to String Theory - Particle Theorytheory.uchicago.edu/~nelia/quarks.pdf · Baryon Octet baryon octet similar to decuplet, except with the corners cut off and the middle doubled since

From Quantum Mechanics to String Theory

Relativity (why it makes sense) ✓

Quantum mechanics: measurements and uncertainty ✓

Smashing things together: from Rutherford to the LHC ✓

Particle Interactions ✓

Quarks and the Strong Force

Symmetry and Unification

String Theory: a different kind of unification

Extra Dimensions

Strings and the Strong Force

Thursday, May 7, 2009

Particle Interaction Summaryquantum mechanics and special relativity together imply the existence of anti-particles

forces are mediated by the exchange of virtual particles, which carry energy and momentum inconsistent with their masses using quantum uncertainty. This leads to a decrease of force strength with distance, and in the case of massive mediators, an effective range for the force

particle interactions are limited by conservation laws: energy, momentum, angular momentum, charge, quark number. These conservation laws lead to particle stability.

virtual electron/positron pairs in the vacuum shield electromagnetic charges, making them seem smaller than they are


Quarks and

the Strong Force


The Particle Zoofor a while it looked like we were close to a complete picture, with just the electromagnetic and nuclear forces, and the particles from last time

In the 1950s and 60s accelerator and cosmic ray experiments produced a proliferation of new particles

heavier particles related to protons, neutrons, and pions


Patternstry arranging the particles by spin, quark number, charge, mass



Quark Number 3 Quark Number 0











Quarksjust like with the periodic table, these patterns of particles indicate some underlying structure

Murray Gell-Mann realized that they could be explained if the particles were made up of smaller particles he called quarks

the quarks that explain these patterns come in three types: up, down, and strange (and their anti-particles)

the particles with non-zero quark number (baryons) have 3 quarks each, the ones with zero quark number (mesons) have one quark, one anti-quark

two of the quarks are very close to identical in the masses they generate, the third causes (generically) larger masses


Baryon Decupletthe ten baryons in this pattern are the ten possible 3-quark combinations of up, down, and strange quarks

by looking at the charges, we see that the charges of the three quarks must be

u: +2/3

d: -1/3

s: -1/3

!++

(uuu)!+

(uud)!0

(udd)!!

(ddd)

!!

(sss)

!!+

(suu)!!0

(sud)!!"

(sdd)

!!0

(ssu)!!"

(ssd)


Baryon Octetbaryon octet similar to decuplet, except with the corners cut off and the middle doubled

since quarks have anti-particle partners, for each of the baryon patterns there is an equivalent pattern made up of anti-baryons

particles in the decuplet tend to be extremely unstable, generically they decay into particles in the octet

p+

(uud)n0

(udd)

!+

(suu)

!0

(sud)!0

(sud)

!!

(sdd)

!0

(ssu)!!

(ssd)


Meson Nonets

the mesons are made up of a quark and an anti-quark. They are arranged directly opposite their anti-particles

the 6 mesons in the centers and to the sides are made up of combinations of

the mesons in the second nonet tend to be highly unstable and decay first to the mesons in the first nonet generally

K+ (su) K0 (sd)

!+ (du) !0, "0 !! (ud)

K0 (ds) K! (us)

K!+ (su) K!0 (sd)

!+ (du) !! (ud)!0, "0

K!0(ds) K!"(us)

!!0

!0

uu, dd, ss


More QuarksDeep Inelastic Scattering Experiments: evidence of 3 quarks in protons, confirmation of their charges

further experiments revealed three more quarks: charmed, top, and bottom (which combine in extremely massive, short-lived mesons and baryons)

quarks and leptons fall into “generations”: each generation needs all four elements to be mathematically consistent

e (electron) νe (neutrino) d (down) u (up)μ (muon) νμ (neutrino) s ( strange) c (charmed)τ (tau) ντ (neutrino) b (bottom) t (top)


The Color Puzzlequarks are spin 1/2 particles (fermions)

fermions satisfy the “pauli exclusion principle”: you cannot have 2 fermions in exactly the same state

consider the particle Δ++, made up of three “u” quarks

it is a spin 3/2 particle, capable of carrying angular momentum in the z-direction equivalent to all three quarks having spin in the same direction (+++)

it looks as if we have three identical quarks, all in the same spin state (u,+)

⇒ there must be some other quantity that the quarks carry

that allows them to be in different states: call it “color”Thursday, May 7, 2009

Colored Quarks

quarks come in 3 colors (and 3 anti-colors)

baryons are made up of one of each color, anti-baryons one of each anti-color

mesons are made up of one color and one anti-color

these are called “colorless” combinations: all natural combinations are colorless

Red Green Blue Anti-Red Anti-Green Anti-Blue Baryons Anti-Baryons

Mesons


The Strong Force & Gluonswhat role (besides explaining the exclusion principle paradox) does color play?

the strong force: color is to the strong force what charge is to the electromagnetic force

the mediators for the strong force are gluons

8 varieties, each a combination of one color and one anti-color--but *not* colorless combinations

gluons are massless and spin 1, like photons. Unlike photons, they are not colorless and therefore interact directly with other gluons


Confinementno particles found in nature have any net color. Why?

gluons are massless, like photons. Classically the strong force should behave the same as the electromagnetic force.

qm shielding is a large effect here, because the gluons themselves carry color

virtual gluons and quarks serve to re-inforce bare colored particles. Classically the force decreases with distance like 1/r^2, but quantum mechanically the force increases with distance like r.

this is spring-like behavior. Colored objects attach to each other as if by a spring--it requires an infinite amount of energy to separate them


Confinementquarks close together feel very little force from each other (like marbles in a sack). The force becomes strong when you start to separate them

what would happen if you tried to pull a meson apart?

Energy

as you begin to separate them, you put more and more energy into the system

eventually, you have put more energy in than is required to produce a quark/anti-quark pair. They are created out of this energy, and what results is two (colorless) mesons coming apart

in accelerators, when energies are high enough to probe the insides of protons and mesons, the result is messier: “jets” of hadrons


The Effective Nuclear Force

can we explain the behavior of the “nuclear force” between protons and neutrons in terms of the strong force and gluons?

the nuclear force is a residual effect of the color structure of objects that have no net color

it dies off quickly with distance because as you get further away the color structure “disappears” (parallel: electromagnetic Van der Walls force)

what about the pion as a nuclear force mediator? Let’s draw a picture of how a proton and a neutron can interact


Pion Exchangecan proton/neutron interaction occur by exchange of a gluon?

the gluon is a colored object, so this interaction must be *extremely* short range (even shorter than the nuclear force range)

but we can make the proton and neutron “exchange” a color neutral object:

this can act over a longer distance (up to what is limited by the pion’s mass) and becomes the dominant effect in the nucleus

d d

dd

dd

uu

u

uu

u

gluon

d d

dd

dd

uu

u

uu

u

pion

exchange


Quark Summarymesons and baryons can be fit into patterns according to quark number, spin, mass and charge: quark structure

baryons are made up of three quarks, mesons are made up of a quark and an anti-quark

quarks have a quantity called color, which is the “charge” of the strong force, mediated by gluons (which also carry color)

quantum shielding causes the strong force to grow with distance, holding colored objects together as if with a spring

the nuclear force and pion exchange is a residual effect from the color structure of baryons which have no net color


Documents

to String Theory - Particle Theorytheory.uchicago.edu/~nelia/quarks.pdf · Baryon Octet baryon octet similar to decuplet, except with the corners cut off and the middle doubled since