The Strong Force Announcements 1. Exam#3 next Monday. (Bring your calculator) 2. HW10 will be posted today. Solutions will be posted Thurs. afternoon (I’m not collecting HW#10) 3. Q&A session on Sunday at 5 pm. 4. Tentative course grades will be posted by Tuesday evening. 5. You can do no worse than this grade if you skip the final (but you could do better if you take it) 6. Final Exam, Friday, May 2 10:15 – 12:15 in Stolkin. 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 ‘Charge’ Electric charge e Electric charge u = +2/3 = -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. Which of these might you expect experiences a larger electrical repulsion? u u e e Strong Force & Color
u u 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! Comparison Strong and EM force Property EM Strong
Force Carrier Photon (g) Gluon (g)
Mass 0 0
Charge ? None Yes, color charge
Charge types +, - red, green, blue Mediates interaction All objects with All objects with between: electrical charge color charge 10-14 [m] Range Infinite ( 1/d2) (inside hadrons) Color of Hadrons
BARYONS q1 q2 RED + BLUE + GREEN = “WHITE” q3 or “COLORLESS”
MESONS q q q GREEN + ANTIGREEN = “COLORLESS” RED + ANTIRED = “COLORLESS” q BLUE + ANTIBLUE = “COLORLESS” A meson can be any one of these combinations !
Hadrons observed in nature are colorless (but there constituents are not) Color of Gluons rb Each of the 8 color combinations have a “color” and an “anti-color” rg bg br gb gr Don’t rr gg2 bb worry about rr gg what this means 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) ! Interactions through Exchange of Color Charge rg
Emission of Gluon Initially After gluon emission RED RED-ANTIGREEN + GREEN (quark) (gluon) (quark)
Re-absorption of Gluon Before gluon absorption After gluon absorption RED-ANTIGREEN + GREEN RED (gluon) (quark) (quark) 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 !
e+ q This cannot happen, because g the gluon does not interact with objects unless they have color charge! e - q Leptons do not have color charge ! 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… Feynman Diagrams (Quark Scattering)
u d Quark-antiquark Annihilation g u d Quark-quark Scattering u u Could also be Quark-antiquark g Scattering or
Antiquark-antiquark d d Scattering time 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 g g because the photon only interacts with g g electrically charged g objects ! BUT GLUONS HAVE COLOR CHARGE !!!
Gluons carry the “charge” of the strong force, which is “color charge”, or just “color” ! Ok, so here’s where it gets hairy!
Since gluons carry “color charge”, they can interact with each other ! (Photons can’t do that)
Gluon-gluon Scattering Gluon-gluon Fusion
g g g g g g
g g g g And quark-gluon interactions as well!
Since both quarks and gluons have color, they can interact with each other !!!
Quark-Antiquark Quark-gluon Scattering Annihilation
u g d d g g
g g u g Where do the gluons come from ?
The gluons are all over Proton inside hadrons!!
u In fact there are a lot more than shown here !!!
Notice sizes here: th u In fact quarks are < 1/1000 d of the size of the proton, so they are still too big in this picture !
~10-15 [m] Even protons and neutrons are mostly empty space !!! 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 ! Hadronization (process of forming hadrons) As quarks move apart, the potential energy stored in the “spring” Hadrons! increases, until its large enough, to ‘snap’ and convert its potential - energy into mass energy (qq pairs) K s s K+ u u u
d d p- d d d In this way, you can see that quarks d are always confined inside hadrons p0 (that’s CONFINEMENT) ! d 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. Food for thought
Recall: Mass of Proton ~ 938 [MeV/c2]
Proton constituents: 2 up quarks: 2 * (5 [MeV/c2]) = 10 [MeV/c2] 1 down quark: 1 * 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 !!!! 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) 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.