The Masses of the Neutrinos

Abstract

If the cosmological limits on the sum of the neutrino masses are taken seriously we have first measurements of the masses of the neutrinos. Using the Planck experiment’s limit P3=1 mi < 230 meV and some simple assumptions on measurement uncertainties the mass of the heaviest neutrino is 63±11 meV and the lightest 40±18 meV for either hierarchy. A recent seminar at Fermilab reviewed the status of the sum of the masses of neutrinos from various cosmological measurements [1]. If those limits are taken seriously then we already have measurements of the masses of the three neutrinos with some precision. This note reduces the simple algebra of the neutrino masses to graphical form to illustrate this. The cosmological limits on the sum of neutrino masses is a long and growing list of measurements [2]. I have chosen to use the latest result of the Planck collaboration [3], M = P 3=1 mi < 230 meV , to work in units of meV since all the interesting numbers are cleanly represented to appropriate precision as integers, and to use the PDG’s averages for the neutrino masssquared differences: �m 2 = m 2 m 2 = 75.3 ± 1.8 meV 2 �m 2 = m 2 m 2 = 2420 ± 60 meV 2 Normal hierarchy �m 2 = m 2 m 2 = 2490 ± 60 meV 2 Inverted hierarchy M = P 3=1 mi = m1 + m2 + m3