Has the Pauli exclusion principle been observed with neutrinos?

Question

score 2 · Answer 1 · answered Sep 22 '23 at 17:59

Cosmology and double-beta decay are a couple of experimental/observational paths to constrain how well neutrinos obey the Pauli Exclusion Principle (PEP), but the current constraints only tell us that neutrino statistics appear to be more fermionic than bosonic. Neutrino PEP violations at the 10% level are not yet experimentally excluded.

If neutrinos do not strictly obey the Pauli Exclusion Principle, this would change their equilibrium distribution in the early universe and affect the cosmic microwave background, baryon acoustic oscillations, and the primordial abundances of light elements. As of 2018, however, available data set only extremely weak cosmological bounds on neutrino statistics, i.e. the possibility that neutrinos actually obey pure Bose-Einstein statistics instead of Fermi-Dirac statistics is only excluded with less than $2 \sigma$ confidence.

The energy and angular distributions of the electrons emitted in ordinary double beta decay $$(Z,A) \rightarrow (Z+2,A)\;\; e^- \,e^- \,\bar{\nu}\,\bar{\nu}$$ depend on the energy and angular distributions of two invisible anti-neutrinos, which would change if the anti-neutrinos do not strictly obey the Pauli Exclusion Principle. If the two neutrino amplitude is parameterized as $$A_{2\beta} = A_f \cos^2\chi + A_b \sin^2 \chi $$ with $A_f$ and $A_b$ the fermionic (antisymmetric) and bosonic (symmetric) contributions, then NEMO-3 data on $^{100}\mathrm{Mo}$ double beta decays set a limit on the neutrino bosonic (i.e. PEP violating) contribution of $$\sin^2 \chi < 0.27 \,\mathrm{(90\% C.L.)}$$

In comparison, the Pauli Exclusion Principle has been tested for electrons in many systems, with the best limits as small as $<10^{-42}$.

Árpád Szendrei · Answer 2 · 2018-05-03T21:07:34.107

-2

Yes it has, but indirectly with math. There has been no direct observation.

it works with the estimation of the density at which the violation of the principle becomes an issue. This density cannot be exceeded. This is the case with White dwarfs, and their electrons. Neutrinos have a momenta $10^{-4}\,\mathrm{eV}/c$, their maximum density is 30 orders smaller then the electrons in White dwarfs. This maximum density is $\rm 225\,cm^{-3}$.

Citation: Richard Wigmans, J. Phys.: Conf. Ser. 633, 012034 (2015)

edited May 03 '18 at 21:07

answered May 03 '18 at 20:37

Árpád Szendrei

28,452

Forgive me, but does this imply the pressure in a White Dwarf is "because" of the neutrinos, not the electrons? – Maury Markowitz May 03 '18 at 20:57
I would say this is just the way to do the mathnsince neutrinos as really hard to interact with – Árpád Szendrei May 03 '18 at 20:59
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Note that Wigmans is discussing relic neutrinos left over from the Big Bang, which are predicted but for which there is only indirect evidence. The degeneracy of these neutrinos is an additional prediction, but since the neutrinos haven't been directly observed then their degeneracy hasn't been directly observed either. – rob May 03 '18 at 21:00
you are right I will edit – Árpád Szendrei May 03 '18 at 21:02
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The question asks whether this has been observed. This answer doesn't address that. – May 03 '18 at 21:05
I edited. I added that there has been no direct observation, just indirect. – Árpád Szendrei May 03 '18 at 21:08
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The PEP puts no upper limit on the density of neutrinos (or any other fermion). – ProfRob May 03 '18 at 21:19

Has the Pauli exclusion principle been observed with neutrinos?

2 Answers2