More on the Standard Model

• Particles from quarks• Particle interactions• Particle decays• More conservation laws• Quark confinement• Spin

The fundamental particles

u c t +2/3 six quarks

d s b -1/3

e µ 0 six leptons

e µ -1

These particles interact through the exchange of a force carrier.

Particles from Quarks

The quarks combine in two ways to form the particles we see in the lab:

Quark-antiquark pairs from mesons:

u and anti-d = +

u and anti-s = K+

and so on, making hundreds of particles.

Quiz: How would I make a neutral K particle?

Particles from Quarks

Three quarks combine to form a baryon such as the proton and neutron

uud = proton

udd = neutron

uds = lambda ()

and so on, making hundreds of baryons

Quiz: What is the charge of the lambda?

Force carriers

Particles interact through the exchange of force carriers.

There are four force carriers:

Photon () for EM interaction

Gluon (g) for the strong interaction

W+, W- and Z0 for the weak interaction

Electromagnetic interaction example

The photon is the force carrier, and it couples to electric charge.

Weak Interaction examples

Quarks can change from one type to another (flavor changing), but ONLY through the exchange of a W.

The Ws and Zs are the carriers of the weak force, and they couple to all known particles

Strong interaction example

The leptons do NOT see the strong interaction.

Only the quarks interact strongly.

Heavier particles decay into ligher particles

But subject to the rules:

conservation of energy, momentum and angular momentum

conservation of electric charge

conservation of the number of baryons and leptons

So for example

n p e e

µ µ

µ e e µ

Particles decay as far as possible

Particles keep on decaying until there is some conservation rule that forbids them from decaying further.

The electron is the lightest charged particle, so it is stable.

But wait…why doesn’t a proton decay into a positron and say a 0 ?

Baryon number/lepton number

In particle physics we have two additional conservation laws that all decays ever observed obey.

The total number of baryons is constant.

The total number of leptons is constant.

Anti-particles carry opposite baryon/lepton number.

n p e e (bar = antiparticle)_

But what about the matter-antimatter asymmetry of the universe?

If the number of baryons is a constant in the universe,and we make matter and antimatter in pairs…

How did we arrive at a matter-dominated universe?

We don’t know the answer completely, but we do know it is related to the violation of the fundamental symmetries of parity (mirror reflection) and charge conjugation (matterantimatter)

Why no free quarks?

There are no free quarks—why?

People have looked for decades for free quarks, butnone have been observed.

We can pull an electron off an atom, so why can’twe pull a quark out of a proton?

The answer has to do with the nature of the force Holding them together, the so-called color force.

Why no free quarks?

The potential energy two electric charges:

U=-kqQ/r

The potential energy between two color charges is Coulomb-like but has an extra term:

U=-kqQ/r+Kr

The PE increases with distance!

Quark- quark potential energy

The quark potential looks like the Coulomb potential close up, but when the separation is large, the linear term dominates

In these units 1=the proton radius.

Quark -quark potential energy

As r gets large, the PE increases without bound and the quark cannot escape!!

We call this

CONFINEMENT!

Electric field between electric charges

Electric Dipole

Color field between color charges

Color Dipole

When the distance beteen the quarks gets large, a great deal of PE is stored in the color field.

Confinement!

When two quarks separate, at some point there is enough energy in the field to create a quark-antiquark pair. Then the color field lines snap, and two mesons are created!

Jet Production

The color charge holding the quarks together is so strong, you can never pull a free quark out of a proton.

The harder you try to pull a quark out of a proton, the more mesons you get!

The stream of mesons that marks the path of a quark we call a jet.

We can see quarks

The jet of particles produced by the quark allows us to get some measure of its energy and momentum.

Spin

All the fundamental particles have one other property-- intrinsic angular momentum. They all have ½ unit of angular momentum, where the unit is h/2.

Particles with ½ integral spin are called fermions.

Particles with integral spin are called bosons.

Combining two spin ½ fermions gives a boson

Adding spins

A state of two electrons will have spin either 1 or 0, both of which are bosons.

Spins add, total spin=1 Spins cancel, spin=0

Fermions and the exclusion principle

Only one fermion can be an any state, which explains most of chemistry…the electrons fill up the energy levels with only one per state. This is the Pauli exclusion principle.

But can’t I put two electrons per state? Yes, but their spins are in different directions, so they are not really in the same state.

Supersymmetry

Supersymmetry is an unproven theory that postulates a boson for every fermion and a fermion for every boson!

It solves some problems deep in the mathematics of the Standard Model.

But…ugh…too many fundamental particles. And where are they anyway? (Must be heavy or we would have seen them by now.)

Supersymmetry and dark matter

Supersymmetric particles are prime candidates to be the dark matter of galactic halos.

But there is as yet no evidence for supersymmetric particles, although we are looking very hard!

Supersymmetry?

Supersymmetry is an offer nature can’t refuse.

D.V. Nanopolus, theorist

There ain’t no Supersymmetry.

Leo Bellantoni, Fermilab physicist

Experiment is the sole judge of scientific truth.

Richard Feynman

Supersymmetric names

The supersymmetric partner of the top quark is called stop.

The supersymmetric partners of any quark is a squark.

The supersymmetric partner of the photon is the photino.

The supersymmetric partner of the W is the …

(I am not making this up..)