Neutrinos stand out among the elementary particles because of their unusually small masses.Various seesaw mechanisms attempt to explain this fact.In this work,applying insights from matrix theory,we are in a position ...Neutrinos stand out among the elementary particles because of their unusually small masses.Various seesaw mechanisms attempt to explain this fact.In this work,applying insights from matrix theory,we are in a position to treat variants of seesaw mechanisms in a general manner.Specifically,using Weyl's inequalities,we discuss and rigorously prove under which conditions the seesaw framework leads to a mass spectrum with exactly three light neutrinos.We find an estimate of the mass of heavy neutrinos to be the mass obtained by neglecting light neutrinos,shifted at most by the maximal strength of the coupling to the light neutrino sector.We provide analytical conditions allowing one to prescribe that precisely two out of five neutrinos are heavy.For higher-dimensional cases the inverse eigenvalue methods are used.In particular,for the CP-invariant scenarios we show that if the neutrino sector has a valid mass matrix after neglecting the light ones,i.e.if the respective mass submatrix is positive definite,then large masses are provided by matrices with large elements accumulated on the diagonal.Finally,the Davis-Kahan theorem is used to show how masses affect the rotation of light neutrino eigenvectors from the standard Euclidean basis.This general observation concerning neutrino mixing,together with results on the mass spectrum properties,opens directions for further neutrino physics studies using matrix analysis.展开更多
We discuss a linear seesaw model with a field content as minimum as possible,introducing a modular S_(4)using gauged U(1)_(B−L) symmetries.Owing to the rank two neutrino mass matrix,we obtain a vanishing neutrino mass...We discuss a linear seesaw model with a field content as minimum as possible,introducing a modular S_(4)using gauged U(1)_(B−L) symmetries.Owing to the rank two neutrino mass matrix,we obtain a vanishing neutrino mass eigenvalue,and only the normal mass hierarchy of neutrinos is favored via the modular S_(4)symmetry.In our numericalΔχ^(2)analysis,we especially determine a relatively sharp prediction on the sum of neutrino masses to be approximately 60 meV,in addition to other predictions.展开更多
The masses of the three generations of charged leptons are known to completely satisfy Koide＇s mass relation,but the question remains of whether such a relation exists for neutrinos.In this paper,by considering the s...The masses of the three generations of charged leptons are known to completely satisfy Koide＇s mass relation,but the question remains of whether such a relation exists for neutrinos.In this paper,by considering the seesaw mechanism as the mechanism generating tiny neutrino masses,we show how neutrinos satisfy Koide＇s mass relation,on the basis of which we systematically give exact values of both left-and right-handed neutrino masses.展开更多
基金Supported partly by the Polish National Science Centre(NCN)under the Grant Agreement 2017/25/B/ST2/01987 and the COST(European Cooperation in Science and Technology)Action CA 16201 PARTICLEFACE。
文摘Neutrinos stand out among the elementary particles because of their unusually small masses.Various seesaw mechanisms attempt to explain this fact.In this work,applying insights from matrix theory,we are in a position to treat variants of seesaw mechanisms in a general manner.Specifically,using Weyl's inequalities,we discuss and rigorously prove under which conditions the seesaw framework leads to a mass spectrum with exactly three light neutrinos.We find an estimate of the mass of heavy neutrinos to be the mass obtained by neglecting light neutrinos,shifted at most by the maximal strength of the coupling to the light neutrino sector.We provide analytical conditions allowing one to prescribe that precisely two out of five neutrinos are heavy.For higher-dimensional cases the inverse eigenvalue methods are used.In particular,for the CP-invariant scenarios we show that if the neutrino sector has a valid mass matrix after neglecting the light ones,i.e.if the respective mass submatrix is positive definite,then large masses are provided by matrices with large elements accumulated on the diagonal.Finally,the Davis-Kahan theorem is used to show how masses affect the rotation of light neutrino eigenvectors from the standard Euclidean basis.This general observation concerning neutrino mixing,together with results on the mass spectrum properties,opens directions for further neutrino physics studies using matrix analysis.
基金Supported by an appointment to the JRG Program at the APCTP through the Science and Technology Promotion Fund and Lottery Fund of the Korean Government。
文摘We discuss a linear seesaw model with a field content as minimum as possible,introducing a modular S_(4)using gauged U(1)_(B−L) symmetries.Owing to the rank two neutrino mass matrix,we obtain a vanishing neutrino mass eigenvalue,and only the normal mass hierarchy of neutrinos is favored via the modular S_(4)symmetry.In our numericalΔχ^(2)analysis,we especially determine a relatively sharp prediction on the sum of neutrino masses to be approximately 60 meV,in addition to other predictions.
基金Supported by National Natural Science Foundation of China(11275017,11172008,11173028)the financial support from Chinese Scholarship Council
文摘The masses of the three generations of charged leptons are known to completely satisfy Koide＇s mass relation,but the question remains of whether such a relation exists for neutrinos.In this paper,by considering the seesaw mechanism as the mechanism generating tiny neutrino masses,we show how neutrinos satisfy Koide＇s mass relation,on the basis of which we systematically give exact values of both left-and right-handed neutrino masses.
