We study Borromean 2n-halo nuclei using effective field theory. We compute the universal scaling function that relates the mean-square matter radius of the 2n halo to dimensionless ratios of two- and three-body energies. We use the experimental value of the rms matter radius of 22C measured by Tanaka et al. to put constraints on its 2n separation energy and the 20C-n virtual energy. We also explore the consequences of these constraints for the existence of excited Efimov states in this nucleus. We find that, for 22C to have an rms matter radius within 1-sigma of the experimental value, the two-neutron separation energy of 22C needs to be below 100 keV. Consequently, this three-body halo system can have an excited Efimov state only if the 20C-n system has a resonance within 1 keV of the scattering threshold.
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