Elementary particles and their forces -- how can we understand them and what do they imply about our early universe? Barbara Hale Physics Department Missouri University of Science & Technology

mass, m ( E = mc 2 ) charge, Q ( units of e) spin : s =½ ℏ (fermion) s = 0, 1, 2 ℏ (boson) flavor ( up, down, top, bottom, charm, strange)

all have spin = ½  they are fermions that’s it!

 electromagnetic (photon) zero mass  weak ( W +, W -, Z 0 )  strong (8 gluons) zero mass  gravitational (graviton) (not yet observed ) all have spin = 1 (or 2 for graviton)  they are bosons

Richard P. Feynman, Nobel Laureate 1965 New Zealand 1979 “Feynman” by J. Ottaviani, L. Myrick and H. Sycamore First Second, NY 2011

…California 1983 … he tries again. It’s just a plane wave!

J J2J2

He’s talking about reflections here.

anti-particles

Sum all these up to get mass of electron.

e eee photon e 2 / ℏ c = 1/137 ℏ = c =1 The way theorists write the interaction The  runs from 0,1,2,3 and you sum over them.

WHY? At the basic level it comes from Maxwell’s equations. The source of all electric and magnetic fields is a charge, static and/or moving. A photon (A) is the particle manifestation of the E&M wave. You can’t produce a photon without a moving charge somewhere! They must interact. So you thought electrons and photons were separate things? They are rather two things intimately coupled. People thought about that. And they gave it a fancy name: Gauge Invariance!

The story goes like this:  You start with the equations that describe free electrons, with wave function/operators,  (r,t). Then, you make an arbitrary “rotation” (a gauge transformation) on these  (r,t). The “angle” of rotation can depend on r, and t.  Next, you demand that the original equations be invariant under this transformation! They are not!  But, if you introduce another particle (called the gauge particle - in this case the photon) the equations become invariant. Gauge Invariance  you must have a photon!  Furthermore they must interact like to produce the invariance!

 ’’ AµAµ AµAµ  ’’  invariance Note that the photon field must also be transformed. 1. Initial state 2. Rotate  3. Transform A4. Final state a picture.. sort of … they interact!

This group of gauge operations/rotations is called U(1). The 1 means only one gauge boson. So we say U(1) “gauge symmetry” gives rise to the photon, QED and all those Feynman diagrams from which we can calculate probabilities of electrons scattering from electrons, electrons from protons, etc. It is totally consistent with Maxwell’s equations. That made it easy – we knew the answer! U(1) Gauge Invariance

What about quarks and electrons? -- invent another gauge symmetry! At this point it was not so clear what “rotation” operations to choose, but there were already some idea. The “rotations” are made in flavor space and called SU(2). Quarks come in flavor “doublets”: Leptons also come in flavor “doublets”. Number of gauge particles: 2 2 – 1 = 3 W + W - Z 0

neutron proton beta decay u d u d d W doesn’t see color u W-W-

decay of  - -- u d - Mesons are composed of quarks and anti-quarks.

p p d u u u u d W  production from - p p p - - W+W+ Following the detection of the W and Z in 1973 almost everyone believed in quarks. e+e+ e u u _ d u _

What about quarks interacting with quarks? -- invent another gauge symmetry! At this point again it was not so clear what “rotation” operations to choose, but the theorists were ready: they invented color. “rotations” are made in color space. Quarks come in colors: red, green and blue SU(3) gauge bosons: = 8 gluons

The red, anti-green gluon The green, anti-blue gluon Note that there are only 8 gluons r gr g grggrg - ggbggb - These interaction terms correspond to the following diagrams.

At any time the proton is color neutral. That is, it contains one red, one blue and one green quark. The gluon forces hold the proton together proton A schematic of the proton’s internal structure.

eight gluons

The Standard Model is obtained by imposing these three local gauge invariances on the quark and lepton field operators: rotation symmetry: gauge boson U(1) “QED”  photon SU(2) weak/favor  W + W - Z 0 SU(3) color  8 gluons This gives rise to spin = 1 force carrying gauge particles and prescribes the interactions of all the quarks and leptons.

Grand Unified (GUT) Theory SU(5) includes all of the Standard Model and extra invariance under the following transformations: quarks  leptons leptons  quarks There is one more “gauge” invariance to know about. It is not well formulated and has some difficulties. But it is usually included in describing the early universe. 24 gauge particles – photon, W, Z, gluons + 6 X, 6Y more

d red u green u blue X + red e+e+ d red - X red - anti-up blue green blue green X +red proton 0 Decay of proton in SU(5) 3-color vertex The Grand Unified Theory predicts the decay of the proton. Unfortunately, the lifetime it predicts is too short.

Another symmetry which is taken seriously SUPER SYMMETRIC (SUSY) THEORY SUSYs contain invariance under operations which change bosons (spin = 01,2,..) fermions (spin = ½, 3/2 …). SUSY  unifies E&M, weak, strong SU(3) and gravity fields. usually includes invariance under local transformations This theory is not yet rigorously formalized.

Supersymmetric String Theories Elementary particles are one-dimensional strings: closed strings open strings L = 2  r L = cm. = Planck Length M planck  GeV/c 2 or See Schwarz, Physics Today, November 1987, p. 33 “Superstrings”.no free parameters The Planck Mass is approximately that mass whose gravitational potential is the same strength as the strong QCD force at r  cm. An alternate definition is the mass of the Planck Particle, a hypothetical miniscule black hole whose Schwarzchild radius is equal to the Planck Length.

Problem: if the gauge particles has mass the invariance is destroyed!! This seems like the end of the models. But, it means something terribly important. It is where the story of particle physics and the universe begins. Early in the universe (just after the big bang) everything was too hot and dense to have a mass. At this time all the invariances were perfect. No particles had mass and the entire small, dense universe was a “soup” of highly energetic waves. But, as the universe expanded and cooled off, the gauge particles “condensed” out of the mass-less soup. When this happened, the perfect symmetry was broken and a “new” physics emerged. Two invariances exist today: both the photon and the gluons remain mass-less. It’s the reason why QED is one of the most rigorous theories we have.

Planck epoch Up to 10 – 43 seconds after the Big Bang At the energy levels that prevailed during the Planck epoch the four fundamental forces— electromagnetism U(1), gravitation, weak SU(2), and the strong SU(3) color — are assumed to all have the same strength, and “unified” in one fundamental force. Little is known about this epoch. Theories of supergravity/ supersymmetry, such as string theory, are candidates for describing this era. The universe evolved through a series of “epochs ”

Grand unification epoch: GUT Between 10 –43 seconds and 10 –36 seconds after the Big Bang T he universe expands and cools from the Planck epoch. After about 10 –43 seconds the gravitational interactions are no longer unified with the electromagnetic U(1), weak SU(2), and the strong SU(3) color interactions. Supersymmetry/Supergravity symmetries are broken. The universe enters the Grand Unified Theory (GUT) epoch. A candidate for GUT is SU(5) symmetry. In this realm the proton can decay, quarks are changed into leptons and all the gauge particles (X,Y, W, Z, gluons and photons), quarks and leptons are mass-less. The strong, weak and electromagnetic fields are unified.

Inflation and Spontaneous Symmetry Breaking. At about 10 –36 seconds and an average thermal energy kT  GeV, a huge phase transition is believed to have taken place. In this phase transition, the vacuum state undergoes spontaneous symmetry breaking. Spontaneous symmetry breaking: Consider a system in which all the spins can be up, or all can be down – with each configuration having the same energy. There is perfect symmetry between the two states and one could, in theory, transform the system from one state to the other without altering the energy. But, when the system actually selects a configuration where all the spins are up, the symmetry is “spontaneously” broken.

When the phase transition takes place the vacuum state transforms into a Higgs particle (with mass) and so-called Goldstone bosons with no mass. The Goldstone bosons “give up” their mass to the gauge particles (X and Y gain masses  GeV). The Higgs keeps its mass (  the thermal energy of the universe, kT  GeV). This Higgs particle has too large a mass to be seen in accelerators. Higgs Mechanism What causes the inflation? The universe “falls into” a low energy state, oscillates about the minimum (giving rise to the masses) and then expands rapidly. When the phase transition takes place, latent heat (energy) is released. The X and Y decay into ordinary particles, giving off energy. It is this rapid expansion that results in the inflation and gives rise to the “flat” and homogeneous universe we observe today. The expansion is exponential in time.

Schematic of Inflation T (GeV/k) R(t) m T=2.7K R  t 1/2 T  t -1/2 R  e Ht R  t 2/3 T  t -2/ time (sec)

After the Big Bang: the first Seconds. GUTSU(2) x U(1) symmetry Planck Era gravity decouple s SUSY Supergravity inflation X,Y take on mass W , Z 0 take on mass.. all forces unified bosons  fermions quarks  leptons all particles massless

Electroweak epoch Between 10 –36 seconds and 10 –12 seconds after the Big Bang The SU(3) color force is no longer unified with the U(1)x SU(2) weak force. The only surviving symmetries are: SU(3) separately, and U(1)X SU(2). The W and Z are massless. A second phase transition takes place at about 10 –12 seconds at kT = 100 GeV. In this phase transition, a second Higgs particle is generated with mass close to 100 GeV; the Goldstone bosons give up their mass to the W, Z and the particles (quarks and leptons). It is the search for this second Higgs particle that is taking place in the particle accelerators at the present time.

After the Big Bang: the first Seconds. GUTSU(2) x U(1) symmetry Planck Era gravity decouple s SUSY Supergravity inflation X,Y take on mass W , Z 0 take on mass.. all forces unified bosons  fermions quarks  leptons all particles massless

..... COBE data 2.7K Standard Model W , Z 0 take on mass.. n, p formed nuclei formed atoms formed 100Gev only gluons and photons are massless

Thank you!

/ Dark Energy:

Dark Energy What Is Dark Energy? More is unknown than is known. We know how much dark energy there is because we know how it affects the Universe's expansion. Other than that, it is a complete mystery. But it is an important mystery. It turns out that roughly 70% of the Universe is dark energy. Dark matter makes up about 25%. The rest - everything on Earth, everything ever observed with all of our instruments, all normal matter - adds up to less than 5% of the Universe. Come to think of it, maybe it shouldn't be called "normal" matter at all, since it is such a small fraction of the Universe.