Identification of the cosmogenic $$^{11}$$ <math> <msup> <mrow></mrow> <mn>11</mn> </msup> </math> C background in large volumes of liquid scintillators with Borexino

Cosmogenic radio-nuclei are an important source of background for low-energy neutrino experiments. In Borexino, cosmogenic $$^{11}$$ 11 C decays outnumber solar pep and CNO neutrino events by about ten to one. In order to extract the flux of these two neutrino species, a highly efficient identification of this background is mandatory. We present here the details of the most consolidated strategy, used throughout Borexino solar neutrino measurements. It hinges upon finding the space-time correlations between $$^{11}$$ 11 C decays, the preceding parent muons and the accompanying neutrons. This article describes the working principles and evaluates the performance of this Three-Fold Coincidence (TFC) technique in its two current implementations: a hard-cut and a likelihood-based approach. Both show stable performances throughout Borexino Phases II (2012–2016) and III (2016–2020) data sets, with a $$^{11}$$ 11 C tagging efficiency of $$\sim 90$$ ∼ 90 % and $$\sim $$ ∼ 63–66 % of the exposure surviving the tagging. We present also a novel technique that targets specifically $$^{11}$$ 11 C produced in high-multiplicity during major spallation events. Such $$^{11}$$ 11 C appear as a burst of events, whose space-time correlation can be exploited. Burst identification can be combined with the TFC to obtain about the same tagging efficiency of $$\sim 90\%$$ ∼ 90 % but with a higher fraction of the exposure surviving, in the range of $$\sim $$ ∼ 66–68 %.