## Monday, February 27, 2023

### Strong Forces: UNIZOR.COM - Physics4Teens - Atoms - Elementary Particles

Notes to a video lecture on http://www.unizor.com

Strong Nuclear Force

Physical concept of a field assumes that there is a characteristic usually called a charge that participates in the creation of a field or its interaction with objects, manifested as a force.

Electricity has two types of charges that we call positive, carried by protons, and negative, carried by electrons.
Strictly speaking, these are just names, they do not imply that electric charges are positive or negative real numbers, but we can measure them using some clever devices and measuring units, resulting in positive or negative numbers, and they act as if we can add them together using the rules of arithmetic.

In particular, equal in magnitude positive and negative charges neutralize each other. For example, an atom of hydrogen has one proton (positively charged) and one electron (negatively charged) that neutralize each other and form an electrically neutral atom.

In quantum field theory the electric field activity is manifested itself in exchange of photons - particles that carry field energy.

Gravity has only one type of charge that we call mass and it's always present, wherever we have a matter. We can measure it using some devices and measuring units, and these charges can be dealt with using their positive numerical values. There is no opposite charge to neutralize gravity.

There is a theory (not yet decisively supported by experiments) that gravitational field's activity is manifested itself in exchange of gravitons - particles that carry gravitational field energy.

In both above cases, electric and gravitation fields, the quantum theory tells that the field interaction is an exchange of particles specific for this field.

Let's consider the strong nuclear forces now.
As we suggested in the previous lecture, following the Standard Model, protons and neutrons are comprised of three quarks each:
+1p = +2/3u + +2/3u + −1/3d
0n = +2/3u + −1/3d + −1/3d
where
p is a proton,
n is a neutron,
u is an UP quark,
d is a DOWN quark and
preceding numbers are the electric charges of corresponding particles.

Earlier in this course we mentioned the existence of strong nuclear forces that hold the nucleus together.
These forces hold triplets of quarks together to form a nucleon (a proton or a neutron), overcoming repelling electric forces between similarly charged quarks (two +2/3u quarks or two −1/3d quarks).
Strong nuclear forces are much stronger than electric forces and prevent protons from separating because of their mutually repelling positive electric charge.

What is the nature of these strong nuclear forces?
As in a case of electric or gravitational fields, there are charges that create the strong nuclear force field and there are particles that carry the energy of strong nuclear forces.

The charges that create a strong force field and interact by exerting the force are called color charges. Below is an explanation of the reasons for calling them using colors.

The particles that carry energy of strong nuclear forces are called gluons because quarks (material particles) are "glued" together into a proton or a neutron by exchanging gluons.
So, gluons are radiation type particles, carriers of strong nuclear forces analogously to how photons carry the force of electromagnetic field.

Color Charge

Strong nuclear forces are manifestations of a force field inside a nucleus that maintains the nucleus integrity. As with other fields, there is a charge that produces it and participates in its interaction.
While electric charges involved in electric forces are of two types (positive and negative) and gravitational charges are of only one type (mass), charges involved in strong nuclear field are of three different types.

Obviously, these three types of strong nuclear field charges have to be named. The types of charges for strong nuclear forces are called color charges. It has nothing to do with colors of visible light, it's just a name used to characterize and differentiate the types of charges participating in the interactions of strong nuclear forces.

According to Standard Model, there are three different types of color charges (or simply colors) participating in strong force field called:
red (R),
green (G) and
blue (B).
Again, these are just the names to differentiate the types of charges, totally unrelated to visible light and its colors.

In the world of electric fields a single charged particle (negatively charged electron or positively charged proton) prefers to find an oppositely charged particle to combine and to neutralize the charge, attaining electric neutrality.
For example, a proton and an electron can combine to form an electrically neutral atom of hydrogen.

Similarly, in the world of strong forces quarks, charged with any one of the main colors, look for stability in terms of combining their type of charge with other quarks of other charges to attain stability. This stability comes when all three types of quarks are together to form a stable particle, like a proton or a neutron.

The color analogy helps in this case because a combination of three lights of three main colors, red, green and blue, produces the white (colorless) light.
R + G + B = 0

In real numbers the opposite number to number X is the number −X that, combined with X, results in zero.
Similarly, in colors the opposite light color (we can call it anti-color) is the one that, combined with original, produces colorless (that is, white) light.
Therefore, the anti-colors are
anti-red R=G+B,
anti-green G=R+B,
anti-blue B=R+G.

These three anti-colors are the colors of anti-charges. Thus, an anti-proton is comprised from three anti-quarks, two anti-up quarks and one anti-down quark. Each of these quarks has a different anti-color, so all three anti-colors are present in the anti-proton particle.

While the term "color" applied to this physical characteristic is just a name, it was not chosen arbitrarily.
There is a similarity between a quantum characteristic of three types of strong nuclear field charges called "color" and three main colors of visible light, combination of which in proper proportion can produce any other color.

That's why we say that
anti-red = cyan (R=G+B),
anti-green = magenta (G=R+B),
anti-blue = yellow (B=R+G).

Analogously, a combination of all three anti-colors produces black (also, colorless, that is neutral, not charged) charge
R + G + B = 0

Quarks can have one of three possible color charges (or just colors) (R, G, B).

Anti-quarks have one of three anti-colors (R, G, B).

Three quarks of three different main colors make up a colorless (that is neutral and observable) proton or neutron.
For example,
p=u+u+d or p=u+d+u,
n=d+d+u or n=u+d+d.

Three anti-quarks of three different anti-colors make up a colorless anti-proton or anti-neutron.
For example,
p=u+u+d or p=d+u+u,
n=d+u+d or n=d+d+u.

We can obtain a colorless combination of a quark of some color and an anti-quark of a corresponding anti-color.
These two quarks, one of the main color and an anti-quark of the corresponding anti-color (like, u+d) make up a particle called meson.

Quarks are usually confined to a combination that has zero color charge, like a triplet of quarks of three main colors in a proton or a duo of quark and anti-quark of a corresponding anti-color in a meson.

Gluons

Gluons, like quarks, are color charged. A very important difference is that gluons carry two different color charges at the same time, while quarks are color charged with only one.
More precisely, gluons have one charge of the main color and another charge of an anti-color.
For example, green (G) and anti-red (R).

Let's see what happens when a quark emits a gluon.

Assume, a green quark emits green/anti-red gluon.
In simple terms, we subtract the green from green quark and subtract anti-red from the result.
Subtracting anti-red is equivalent to adding red. Therefore, a quark becomes a red one.
quark(G) → gluon(G,R) =
=
quark(GGR) =
=
quark(GG + R) =
=
quark(R)

If this gluon is subsequently absorbed by a red quark, we add to its color charge green and anti-red. Adding anti-red is equivalent to subtracting red. The original red color, therefore, disappears, but green will be added, so this quark becomes green.
qluon(G,R) → quark(R) =
quark(G + R + R) =
=
quark(GR + R) =
=
quark(G)

The emitting of a green/anti-red gluon by a green quark and subsequent absorbing it by a red quark results in exchange of colors between these quarks. A green quark becomes red and red one becomes green.

So, quarks can change color by emitting or absorbing gluons.
If this happens inside a nucleon (a proton or a neutron), the color neutrality of this nucleon is preserved. This is a conservation of color during this process of emitting and absorbing of a gluon.

Quarks inside a nucleon constantly exchange gluons, thus establishing a strong force that is responsible for the integrity of a nucleon.

While quarks exchange the color charges, a nucleon as a whole always remains color neutral, stable and observable.

Residual Strong Force

As we stated above, three quarks make up a nucleon, uud for a proton or udd for a neutron.
Inside a nucleon these quarks have different color charges (R, G and B) and exchange gluons to maintain their nucleon's color charge as a whole neutral (R+G+B = 0), exerting strong forces to assure a nucleon is stable and observable.

The question is, what keeps different nucleons together?

The answer, as we understand it today, is related to the same strong force and is the force called residual strong force.

Let's start with a process inside a proton, the particle #1 in an interaction we analyze and use a symbol p1 for it. Its three quarks uud constantly exchange gluons, which constantly exchanges their color charge.

(a) For some reason during this process a pair of quark d and anti-quark d are born as a result of these interactions.
p1(uud)p1(uud) + d + d

(b) The next step is a replacement of one quark u inside a proton with quark d born above, which effectively changes quark set from uud (proton) to udd (neutron) and releases quark u.
This released quark u combines with anti-quark d born above making a virtual (very short lived) π-meson (short name is pion) π(ud).
p1(uud) + d + d
n1(udd) + π(ud)

(c) Now a proton (particle #1) has transformed into a neutron and π-meson π(ud) that immediately contacted a neighboring particle #2 which is neutron n2(udd).
An anti-quark d of π-meson annihilates with quark d of this neutron (particle #2) leaving an empty spot in a neutron.
Quark u from π-meson takes an empty spot, effectively converting the whole particle into proton p2(uud).
π(ud) + n2(udd)p2(uud)

Analogous transformation of a particle #1, neutron, transforming into a proton, and, subsequently, a particle #2, proton, transforming into a neutron, is possible as well:
(a)n1(udd)n1(udd) + u + u
(b) n1(udd) + u + u
p1(uud) + π(du)
(c) π(du) + p2(uud)n2(udd)

The above process of transformation of a proton into a neutron and a neighboring neutron into a proton with corresponding exchange of quarks is the manifestation of residual strong forces that keep the nucleons (protons and neutron) together inside a nucleus.

That's why we observe neutrons inside any multiple protons nuclei, they are the results of constant transformation and interaction with protons, carriers of electric properties of an atom.
That's why the number of neutrons is equal (for lighter nuclei) or greater (for heavier nuclei) than the number of protons.

Obviously, residual strong forces on distances comparable with a radius of a proton should be stronger than electric repulsion between protons to keep the nucleus from disintegration.