The Strong Force Announcements1. 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 210:15 – 12:15 in Stolkin.

The Strong ForceWhy do protons & protons, protons & neutrons, andneutrons & neutrons all bind together in the nucleusof an atom?

Why do protons & protons, protons & neutrons, andneutrons & neutrons all bind together in the nucleusof 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!)

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, thetheoretical calculations agree with experimental observations toincredible accuracy.

Build a similar theory of the strong interaction, based on force carriers

‘Charge’

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.

u Electric charge = +2/3

e Electric charge = -1

The ‘strength’ of the interaction depends on the amount of charge.

u u

e e

Which of these might you expect experiences a larger electricalrepulsion?

Strong Force & Color

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 easyto 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 strongforce carries ‘color charge’. Recall the photon is electrically neutral!

u u u

Comparison Strong and EM force

Property EM Strong

Force Carrier Photon () Gluon (g)

Mass 0 0

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)

Color of Hadrons

q1 q2

q3

RED + BLUE + GREEN = “WHITE” or “COLORLESS”

BARYONSBARYONS

GREEN + ANTIGREEN = “COLORLESS”RED + ANTIRED = “COLORLESS”BLUE + ANTIBLUE = “COLORLESS”

MESONSMESONS

q

q

q

q

q

q

Hadrons observed in nature are colorless (but there constituents are not)

A meson can be any one of these combinations !

Color of Gluons

2

rb

rg

bg

br

gb

gr

rr gg bb

rr gg

2

rb

rg

bg

br

gb

gr

rr gg bb

rr gg

Each of the 8 color combinationshave a “color” and an “anti-color”

Don’tworryaboutwhat thismeans

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 Chargerg rg rg

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

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 leptonsbecause leptons do not have color charge !

qe+

g

e - q

This cannot happen, becausethe gluon does not interact withobjects unless they have color charge! Leptons do not have color charge !

Feynman Diagrams forthe 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 theflow of color charge (oh goody). It’s understood to be occurring though.

Let’s look at a few Feynman diagrams…

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 theflow of color charge (oh goody). It’s understood to be occurring though.

Let’s look at a few Feynman diagrams…

Feynman Diagrams (Quark Scattering)

g

u

Quark-antiquarkAnnihilation

Quark-antiquarkAnnihilation

g

Quark-quarkScattering

Could also beQuark-antiquark

Scatteringor

Antiquark-antiquarkScattering

Quark-quarkScattering

Could also beQuark-antiquark

Scatteringor

Antiquark-antiquarkScattering time

Pos

itio

nu

d

d

d d

u u

Flashback to EM InteractionsRecall 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 photononly interacts withelectrically chargedobjects !

BUT GLUONS HAVE COLOR CHARGE !!!

Gluons carry the “charge” of the strong

force, which is “color charge”, or just

“color” !

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)

Since gluons carry “color charge”, they can interact with each other !

(Photons can’t do that)

g

g

g

g

g

Gluon-gluon Scattering

g

g

g

g

Gluon-gluon Fusion

g

And quark-gluon interactions as well!

g

g

d

g

d

Quark-gluon Scattering

g

gu

Quark-AntiquarkAnnihilation

g

u

Since both quarks and gluons have color, they can interact witheach other !!!

Where do the gluons come from ?

The gluons are all overinside 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 neutronsare mostly empty space !!!

u

u

d

~10-15 [m]

Proton

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 !

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)

u

d

u

d

d

u

u

u

0

-

-

+

Hadrons!

d

u

s

u

s

u

d

d

As quarks move apart, the potentialenergy stored in the “spring”increases, until its large enough, to‘snap’ and convert its potentialenergy into mass energy (qq pairs)

u

d

In this way, you can see that quarksare always confined inside hadrons

(that’s CONFINEMENT) !

What holds the nucleus together?

The strong force !The strong force !

Inside the nucleus, the attractive strong force is stronger thanthe repulsive electromagnetic force.

Protons and neutrons both “experience” the strong force.

The actual binding that occurs between proton-proton andproton-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 thestrong force, the gluon.

The gluon is massless like the photon, but differs dramaticallyin that:

It has color charge It’s force acts over a very short range (inside the nucleus)

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 thestrong force, the gluon.

The gluon is massless like the photon, but differs dramaticallyin 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. Theremaining 50% is carried by gluons.

We learn about the strong force by hadron-hadron scatteringexperiments.

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. Theremaining 50% is carried by gluons.

We learn about the strong force by hadron-hadron scatteringexperiments.