# Physics 226 (Fall 2001) Lecture #1

The Standard Model
(The Standard Theory of Particle Physics)

The theory of quarks and leptons (matter fields), and their interactions.
• Understanding the structure of the natural universe
• identify the basic particles that are consistuents of matter (quarks and leptons)
• know what forces they feel
• know how to calculate the behavior of the particles given the forces (in particle physics the word "force" and "interaction" are used interchangeably)
• Although the S.M. describes all known experiments and particle interactions, there are many questions that can be rased about
• the values of the parameters it depends on
• the form it takes.
• We hope for and expect a number of future developments to help answer such questions:
• how they fit into the S.M.
• how they extend the S.M.
Relativistic Quantum Field Theory
• Theorists have learned how to deal with difficult problems such as mass and renormalization.
• There has been steady and extraordinary progress in particle physics, both
• in understanding quantum field theory
• in learning what to include in the Lagrangian
• The theories which describe the particles and their interactions seem to be gauge theories, a special class of quantum theories where there is an invariance principle that necessarily implies the existance of interactions mediated by guage bosons.
• In gauge theories the interaction Lagrangian is, in a sense, inevitable rather than being introduced in an "ad hoc" way as in quantum theory.

Brief description of the structure the theory takes and introduces the quarks and leptons, the gauge bosons, and the forces,
to give an overview so it is more clear where we are heading.

The Framework
• In classical theory
• recall the way in which force enters in Newton's laws. F = ma is used to compute the motion of an object, givin any force F on the object.
• And specific classical forces have been discovered, such as grivity with F = GmM/r^2, Coulomb's law with F = KqQ/r^2, ...
• Hamilton's or Lagrange's equations are equivalent to F = ma in a different formalism.
• In quantum theory
• There is an analogous structure.
• The Schrodinger equation, H psi = i del(psi) / del(t), is like F = ma.
• It holds for any Hamiltonian. Specific forces lead to specific Hamiltonians.
• In particle physics
• The formalism, analogous to F = ma or the Schrodinger equation, that allows one to start with any Lagrangian and compute "the motion", i.e. to compute cross sections and decay rates.
• In practice that means extracting Feynman rules to write matrix elements, and converting the matrix elements into transition probabilities.
• The specific Lagrangians for the electroweak force and the strong force are what is particularly new about the Standard Model. These Lagrangians are somewhat more complicated than GmM/r. To say differently, the Hamiltonians that describe all the known interactions of particles have been found in recent years. There has also been much progress in understanding the structure of the quantum field theory equivalent, of the Schrodinger equation.
• Quantum Field Theory
• The combination of quantum theory and relativity leads to the introduction of quantum fields and of associated particles.
• Suppose various particles can interact with one another, and you give one particle a push. The forces, due to that particle, that act on nearby particles can not produce instantaneous changes in their motions, since no signal can travel faster than the speed of light.
• Instead, as with electromagnetism and gravity, we say the pushed particle is the source of various fields which carry energy, and perhaps other quantum numbers, through the surrounding space; eventually the fields interact with other particles.
• Because of the quantum theory, the energy and other quantum numbers are carried by discrete quanta, which become identified with the particles transmitting the force.
• Thus in a quantum field theory, the elementary particle interactions are interpreted in terms of exchanges of some of the particles themselves.
• Gauge theories
• Gauge theories are a special class of quantum field theories where there is an invariance principle that necessarily requires the existence of interactions among the particles.
• Gauge forces mean forces which respect a gauge symmetry and in addition, forces whose strengths are proportional to a "charge" of some kind.
• e.g. in electrodynamics the charge (the fine structure constant alpha) measures the strength of the electromagnetic force.
• The amount of charge can be given to particles ; 0, +-1/3 e, +-2/3 e, +-e, ...
• For other forcies, new charges arise which play both the above roles.
• The basic view of a particle interaction

(Feynman diagram of an electron emitting a photon which is absorbed by another electron)

• For electrodynamics a charged particle emits a photon and recoils; the photon is absorbed by another charged particle, which changes its motion as a consequence.
• Such diagrams (Feynman diagrams) are useful pictures of what is occuring. More than that. When a set of rules (Feynman rules of the theory) is givin to convert each diagram into a matrix element, and to calculate transition probabilities, the theory can be summarized in its diagrams (assuming situations where perturbative calculations are relevant).
• In the case of electromagnetism, the matrix element, in the non-relativistic limit, gives Coulomb's law.
The Forces
• The progress in particle physics, both theoretical and experimental, in 1970's and 1980's has been remarkable.
 --------------- ------------- --------------------------- ------- Forces 1970 now soon ? Real theory ? --------------- ------------- --------------------------- ------- Gravity yes but classical unchanged ? Electromagnetism yes (QED) united into a single theory (electroweak) GUT Weak Interactions no united into a single theory (electroweak) GUT Strong Interactions no yes (QCD) GUT --------------- ------------- --------------------------- -------
GUT : Grand Unified Theories
Real Theory --> Does a Lagrangian Quantum Field Theory exist in which all observables are finite ?

• Gravity
• The theory of general relativity was fully satisfactory but unconnected with the other forces.
• A quantum theory has not yet been constructed. That is unchanged today. Various approaches to constructing a quantum theory of gravity and to unifying gravity with other forces are being pursued actively.
• Weak Intractions
• no theory in 1970 although observed to exist : neutron beta-decay n --> p e nu-bar
• They play a critical role in the process of generation of energy in the Sun, and in the building up of heavy elements. Life on earth could not exist in the absence of the weak interactions (or if any of the other known forces were missing, for that matter).
• The Sun as energy source on Earth
• The Sun originally condensed under gravity from a cloud of hydrogen, until the core reached by compression a high enough temperature (10^7 degrees) for thermonuclear fusion reactions to begin: hydrogen is converted to helium.
• The first stage reaction involves weak interactions (p + p --> d + e- + nu).
• Subsequent stages involve strong nuclear interactions.
• They are called "weak" because the typical time scale on which they occur is much longer (of order 10^-13 sec) than for electromagnetic processes (of order 10^-19 sec).
• Now the weak and electromagnetic interactions have been unified into one force.
• Strong Interactions
• no theory in 1970
• Nuclear force has been known since ~ the 1930's : a nucleus containing several protons would hold together in spite of their electrical repulsion. Consequently, another attractive force, stronger than electromagnetism, must exit.
• Since the force was strong, it was expected that perturbative calculations would not apply to observable phenomena.
• Now a real theory of strong interactions exists and experimentally checked in a variety of ways.
• It is quarks that undergo the strong interactions, "color" force (QCD, quantum chromodynamics).
• The quarks carry the color charge and combine to make color neutral hadrons just as an electrically charged nucleus and electrons combine to make electrically neutral atoms.
• The residual color field outside of protons and neutrons is the force that forms nuclei, just as a residual electric field outside neutral atoms causes them to combine into molecules.
• Many other hadrons would form nuclei if they lived long enough, but they are unstable because of the strong or weak forces.
• Unification
• Success in unification
• Electricity and magnetism into electromagnetism
• Electromagnetism and weak interactions into the electroweak theory
• The electroweak theory and QCD into one theory "grand unified theory" ??
• Candidate theories exist ?!
Particles
• matter particles : quarks and leptons (spin 1/2 fermions)
 ---------- ---------- ---------- ----------- ------- -------- 1st generation 2nd generation 3rd generation electric charge # of colors Baryon # (family) (family) (family) ---------- ---------- ---------- ----------- ------- -------- u c t +2/3 3 1/3 d s b -1/3 3 1/3 ---------- ---------- ---------- ----------- ------- -------- nu_e nu_mu nu_tau 0 0 0 e mu tau -1 0 0 ---------- ---------- ---------- ----------- ------- --------
• Flavors
• six quark flavors (up, down, strange, charm, bottom, top)
• six lepton flavors (e, nu_e, mu, nu_mu, tau, nu_tau)
• It is not understood why there are six.
• Lepton # (L_e, L_mu, L_tau)
• As far as is known, the separate lepton types do not undergo transitions into one another. A lepton number defined for each family is observed experimentally to be conserved.
• Fundamental reasons why it should be conserved are not known.
• Baryon #
• observed experimentally to be conserved to a very good accuracy
• but no reason is known why.
• The requirements of the Electroweak theory
• the total charge of the u,c,t quarks = 3(# of colors) x 3 (3 quarks) x (2/3) = 6
• the total charge of the d,s,b quarks = 3(# of colors) x 3 (3 quarks) x (-1/3) = -3
• the total charge of the leptons = 3 (e, mu, tau) x (-1) = -3
• The total charge of all the fermions = 0.
• The Standard Model should be free of so-called "anomalies" (renormalisable field theory)
• After the discovery of the bottom quark in 1977, the top quark was required in the Standard Model.
Recall the several accelerators built to search for the top quark before it was observed at Tevatron by the CDF and D0 experiments.
• It turns out that it is also a property of the grand unified theories.
• Any colored particle is permanently bound inside a colorless hadron.
• It makes quantitative determination of quark masses a subtle point when the quark masses are smaller than the typical hadronic masses of ~1 GeV.
• free quark masses (current algebra masses)
• constituent quark masses
• constituent mass = free quark mass + ~300 MeV
• gauge bosons : photon, W+-, Z, gluons (spin 1 bosons), gravitons (spin 2 bosons)
• the bosons tht transmit the forces.
• Since the quantum field theory that allows us to calculate the behavior of the particles is a gauge theory, they are called "gauge bosons".
• Gravitons, gauge bosons for gravity, interact too weakly to be detected singly; their existence and properties are inferred from the structure of the theory, in the same way that quantum electrodynamics leads to a photon.
• All the other gauge bosons have been discovered.
• The known universe is made of u-quarks, d-quarks, electrons, electron neutrinos, and the gauge bosons.
• The other quarks and leptons have been made at accelerators (and occasionally by collisions of energetic cosmic rays in the earth's atmosphere), and existed at an early stage of the universe, but are very short-lived and play no known role in the universe today.
• Anti-particles
• Each particle has an antiparticle.
• opposite : electric charge, color charge, flavor
• same : mass, spin
• Photon and pi-0 are their own antiparticles.
• Anti-particles are just particles !!
• Higgs bosons
• one more class of particles is needed to make a consistent theory of particle masses and interactions.
• The spin-0 or scalar bosons called Higgs bosons, which are responsible for particles' masses.
• The electroweak theory requires one electrically neutral Higgs boson, but more could exist.
• The Standard Model Higgs mechanism does not tell us the values of masses.
• Flavor mixing
Units
• natural units
• h-bar = c = 1 = mu_0 = epsion_0
• All quantities have the dimension of a power of energy.
• E = energy unit
• [momentum] = E / c = E
• [mass] = E / c^2 = E
• [time] = h-bar / E = 1/E
• [length] = h-bar c / E = 1/E
• The actual expressions for h-bar and c provide the conversion factors.
• example
• proton mass = 1 GeV
• proton size = 1 fm = 5 GeV-1
• top quark lifetime = 10^-25 sec = 1 GeV-1