The Standard Model of Particle PhysicsTopics

Classically known particles;Cosmic forces;The Heisenberg Uncertainty Principle;Forces mediated by virtual particles;The Particle Zoo;The Standard Model.

MotivationWhat are the forces of the Universe?What are the particles of the Universe?

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Basic atomic particles

Baryons (high mass particles, spin = +½)Proton: positive charge, m=1.007 u;Neutron: zero charge, m=1.008 u.

Lepton (low mass particle, spin = +½) Electron: negative charge, m=0.000548 u;

Boson (spin=1)Photon: the particle of energy.

Example13C = 6 protons, 7 neutrons (13-6=7), 6 electrons.

This system was beautiful, simple, and complete.

This explained all the elements, all of matter, all of energy, for many years.

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Also, there are four forcesElectromagnetism—classic knowledge

– Known since ancient times.

– Originally viewed as two separate force fields: electricity and magnetism.

– Unified by Maxwell’s laws.

– Electromagnetism affects particles that have positive or negative charge, such as protons and electrons.

Preview facts (spoilers!)

– Maxwell discovered that photons are related to electromagnetism, but it goes beyond that—it will be seen that photons are carriers for the electromagnetic force.

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Also, there are four forcesGravity—classic knowledge

– Known since ancient times.– Originally described by Newton’s law of

gravity, acting as an instantaneous force.– Gravity was long known to affect all

particles that have mass.– An enormous source of frustration to

Einstein, in that it violated Special Relativity (it exceeded the speed of light).

– Extremely weak, but since there are no “negative” gravity charges, this force adds up over distance.

Preview facts (spoilers!)– Einstein ultimately expanded gravity’s

influence, to say that gravity affected energy, such as photons, the same way it affects matter.

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Also, there are four forcesStrong force—classic knowledge

– Quantified in 1934.– Only important within atoms, affecting protons/neutrons.– Drops off exponentially.– Changes in energy stored in strong force releases energy.

Preview facts (spoilers!)– Affects all “hadrons” (i.e., quark-matter).– Really, just a side-effect of the “strong interaction” (which

is also known as the “color force”).

Also, there are four forces

Weak force—classic knowledge– Quantified in 1930s.– Best known for β- decay.

n → p + e- + νe

– Weakest of the forces, except for gravity.

Preview facts (spoilers!)– To be united with the electromagnetic force.– Affects hadrons and leptons, including neutrinos.

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Heisenberg uncertainty principleTo understand forces of the Universe, we will have to digress slightly.

Recall the de Broglie wavelength for an electron:

λ=h/p → λp=h

With some work (Heisenberg, 1927), this can be used to derive something remarkable, specifically the uncertainty principle:

Δx Δp ≥ ħ/2 where ħ = h/2π

This means that, on a ultra-microscopic level, there is a limit on measurement accuracy. In order to identify the position (Δx) of an object very well, you will lose accuracy on how well you can know its momentum (Δp).

This is not a comment on measuring technology—it is not something you can circumvent with better equipment…it is a limitation imposed by the physics of the Universe.

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Uncertainty principleExample: Suppose you are studying a moving electron, and wish to defy the uncertainty principle. You plan to measure its momentum and position as accurately as possible….

– To learn its position, you bombard it with high-energy photons. (High-energy = small λ → accurate locations). Such high-energy photons will disturb the electron’s momentum.

→ Good position information, bad momentum information

– You switch to lower-energy photons, so the electron’s momentum is disturbed less. Low-energy photons have larger wavelengths, so are less precise about position.

→ Bad position information, good momentum information

– Using photon bombardment to learn its speed via the Doppler effect encounters the same problems—low-disturbing, long λ photons give good momentum information but terrible position information.

Uncertainty principle

The uncertainty principle can be written two ways

Δx Δp ≥ ħ/2 AND ΔE Δt ≥ ħ/2

The second version says that, in a similar way, there is a limitation of how well you can simultaneously determine—over the small period of time (Δt)—how much energy (ΔE) a particle has.

Written this way, the uncertainty principle leads us to extremely profound consequences…

The total energy of a subatomic particle can vary over time, in violation of the law of conservation of energy, just as long as the variation happens over a very small time!!!

In quantum physics, the Universe no longer plays by what we consider to be the rules; the Universe breaks the rules if it can get away with it without being caught!

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Uncertainty principle and virtual particlesEVEN WEIRDER… ΔE Δt ≥ ħ/2

Recall that energy and matter are interchangeable:

E = mc2 → ΔE = Δmc2 → (Δmc2)Δt ≥ ħ/2.

Particles and their anti-matter twins can pop into existence, out of nothing, in a perfect vacuum, just as long as they recombine in a short time Δt.

The tinier the particles, the longer they can last.

The Universe, on a microscopic level, is seething with an infinite sea of virtual particle pairs and virtual photons popping into existence, then disappearing as they recombine back into nothing.

“Created and annihilated, created and annihilated—what a waste of time” —Richard Feynman

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Forces mediated by virtual particles So how do forces really work?

Two particles interact by constantly exchanging particles. This steady stream of particles is what expresses the force. The particles are said to “mediate” the force.

The particles are virtual particles, created out of nothing.

Example: Electromagnetic force

– Two electrons are separated by a small distance. They constantly produce virtual photons in all directions.

– The virtual photons that reach the partner particle are absorbed, thus transmitting information about the emitting particle.

– If the photons miss the partner particle (by being sent in the wrong direction), that is not a problem because they were virtual particles, and were not sent in the first place after all!

– Photons are massless, so the range of this force is infinite.

Does this disturb you? It should! 11

Back to matter: probing subatomia

How accelerators work

– Charged particles are deflected by magnetic fields.

– A suitable arrangement of electromagnets can force particles into circular paths.

– Electric fields accelerate the particles.

– Recall the relativistic energy: E2 = (pc)2 + (mc2)2

– Energies can be driven to values exceeding rest masses of other particles.

– BLAM! They can transform into these other particles via: E = mc2

– Accelerators are rated in power: 1 eV (1.6 ×10-19 J).

– 14 TeV is the energy of a 1 gram object falling 0.2 mm in 1g.

More powerful accelerators →

more energy →

creation of more massive particles.12

What they have discovered

Neutrinos: zero charge, essentially massless; predicted in 1931; discovered in 1956; found to be hyper-relativistic in 2011?

– Muons: negative charge, 0.1 u; discovered in 1936.

– Π-mesons: neutral, positive, negative charge, 0.1 u; discovered in 1947.

– K-mesons (kaons): neutral, positive, negative charge, 0.53 u; discovered in 1947.

– Λ-baryons: 1.2 u, neutral; discovered in 1947.

– Xi-baryons: 1.3 u, neutral; discovered in 1964.

– J/Ψ meson, τ, upsilon meson, gluon, W and Z meson, and others followed.

– Current list of mesons

– Current list of baryons

Surely, as this continued, physicists concluded the so-called “elementary” particles must in fact be composite articles.

What are the real core particles? 13

The Standard Model of particle physics

The Standard Model of particle physics was developed by Sheldon Glashow (1960); Steven Weinberg and Abdus Salam (1967). It treats electromagnetism, strong, and weak interactions, but not gravity. Major successes include correctly predicting the mass of W and Z bosons. Even so, it has flaws, and is clearly not the final solution.

Charge Family 1 Family 2 Family 3Quarks: +2/3 up (u) charm (c) top (t)

-1/3 down (d) strange (s) bottom (b)

Leptons: -1 electron (e-) muon (μ-) tau (τ-)

0 electron neutrino (νe) muon neutrino (νμ) tau neutrino (ντ)

Family 1 includes the familiar forms of matter: protons, neutrons, electrons, neutrinos.14

QuarksProposed by Gell-Mann and Zweig in 1964; first observed in 1968 by deep inelastic scattering experiments which probed the interior structure in protons and neutrons, and found three mass-globs inside these baryons.

Therefore their subatomic compositions are:– Proton = u + u + d

Charge = (+2/3) + (+2/3) + (-1/3) = 1

– Neutron = u + d + dCharge = (+2/3) + (-1/3) + (-1/3) = 0

– Leptons (neutrinos and electrons) are still considered elementary.

The presence of mesons (which are unstable, and were found to contain two quarks), ultimately demanded the introduction of four more quarks.

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Quarks and forcesIn quantum mechanics, particles interact with each other by fields, but also interactions can be thought of as the continual exchange of mediating particles.

ElectromagnetismWe have seen that the mediating particles are virtual photons.

The weak interaction Mediated by the exchange of Z, W+, and W- bosons.

The strong interaction Mediated by the exchange of gluons.

As a detailed example, let’s look at how quarks interact with each other…

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Quark color – Quarks have a special, additional quantum characteristics called “color.”

– Any quark can assume any color.

– The colors are called red, green, and blue.

– There are three anti-colors: anti-red, anti-green, and anti-blue.

No Net Color is Allowed

Quarks combine so that there is no “net color” in the resulting particle.

In particles that consist of three quarks (such as protons, neutrons), the three quarks must either be (red, green, and blue), or they must be (anti-red, anti-green, and anti-blue).

Particles such as mesons that consist of only two quarks contain a color-anticolor pair: (red + anti-red), (green + anti-green), (blue + anti-blue).

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Quark color as a force: “quantum chromodynamics”

Quarks can change color by exchanging gluons.

A gluon consists of a packet of color and an anticolor.

Consider a particle containing a blue (#1), red (#2), and green (#3) quark.

1. The blue quark (#1) emits a gluon that contains blue color and anti-red.The emission of the blue makes the quark “grey”;The emission of the anti-red turns the quark (#1) red.

2. The gluon is absorbed by the red quark (#2).The absorption of the anti-red part turns the quark “grey”;The absorption of the blue turns the quark (#2) blue.

This “color force” holds the proton, neutron, or meson together.

A relatively weak echo of this force from one proton (or neutron) can affect nearby protons (or neutrons). This is the origin of the “strong nuclear force!”

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Separating quarks

An interesting characteristic of the color force is that it does not drop off with distance.

Suppose you tried to pull a quark out of a proton…

You would have to pull so hard, for so far, that the energy required would be equivalent to the rest-energy of three quarks, in a new atom.

If you managed to pull a quark out of an atom, you’d discover you simply had two new atoms, each with three quarks, and that you had pointlessly expended a great deal of energy.

You cannot isolate quarks.

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Standard Model: summary Fermions

– 6 quarks: up, down, charm, strange, top, bottom

– Hadrons (quark-matter): baryons (p, n, etc.) (3 quarks) and mesons (2 quarks)

– Leptons: electrons, muons, tau, and three neutrinos

Bosons (force particles)

– Photon (electromagnetic)

– W+, W-, Z boson (weak interaction)

Three families (or generations) of particles

– Family 1 contains all the particles encountered in everyday matter

– Family 1 particles: up, down (proton, neutron), electron, electron neutrino

– Families 2, 3 include bizarre, unstable particles

Forces

– Electroweak (electromagnetic and weak)

– Strong force (a side-effect of the color force)

– Gravity (not yet incorporated into the theory) from massless bosons: gravitons20

The Higgs boson– This particle is predicted by the Standard Model.

– The Higgs boson has spin = 0 (all other bosons are spin=1)

– It creates the “Higgs field”

• Particles passing through the Higgs field feel a kind of drag.

• This drag is what we call mass.

• Even the Higgs boson feels this drag (and hence has mass).

The Standard Model predicts its mass to be something below 1.4 TeV, probably 80-200 GeV (~85-215 protons). In 2012, two separate experiments at the LHC detected a particle with a mass of 125-126 GeV; uncertainly about 5σ.

1p = 0.938 GeV, so the Higgs-like particle has a mass of about 133 protons.

Depending upon its existence, mass, and frequency, the weakly interacting Higgs boson might be common enough to explain dark matter in the Universe.

Annoyingly called the “god particle” by the press, physicists prefered calling it the “champagne-bottle boson” because its detection marked a joyous day! 21

Appendix: Ancient concepts of the elementsAristotle (Greece: 384-322 BC) defined the elements to be air, fire, water, earth, and quintessence (the immutable material of the cosmos)

Ancient China saw a single underlying form of energy that could appear in one of five different, inter-changing forms: earth, fire, water, metal, wood.

Babylonia saw earth, sea, sky, wind.

Modern elements

Lavoisier (1789): 33 elements

Berzelius (1818): 49 elements

Mendeleev (1869): 66 elements

(1919): 72 elements

(1955): 101 elements

(2014): 118 elements (most massive several not officially approved)

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