# Why does the Standard Model predict Neutrinos are massless?

Why are neutrinos massless in the Standard Model? Is it connected with experimental fact that neutrinos always have only one direction of projection of spin on motion direction?

• – glS
Feb 27, 2015 at 23:35
• ps.uci.edu/~superk/oscillation.html This is the site I found quite enlightening on subject how people found out neutrinos must have mass (in layman terms!). Standard Model doesn't really predict this, instead math describing model had to be slightly changed, as answers point out.
– Rena
Feb 28, 2015 at 0:00

Standard model doesn't predict that neutrinos are massless. It's a "Model", where initially neutrinos are considered massless, because no mass was observed.

The way we know, now, that neutrinos have masses, is through the mixing between the different neutrino types, through a matrix called the PMNS matrix (similar to the CKM matrix for quarks). This mixing explains the number of neutrinos that come from the sun, and sets a lower limit for the masses. But no one has done a real measurement for the masses of neutrinos... dealing with neutrinos is really hard.

• I thought all particles in the SM start off massless and they acquire mass via either the Higss, Dirac, or Majorana mechanisms and for Neutrinos it was assumed none of the mechanisms applied / mattered but with oscillations we now think the Majorana mechanism is at play. Nov 25, 2013 at 20:53
• @BrandonEnright I'm not sure about all particles, cuz in all problems I solved (QED, QCD, ...) we presume that we know their mass (experimentally). U may explain the mass with a Higgs field that you add to your Lagrangian, but u have to separate this from interaction problem you solve. Doing everything from scratch no one does ever! So people usually gain explanation of mass and make sure it's compatible with the Lagrangian of the theory, and then they forget about all those additional fields, cuz you can always decompose your interaction in terms of perturbation theory (at least in QED). Nov 26, 2013 at 10:07
• @BrandonEnright You are correct that at very high energies all masses of the SM are 0 and stay that way if there were no Higgs mechanism. The crux is that the SM has very many parameters which allow to input in fact the observed masses. The neutrino, from experimental measurements had a mass compatible with zero. It is only the oscillations between different lepton number neutrinos that point to a very small mass. Nov 27, 2013 at 6:25
• Ok. I can rewrite my question in following form: why in "native" SM neutrinos can't be massive? Nov 28, 2013 at 16:04
• @AndrewMcAdams It's not "can't", it's an input. We found experimentally that neutrinos are massless, and we thought that was right because our measurements were not precise enough (and still), and now we found that with some theory, which is confirmed by observations, that neutrinos should have some small mass. So, all we do now is we change the input in SM. That doesn't destroy SM. You can just add the mass term to the Lagrangian of Neutrinos, and problem fixed. However, practically, we don't need to do that, because the error that would come from that is very small compared to other errors. Nov 28, 2013 at 17:42

I agree with the answer of Quantum physicist , that zero mass for neutrinos was an input to the standard model , not a prediction, because measurements showed a mass compatible with zero.

But I will add that the discovery that neutrinos must have mass does not destroy the Standard Model, just different Lagrangian for the neutrinos has to be included.

However the experimentally established phenomenon of neutrino oscillation, which mixes neutrino flavour states with neutrino mass states (analogously to CKM mixing), requires neutrinos to have nonzero masses. Massive neutrinos were originally conceived by Bruno Pontecorvo in the 1950s. Enhancing the basic framework to accommodate their mass is straightforward by adding a right-handed Lagrangian. This can be done in two ways. If, like other fundamental Standard Model particles, mass is generated by the Dirac mechanism, then the framework would require a SU(2) singlet. This particle would have no other Standard Model interactions (apart from the Yukawa interactions with the neutral component of the Higgs doublet), so is called a sterile neutrino. Or, mass can be generated by the Majorana mechanism, which would require the neutrino and antineutrino to be the same particle.

In standard model, the mass of a particle can be explain by either Dirac or Weyl equation. The first thing is that neutrinos are can't be described by any of the above equations (Dirac equation or Weyl equation) in the standard model because no right handed neutrinos are observed. Dirac equation needs four spinors to explain the mass of any particle. But in case of neutrinos, we have only two spinors. On the other hand, Weyl equations are only for the massless particles. Thus, neither the Dirac equation nor the Weyl equation can explain the neutrinos. Simply that why neutrinos are massless in standard model according to me.

I agree with Curious about the reason why neutrino was assumed to be massless in standard model. I would only like to add that this assumption holds only for a spinor or a spin 1/2 particle which is also a fermion.