EXPLANATION OF THE NATURE OF
LEPTON DOUBLETS OF THE
STANDARD MODEL WITHIN THE
FRAMEWORK OF A NONHERMITIAN THEORY WITH A
FUNDAMENTAL MASS
V.N. Rodionov, A.M. MandelQuestions,that are not customary to ask in the SM :1) Why do leptons in the SM form doublets - neutrinos of the corresponding typeand a charged lepton?
2) Why are charged leptons chirally symmetric in mass, but there are nochirally symmetric partners in mass among the neutrinos?
3) Why are the mass of left-handed neutrinos are very small on the leptonmass scale, however for the right-handed neutrino masses are very large (ifthey exist at all)? Can this be explained this phenomenon without fine-tuningin the mass sector?
4) How is the mass difference between the chiral components related to theelectric charge of the particle?

The answers to these questions (simple andnatural) are given by a small non-Hermitian
extension of the SM

Its essence is best expressed by themodified Dirac equation
(i    m1  5m2 )(r , t )  0
the last term here is anti-Hermitian,We will use linear superposition of these masscomponents for particles with a certain chirality

Two modern directions of development of nonHermitian theory• no restrictions on masscomponents• with the additional
condition

M - fundamental mass

Following V.G. Kadyshevsky, we adhere to the second
direction with a fundamental mass. There are anumber of reasons for this. The main reason is therequirements of the principle of equivalence. Someof its violations in non-Hermitian theories areinevitable, and the magnitude of the fundamental
mass M limits the scale of these violations.

The role of the mass corresponding to the thresholdfor the production of a chiral symmetric particle isplayed by the following combination of chiralcomponents

It is usually associated with gravitational mass.

The role of the dynamic (inert) mass, which
determines the mobility of particles in external
fields, is played by another combination of chiralcomponents

There are two different ways of forming theHermitian and non-Hermitian components of themass, and, accordingly, two ways of forming theobserved mass of particles. Introducing thedimensionless "observable mass"

they can be described by the following expressions

Here are the relevant graphs

Very important: in the Dirac limit
only the components of the first type (lower curves)and the particles composed of them survive.

V.G. Kadyshevsky called such particles, which are"compatible" with the SM and the ordinary Hermitian
theory of Dirac, ORDINARY. Their main feature is theclose chiral components at

Particles of the second type, disappearing in the Diraclimit, V.G. Kadyshevsky called "EXOTIC". Theyare incompatible with SM and Hermitian theory. Theirmain feature is the huge difference in the masses of
the chiral components at

The main idea of our report:
neutrinos are "exotic
Kadyshevsky particles".
It is this point of view that makes
it easy and natural to answer thequestions named at the beginningof the report.

This behavior of the masses of elementary particles
is not typical for the SM. But it is in many ways
analogous to the behavior of particles in Solid State
Physics. For example, the phonon dispersion curve

Compare with the formula for the massconstituents of non-Hermitian theoryDispersion curve of phonons

compare with slide 8

Very important: in the Dirac limit
exotic particles disappear, and the mass spectrumof ordinary particles grows indefinitely. In the limitof a continuous string (lattice constant d→0) the
acoustic branch grows indefinitely, while theoptical branch disappears.
In the limit of a continuous string d = 0, it isimpossible to understand the nature of opticalphonons. In our opinion, in the same way in the
Hermitian SM it is impossible to understand thetrue nature of exotic particles - neutrinos.

Let's summarize. Answers on questions
Why do SM leptons form doublets consisting of one
neutrino and one charged particle? Because themass of a lepton can be formed in two ways - fromvery close chiral components
and from very distant from each other
The first possibility corresponds to an ordinary
charged lepton, the second - to an exotic neutrino
particle.

Why is the mass of left-handed neutrinos so small
on the lepton mass scale, and why is the righthanded neutrino mass very large? Because themass of the left-handed neutrino is related to themass of the corresponding lepton as
It is small on the lepton scale because it is suppressed by the factor
No fine tuning is required for this. The mass ofright-handed neutrinos is of the order of thefundamental mass, which explains its very highvalue.

Why can only an ordinary particle in a doublet
have an electric charge? Because wheninteracting with photons (massless vectorbosons), a lepton should easily change its
chirality. Ordinary particles can do this, exotic
ones cannot. Therefore, exotic particles can onlyinteract with much more massive vector bosons.