figure 2

Lab frame electron neutrino flux from the $\mathrm{C}\nu \mathrm{B}$.

Figure 3

Event rate enhancement for a PTOLEMY-on-a-beam type experiment (blue) as a function of the beam energy $E$ using $m_{\nu }=0.1\mathrm{eV}$, alongside the rate for the inverse process on a beam (orange), assuming $N_T^{\mathrm{beam}}=N_T^{\mathrm{rest}}$. Also shown by the dotted line is the decrease in the tritium decay rate as a function of the beam energy.

Figure 4

Isobar triplets with “stable-unstable-stable” configurations are candidates for 3-state systems for resonant neutrino capture. Graphic taken in part from [35].

Figure 5

Fraction of parent ions converted to signal ($D$ or $F$ states) for different resonant systems, all with $\chi =1$, $J_D=J_P$, $m_{\nu }=0.1\mathrm{eV}$, $Z=50$, $A=100$, ${\delta }_b=0$ and ${\mathcal{B}}_{EC}=0.5$ where appropriate. For the GS systems, $Q=100\mathrm{keV}$, whilst the ES systems use $Q=0.1\mathrm{keV}$ and $\eta ={10}^9$. Finally, for the 3-state systems we plot $N_F$ using a solid line, and $N_F+N_D$ using a dotted line.

Figure 6

Effect of the neutrino mass uncertainty on $R_{\tau }$, with respect to its maximum value. For simplicity, we set $R_{\tau }=1/\sqrt{{\delta }_{\nu }^2+{\delta }_b^2}$. As before, we use ${\delta }_{\nu }=0.00334$, corresponding to $m_{\nu ,\mathrm{true}}=0.1\mathrm{eV}$ and $T_{\nu }=T_{\nu }^0$. The solid white contours denote the value of ${\delta }_b$ that maximizes $R_{\tau }$ at a given value of ${\delta }_m$, whilst the white dotted contours are located at $|{\delta }_m|={\delta }_{\nu }$.

Figure 7

Dependence of the bound beta decay branching ratio on $K(Q,Z)$. We choose $A=2Z$, $n_f=2$ and set $Q_{\mathrm{C}\beta }=Q_{\mathrm{B}\beta }=Q$.

Figure 8

Temperature and plasma frequency profiles of the sun.