Neutrino theory regarding rest masses

In summary, the difference in the three-neutrino models is that the authors of the 1404.1740 paper include the sterile neutrino in their analysis, while the authors of the 1308.5870 paper do not. The results of the two analyses are different, with the 1404.1740 paper giving a result that is marginally within the error range of the 1308.5870 paper's result of 0.23 eV.
  • #106
Buzz Bloom said:
Does the quote mean that the PMNS mass mixing matrix includes values for probabilites that take into account both of two currently undecided possibilites regarding the nature of a neutrino's mass type: Majorana or Dirac?
This makes no sense. I suggest you pick up a basic book in quantum mechanics before even attempting questions regarding neutrino oscillations. The PMNS matrix is not a matrix of probabilities, it is a mixing matrix. The PMNS matrix is equally applicable to Majorana and Dirac neutrinos, with some additional physical phases for Majorana neutrinos.
 
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  • #107
Hi @Orobruin:

Orodruin said:
The PMNS matrix is not a matrix of probabilities, it is a mixing matrix. The PMNS matrix is equally applicable to Majorana and Dirac neutrinos, with some additional physical phases for Majorana neutrinos.
(underlining is mine)

Here is another quote from https://en.wikipedia.org/wiki/Pontecorvo–Maki–Nakagawa–Sakata_matrix#Parameterization .
The PMNS matrix describes the amplitude that a neutrino of given flavor α will be found in mass eigenstate i. The probability that a neutrino of a given flavor α to be found in mass eigenstate i is proportional to |Uαi|2 (underlining is mine)​
I am not certain how to reconcile the first underlined text from above quote from your post with the underlined text from Wikipedia quote. Are you simply making the technical distinction between an amplitude and it's absolute value square, that is, a probability. I am also not sure I understand exactly what you mean by "equally applicable" in the second underlined text from your post quote. Does this mean the following?
The form of the PMNS matrix can be applied equally well to both Dirac and Majorana neutrinos, but for the Majorana neutrinos some additional terms representng additional physical phases need to be included. Therefore the values of the matrix components would not be the same.​

The following concept is the reason I have made the interpretation in the above text. Dirac and Majorana neutrinos are not two differnt kinds of neutrinos, both of which existing in our real universe. Rather, they are two different theorectical possibilies regarding the nature of real neutrinos. Therefore, it would not make sense that a matrix of specific amplitude values would be applicable for both theories. Your post was helpful to me thinking about the question I asked in my previous post, and arriving at this concept. I believe my problem in understanding the Wikiedia quote in my previous post was a matter of what I see as ambiguous use of language, a common problem for me in learning from Wikikpedia articles.

Orodruin said:
I suggest you pick up a basic book in quantum mechanics before even attempting questions regarding neutrino oscillations.

I think this is an excellent suggesion. I have asked my town library to get a copy for me of Quantum mechanics : the theoretical minimum by Leonard Susskind and Art Friedman, and it is currently in transit from another library. I expect to start learning from it in a few days. This book was recommended by someone on the forum when I requested a suggestion, but I can't find that post now, so I can't tell you who made the recommendation.

Thanks for your post,
Buzz
 
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  • #108
Buzz Bloom said:
I am not certain how to reconcile the first underlined text from above quote from your post with the underlined text from Wikipedia quote. Are you simply making the technical distinction between an amplitude and it's absolute value square, that is, a probability. I am also not sure I understand exactly what you mean by "equally applicable" in the second underlined text from your post quote. Does this mean the following?
It is simply not a matrix of probabilities. You can compute some pribabilities from it, but you need to take care due to oscillations.
 
  • #109
Hi Orodruin:

Orodruin said:
It is simply not a matrix of probabilities. You can compute some pribabilities from it, but you need to take care due to oscillations.

I get it. Calling it probabilities was an incorrect way of using the vocabulary.

BTW, the recommendation of Quantum mechanics : the theoretical minimum was made by bhobba in post #211 in the thread "is the cat alive, dead, both or unknown".

Thanks for the clarification re "probability",
Buzz
 
<h2>1. What is a neutrino?</h2><p>A neutrino is a subatomic particle that has a very small mass and is electrically neutral. It is one of the fundamental particles that make up the universe, along with electrons, protons, and neutrons. Neutrinos are known for their elusive nature and their ability to pass through matter without interacting.</p><h2>2. What is the theory regarding the rest masses of neutrinos?</h2><p>The theory regarding the rest masses of neutrinos is that they are extremely small, but not zero. This means that they do have some mass, but it is difficult to measure due to their weak interactions with other particles. The Standard Model of particle physics predicts that neutrinos have a rest mass, but its exact value is still unknown.</p><h2>3. How are neutrinos related to the Higgs field and the Higgs boson?</h2><p>Neutrinos are related to the Higgs field and the Higgs boson through the mechanism of mass generation. The Higgs field is a fundamental field that permeates the universe and gives particles their mass. The Higgs boson is the particle associated with this field, and its interactions with other particles, including neutrinos, give them their mass.</p><h2>4. Why is the study of neutrino masses important?</h2><p>The study of neutrino masses is important for several reasons. First, it helps us understand the fundamental properties of the universe and the particles that make it up. Second, it has implications for the Standard Model of particle physics and may lead to the discovery of new physics beyond the Standard Model. Finally, neutrino masses have implications for astrophysics and cosmology, as they play a role in the evolution of the universe.</p><h2>5. How do scientists measure the rest masses of neutrinos?</h2><p>Scientists measure the rest masses of neutrinos through a variety of methods, including studying their interactions with other particles, observing their behavior in particle accelerators, and studying the effects of neutrino oscillations. However, due to the extremely small mass of neutrinos, these measurements are challenging and require sophisticated experiments and technologies.</p>

1. What is a neutrino?

A neutrino is a subatomic particle that has a very small mass and is electrically neutral. It is one of the fundamental particles that make up the universe, along with electrons, protons, and neutrons. Neutrinos are known for their elusive nature and their ability to pass through matter without interacting.

2. What is the theory regarding the rest masses of neutrinos?

The theory regarding the rest masses of neutrinos is that they are extremely small, but not zero. This means that they do have some mass, but it is difficult to measure due to their weak interactions with other particles. The Standard Model of particle physics predicts that neutrinos have a rest mass, but its exact value is still unknown.

3. How are neutrinos related to the Higgs field and the Higgs boson?

Neutrinos are related to the Higgs field and the Higgs boson through the mechanism of mass generation. The Higgs field is a fundamental field that permeates the universe and gives particles their mass. The Higgs boson is the particle associated with this field, and its interactions with other particles, including neutrinos, give them their mass.

4. Why is the study of neutrino masses important?

The study of neutrino masses is important for several reasons. First, it helps us understand the fundamental properties of the universe and the particles that make it up. Second, it has implications for the Standard Model of particle physics and may lead to the discovery of new physics beyond the Standard Model. Finally, neutrino masses have implications for astrophysics and cosmology, as they play a role in the evolution of the universe.

5. How do scientists measure the rest masses of neutrinos?

Scientists measure the rest masses of neutrinos through a variety of methods, including studying their interactions with other particles, observing their behavior in particle accelerators, and studying the effects of neutrino oscillations. However, due to the extremely small mass of neutrinos, these measurements are challenging and require sophisticated experiments and technologies.

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