Understanding Neutrino Mass and its Impact on Beta Decay Observations

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Discussion Overview

The discussion revolves around the topic of neutrino mass and its implications for observations of beta decay. Participants explore the relationship between missing energy and momentum in beta decay events and the challenges in determining the mass of neutrinos, including theoretical and experimental considerations.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant suggests that knowing the missing momentum and energy in beta decay should allow for the determination of neutrino mass, questioning why it remains unknown.
  • Another participant corrects the initial claim about the energy-momentum relationship, stating that for ultrarelativistic neutrinos, the mass term is negligible, and thus mass cannot be extracted from the data.
  • A participant acknowledges the clarification and expresses gratitude for the response.
  • Another participant discusses the relationship between mass and momentum using the equation E² = p²c² + m²c⁴, noting that experimental data are consistent with a neutrino mass of zero and mentioning an upper bound of about 2 eV for neutrino mass based on decay spectrum analysis.
  • A further contribution highlights the use of the Kurie plot in studying the electron energy spectrum in beta decay, indicating that any curvature could suggest a finite neutrino mass.

Areas of Agreement / Disagreement

Participants express differing views on the implications of missing energy and momentum in beta decay and the feasibility of determining neutrino mass. There is no consensus on the exact nature of neutrino mass or its implications for beta decay observations.

Contextual Notes

Participants note limitations in current experimental approaches and the challenges in measuring neutrino mass, including the rarity of events that would provide clear data on neutrino energy.

granpa
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when beta decay is observed it is noticed that some of the energy and some of the momentum is missing.
it is thought that this missing energy and momentum is carried away by a neutrino.
the neutrino mass is still unknown.

if you know how much momentum (mv) is missing and
you know how much energy (mc<sup>2</sup> + mv<sup>2</sup>) is missing then
dont you automatically know how much mass the neutrino must have?

why is the neutrino mass still unknown?
 
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Relativistic energy is not given by E=mc^2+mv^2, it's E=\sqrt{m^2+p^2} (in units with c=1). The neutrinos emitted in radioactive decay are ultrarelativistic, so m2 is negligible compared to p2, and E=p to an extremely good approximation. Therefore you can't extract any information about m.

Neutrino masses are not completely unknown. We know that there are mass differences between neutrino flavors.
 
:-(

hmm. well, that clears it up.
Thanks for the reply.
 
The mass and momentum are related by the relation E^2 = p^2 c^2 + m^2 c^4 . In a typical beta decay, the energy and momentum are both in the MeV range, and since the neutrino mass is in the eV range or less, within experimental error the data are related by E^2=p^2 c^2. In other words, the experimental data are consistent with a neutrino mass of zero. There have been attempts to look at the very end of the decay spectrum, where the electron carries away almost all of the energy, and the neutrino has only a very small energy, but only about 1 in 10^14 decay events are in this range. The best that has been done this way, to my knowledge, is to put an upper bound on the neutrino mass of about 2eV.
 

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