Elementary Particles:Physical Principles

Benjamin SchumacherPhysics 145

29 April 2002

Particles and antiparticlesParticles and antiparticles

For every type of elementary particle, there exists a corresponding antiparticle.

The antiparticle has exactly the same mass and spin as the particle, but opposite electric charge, etc.

Example: The antiparticle of an electron e- is a positron e+

A few (but not all) uncharged elementary particles (such as the photon ) are their own antiparticles.

Dirac’s dilemmaDirac’s dilemma

• 1927 - Paul Dirac develops relativistic quantum theory. (Predicts spin of the electron, etc.) But there is a problem....

0

+mc2

- mc2

possible energy states

Puzzle: Dirac’s equation predicts positive and negative electron energies, but we only ever see positive energies.

- mc2

The Dirac “sea”The Dirac “sea”

• Dirac’s idea: All negative energy states are already filled. By the Pauli exclusion principle, no additional electrons can have negative energies.

0

+mc2

• The universe contains a vast invisible “sea” of negative energy electrons.

Holes in the Dirac SeaHoles in the Dirac Sea

• Suppose there is a “hole” or “bubble” in the Dirac sea of negative energy electrons.

0

+mc2

- mc2

• Hole behaves like a particle with

• positive energy (hole is a “lack of a negative energy electron”)

• positive charge (absence of a negative charge)

• Anti-electron = positronpositron ee++

• Discovered by Anderson in 1932

Creation and annihilationCreation and annihilation

• Pair creaton

Input one or more photons (total energy at least 2 mc2) and create both an electron and a positron.

0

+mc2

- mc2

ee--

ee++

Creation and annihilationCreation and annihilation

• Pair creaton

Input one or more photons (total energy at least 2 mc2) and create both an electron and a positron.

0

+mc2

- mc2

ee--

ee++

• Pair annihilation

Electron and positron meet; electron “fills the hole” and releases energy (photons).

Two photons are produced (momentum conservation).

A slightly different view . . .A slightly different view . . .

Basic “Feynman diagramsFeynman diagrams”

e-

e-

e-

e-

time

Photon emitted Photon absorbed

A slightly different view . . .A slightly different view . . .

An antiparticle is a particle An antiparticle is a particle “going backwards in time”.“going backwards in time”.

e- e+e-

e-

time

Compton scattering Pair annihilation

Fundamental forcesFundamental forces• Strong nuclear (hadronic) force

relative strength 1, short range, affects only hadrons

• Electromagnetic force

relative strength 10-2, long range, affects charges

• Weak nuclear force

relative strength ~10-13, short range, affects both hadrons and leptons

• Gravitational forcerelative strength ~10-43, long range, affects all particles

Two principlesTwo principles

• The stronger the force, the quicker the process.The stronger the force, the quicker the process.

The rate at which a process (e.g., a particle decay) proceeds is related to the strength of the fundamental interaction responsible.

•Anything that is not forbidden is compulsory.Anything that is not forbidden is compulsory.

Any particle process that is not actually forbidden by some physical law (e.g., a conservation law) has some probability of occuring.

If a process that looks possible does not occur, then there must be a physical law that prevents it.

Virtual particlesVirtual particles Forces are mediated by the exchange of virtual particles

Example: Electromagnetic forces mediated by the exchange of virtual photons

e-

e-

e-

e-

Where does the energy for the virtual particle come from?

Virtual particles live “underneath” the Uncertainty Principle:

Et

Yukawa and the mesonYukawa and the meson

H. Yukawa (1935) : Short range nuclear forces should be mediated by a massive particle.

p,n

2cmc

EctcR

p,n p,n

p,n

range of force

mass of

R = 1.5 fm mc2 = 130 MeV

““Who ordered that?”Who ordered that?”

• 1936 -- New particles (, or “muons”) are detected in cosmic rays.

Rest energy: 106 MeV

Muon is not a hadron -- cannot be Yukawa’s meson

• Actual mesons (rest energies 130-140 MeV) discovered in 1947.

• Since 1940’s -- Many, many new particles discovered.

Many successful predictions of theory

A few surprises!

Elementary Particles:The Particle Zoo

Benjamin SchumacherPhysics 1451 May 2002

Particle TaxonomyParticle Taxonomy

All particles

others

“Field particles”

Leptons

Hadrons

Mesons

Baryons

(, ...)

(e±, ±, ...)

(±, ...)

(p, n, ...)

Bosons

Particle TaxonomyParticle Taxonomy

All particles

others

“Field particles”

Leptons

Hadrons

Mesons

Baryons

(, ...)

(e±, ±, ...)

(±, ...)

(p, n, ...)

Fermions

Field particlesField particles

g gluons 0* 0 1 strong nuclear

particlemc2

(GeV) q s force

W± “vector bosons”

79.8 ±1 1weak nuclear

91.2 0 1Z0

photon 0 0 1 electromagnetic

gravitons 0 0 2 gravitational

LeptonsLeptons

e- electron 0.511 -1 1/2 e+

particlemc2

(MeV) q smean

lifetimeanti-particle

- muon 106 -1 1/2 2.2 s +

- tau 1780 -1 1/2 very short +

e e-neutrino 0 1/2

muonzero?very

small?1/2

tau 1/2

stable?oscillation?0

0

e

BaryonsBaryons

p proton 938.3 +1 1/2

particlemc2

(MeV) q smean

lifetime

n neutron 939.6 0 1/2 930 s

lambda 1116 0 1/2 0.25 ns

sigma ~11900 1/2 10-20 s

±1 1/2 ~ 0.1 ns

xi ~13200 1/2 0.3 ns

-1 1/2 0.17 ns

omega 1672 -2 3/2 0.13 ns

anti-particle

p

n

MesonsMesons

particlemc2

(MeV) q smean

lifetimeanti-particle

pions

139.6 +1 0 26 ns

135 0 0 ~10-16 s

Kkaons

497.7 +1 0 12.4 ns

K 493.7 0 0 peculiar

K

K

eta 549 0 0 ~10-19 s

Particle decay mechanismsParticle decay mechanisms

• Strong (hadronic) force decays proceed very fast (~10-23 s) -- no such “particles” listed above.

• Electromagnetic decays: Involve photons!

10-20 s

0.8 ×10-16 s

2 ×10-19 s

fastest decay times listed

• Weak force decays are much slower -- these include all other decays listed (~0.1 ns or longer)

Conservation laws (exact)Conservation laws (exact)

Baryon number+1 for baryons-1 for antibaryons 0 for all others

• Energy, momentum, angular momentum

• Electric charge

Why not p e+ ?

Lepton number+1 for leptons-1 for antileptons 0 for all others

• Conservation of baryon number, lepton number!

ApproximateApproximate conservation laws conservation laws

The reaction K does occur, but not fast . . .

. . . even though all three particles can participate in hadronic forces!

Something strange going on!Idea: There is a quantity (“strangeness”, or S ) that is

conserved by strong and EM forces, but not by the weak force. (K+ has strangeness -1.)

More approximately conserved quantities: Charm, etc.

QuarksQuarks

Hadrons (baryons, mesons) are composite particles, like atoms.

quarkmc2

(MeV) q B

u up ~340 +2/3 1/3 constituents of nucleons (p,n)

d down ~340 -1/3 1/3

c charmed +2/3 1/3

s strange -1/3 1/3

t top +2/3 1/3

b bottom -1/3 1/3

more m

assive

Constructing hadronsConstructing hadrons

All hadrons are composed of quarks and antiquarks.

1 baryon = 3 quarks

uu uu

ddproton

uu dd

ddneutron

1 meson = 1 quark + 1 antiquark

uud d pion (+)

ssu u kaon (K-)