to String Theory - Particle Theorytheory.uchicago.edu/~nelia/quarks.pdf · Baryon Octet baryon...
Transcript of to String Theory - Particle Theorytheory.uchicago.edu/~nelia/quarks.pdf · Baryon Octet baryon...
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
Thursday, May 7, 2009
Quarks and
the Strong Force
Thursday, May 7, 2009
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
Thursday, May 7, 2009
Patternstry arranging the particles by spin, quark number, charge, mass
Thursday, May 7, 2009
Patternstry arranging the particles by spin, quark number, charge, mass
Quark Number 3 Quark Number 0
Thursday, May 7, 2009
Patternstry arranging the particles by spin, quark number, charge, mass
Quark Number 3 Quark Number 0
Thursday, May 7, 2009
Patternstry arranging the particles by spin, quark number, charge, mass
Quark Number 3 Quark Number 0
Thursday, May 7, 2009
Patternstry arranging the particles by spin, quark number, charge, mass
Quark Number 3 Quark Number 0
Thursday, May 7, 2009
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
Thursday, May 7, 2009
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)
Thursday, May 7, 2009
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)
Thursday, May 7, 2009
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
Thursday, May 7, 2009
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)
Thursday, May 7, 2009
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
Thursday, May 7, 2009
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
Thursday, May 7, 2009
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
Thursday, May 7, 2009
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
Thursday, May 7, 2009
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
Thursday, May 7, 2009
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
Thursday, May 7, 2009
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
Thursday, May 7, 2009