Talk:Pontecorvo–Maki–Nakagawa–Sakata matrix

The PMNS matrix was not introduced in 1962. In the referred paper MNS proposed neutrino mixing for the weak flavour. 1967 Pontecorco proposed flavour oscillations for the 2 neutrino case. I have problems to find the paper from 1969 but it seems then the PMNS matrix in its current form was proposed.

Error in refs
Refs 2 & 3 have an apparent linking error. Two is:

B. Pontecorvo (1957). "Mesonium and anti-mesonium". ''Zh. Eksp. Teor. Fiz.'' 33: 549–551. reproduced and translated in ''Sov. Phys. JETP'' 6: 429. 1957.

Both journals link to the same title, Journal of Experimental and Theoretical Physics. However, that doesn't fit with volumes 33 and 6 both coming out in 1957. — kwami (talk) 01:22, 18 October 2010 (UTC)


 * I don't see what the problem is really (the information is accurate). Soviet Physics JETP is the translation of Zhurnal Eksperimental'noi i Teoreticheskoi Fiziki. This most likely means that the first 27 volumes of the Russian version were not translated, or that the translated edition was published less frequently than the Russian edition, or both. Headbomb {talk / contribs / physics / books} 01:40, 18 October 2010 (UTC)


 * I get it now. I thought the maybe article was republished in another journal with a similar name. — kwami (talk) 04:45, 18 October 2010 (UTC)

There is another problem with these references, which is that they are not appropriate for the text they refer to. [2] is Pontecorvo's prediction of neutrino-antineutrino oscillation in analogy with the neutral K system, and [3] discusses experimental tests of neutrino oscillation well after the theory was already established. The correct reference is "Inverse beta processes and nonconservation of lepton charge" from Zh.Eksp.Teor.Fiz. 34 (1957) 247 / Sov.Phys.JETP 7 (1958) 172-173, I updated it. Jasondet (talk) 09:48, 25 August 2015 (UTC)

Contradictory values
We have: "Θ13=9 degrees."

...and: "Θ13=0, which before 2011 was in good agreement with experiments, but thanks to T2K, Double Chooz and Daya Bay[6] it is known to be around 4.4 deg"

Which is it? -24.13.168.97 (talk) 01:59, 11 July 2012 (UTC)

I don't think 4.4 deg is right either. "In the space of ten months five experiments have produced results consistent with a value of sin^2(2 theta13)~ 0.1." from http://arxiv.org/pdf/1209.3884v2.pdf (September 12, 2012). The square root of 0.1 is about 0.32. Sine 19 deg is about 0.32. So, for theta13 equal to 9.5 deg, sin^2(2*theta13)=0.1. Ohwilleke (talk) 15:34, 4 April 2013 (UTC) Another global fit which provides a value of about 9.2 degrees and provides updated as of Dec 2012 values (not yet incorporated by me in the table on the page) is here: http://arxiv.org/pdf/1209.3023v3.pdf Ohwilleke (talk) 15:54, 4 April 2013 (UTC)

Latest parameter values
As of 2015, there are tighter bounds, but I don't feel competent to update the following discussion (especially about the significance of δCP), so I haven't dropped these in yet. The Particle Data Group link is dead; the current one is http://pdg8.lbl.gov/rpp2014v1/pdgLive/Particle.action?node=S067



\begin{align} \sin^2 2\theta_{12} & = 0.846 \pm 0.021 && (\textrm{was}~0.857 \pm 0.024) \\ \sin^2 2\theta_{23} & = 0.999^{+0.001}_{-0.018} && (\textrm{was} > 0.95) \\ \sin^2 2\theta_{13} & = 0.093 \pm 0.008 && (\textrm{was}~0.095 \pm 0.010) \\ \end{align} $$

The current NuFit values, which were apparently updated after the Neutrino 2014 conference (which I'm not sure if they're based on the same source data as the PDG, and I'm not sure if I should be using the free or Huber flux fit) are:



\begin{align} \theta_{12} [^\circ] & = 33.48^{+0.77}_{-0.74} && (\textrm{was}~33.36^{+0.81}_{-0.78}) \\ \theta_{23} [^\circ] & = 42.2^{+0.1}_{-0.1}~\textrm{or}~49.4^{+1.6}_{-2.0} && (\textrm{was}~40.0^{+2.1}_{-1.5}~\textrm{or}~50.4^{+1.3}_{-1.3}) \\ \theta_{13} [^\circ] & = 8.52^{+0.20}_{-0.21} && (\textrm{was}~8.66^{+0.44}_{-0.46}) \\ \delta_{\textrm{CP}} [^\circ] & = 251^{+67}_{-59} && (\textrm{was}~300^{+66}_{-138}) \\ \end{align} $$ 71.41.210.146 (talk) 13:54, 23 April 2015 (UTC) Ohwilleke (talk) 06:34, 30 July 2015 (UTC) I will try to drop in the new data points and update the commentary in the near future.

PDG now gives the mixing angles in terms of $$\sin^2 \theta_{ij}$$ and splits $$\theta_{23}$$ and $$\delta_{\textrm{CP}}$$ into the inverted and normal hierarchy cases. The values as of the October 2016 (latest) edition are:

\begin{align} \sin^2 \theta_{12} & = 0.304 \pm 0.014 \\ \sin^2 \theta_{23} & = 0.51 \pm 0.05 \textrm{ (normal)} \\ \sin^2 \theta_{23} & = 0.50 \pm 0.05 \textrm{ (inverted)} \\ \sin^2 \theta_{13} & = 0.0219 \pm 0.0012 \\ \delta_{\textrm{CP}} / \pi & = 1.35^{+0.64}_{-0.43} \textrm{ (normal)}\\ \delta_{\textrm{CP}} / \pi & = 1.32^{+0.67}_{-0.49} \textrm{ (inverted)} \\ \end{align} $$ The ranges on $$\delta_{\textrm{CP}}$$ are the $$3\sigma$$ level. Clearlyfakeusername (talk) 19:33, 12 May 2017 (UTC)

New $$\delta_{\textrm{CP}}$$ measurements are given in Abe, K., Akutsu, R., Ali, A. et al. Constraint on the matter–antimatter symmetry-violating phase in neutrino oscillations. Nature 580, 339–344 (2020). https://doi.org/10.1038/s41586-020-2177-0 Somebody more familiar with particle physics please update the article, thanks. — Preceding unsigned comment added by 193.197.56.193 (talk) 12:43, 2 June 2020 (UTC)