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The Radius of the Proton in the Self-consistent Model

January 2012
Hadronic Journal 35(4):349

Authors:

Perm scientific site

Hadronic Journal, 2012, Vol. 35, No. 4, P. 349 – 363. Based on the notion of strong gravitation, acting at the level of elementary particles, and on the equality of the magnetic moment of the proton and the limiting magnetic moment of the rotating non-uniformly charged ball, the radius of the proton is found, which conforms to the experimental data. At the same time the dependence is derived of distribution of the mass and charge density inside the proton. The ratio of the density in the center of the proton to the average density is found, which equals 1.57.

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THE RADIUS OF THE PROTON

IN THE SELF-CONSISTENT MODEL

Sergey G. Fedosin

e-mail: intelli@list.ru

Perm, Perm Region, Russia

Sviazeva Str. 22-79

Abstract

Based on the notion of strong gravitation, acting at the level of elementary

particles, and on the equality of the magnetic moment of the proton and the limiting

magnetic moment of the rotating non-uniformly charged ball, the radius of the proton

is found, which conforms to the experimental data. At the same time the dependence is

derived of distribution of the mass and charge density inside the proton. The ratio of

the density in the center of the proton to the average density is found, which equals

1.57.

Keywords: strong gravitation; de Broglie waves; magnetic moment; proton radius.

1 Introduction

Since the discovery of the proton in 1917 the question arose how to

determine the radius of this elementary particle. There are many theoretical

models to estimate the radius of the proton. Most of these models is associated

with the concept of the electromagnetic form factors as the amendment by

which the scattering amplitude of particles by proton is different from the

scattering amplitude by a point particle. The calculation of the form factors is

complex and requires taking into account many factors, including the radial

density distribution of charge and magnetic moment, the dynamics of quarks,

partons and virtual particles. There may be a variety of approaches – scattering

theory, chiral perturbation theory, lattice QCD, etc., description of which can

be found in [1], [2]. Form factors are determined from scattering experiments,

depend on the energy of the interacting particles, and allow us to find the root

mean square of the charge distribution and magnetic moment as a measure of

particle’s size. Information on the radius of the proton can be extracted from

the analysis of the Lamb shift in hydrogen and in a coupled system of a proton

and a negative muon [3].

2 Other estimates of proton radius

Consider some simple methods for determining the radius of the proton.

One of them is based on the fact that in the particles, when they are excited,

standing electromagnetic waves emerge. The maximum energy of these

standing waves does not exceed the rest energy in order to avoid the decay of

particles. From this it can be derived that the de Broglie waves are

electromagnetic oscillations, detectable in the laboratory frame in the

interaction of moving particles. To describe these oscillations it is necessary to

apply the Lorentz transformations to the standing waves inside the particles and

to find their form in the laboratory reference frame [4], [5].

In the simplest case the spherical standing waves are modeled by two

waves, one of which runs from the center to the surface of the particle and the

other at the same time is moving backwards. We can assume that in the

direction of a specified axis, for example OX , there are two counter-

propagating waves of the following form:

)sin( 101

′′

−

′′

=xKtUU , )sin( 202

′′

=xKtUU ,

⎟

⎠

⎞

⎜

⎝

⎛+

′′

⎟

⎠

⎞

⎜

⎝

⎛−

−

′′

=+= 2

sin

cos2 2121

021

ϕϕ

txKUUUU , (1)

here 1

, 2

are the initial phases of the oscillations with 0tx

′′

, 0

U is

the amplitude of the periodic function,

′ and

′ denote the angular

frequency and wave number and the primes over the variables mean that they

are considered in the rest frame of the particle.

As U any periodic function can be used, which satisfies the wave equation.

For example, it can be the strength or the field potential of the wave. The

phases of the waves in (1) must be shifted to

for emerging of the standing

wave. If 1

=, 20

=, then in the center of the particle with 0x′= there will

be always a node as the absence of visible oscillations, and (1) becomes as

follows:

()()

txKUU ′′′′

cossin2 0. (2)

As a result of oscillations (2) velocities of charges of the particle substance

and the field potentials can periodically change inside the particle. This leads

inevitably to periodic oscillations of the field potentials also outside the particle

in the surrounding space.

Now we shall assume that the particle moves together with its standing

wave along the axis OX in the laboratory reference frame at the velocity u.

How are the field oscillations modified inside and outside the particle with

respect to its movement? We should express in (2) the primed coordinates and

the time inside the moving particle through the coordinates and the time in the

laboratory reference frame using the Lorentz transformations ( c refers to the

speed of light):

cxut

t−

−

′, 22

1cu

tux

−

′, yy =

′, zz =

′,

⎟

⎠

⎞

⎜

⎝

⎛

−

′

⎟

⎠

⎞

⎜

⎝

⎛

−

′

=22

)/(

cos

)(

sin2

cxut

tuxK

. (3)

From (3) we see that as a result of displacement of the standing wave with

the particle for the external motionless observer in the laboratory frame the

wavelength and the frequency will change. More precisely, on the observed

wave additional antinodes appear, with a wavelength between them, differing

from the wavelength 2

′=′ in the reference frame of the particle. We shall

stop the wave (3) for a moment with 0t= and shall find the wavelengths as

the spatial separation between the points of the wave in the same phase. When

0x= the sine in (3) will be zero, while when 1

= the phase of the sine will

change from 0 to 2

. Hence we obtain:

()

2sin

sin 22

⎟

⎠

⎞

⎜

⎝

⎛

−

′

K, 22

12 cu

cu −

′

−

. (4)

Similarly for the wavelength of the cosine in (3) we find:

()

λω

2cos

cos 22

2−=

⎟

⎠

⎞

⎜

⎝

⎛

−

′

−

cu , u

cuc

′

−

222

12 . (5)

We shall now estimate the temporal separation between the points of the

wave in one phase with 0x=, considering this separation as the corresponding

period of the wave:

()

2sin

sin 22

1−=

⎟

⎠

⎞

⎜

⎝

⎛

−

′

−

TuK , uK

T′

−

. (6)

()

2cos

cos 22

⎟

⎠

⎞

⎜

⎝

⎛

−

′

T, 22

21cuTT −

′

=. (7)

From (4) − (7) we obtain the following expressions for the velocities:

, b

2. (8)

As we see from (8) the oscillations of the wave (3) associated with the

cosine, are propagating at the phase velocity of de Broglie b

. Besides, the

oscillations of the wave (3) associated with sine, move in space at the same

velocity u as the particle itself. The wavelength 2

in (5) can be transformed

so as to bring it to the standard form for the de Broglie wavelength. We shall

associate the angular frequency of the oscillations inside the particle, similarly

to the electromagnetic wave, with the energy of oscillations: W

′′

==, where

== is Dirac constant, h is Planck constant. This gives the following:

cuch

′

−

222

. (9)

Similarly from (4) we have:

cuch

′

−

. (10)

In the limiting case when the oscillation energy is compared with the rest

energy of the particle, 2

Wmc

′′

===, from (9) it follows:

huc

−

℘, (11)

where m is the mass of particle, ℘ is relativistic momentum of the particle.

The formula (11) defines de Broglie wavelength with the help of particle

momentum. We shall note that de Broglie wrote (11) on condition that the

energy of the particle

−

is equal to the energy of the wave

accompanying the particle. According to the obtained expression (9), the

wavelength 2

must be present in the particle also at low excitation energy

.W′ In this case as the excitation energy decreases, the wavelength should

increase.

As a rule in the experiments only 2bf

λλ

℘ is found from (11), and not

the wavelength 2

from (9). This can occur because among the number of

interacting particles at the same time there are particles with different

excitation energies W′ and different 2

, so that the wave phenomena are

blurred. The same is true for the waves with wavelength 1

in (10). Only for

the most actively interacting particles, the excitation energies W′ of which are

close to the rest energy of the particles, the limiting value of the wavelength is

reached equal to the de Broglie wavelength. Thus this wavelength is revealed

in the experiment. When 2

Wmc

′′

=== we can also predict for the particles

the wave phenomena with the critical wavelength

huc

−

=. In

particular, c

= is the Compton wavelength, discovered in the Compton

effect. According to our point of view, emerging of de Broglie wave should be

treated as a purely relativistic effect, which arises as a consequence of the

Lorentz transformation of the standing wave, moving with the particle.

As a result, we have to assume that the wave-particle duality is realized in

full only in those particular particles, the excitation energies of which reach

their rest energies. In this case the difference of particles and field quanta, if

they are treated from the point of view of their wave properties, becomes

minimal. At low excitation energies the particles can not emit their energy

greatly, and the amplitudes of the oscillations of the field potentials near the

particles are small. Then the particles would interact with each other not in the

wave way, but rather in the usual way, and the wave phenomena become

invisible.

If we assume that the length of the standing wave is equal to 2R

′= ,

where

is the radius of the proton, then from the equality of the wave energy

and the rest energy of the proton we obtain:

′==

′, 2

Mc h

′

==, 16

6.6 10

RMc

−

==⋅

here

′ is the oscillation frequency, p

is the mass of the proton.

Another way to estimate the radius of the proton assumes that the difference

between the rest energy of the neutron and the proton is due to the electrical

energy of the proton charge. In this case, it should be:

()

MMc

πε

−= , (12)

where n

is the mass of the neutron, e is the elementary charge, 0

is the

vacuum permittivity.

In (12) for the case of the uniform distribution of the charge in the volume

of the proton 0.6k=, as a result the estimation of the proton radius gives the

value of 16

6.68 10R−

=⋅ m.

In [6] and [7], the radius of the proton was found from the condition that the

limiting angular momentum of the strong gravitation field inside the proton is

equal in magnitude to the spin of the proton. This leads to the following

formula:

56.7 10

ΓM

−

==⋅ m. (13)

In (13) the strong gravitational constant

is used. According to [4], this

constant is determined from the equation of electric force and the force from

the strong gravitation field, acting in the hydrogen atom on the electron with

the mass e

, which is located in the ground state on the Bohr radius B

πε

1.514 10

4pe

ΓMM

πε

==⋅

m3·kg–1·s–2, (14)

In addition to the attractive forces from gravitation and the charges of the

nucleus and the electron, in the hydrogen atom the electron substance in the

form of the rotating disc is influenced by the repulsive forces acting away from

the nucleus. One of these forces is the electric force of repulsion of the charged

substance of the electron cloud from itself. In the rotating non-inertial reference

frame in which an arbitrary part of the electron substance is at rest, there is also

the force of inertia in the form of the centrifugal force, which depends on the

velocity of rotation of this substance around the nucleus. In the first

approximation, these forces are equal in magnitude, which leads to (14).

We shall remind that the idea of strong gravitation was introduced into

science in the works of Abdus Salam and his colleagues [8], [9] as the

alternative explanation of the strong interaction of the particles. Assuming that

hadrons can be represented as Kerr-Newman black holes, they estimated the

strong gravitational constant as 27

6.7 10⋅ m3·kg–1·s–2.

With the help of the strong gravitation constant (14) we can express the fine

structure constant:

137.035999

ΓMM

Another estimate of the radius of the proton follows from the equality of the

rest energy and the absolute value of the total energy, which, taking into

account the virial theorem, is approximately equal to the half of the absolute

value of the strong gravitation energy associated with the proton [4]:

=. (15)

If we take 0.6k= for the case of the uniform mass distribution, then from

(15) it follows that 16

8.4 10R−

=⋅ m.

All of the above estimates are based on the classical approach to the proton

as to the material object of small size in the form of the ball with the radius

It is assumed that the strong gravitation acts at the level of elementary particles

in the same way as ordinary gravitation at the level of planets and stars.

In the Standard model of elementary particles and in quantum

chromodynamics it is assumed that the nucleons and other hadrons consist of

quarks, and baryons have three quarks, while mesons have two quarks. Instead

of the strong gravitation, the action of gluon fields is assumed to hold the

quarks in hadrons. Quarks are considered to be charged elementary particles,

therefore as the radius of the proton the charge and magnetic root mean square

radii are considered. These radii are determined by the electric and magnetic

interactions of the proton and can differ from each other.

The estimate of the proton charge radius can be made with the help of the

experiments on the scattering of charged particles on the proton target [10]. In

such experiments the total cross sections of interaction of the particles

are

found. For the case of the protons scattering on nucleons with energies more

than 10 GeV we can assume that 2

σπ

=, and 30

3.8 10

−

=⋅ m

2. Hence we

obtain 16

7.8 10R−

=⋅ m.

3 The self-consistent model

Our aim will be to find a more exact value of the radius of the proton by

using classical methods. In the calculations we shall use only the tabular data

on the mass, charge and magnetic moment of the proton. The proton will be

considered from the standpoint of the theory of infinite nesting of matter [11],

in which the analogue of the proton at the level of stars is a magnetar or a

charged neutron star with a very large magnetic and gravitational field.

Similarly to the magnetar, the substance of the proton must be magnetized and

held by a strong gravitation field.

To take into account the non-uniformity of the substance density inside the

proton we shall use the simple formula in which the substance density changes

linearly increasing to the center:

(1 )

cAr

ρρ

=−, (16)

where c

is the central density,

is the current radius, R

0<< is the

coefficient which should be determined.

Formula (16) should be considered as a first approximation to the actual

distribution of the density of matter inside the proton. Approximate linear

dependence of the density of matter in neutron stars has been shown in [12],

and we assume that this is also true for the proton as an analogue of the neutron

stars.

To estimate the values

and the radius

we shall consider the integral

for the proton mass in the spherical coordinates:

243

(1 ) sin 1

MArrdrdd

πρ

ρθθϕ

⎛⎞

=− = −

⎜⎟

⎝⎠

∫. (17)

For accurate calculation of state of neutron stars, and thus protons as their

analogues we should consider the curvature of spacetime in a strong

gravitational field, as well as the contribution of the energy of the gravitational

field to the total mass-energy. We shall assume that in (16), in dependency of

matter density on the radius all relativistic effects are taken into account, and

the mass of the proton (17) is the gravitational mass from the point of view of a

distant observer.

In (17) there are three unknown quantities, to obtain which two more

equations are required. We shall assume the virial theorem to be valid and

equate the rest energy of the proton to the half of the absolute value of the

energy of the static field of strong gravitation:

216

cdVGdV

επ

∞∞

=− =

∫∫

, (18)

where

επ

=− is the energy density of the strong gravitation field

according to [4], G is the gravitational acceleration or strength of gravitational

field.

In (18), the integration of the energy density of the field should be done

both inside and outside of the proton. The value G inside the proton can be

conveniently found by integrating the equation for the strong gravitation field

Γ4−=⋅∇ G, which is part of the equations of the Lorentz-invariant theory

of gravitation [13]. After integrating over the spherical volume with the radius

≤, and then using the Gauss theorem, that is making transition to

integrating over the area of the indicated sphere inside this proton, in view of

(17) we obtain:

ii i

dV dS r G

ππρ

∇⋅ = ⋅ = =−

∫∫ ∫

GGn ,

⎟

⎠

⎞

⎜

⎝

⎛−−= 4

4rA

Γcr

ρπ

. (19)

Outside the proton the gravitational acceleration is equal to:

MΓpr

Go−= . (20)

Substituting (19) and (20) in (18), we obtain the relation:

MΓ

RARA

RΓcM p

cp 41123645

5222 +

⎟

⎠

⎞

⎜

⎝

⎛+−=

ρπ

. (21)

In (21) we can eliminate the value c

using (17), which give the

dependence of A on R in the form of the quadratic equation:

414

222

22 =−+

⎟

⎠

⎞

⎜

⎝

⎛+−+

⎟

⎠

⎞

⎜

⎝

⎛−cR

MΓ

RA ppp .

The analysis of this equation shows that it has the following solution:

45360

9453

222

MΓ

MΓcRMΓ

MΓ

ppp

−

−+−

=, (22)

on condition that when

213

0.3 0.371

ΓM

<<≈

, then accordingly

01AR<<

We shall now turn to the magnetic moment of the proton. As in [4], we

assume that the magnetic moment of the proton is equal to the magnetic

moment, which is formed due to the maximum rapid rotation of the charged

substance of the proton. In spherical coordinates, the magnetic moment can be

approximately calculated as the sum of the elementary magnetic moments of

the separate rings with their radius

sinr, which have the magnetic moment

due to the current di flowing in them from the rotation of the charge:

22 22

22 2

sin sin

sin (1 ) sin 1 .

15 6

Lqc

PdP r di r dt

dAR

rArrdrd

πθπθ

πωρ

πθρ θθ

== = =

⎛⎞

=− =−

⎜⎟

⎝⎠

∫∫ ∫

∫

(23)

The angular velocity L

= of the maximum rotation of the proton can

be found from the condition of limiting rotation, with the equality of the

centripetal force and the gravitation force at the equator: R

MГ

=. Further

we believe that for the charge density and the substance density the equation

holds, and we use (17). This gives the following:

()

RARMГe

m3430

564

−

=. (24)

4 Conclusions

The relation (24) together with (22) allow us to find the radius of the proton

8.73 10R−

=⋅ m, as well as the value 0.48

=. From (17) we obtain then the

central substance density 17

9.4 10

=⋅ kg/m3, which exceeds the average

density of the proton 1.57 times. The maximum angular velocity of rotation of

the proton in view of (23) is equal to 23

6.17 10

=⋅

rad/s. At the same time, if

the spin of the proton in the approximation of the uniform density of substance

would be equal to the standard value for the spin of the fermion

0.4 2

LMR

=, then the angular velocity of rotation 23

1.03 10

=⋅

rad/s

would correspond to this spin.

For comparison with the experimental data we shall point to the results of

calculations of electron scattering from [14], where the charge radius

8.7 10

R−

=⋅ m is obtained taking into account only the scattering on

protons, 16

8.71 10

R−

=⋅ m – taking into account the data on the pion

scattering, and 16

8.8 10

R−

=⋅ m – taking into account the data on the neutron

scattering. In [3] the charge radius 16

8.4184 10

R−

=⋅

m was found in the study

of the coupled system of the proton and the negative muon. The study of the

scattering cross section of polarized photons by protons [15] gives the charge

radius 16

8.75 10

R−

=⋅ m and the magnetic radius 16

8.67 10

R−

=⋅ m. The

charge radius 16

8.77 10

R−

=⋅ m and the magnetic radius 16

7.77 10

R−

=⋅ m

of the proton are listed on the site of Particle data group [16]. In the database

CODATA [17] the proton charge radius is equal to 16

8.775 10

R−

=⋅

The value 16

8.73 10R−

=⋅ m obtained in the framework of the self-consistent

model is close to the experimental values of the radius of the proton, which

confirms the possibility of applying the idea of strong gravitation to describe

the strong interaction of elementary particles.

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Jan 2024

Mikhail Batanov-Gaukhman

This article is the fifth part of a scientific project under the general title "Geometrized vacuum physics based on the Algebra of Signatures". In this article, Einstein's vacuum equations are used as conservation laws, and their solutions as metric-dynamic models of stable vacuum formations. Sets of metrics-solutions of vacuum equations are considered, and methods of extracting information from these metrics based on Algebra of Signature (Alsigna) are proposed. For convenience of perception of intra-vacuum processes, a change in the interpretation of the zero components of the metric tensor was used. Instead of curved space-time continua, “colored” elastoplastic continuous pseudo-mediums are introduced into consideration. In this case, the zero components of the metric tensor determine not the change in the rate of flow of local time, but the speed of flow of intra-vacuum current in the local region of the elastoplastic pseudo-medium. At the end of the article, an extended (third) Einstein vacuum equation is proposed, which allows us to consider metric-dynamic models of a variety of stable corpuscular vacuum formations. Alsigna's infinitely deepening intertwined fabric of space-time continuum, taking into account all 16 signatures (i.e. 16 types of topologies), is in many ways similar to the spin network of loop quantum gravity and to 6-dimensional Calabi-Yau manifolds. In this sense, the Algebra of Signatures can serve as a link that unites different directions in the development of quantum gravity.

The Gravitational Field in the Relativistic Uniform Model within the Framework of the Covariant Theory of Gravitation

Article

Full-text available

Apr 2018

Sergey G. Fedosin

For the relativistic uniform system with an invariant mass density the exact expressions are determined for the potentials and strengths of the gravitational field, the energy of particles and fields. It is shown that, as in the classical case for bodies with a constant mass density, in the system with a zero vector potential of the gravitational field, the energy of the particles, associated with the scalar field potential, is twice as large in the absolute value as the energy defined by the tensor invariant of the gravitational field. The problem of inaccuracy of the use of the field’s stress-energy tensors for calculating the system’s mass and energy is considered. The found expressions for the gravitational field strengths inside and outside the system allow us to explain the occurrence of the large-scale structure of the observable Universe, and also to relate the energy density of gravitons in the vacuum field with the limiting mass density inside the proton. Both the Universe and the proton turn out to be relativistic uniform systems with the maximum possible parameters. The described approach allows us to calculate the maximum possible Lorentz factor of the matter particles at the center of the neutron star and at the center of the proton, and also to estimate the radius of action of the strong and ordinary gravitation in cosmological space.

Prediction of Rms Charge Radius of Proton Using Proton–Proton Elastic Scattering Data at TeV

Article

Full-text available

May 2021

Using proton–proton elastic scattering data at TeV and squared four-momentum transfer 0.36 < -t < 0.76 (GeV/c)2 for 13 σBeam distance and 0.07 < -t < 0.46 (GeV/c)2 for 4.3 σBeam distance, form factor of proton is predicted. Simplest version of Chou–Yang model is employed to extract the form factor by fitting experimental data of differential cross section from TOTEM experiment (for 13σBeamand 4.3 σBeam distance) to a single Gaussian. Root mean square (rms) charge radius of proton is calculated using this form factor. It is found to be equal to 0.91 fm and 0.90 fm respectively. Which is in good agreement with experimental data and theoretically predicted values.

On the structure of the force field in electro gravitational vacuum

Article

Full-text available

Jan 2021

Sergey G. Fedosin

Analysis of the field equations for the tensors of the mass and charge components of the general field shows that their source is the charge four-current. In this connection, an assumption is made that it is the charge component of the force field of the electrogravitational vacuum in the form of fluxes of charged particles within the framework of Le Sage's theory of gravitation, which is mainly responsible for both electromagnetic and gravitational interactions, as well as for the action of other fields inside bodies. The parameters of the vacuum’s charged particles can be determined quite accurately using the theory of similarity within the theory of infinite nesting of matter, so that the description of the cause of emergence of electromagnetic and gravitational forces is filled with specific content.

On the Dependence of the Relativistic Angular Momentum of a Uniform Ball on the Radius and Angular Velocity of Rotation

Article

Full-text available

Feb 2020

Sergey G. Fedosin

In the framework of the special theory of relativity, elementary formulas are used to derive the formula for determining the relativistic angular momentum of a rotating ideal uniform ball. The moment of inertia of such a ball turns out to be a nonlinear function of the angular velocity of rotation. Application of this formula to the neutron star PSR J1614-2230 shows that due to relativistic corrections the angular momentum of the star increases tenfold as compared to the nonrelativistic formula. For the proton and neutron star PSR J1748-2446ad the velocities of their surface’s motion are calculated, which reach the values of the order of 30% and 19% of the speed of light, respectively. Using the formula for the relativistic angular momentum of a uniform ball, it is easy to obtain the formula for the angular momentum of a thin spherical shell depending on its thickness, radius, mass density, and angular velocity of rotation. As a result, considering a spherical body consisting of a set of such shells it becomes possible to accurately determine its angular momentum as the sum of the angular momenta of all the body’s shells. Two expressions are provided for the maximum possible angular momentum of the ball based on the rotation of the ball’s surface at the speed of light and based on the condition of integrity of the gravitationally bound body at the balance of the gravitational and centripetal forces. Comparison with the results of the general theory of relativity shows the difference in angular momentum of the order of 25% for an extremal Kerr black hole.

THE BINDING ENERGY AND THE TOTAL ENERGY OF A MACROSCOPIC BODY IN THE RELATIVISTIC UNIFORM MODEL

Article

Full-text available

Jun 2019

Sergey G. Fedosin

Middle East Journal of Science, Vol. 5, Issue 1, pp. 46-62. The total energy, binding energy, energy of fields, pressure energy and the potential energy of the system consisting of particles and four fields is precisely calculated in the relativistic uniform model. These energies are compared with the kinetic energy of particles. The relations between the coefficients of the acceleration field and the pressure field independent of the system’s properties are found, which can be expressed in terms of each other and in terms of the gravitational constant and the vacuum permittivity. A noticeable difference is shown between the obtained results and the relations for simple systems in classical mechanics, in which the acceleration field and pressure field are not taken into account or the pressure is considered to be a simple scalar quantity. The conclusion is substantiated that as increasingly massive relativistic uniform systems are formed, the average density of these systems decreases as compared to the average density of the particles or bodies making up these systems. In this case the inertial mass of the massive system is less than the total inertial mass of the system’s parts.

General Solution of the Schrödinger Equation

Article

Oct 2024

Mikhail N. Sergeenko

Strong gravity, black holes, and hadrons

Article

Full-text available

Sep 1977

Certain similarities and analogies between the properties of black holes and elementary particles are considered in the framework of the strong gravitational field. Properties examined include measurable parameters (mass, angular momentum, charge), the metrical properties of space-time in the region near an elementary particle, mass formulas, thermodynamical phenomena, and black-hole radiation. An upper limit for the temperature of black holes is derived which is the same as the limiting temperature arising in thermodynamic bootstrap models of hadrons.

Electromagnetic and Gravitational Pictures of the World

Article

Full-text available

Oct 2007
Apeiron

Sergey G. Fedosin

The review of the theory of electromagnetic field together with the special and general theories of relativity has been made. The similar theory of gravitation has been presented which has the property of Lorentz-invariancy in its own representation in which the information is transferred at the speed of propagation of the gravitational field. Generalization of the specified gravitation theory on noninertial reference systems has been made with the help of the mathematical apparatus of the general relativity. It allows to avoid some drawbacks of the standard general relativity theory and to expand its applicability. The possibility of complementary descriptions of the physical phenomena with the help of simultaneous use of the theories of gravitational and electromagnetic fields has been shown.

The Moment of Momentum and the Proton Radius

Article

Full-text available

May 2002

The theory of nuclear gravitation is used to calculate the moment of momentum of the gravitational field of a proton, which is compared to the corresponding moment of momentum of the electromagnetic field. As a result, the proton radius is estimated and a relation for the moment of momentum of the field is established, which coincides in form with the expression of the virial theorem for energy.

Review of Particle Physics

Article

Jul 2012

This biennial Review summarizes much of particle physics. Using data from previous editions, plus 2658 new measurements from 644 papers, we list, evaluate, and average measured properties of gauge bosons, leptons, quarks, mesons, and baryons. We summarize searches for hypothetical particles such as Higgs bosons, heavy neutrinos, and supersymmetric particles. All the particle properties and search limits are listed in Summary Tables. We also give numerous tables, figures, formulae, and reviews of topics such as the Standard Model, particle detectors, probability, and statistics. Among the 112 reviews are many that are new or heavily revised including those on Heavy-Quark and Soft-Collinear Effective Theory, Neutrino Cross Section Measurements, Monte Carlo Event Generators, Lattice QCD, Heavy Quarkonium Spectroscopy, Top Quark, Dark Matter, Vcb & Vub, Quantum Chromodynamics, High-Energy Collider Parameters, Astrophysical Constants, Cosmological Parameters, and Dark Matter.A booklet is available containing the Summary Tables and abbreviated versions of some of the other sections of this full Review. All tables, listings, and reviews (and errata) are also available on the Particle Data Group website: http://pdg.lbl.gov/.The 2012 edition of Review of Particle Physics is published for the Particle Data Group as article 010001 in volume 86 of Physical Review D.This edition should be cited as: J. Beringer et al. (Particle Data Group), Phys. Rev. D 86, 010001 (2012).

Article

Jun 2008

This paper gives the 2006 self-consistent set of values of the basic constants and conversion factors of physics and chemistry recommended by the Committee on Data for Science and Technology (CODATA) for international use. Further, it describes in detail the adjustment of the values of the constants, including the selection of the final set of input data based on the results of least-squares analyses. The 2006 adjustment takes into account the data considered in the 2002 adjustment as well as the data that became available between 31 December 2002, the closing date of that adjustment, and 31 December 2006, the closing date of the new adjustment. The new data have led to a significant reduction in the uncertainties of many recommended values. The 2006 set replaces the previously recommended 2002 CODATA set and may also be found on the World Wide Web at physics.nist.gov/constants.

STRONG GRAVITY APPROACH TO QCD AND CONFINEMENT

Article

Nov 2011
MOD PHYS LETT A

A Weyl type of action which is scale free and quadratic in the curvature is suggested for strong gravity. The corresponding field equations have solutions which imply confinement. At the QCD scale, the scale invariance is broken inducing a Hilbert type term which describes the short distance behavior. This approach may provide a strong gravity basis for QCD.

Article

Oct 2008

Savely G. Karshenboim

Up-to-date data on the fundamental physical constants are briefly reviewed, as are the results of their combined analysis, namely, the new recommended values of the fundamental physical constants [Mohr P J, Taylor B N, Newell D B, "CODATA recommended values of the fundamental physical constants: 2006" Rev. Mod. Phys. 80 633 (2008)]. Following an approach presented previously (Usp. Fiz. Nauk 175 271 (2005) [Phys. Usp. 48 255 (2005)]), the author divides the data into blocks. The same block approach is used to discuss new theoretical and experimental results and their implications for the new recommended values of the constants. A comparison with the previous (1998 and 2002) sets of the recommended values of the constants is given.

The Size of the Proton

Article

Oct 2012

Randolf Pohl

We have measured the charge radius of the proton via laser spectroscopy of the exotic "muonic hydrogen" atom. Our value is 10 times more precise but 5 sigma away from the CODATA value.

Neutron star equilibrium configurations within a fully relativistic theory with strong, weak, electromagnetic, and gravitational interactions

Article

Feb 2012
NUCL PHYS A

We formulate the equations of equilibrium of neutron stars taking into account strong, weak, electromagnetic, and gravitational interactions within the framework of general relativity. The nuclear interactions are described by the exchange of the sigma, omega, and rho virtual mesons. The equilibrium conditions are given by our recently developed theoretical framework based on the Einstein-Maxwell-Thomas-Fermi equations along with the constancy of the general relativistic Fermi energies of particles, the "Klein potentials", throughout the configuration. The equations are solved numerically in the case of zero temperatures and for selected parametrization of the nuclear models. The solutions lead to a new structure of the star: a positively charged core at supranuclear densities surrounded by an electronic distribution of thickness

\sim \hbar/(m_e c)

of opposite charge, as well as a neutral crust at lower densities. Inside the core there is a Coulomb potential well of depth

\sim m_\pi c^2/e

. The constancy of the Klein potentials in the transition from the core to the crust, impose the presence of an overcritical electric field

\sim (m_\pi/m_e)^2 E_c

, the critical field being

E_c=m^2_e c^3/(e \hbar)

. The electron chemical potential and the density decrease, in the boundary interface, until values

\mu^{\rm crust}_e < \mu^{\rm core}_e

and

\rho_{\rm crust}<\rho_{\rm core}

. For each central density, an entire family of core-crust interface boundaries and, correspondingly, an entire family of crusts with different mass and thickness, exist. The configuration with

\rho_{\rm crust}=\rho_{\rm drip}\sim 4.3\times 10^{11}

g/cm

^3

separates neutron stars with and without inner crust. We present here the novel neutron star mass-radius for the case

\rho_{\rm crust}=\rho_{\rm drip}

and compare and contrast it with the one obtained from the Tolman-Oppenheimer-Volkoff treatment.

High Precision Measurement of the Proton Elastic Form Factor Ratio at Low

Q^2

Article

Aug 2011

Xiaohui Zhan

Jefferson Lab experiment E08-007 measured the proton elastic form factor ratio

\mu_pG_E/G_M

in the range of

Q^2=0.3-0.7(\mathrm{GeV}/c)^2

by recoil polarimetry. Data were taken in 2008 at the Thomas Jefferson National Accelerator Facility in Virginia, USA. A 1.2 GeV polarized electron beam was scattered off a cryogenic hydrogen target. The recoil proton was detected in the left HRS in coincidence with the elasticly scattered electrons tagged by the BigBite spectrometer. The proton polarization was measured by the focal plane polarimeter (FPP). In this low

Q^2

region, previous measurement from Jefferson Lab Hall A (LEDEX) along with various fits and calculations indicate substantial deviations of the ratio from unity. For this new measurement, the proposed statistical uncertainty (

<1%

) was achieved. These new results are a few percent lower than expected from previous world data and fits, which indicate a smaller

G_{Ep}

at this region. Beyond the intrinsic interest in nucleon structure, the new results also have implications in determining the proton Zemach radius and the strangeness form factors from parity violation experiments.

The Radius of the Proton in the Self-consistent Model

Abstract

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