Cosmogenic ${}^{11}\mathrm{C}$ production and sensitivity of organic scintillator detectors to $\mathit{pep}$ and CNO neutrinos

Several possible background sources determine the detectability of pep and CNO solar neutrinos in organic liquid scintillator detectors. Among such sources, the cosmogenic ${}^{11}\mathrm{C}$ nuclide plays a central role. ${}^{11}\mathrm{C}$ is produced underground in reactions induced by the residual cosmic muon flux. Experimental data available for the effective cross section for ${}^{11}\mathrm{C}$ by muons indicate that ${}^{11}\mathrm{C}$ will be the dominant source of background for the observation of pep and CNO neutrinos. ${}^{11}\mathrm{C}$ decays are expected to total a rate 2.5 (20) times higher than the combined rate of pep and CNO neutrinos in Borexino (KamLAND) in the energy window preferred for the pep measurement between 0.8 and 1.3 MeV. This study examines the production mechanism of ${}^{11}\mathrm{C}$ by muon-induced showers in organic liquid scintillators with a novel approach: for the first time, we perform a detailed ab initio calculation of the production of a cosmogenic nuclide, ${}^{11}\mathrm{C}$, taking into consideration all relevant production channels. Results of the calculation are compared with the effective cross sections measured by target experiments in muon beams. This article also discusses a technique for reduction of background from ${}^{11}\mathrm{C}$ in organic liquid scintillator detectors, which allows to identify on a one-by-one basis and remove from the data set a large fraction of ${}^{11}\mathrm{C}$ decays. The background reduction technique hinges on an idea proposed by Martin Deutsch, who suggested that a neutron must be ejected in every interaction producing a ${}^{11}\mathrm{C}$ nuclide from ${}^{12}\mathrm{C}$. ${}^{11}\mathrm{C}$ events are tagged by a threefold coincidence with the parent muon track and the subsequent neutron capture on protons.

Figure 1

Energy spectrum of electrons scattered by pep (dotted line) and CNO neutrinos (dash-dotted line), for the MSW-LMA solution of the solar neutrino problem. The total spectrum for all solar neutrinos (including $\mathrm{pp},{}^7\mathrm{Be}$, and ${}^8\mathrm{B}$ neutrinos, not shown separately) is also shown (continuous line). Neutrino fluxes for the spectra shown are from the BP04 version of the standard solar model (see Ref. 11). The background signal expected from cosmogenic ${}^{11}\mathrm{C}$ at Gran Sasso depth is superimposed (dashed line). For all the neutrino and the ${}^{11}\mathrm{C}$ spectra, we assume that the energy resolution of the detector is 5% at 1 MeV and varies with the energy E as $1/\sqrt{E}$.

Figure 2

Cross sections for ${}^{11}\mathrm{C}$ production from ${}^{12}\mathrm{C}$ as a function of energy.

Figure 3

Cumulative path of secondaries generated in showers induced by negatively charged muons at 320 GeV. Results are quoted in cm of range per meter of μ track per energy bins of 1 MeV.

Figure 4

Energy distribution for neutrons produced in association with ${}^{11}\mathrm{C}$ nuclides.

Figure 5

Range of neutrons produced in association with ${}^{11}\mathrm{C}$ nuclides.

Figure 6

(Color online) Correlation between the signal to reduced background ratio (R) and the dead mass-time fraction for Borexino, as a function of spatial (ζ) and time (η) efficiencies of ${}^{11}\mathrm{C}$ events rejection. The only background considered in the pep energy window (0.8–1.3 MeV) is the ${}^{11}\mathrm{C}$ background surviving the cuts described in the text. Isocontours for the ratio R (for values $R=1,2,5$) and for the dead mass-time fraction D (for values $D=1\%,10\%,50\%$) are shown in the graph.