Pontecorvo–Maki–Nakagawa–Sakata matrix: Difference between revisions
th13 != 0 now |
Puzl bustr (talk | contribs) Replaced bare link with arxiv citation |
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As a starting point, one recent particle physics course<ref>http://www.hep.phy.cam.ac.uk/~thomson/partIIIparticles/handouts/Handout11_2010.pdf</ref> provided the following |
As a starting point, one recent particle physics course<ref>http://www.hep.phy.cam.ac.uk/~thomson/partIIIparticles/handouts/Handout11_2010.pdf</ref> provided the following |
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estimated values for the matrix (assuming the mixing angle Θ<sub>13</sub>=0, which before 2011 was in good agreement with experiments, but thanks to [[T2K experiment|T2K]], [[Double Chooz]] and Daya Bay |
estimated values for the matrix (assuming the mixing angle Θ<sub>13</sub>=0, which before 2011 was in good agreement with experiments, but thanks to [[T2K experiment|T2K]], [[Double Chooz]] and Daya Bay<ref>{{cite arxiv|author=Daya Bay Collaboration|eprint=1203.1669|title=Observation of electron-antineutrino disappearance at Daya Bay|date=8 March 2012}}</ref> it is known to be around 4.4 deg): |
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:<math>\begin{bmatrix} U_{e 1} & U_{e 2} & U_{e 3} \\ U_{\mu 1} & U_{\mu 2} & U_{\mu 3} \\ U_{\tau 1} & U_{\tau 2} & U_{\tau 3} \end{bmatrix} |
:<math>\begin{bmatrix} U_{e 1} & U_{e 2} & U_{e 3} \\ U_{\mu 1} & U_{\mu 2} & U_{\mu 3} \\ U_{\tau 1} & U_{\tau 2} & U_{\tau 3} \end{bmatrix} |
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= \begin{bmatrix} 0.85 & 0.53 & 0 \\ -0.37 & 0.60 & 0.71 \\ 0.37 & -0.60 & 0.71 \end{bmatrix} \ </math>. |
= \begin{bmatrix} 0.85 & 0.53 & 0 \\ -0.37 & 0.60 & 0.71 \\ 0.37 & -0.60 & 0.71 \end{bmatrix} \ </math>. |
Revision as of 14:18, 18 March 2012
Flavour in particle physics |
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Flavour quantum numbers |
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Related quantum numbers |
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Combinations |
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Flavour mixing |
In particle physics, the Pontecorvo–Maki–Nakagawa–Sakata matrix (PMNS matrix), Maki–Nakagawa–Sakata matrix (MNS matrix), lepton mixing matrix, or neutrino mixing matrix, is a unitary matrix[note 1] which contains information on the mismatch of quantum states of leptons when they propagate freely and when they take part in the weak interactions. It is important in the understanding of neutrino oscillations. This matrix was introduced in 1962 by Ziro Maki, Masami Nakagawa and Shoichi Sakata,[1] to explain the neutrino oscillations predicted by Bruno Pontecorvo.[2][3]
The matrix
For three generations of leptons, the matrix can be written as:
- .
On the left are the neutrino fields participating in the weak interaction, and on the right is the PMNS matrix along with a vector of the neutrino fields diagonalizing the neutrino mass matrix. The PMNS matrix describes the probability of a neutrino of given flavor α to be found in mass eigenstate i. These probabilities are proportional to |Uαi|2.
Various parametrizations of this matrix exist,[4] however due to the difficulties of detecting neutrinos, it is much more difficult to determine the individual coefficients than in the equivalent matrix for the quarks (the CKM matrix). The matrix is most commonly parameterized by three mixing angles (Θ12, Θ23 and Θ13) and a single phase. Experimentally, the mixing angles were established to be approximately Θ12=45 degrees, Θ23=34 degrees, and Θ13<4 degrees.
As a starting point, one recent particle physics course[5] provided the following estimated values for the matrix (assuming the mixing angle 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):
- .
See also
Notes
- ^ The PMNS matrix is not unitary in the seesaw model
References
- ^
Z. Maki, M. Nakagawa, and S. Sakata (1962). "Remarks on the Unified Model of Elementary Particles". Progress of Theoretical Physics. 28: 870. Bibcode:1962PThPh..28..870M. doi:10.1143/PTP.28.870.
{{cite journal}}
: CS1 maint: multiple names: authors list (link) - ^
B. Pontecorvo (1957). "Mesonium and anti-mesonium". Zh. Eksp. Teor. Fiz. 33: 549–551. reproduced and translated in Sov. Phys. JETP. 6: 429. 1957.
{{cite journal}}
: Missing or empty|title=
(help) - ^
B. Pontecorvo (1967). "Neutrino Experiments and the Problem of Conservation of Leptonic Charge". Zh. Eksp. Teor. Fiz. 53: 1717. reproduced and translated in Sov. Phys. JETP. 26: 984. 1968. Bibcode:1968JETP...26..984P.
{{cite journal}}
: Missing or empty|title=
(help) - ^ J.W.F. Valle (2006). "Neutrino physics overview". Journal of Physics: Conference Series. 53: 473. arXiv:hep-ph/0608101. Bibcode:2006JPhCS..53..473V. doi:10.1088/1742-6596/53/1/031.
- ^ http://www.hep.phy.cam.ac.uk/~thomson/partIIIparticles/handouts/Handout11_2010.pdf
- ^ Daya Bay Collaboration (8 March 2012). "Observation of electron-antineutrino disappearance at Daya Bay". arXiv:1203.1669.