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Analytic Neutrino Oscillation Probabilities

by Chee Sheng Fong

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Authors (as registered SciPost users): Chee Sheng Fong
Submission information
Preprint Link:  (pdf)
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Date submitted: 2022-11-04 15:23
Submitted by: Fong, Chee Sheng
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • High-Energy Physics - Phenomenology


In the work, we derive exact analytic expressions for $(3+N)$-flavor neutrino oscillation probabilities in an arbitrary matter potential in term of matrix elements and eigenvalues of the Hamiltonian. With radical solutions for a quartic polynomial, we obtain the first exact analytic oscillation probabilities for the $(3+1)$-flavor scenario in an arbitrary matter potential. With the analytic expressions, we demonstrate that nonunitary and nonstandard neutrino interaction scenarios are physically distinct: they satisfy different identities and can in principle be distinguished experimentally. The analytic expressions are implemented in a public code NuProbe, a tool for probing new physics through neutrino oscillations.

Current status:
Has been resubmitted

Reports on this Submission

Anonymous Report 1 on 2023-1-17 (Invited Report)

  • Cite as: Anonymous, Report on arXiv:2210.09436v2, delivered 2023-01-17, doi: 10.21468/SciPost.Report.6544


1. Clearly written
2. Has utility for the community


1. Certain points could be clarified as detailed in the report


This paper derives analytic formula for neutrino oscillations in the (3+N)flavour scenario. It also considers the differences between the NSI and non-unitary PMNS (i.e. 3+N flavour) scenarios. It would be helpful if the author could clarify:

1. The author states that the two scenarios are qualitatively and quantitively different. Could this be demonstrated in a plot? The two figures show the different NHS and unitary behaviours of each scenario separately i.e. what would we expect to measure for the NHS/Jarlskog identities.

2. The paper discusses how the non-unitary / non-diagonal NSI scenarios can be differentiated, however using this method it does not seem possible to distinguish between a diagonal or non-diagonal potential in the non-unitary scenario. Is there any possible resolution to this problem? How does the NHS identity behave in this in this scenario?

3. How is the NHS identity affected by non-unitarity? It may be helpful to the reader if the author produces a figure similar to Fig 1 but for the NHS identity in the non-unitary scenario.

  • validity: high
  • significance: good
  • originality: good
  • clarity: good
  • formatting: excellent
  • grammar: excellent

Author:  Chee Sheng Fong  on 2023-01-20  [id 3254]

(in reply to Report 1 on 2023-01-17)
answer to question

I would like to thank the referee for highlighting the important points of differentiating between nonunitary and NSI scenarios.

1) In the unitary case, the quantities in Figure 1 will be exactly zero since the unitary relations (29) will hold. And the NHS identity (31) will also be satisfied if the potential remains diagonal.

2) This is an important and difficult question! A reasonable strategy is to first verify if unitary relations (29) hold. On the one hand, if nonunitarity is discovered, then one would proceed to a more challenging task, but doable in principle, to determine if there is also NSI. For example, in the general eq. (32), on top of nonunitary parameters, if further NSI parameters are need in the Hamiltonian. On the other hand, if unitary relations (29) hold to a great precision, then one could go on to verify if the matter potential is diagonal or not.

3) In the attached figure, the NHS combinations for the case of nonunitarity are shown. The solid black thin line is the reference line for the unitary case with any diagonal potential (including zero). It is true that this can be confused with the case of NSI (Figure 2), especially if there are both nonunitary and NSI. So, the key is really to first identify if unitary relations hold as mentioned in the previous point and then go on from there.


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