1. The Strong Force

2. The Strong Force
Why do protons & protons, protons & neutrons, and neutrons & neutrons all bind together in the nucleus of an atom?
Electromagnetic? No, this would cannot cause protons to bind to one another. Gravity ? NO, way too feeble (even weaker than EM force)
Need a force which: A) Can overcome the electrical repulsion between protons.
B) Is ‘blind’ to electric charge (i.e., neutrons bind to other neutrons!)
Quantum theory of EM Interactions is incredibly precise. That is, the theoretical calculations agree with experimental observations to incredible accuracy.
 Build a similar theory of the strong interaction, based on force carriers

3. ‘Charge’ e u u e Electric charge = +2/3 Electric charge = -1
What does it really mean for a particle to have electric charge ?
It means the particle has an attribute which allows it to talk to (or ‘couple to’) the photon, the mediator of the electromagnetic interaction.
The ‘strength’ of the interaction depends on the amount of charge. u e
Which of these might you expect experiences a larger electrical repulsion?

4. Strong Force & Color u
We hypothesize that in addition to the attribute of ‘electric charge’, quarks have another attribute known as ‘color charge’, or just ‘color’ for short. The attribute’s name, color, is just by convention. It’s easy to visualize this attribute and how colors combine…(coming up)
The property of color allows quarks to talk to the mediator of the strong interaction, the gluon (g).
Unlike electric charge, we find (experimentally) that there are 3 values for color: We assign these possible values of color to be: red, green, blue
Also, unlike Electromagnetism, we find that the carrier of the strong force carries ‘color charge’. Recall the photon is electrically neutral!

5. Comparison Strong and EM force
Property EM
Strong
Force Carrier
Photon (g)
Gluon (g)
Mass
Charge ?
None
Yes, color charge
Charge types
+, -
red, green, blue
Mediates interaction between:
All objects with electrical charge
All objects with color charge
Range
Infinite ( 1/d2)
10-14 [m] (inside hadrons)

6. Color of Hadrons q1 q2 q3 RED + BLUE + GREEN = “WHITE” or “COLORLESS”
BARYONS
GREEN + ANTIGREEN = “COLORLESS” RED + ANTIRED = “COLORLESS”
BLUE + ANTIBLUE = “COLORLESS”
MESONS q
A meson can be any one of these combinations !
Hadrons observed in nature are colorless (but there constituents are not)

7. Color of Gluons
Each of the 8 color combinations have a “color” and an “anti-color”
In the first 6 cases, there is a definite change in the color of the initial quark.
In the exchange of gluons, color charge is conserved.
If the initial quark is RED, and it emits a RED-ANTIGREEN gluon, it must turn GREEN. This is most easily seen as follows:
Initially After gluon emission
RED = RED-ANTIREEN GREEN
(quark) (gluon) (quark)
Don’t worry too much about the last couple two gluon colors.
Simply think of them as exchanging gluons while keeping the same color.
Don’t worry about what this means

8. Color Exchange Quarks interact by the exchange of a gluon.
Since gluons carry color charge, it is fair to say that the interaction between quarks results in the exchange of color (or color charge, if you prefer) !

9. Interactions through Exchange of Color Charge
Initially After gluon emission
RED  RED-ANTIGREEN GREEN
(quark) (gluon) (quark)
Emission of Gluon
Before gluon absorption After gluon absorption
RED-ANTIGREEN + GREEN  RED
(gluon) (quark) (quark)
Re-absorption of Gluon
Note that color charge is “conserved” at each stage. Color charge is always conserved.

10. Gluons – Important Points
Gluons are the “force carrier” of the strong force.
They only interact with object which have color, or color charge.
Therefore, gluons cannot interact with leptons because leptons do not have color charge !
This cannot happen, because the gluon does not interact with objects unless they have color charge! Leptons do not have color charge ! q e+ g
e -

11. Feynman Diagrams for the Strong Interaction
As before, we can draw Feynman diagrams to represent the strong interactions between quarks.
The method is more or less analogous to the case of EM interactions.
When drawing Feynman diagrams, we don’t show the flow of color charge (oh goody). It’s understood to be occurring though.
Let’s look at a few Feynman diagrams…

12. Feynman Diagrams (Quark Scattering)
Quark-antiquark Annihilation g d
Quark-quark Scattering
Could also be Quark-antiquark Scattering or Antiquark-antiquark Scattering u u
It is usually understood that time runs along the X-axis, and position along the Y-axis. From now on, I will not draw it.
In the quark-antiquark annihilation diagram, you can imagine that we have the annihilation of a green quark with an antired antiquark, which produces a green-antired gluon. Then this gluon decays back into a green quark and an antired antiquark.
In the bottom diagram, you can imagine the incoming quark (top left) could be blue. It could emit a blue-antred gluon, and in the process turns into a red quark (top right). The other incoming quark (bottom left) might be red initially, and then it absorbs the (blue-antired) gluon, which converts it into a blue quark.
There you see, the quarks have exchanged color!!
Position g d d
time

13. Flashback to EM Interactions
Recall that photons do not interact with each other. Why?
Because photons only interact with objects which have electric charge, and photons do not have electric charge !
This can’t happen because the photon only interacts with electrically charged objects ! g

14. BUT GLUONS HAVE COLOR CHARGE !!!
Gluons carry the “charge” of the strong force, which is “color charge”, or just “color” !

15. Ok, so here’s where it gets hairy!
Since gluons carry “color charge”, they can interact with each other ! (Photons can’t do that) g
Gluon-gluon Scattering g
Gluon-gluon Fusion
Called gluon-gluon “fusion” because the two gluons “fuse” into one.
Note that we can just flip the “gluon-gluon fusion” diagram by ¼ turn, and it becomes the gluon-gluon scattering diagram! This is a powerful time-saving tool for theorists in calculating the probabilities for these processes to occur!

16. And quark-gluon interactions as well!
Since both quarks and gluons have color, they can interact with each other !!! g u
Quark-Antiquark Annihilation g d
Quark-gluon Scattering
In the first diagram the red quark emits a red-antigreen gluon, and turns into a green quark. The red-anti-green gluon then scatters off another gluon, and they fuse together…
IN the second diagram, the quark and antiquark annihilate and produce a gluon. That gluon travels for some time, and then splits to 2 gluons. I will spare you the details, but the gluon for this latter diagram has to split in order to conserve energy. The details are beyond the scope of this course.

17. Where do the gluons come from ?
The gluons are all over inside hadrons!!
In fact there are a lot more than shown here !!!
Notice sizes here:
In fact quarks are < 1/1000th of the size of the proton, so they are still too big in this picture !
Even protons and neutrons are mostly empty space !!! u d
~10-15 [m]
Proton
Years of experimentation on the quarks inside protons have shown that the quarks only carry about 50% of the energy of the proton.
More detailed investigations have revealed that the other 50% is carried by the gluons.
So, when we collide hadrons (ie., protons into antiprotons, for example), we are colliding objects which are “bags of quarks and gluons”
So, hadron-hadron scattering is a tough business!

18. Confinement
Since the strong force increases as quarks move apart, they can only get so far… The quarks are confined together inside hadrons. Hadron jail !
Think of the two charm quarks as being connected by a tight spring. As the spring stretches, the energy stored in it increases. If you keep on pulling, eventually, the spring “snaps”. In the case of quarks, as they separate, the energy stored in the “gluon spring” increases until it eventually “snaps”. When it does, the energy stored in this spring is converted into mass in the form of a quark-antiquark (down-antidown quarks) pair. So, the initial charm-anticharm state has now become two particles, a charm-antidown + a down-anticharm.
An example of conversion of energy into mass!
Also note that the strong interaction can only produce quark-antiquark pairs of the same type. That is (down-antidown, up-antiup, strange-antistrange, etc)
As quarks move apart from one another, the energy stored I the

19. Hadronization (process of forming hadrons)
As quarks move apart, the potential energy stored in the “spring” increases, until its large enough, to ‘snap’ and convert its potential energy into mass energy (qq pairs) p0 p- K- K+
Hadrons! d s u d u d d d
In this way, you can see that quarks are always confined inside hadrons (that’s CONFINEMENT) !

20. What holds the nucleus together?
The strong force !
Inside the nucleus, the attractive strong force is stronger than the repulsive electromagnetic force.
Protons and neutrons both “experience” the strong force.
The actual binding that occurs between proton-proton and proton-neutron and neutron-neutron is the residual of the strong interaction between the constituent quarks.

21. It’s incorporated in the binding energy associated with the gluons !
Food for thought
Recall: Mass of Proton ~ 938 [MeV/c2]
Proton constituents:
2 up quarks: * (5 [MeV/c2]) = 10 [MeV/c2]
1 down quark: * 10 [MeV/c2] = 10 [MeV/c2]
Total quark mass in proton: ~ 20 [MeV/c2]
Where’s all the rest of the mass ?????
It’s incorporated in the binding energy associated with the gluons !
 ~98% of our mass comes from glue-ons !!!!

22. Summary (I)
The property which gives rise to the strong force is “color charge”
There are 3 types of colors, RED, GREEN and BLUE.
Quarks have color charge, and interact via the mediator of the strong force, the gluon.
The gluon is massless like the photon, but differs dramatically in that:
It has color charge
It’s force acts over a very short range (inside the nucleus)

23. Summary (II)
Because gluons carry color charge, they can interact among themselves.
Quarks and gluons are confined inside hadrons because of the nature of the strong force.
Only ~50% of a proton’s energy is carried by the quarks. The remaining 50% is carried by gluons.
We learn about the strong force by hadron-hadron scattering experiments.