2018/01/01 by R. Krishnan, Rama Krishnan, P. F. Harrison +1
Mathematics · Physics and Astronomy · #Astrophysics and Cosmic Phenomena #Combinatorics #MAJORANA #Mass matrix #Mathematics #Mixing (physics) #Neutrino #Neutrino Physics Research #Particle physics #Particle physics theoretical and experimental studies #Physics #Quantum mechanics #Type (biology) #hep-ph
paper · pdf · doi:10.1140/epjc/s10052-018-5516-7
published as Eur. Phys. J. C (2018) 78: 74 · 20 pages, 1 figure. arXiv admin note: substantial text overlap with arXiv:1402.0857
openalex publication_date 2018/01/01 · arxiv created 2018/01/26 · arxiv updated 2018/02/01 · openalex created_date 2018/03/29 · openalex updated_date 2026/08/05
In 2002, two neutrino mixing ansatze having trimaximally mixed middle ( ν 2 ) columns, namely tri-chi-maximal mixing ( \text Tχ \text M ) and tri-phi-maximal mixing ( \text Tφ \text M ), were proposed. In 2012, it was shown that \text Tχ \text M with χ =± (π )/(16) as well as \text Tφ \text M with φ = ± (π )/(16) leads to the solution, sin 2 θ 13 = (2)/(3) sin 2 (π )/(16) , consistent with the latest measurements of the reactor mixing angle, θ 13 . To obtain \text Tχ \text M(χ =± (π )/(16)) and \text Tφ \text M(φ =± (π )/(16)) , the type I see-saw framework with fully constrained Majorana neutrino mass matrices was utilised. These mass matrices also resulted in the neutrino mass ratios, m1:m2:m3=(( 2+√(2)) )/(1+√(2(2+√(2)))):1:(( 2+√(2)) )/(-1+√(2(2+√(2)))) . In this paper we construct a flavour model based on the discrete group \varSigma (72× 3) and obtain the aforementioned results. A Majorana neutrino mass matrix (a symmetric 3× 3 matrix with six complex degrees of freedom) is conveniently mapped into a flavon field transforming as the complex six-dimensional representation of \varSigma (72× 3) . Specific vacuum alignments of the flavons are used to arrive at the desired mass matrices.