Elementary Particles and our Universe Barbara Hale Physics
Elementary Particles and our Universe Barbara Hale Physics Department Missouri University of Science & Technology Elementary particles and their forces -- how can we understand them and what do they imply about our early universe? Elementary particle:
.. not able to be further broken down with a unique set of properties. mass, m charge, Q spin : s = ( E = mc2 ) ( units of e) (fermion)
s = 0, 1, 2 (boson) flavor ( up, down, top, bottom, charm, strange) the elementary particles (as far as we know at this time) six quarks (up down c s t b) (heavy, strongly interacting ) six leptons (e ne m nm t
(little light ones, weakly interacting) nt) all have spin = they are fermions thats it! The forces and particles (gauge bosons) which produce them electromagnetic (photon)
zero mass weak ( W+ , W- , Z0) strong (8 gluons) zero mass gravitational (graviton) (not yet observed) all have spin = 1 (or 2 for graviton) they are bosons How are the interactions explained?
we turn to Feynman and the interactions between photons, , and electrons, e. This theory is called QED Quantum Electrodynamics. 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. Its just a plane wave! J
J2 Hes talking about reflections here. anti-particles Sum all these up to get mass of electron.
photon e2/c = 1/137 = c =1 The way theorists write the interaction The m runs from 0,1,2,3 and you sum over them. e
photon e photon e e WHY?
At the basic level it comes from Maxwells 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 cant 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! Gauge Invariance QED
The story goes like this: You start with the equations that describe free electrons, with wave function/operators, (r,t). r,t). Then, you make an arbitrary rotation (r,t). a gauge transformation) on these (r,t). 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 (r,t). 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 the invariance! to produce 1. Initial state a picture .. sort of 2. Rotate A
A 3. Transform A 4. Final state
they interact! invariance Note that the photon field must also be transformed. U(r,t). 1) Gauge Invariance This group of gauge operations/rotations is called
U(r,t). 1). The 1 means only one gauge boson. So we say U(r,t). 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 Maxwells equations. That made it easy we knew the answer! 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(r,t). 2) . Quarks come in flavor doublets: Leptons also come in flavor doublets. Number of gauge particles: 22 1 = 3 W+ W- Z0 beta decay u
d u d d Wneutron W doesnt see color u proton Mesons are composed of quarks and anti-quarks.
decay of - u d - Following the detection of the W and Z in 1973 almost everyone believed in quarks. W
p d u u p production from
-pp -d u u d u W+ e+
ne _ u _ 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(r,t). 3) gauge bosons: 32-1 = 8 gluons These interaction terms correspond to the following diagrams.
Note that there are only 8 gluons grrggggb- The red, anti-green gluon The green, anti-blue gluon A schematic of the protons internal structure. The gluon forces hold the
proton together proton At any time the proton is color neutral. That is, it contains one red, one blue and one green quark. eight gluons
The Standard Model theory of everything The Standard Model is obtained by imposing these three local gauge invariances on the quark and lepton field operators: rotation symmetry: U(r,t). 1) SU(r,t). 2) SU(r,t). 3)
QED weak/favor color gauge boson photon + W W- Z 0 8 gluons
This gives rise to 1 + 3 + 8 spin = 1 force carrying gauge particles and prescribes the interactions of all the quarks and leptons. 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. Grand Unified (r,t). GUT) Theory SU(r,t). 5) includes all of the Standard Model and extra invariance under the following transformations:
quarks leptons leptons quarks 24 gauge particles photon, W, Z, gluons + 6 X, 6Y more Decay of proton in SU(5)
d red d red - u green u blue proton
d red - green Xred X+ red 3-color vertex
anti-up 0 blue e+ X +red green blue
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 = , 3/2 ). SUSY unifies E&M, weak, strong SU(r,t). 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: open strings closed strings
.no free parameters or L = 2r L = 10-33 cm. = Planck Length Mplanck 1019 GeV/c2 See Schwarz, Physics Today, November 1987, p. 33
Superstrings The Planck Mass is approximately that mass whose gravitational potential is the same strength as the strong QCD force at r 10-15 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. Its the reason why QED is one of the most rigorous theories we have. The universe evolved
through a series of epochs 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.
Grand unification epoch: GUT Between 1043 seconds and 1036 seconds after the Big Bang The 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 1036 seconds and an average thermal energy kT 1015 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. Higgs Mechanism 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 1015 GeV). The Higgs keeps its mass ( the
thermal energy of the universe, kT 1015 GeV). This Higgs particle has too large a mass to be seen in accelerators. 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
10 19 T (GeV/k) R(t) m Rt2/3 Rt1/2 T t-1/2
R eHt 1014 T t-1/2 Rt1/2 Tt-2/3 T=2.7K 10-13
10-43 10-34 10-31 time (sec) 10 After the Big Bang: the first 10-6 Seconds Planck Era
SUSY Supergravity inflation gravity decouple .X,Y take on mass s GUT W , Z0 take
on mass SU(2) x U(1) symmetry . all forces unified bosons fermions quarks leptons all particles massless .
Electroweak epoch Between 1036 seconds and 1012 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 1012 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 10-6 Seconds Planck Era SUSY Supergravity inflation gravity decouple .X,Y take on mass s GUT
W , Z0 take on mass SU(2) x U(1) symmetry . all forces unified bosons fermions quarks leptons
all particles massless . . W , Z0 take on mass COBE data 2.7K
Standard Model . 100Gev . . .
. . only gluons and photons are massless n, p formed nuclei formed atoms formed Thank you!
Dark Energy: http://science.nasa.gov/astrophysics/focus-areas/what-is-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.
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