New research has found that the neutrino has a non-zero mass - but this requires a modification to the Standard Model of particle physics. The non-zero mass also means that neutrinos cannot travel at light-speed as photons do.

Although neutrinos were long believed to be massless, it is now known that there are three discrete neutrino masses with different tiny values, but they don't correspond uniquely to the three flavors. A neutrino created with a specific flavor is in an associated specific quantum superposition of all three mass states"
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Additionally, it's thought that in order to acquire mass, all fermions (including neutrinos) of both 'handedness' must interact with the Higgs boson.

In the Standard Model of particle physics, fermions only have mass because of interactions with the Higgs field. These interactions involve both 'left-handed' and 'right-handed' versions of the fermion. However, only left-handed neutrinos have been observed so far."

Source :Wikipedia

Further, the mass that neutrinos do have has not yet been measured :

It might seem absurd that physicists don't know how much neutrinos weigh, given that the universe contains more of them than any other type of matter particle. However, it's impossible to capture neutrinos, so there's no simple way to measure their mass."

Source : Science, Vol. 356, Issue 6345, pp. 1322-1326, 2017

The mass which they have must be acquired via the Higgs boson (according to the current 'Standard Model') - but there are theoretical conflicts regarding neutrinos :

The Higgs boson is responsible for giving mass to a certain class of particles that feature in the theory of the so-called electroweak interaction: a unified description of two of the four fundamental forces, electromagnetism and the nuclear weak force. Because the weak force underlies the beta decay process in which neutrinos are formed, neutrinos are implicated in this 'Higgs mechanism'. In short, the non-zero mass of the three types of neutrino and the oscillations that cause switches between them can’t be fully squared with the Higgs mechanism, and seem to demand some kind of physics beyond the Standard Model."

Philip Ball, Prospect Magazine, 2007

One proposed solution to the anomaly was the 'invention' of a particle called the Sterile Neutrino. But, according to 2023 research published in the journal Nature, the existence of this hypothetical particle has now been ruled out.

An anomalous measurement from a nuclear reactor triggered a three-year campaign to find an elusive particle called the sterile neutrino. The search shows definitively that sterile neutrinos don’t exist — but the anomaly persists

Nature, News and Views , Jan 2023.

The Karlsruhe Tritium Neutrino (KATRIN ) detector in Germany, has put an upper bound on the mass as being 0.8 eV c^–2 but its maximum sensitivity is around 0.2 eV, and so more sensitive detection systems are now proposed for a more accurate figure.

Also see Radioactive decay neutrino anomalyplugin-autotooltip__plain plugin-autotooltip_bigRadioactive decay neutrino anomaly

Around yr2000, researchers at Purdue University, US, noticed that some radioactive sources - which should decay completely randomly - sometimes show peaks and troughs (i.e. cyclic variations) in the averaged radiation they produce over time. Subsequent tests carried out the Brookhaven National Laboratory and the Federal Physical and Technical Institute in Germany confirmed the phenomenon - which could not be explained by any conventional theory. and Anti-Neutrinosplugin-autotooltip__plain plugin-autotooltip_bigAnti-Neutrinos

"The electron neutrino has a corresponding antiparticle, the electron antineutrino (νe), which differs only in that some of its properties have equal magnitude but opposite sign. One open question of particle physics is whether or not neutrinos and anti-neutrinos are the same particle,

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