_{1}

^{*}

In this paper we consider a model in which the masses of elementary particles are formed and stabilized thanks to confining potential, which is caused by recoil momentum at emission of specific virtual bosons by particle itself. The calculation of this confining potential
*Ф*(
*R*) is carried out. It is shown that
*Ф*(
*R*) may be in the form const
or const
depending on continuous or discrete nature of the spectrum of emitted bosons.

In the article the model of formation of mass of elementary particles is offered as a result of emitting of the special virtual bosons as spherical waves (conditionally we will name them as the bosons of Higgs). It is supposed here that confining potential which is necessary for stabilizing of particle mass appears because of effect of impulse recoil, especially for electron, muon, pion, kaon and neutrino.

In due time Poincare, proceeding from common sense, entered supposition about a presence in the structure of electron of some elastic elements due to which the charge of electron holds out in a small volume. This model was later used by many authors. We will consider it more detailed, following [

In accordance with [

The radius of electron, corresponding to a minimum of energy (1) of the system, is determined from equation

From Equations (1) and (2) the mass of electron is

(3)

It is possible also to write down that

and coefficient

In Equation (1) the value

Preliminary we will represent information about the calculation of the masses for several elementary particles and then pass to more detailed consideration of confining potential.

In [

radius of elastic shell, σ is the coefficient of surface tension, the same that is in Equations (1)-(4). In [

where ρ is a radius of the compressed electric cloud, and N is the number of neutrino quanta that is determined from the decay scheme: N = 2 for muon, 3―for pion, and 21―for kaon. The masses of particles and characteristic sizes ^{0 }and K^{0} are in relation 0.547: 105.707: 134.963: 493.87 (MeV) (by attachment to mass of neutral pion), that is in accord with experience data. It is shown that the masses of all considered particles, as well as for an electron, are proportional to the square of their equilibrium size

It is assumed in the Standard Model that the masses of row of elementary particles can be represented in the form:

(7)

where H = 246 GeV is the characteristic energy in the model of Higgs [

where unknown size

The result of the Formula (6) was used in [_{w} = 80.4 GeV [

where

To define the masses of neutrino in [

1. Although neutrinos do not have an electric charge, they seems to have small electrostatic energy due to that spacial distributions of diverse charges produced by virtual pairs _{ }

2. Virtual rest-energy of neutrino consists of the confining potential

3. The value of s is identical for all neutrinos.

Similarly, as for an electron, mass of neutrino would be found at being of a minimum of virtual energy (11):

but as a value ^{ }is unknown, for determination of the neutrino masses we will take advantage of theoretical results [

Similar values for three neutrino mass eigenstates (ν_{1}, ν_{2}, ν_{3}) were received in [

Values

We will notice that as

where a dimensionless factor

θ_{w}―is the angle of Weinberg,

and are equal to:

In Equation (5), also as in (1), the value ^{2}; however, physical reason for the origin of confining potential is not clear. A model is offered in this article, explaining the origin of this potential and holding pressure due to the effect of impulse recoil of the special emitted virtual bosons.

So then for the ground of this model we will enter next suppositions:

1. By analogy with the model of Poincare we will suppose that every elementary particle has confining potential

2. Every elementary particle radiates the special virtual bosons as spherical waves

3. We will suppose that mass of such bosons ^{0}, where Z^{0} is a neutral carrier of the weak interaction with mass 91.2 GeV [

tence of such virtual bosons τ is much smaller than

4. Every elementary particle is the inexhaustible source of such virtual spherical waves, but the mass of the particle-source does not decrease, because virtual bosons through an instant τ return back into a source, due to interacting with the fields of vacuum.

5. We suppose that complete amount of the bosons emitted by a particle in a unit of time N_{H} is proportional to area of particle surface with a coefficient

As every moving wave carries an impulse, it ensues from these suppositions, that on the surface of elementary particle because of the effect of impulse recoil, spherical waves are creating holding force of pressure F(R) and confining potential

We will consider 2 cases for forms of boson spectrum:

a) the emitted bosons have a continuous spectrum of radiation in the interval of

b) the emitted bosons have a discrete spectrum of radiation : ^{2}.

Let’s consider the case of a). We will enter the condition of normalizing for ^{2} is equal to:

Consequently confining potential for the case of a) is:

where

For the case of b) we will enter the condition of normalizing for^{2} is equal to:

The sum

Thus, in the article it’s assumed that every elementary particle produces the special bosonic field that is present only in a thin layer at the surface of a particle. It is shown that this field can create the confining potential, stabilizing the mass of particle during the time of its life.

Lev I.Buravov, (2016) Confining Potential and Mass of Elementary Particles. Journal of Modern Physics,07,129-133. doi: 10.4236/jmp.2016.71013