Neutrino properties 1

Neutrino Properties
Revised July 2023 by P. Vogel (Caltech) and A. Piepke (University of Alabama).
The Neutrino Properties Listings concern measurements of various propertiesof neutrinos. Nearly all of the measurements, so far only limits, actually concern
superpositions of the mass eigenstates νi , which are in turn related to the weakeigenstates νℓ , via the neutrino mixing matrix
X|νℓ i =Uℓi |νi i .
iIn the analogous case of quark mixing via the CKM matrix, the smallness of theoff-diagonal terms (small mixing angles) permits a “dominant eigenstate” approximation.
However, the results of neutrino oscillation searches show that the mixing matrix contains
two large mixing angles and a third angle that is not exceedingly small. We cannot
therefore associate any particular state |νi i with any particular lepton label e, µ or τ .
Nevertheless, note that in the standard labeling the |ν1 i has the largest |νe i component(∼ 2/3), |ν2 i contains ∼ 1/3 of the |νe i component and |ν3 i contains only a small ∼ 2.5%
|νe i component.
Neutrinos are produced in weak decays with a definite lepton flavor, and are typicallydetected by the charged current weak interaction again associated with a specific lepton
flavor. Hence, the listings for the neutrino mass that follow are separated into the threeassociated charged lepton categories. Other properties (mean lifetime, magnetic moment,charge and charge radius) are no longer separated this way. If needed, the associatedlepton flavor is reported in the footnotes.
Measured quantities (mass-squared, magnetic moments, mean lifetimes, etc.) all
depend upon the mixing parameters |Uℓi |2 , but to some extent also on experimental
conditions (e.g., on energy resolution). Many of these observables, in particular masssquared, cannot distinguish between Dirac and Majorana neutrinos and are unaffected byCP phases.
Direct neutrino mass measurements are usually based on the analysis of the kinematics
of charged particles (leptons, pions) emitted together with neutrinos (flavor states) invarious weak decays. The most sensitive neutrino mass measurement to date, involvingelectron type antineutrinos, is based on fitting the shape of the beta spectrum. TheP2(ef f )quantity mνe= i |Uei |2 m2νi is determined or constrained, where the sum is over
all mass eigenvalues mνi that are too close together to be resolved experimentally.
q2(ef f )ef f
is often denoted hmβ i in the literature.) If the energy(The quantity mνe ≡ mνe2resolution is better than ∆mij ≡ m2νi − m2νj , the corresponding heavier mνi and mixing
parameter could be determined by fitting the resulting spectral anomaly (step or kink).
The dependence of mνe on the mass of the lightest neutrino is shown in Fig. 14.11 of
the Neutrino Masses, Mixing, and Oscillations review. In the case of inverted ordering
pef f
ef f
there is a minimum possible value of mνe , approximately (∆m232 ) ∼ 50 meV. If mνe
is found to be larger than this value, it is impossible, based on this information only, toef f
decide which ordering is realized in nature. On the other hand, if the mνe is less than
∼50 meV, only the normal mass ordering is possible.
S. Navas et al. (Particle Data Group), Phys. Rev. D 110, 030001 (2024)
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Neutrino properties

22(ef f )A limit on mνeimplies an upper limit on the minimum value m2min of m2νi ,2(ef f )independent of the mixing parameters Uei : m2min ≤ mνe. However, if and when2(ef f )the value of mνe
is determined then its combination with the results derived fromneutrino oscillations that give us the values of the neutrino mass-squared differences∆m2ij ≡ m2i − m2j , including eventually also their signs, and the mixing parameters |Uei |2 ,P2(ef f )the individual neutrino mass squares m2νj = mνe− i |Uei |2 ∆m2ij can be determined.

So far solar, reactor, atmospheric and accelerator neutrino oscillation experiments canbe consistently described using three active neutrino flavors, i.e. two mass splittings andthree mixing angles. However, several experiments with radioactive sources, reactors,and accelerators imply the possible existence of one or more non-interacting, i.e. sterile,neutrino species that might be observable since they couple, albeit weakly, to the flavor
neutrinos |νl i. In that case, the neutrino mixing matrix would be n × n unitary matrix
with n > 3.
Combined three neutrino analyses determine the squared mass differences andall three mixing angles to within reasonable accuracy. For given |∆m2ij | a limit on2(ef f )mνefrom beta decay defines an upper limit on the maximum value mmax of mνi :P2(ef f )m2max ≤ mνe+ i<j |∆m2ij |. The analysis of the low energy beta decay of tritium,combined with the oscillation results, thus limits all active neutrino masses. Traditionally,experimental neutrino mass limits obtained from pion decay π + → µ+ + νµ or the shapeof the spectrum of decay products of the τ lepton did not distinguish between flavor andmass eigenstates. These results are reported as limits of the µ and τ based neutrino mass.
After the determination of the |∆m2ij |’s and the mixing angles θij , the corresponding
neutrino mass limits are no longer competitive with those derived from low energy beta
decays.
The spread of arrival times of the neutrinos from SN1987A, coupled with themeasured
q neutrino energies, provided a time-of-flight limit on a quantity similar to2(ef f )hmβ i ≡ mνe. This statement, clothed in various degrees of sophistication, has been
the basis for a very large number of papers. The resulting limits, however, are no longer
comparable with the limits from tritium beta decay.
Constraint, or eventually a value, of the sum of the neutrino masses mtot can be
determined from the analysis of the cosmic microwave background anisotropy, combinedwith the galaxy redshift surveys and other data. These limits are reported in a separatetable ( Sum of Neutrino Masses, mtot ). Obviously, mtot represents an upper limit for all
mi values. Note that many reported mtot limits are considerably more stringent thanef f
the listed mνe limits. Discussion concerning the model dependence of the mtot limit iscontinuing.

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