Physics Beyond the Standard Model

1
Physics Beyond the Standard Model
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Where Does Mass Come From?

• The electroweak gauge theory only has conserved
  currents for its weak charges if the Ws and Z
  are massless, like the photon is. It also helps
  if quarks and leptons are massless.
• To maintain this, but yet have physical masses,
  we fill the vacuum with some sludge. A
  particles mass is then proportional to the
  amount each particle couples to this sludge.
• The sludge is the everywhere constant vacuum
  value of the neutral Higgs.

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The Higgs Fields in the SM

• Three extra Higgs fields, H, H-, anti-H0 make up
  the extra component of the W and Z spins needed
  to make them massive.
• The Ws have a mass of 81 GeV, and the Z of 90
  GeV.
• The H0 has a constant vacuum density, and can
  also make a physical particle.

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How to Find the Higgs

• The Higgs vacuum value is uniform, neutral,
  appears the same at all velocities, and
  undetectable except for the fact that it gives
  mass to everything.
• A particles mass is proportional to its coupling
  to the Higgs and therefore to its vacuum density.
• The excitations of the Higgs is a real particle,
  predicted to be at about 115-130 GeV.
• This should show up in the LHC in some rare
  decays.
• It would have shown up at the Fermilab Tevatron,
  except that the intensity has not met
  expectations.

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Increasingly General Theories

• Grand Unified Theories of electroweak and strong
  interactions
• Supersymmetry
• Superstring Theories 10 dimensions with gravity
• Superstring Unification to M Theory

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Running Coupling Constants

• Charged particles have virtual quantum allowed
  clouds around them of photons and
  electron-positron pairs.
• Colored particles have virtual gluons and
  q-anti-q pairs.
• So the total coupling at long distance or
  charge, is different from the coupling at short
  distance, where the cloud is penetrated.
• Electromagnetic coupling increases with energy
  from 1/137 to 1/40 at 1017 GeV Unification Scale
• Strong coupling decreases from 1 to 1/40
• Weak coupling to Ws also reaches 1/40
• So couplings come together at unification scale

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Running Gluonic Coupling
g3
g3
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Running Couplings
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Fundamental Particles for Unification

• Unification means that at a GUT scale, where
  masses can be ignored, all fundamental particles
  appear in the same multiplet.
• This allows their charges to be the same or given
  fractions of each other, and accounts for the
  proton and electron charge being equal.
• The particles from the SM to include for the
  first generation are the 16 (left handed)
• ur ug ub dr dg db anti-(ur ug ub dr dg db)
• ?e e- anti-?e e
• In the GUT, there are vector bosons that take
  fundamental particles into another in the
  multiplet.

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Sequence of GUTS

• Standard Model of electroweak doublets for quarks
  and leptons plus photon (SU(2)xU(1)) and three
  colors (xSU(3)). It has photon, W, Z, and 8
  gluons as bosons.
• Combine 3 colors and electroweak doublet (SU(5))
  ruled out as causes proton decay at level not
  seen has 5 10 fundamental particles. It has
  24 bosons.
• Add extra neutrino mode for massive neutrinos
  16 fundamental (SO(10))
• There are 45 gauge bosons in SO(10).
• 27 fundamentals (E6), including singlet quarks
  and neutrinos.
• E7, E8 (heterotic string)
• Three generations of each fundamental multiplet

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A Bit of History of Unification

• Electricity unified with magnetism (M. Faraday
  and J. C. Maxwell).
• Relativity and General Relativity (A. Einstein).
• Quantum Mechanics (Planck, Bohr, Schrodinger and
  Heisenberg).
• Relativistic quantum mechanics (P. Dirac).
• Quantum Electrodynamics (R. Feynman, Tomonaga,
  Schwinger).
• Quarks and Quantum Chromodynamics (Nemann, M.
  Gell-Mann and G. Zweig).
• Unification of Electromagnetism with Weak
  Interactions to form Electroweak theory (S.
  Weinberg, A. Salam).
• Grand Unified Theories
• Supersymmetry
• Superstring Theory of Everything including
  gravity.

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Proton Decay

• In a GUT there are X and Y gauge bosons that can
  transform a quark into an antiquark, and a quark
  into a lepton, since they are in the same
  multiplet.
• This allows a proton to decay into a lighter pi
  or K meson and a lepton.
• Dont worry, the lower limit on the lifetime is
  1034 years, far longer than the age of the
  universe of 1010 years.
• It takes a detector the size of Super-K to see a
  few proton decays a year in these theories.

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Proton Decay
dr
dr
p0
anti-danti-r
ug
P
Xanti-r
ub
e
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Particle Spin

• angular momentum is quantized to integer units of
  Plancks constant over 2?.
• Quarks and leptons have half a unit of angular
  momentum as spin, or are spin 1/2 particles, also
  called fermions.
• Photons and Ws and Z are spin 1 particles, also
  called bosons.
• Gravitons have spin 2, and are bosons.

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Particle Supersymmetry

• In a Grand Unified Theory, all quarks and leptons
  are in a generation and are united into one
  family.
• The GUT gauge bosons transform one quark or
  lepton to another, such as gluon changing one
  color quark into another.
• A grander symmetry would be to transform all
  gauge bosons to fermions with the same charges,
  and vice versa.
• Thus for every spin ½ fermion there would be a
  spin 0 boson with the same charges and flavor,
  and to every gauge boson, there would be a like
  charged and coupled spin ½ fermion.
• These look-alikes, except for spin, are called
  sparticles.

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Conserved Supersymmetry

• If supersymmetryness is conserved, sparticles can
  only be created or destroyed in pairs
• Sparticles would then decay to the ordinary
  particles plus another sparticle,
• until they reach the lightest supersymmetric
  particle (LSP)
• The LSP should be neutral and is a leading dark
  matter candidate
• They should have masses about 1 TeV
• They should be produced in pairs at the LHC in
  2007
• The Next Linear Collider (NLC) will be needed to
  map out the sparticles and Higgs interactions in
  detail.

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Sparticle Names

• Thus with quarks there would be spin 0 squarks
• Leptons would have spin 0 sleptons (selectron and
  sneutrino)
• The photon also would have a spin ½ photino
• The Ws and Zs would have spin ½ Winos and Zinos
  
• Spin 0 Higgs would have spin ½ Higgsinos
• In a supergravity theory, spin 2 gravitons have
  spin 3/2 gravitino look-alikes.

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Why Supersymmetry (SUSY)?

• Its believers think it is a beautiful symmetry
  between fermions and bosons, and should be a part
  of nature.
• If the sparticles are at about 1 TeV, then the
  running coupling constants actually do meet at a
  GUT scale of 1017 GeV.
• GUT scale (mass) Higgss would normally couple to
  the light SM Higgs and bring its mass up to the
  GUT scale.
• Adding sparticles to particles cancel this
  coupling to leave the SM Higgs light, solving the
  so-called Heirarchy problem.
• String Theory requires SUSY, again for similar
  cancellations.

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Minimal SUSY Standard Model

• The MSSM has two Higgs doublets, as opposed to
  the one in the standard model.
• The doublets also have distinct anti-Higgs.
• Thus there are 8 Higgs particles.
• Three are eaten to make the W and Z massive.
• One makes the neutral mass generating Higgs.
• Four more are observable, of which two are
  charged.

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Evolution of Gauge Couplings (reciprocals)
Standard Model
Supersymmetry
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Meeting of the Running Couplings (reciprocals) in
MSSM
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What is String Theory?

• It is the theory that elementary particles are
  really strings with tension, that obey relativity
  and quantum mechanics.
• By dispersing the particle away from a point, it
  avoids infinities in the treatment of gravity or
  gravitons by pointlike particles.
• The string size is close to the Planck size of
  10-32 cm, which is the smallest size where
  gravity becomes strong.
• To avoid anomaly infinities requires
  supersymmetry and 10 dimensions (1 time and 9
  space dimensions).
• String theory then provides a quantum theory of
  gravity.
• Andre Neveu, John Schwarz, Michael Green and
  Pierre Ramond were founders.

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Pictures of John Schwarz and Ed Witten
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Types of Superstring Theories

• There are five superstring theories.
• There is one open superstring theory with left
  (L) moving waves (SO(32)).
• There are two closed superstring theories
• Type IIA L-R parity symmetric
• Type IIB L only, parity violating
• There are two heterotic string theories of a
  product of a string theory in 26 dim (with L
  moving waves) x a superstring in 10 dim (with R
  moving waves).
• (SO(32)) and (E8 x E8).

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Unification of Superstring Theories

• Recently, in the second string revolution, it was
  discovered that there are transformations between
  all five superstring theories. (Ed Witten)
• This means they are all views of a larger theory
  which is not well understood, but is called M
  theory. It may be in 11 dimensions.
• For further information, see
• http//superstringtheory.com/, run by
  Patricia Schwarz, John Schwarzs wife.
• The Elegant Universe by Brian Greene,
• http//www.pbs.org/wgbh/nova/elegant

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Towards Verification of Superstring Theory

• Since superstring theory included the three
  unified forces of GUTS and gravity, it has been
  called the Theory of Everything.
• It has not been possible to solve superstring
  theory to find a unique physical model.
• There are a half-million ways to topologically
  compactify the extra six dimensions to very
  short distances, and leave the four dimensional
  world that we live in.
• So many GUTS and breakup paths of GUTS to the SM
  are still possible

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Verification of Superstring Theory

• The masses of sparticles are not well predicted.
• If they are in the TeV range, they will appear in
  the LHC.
• Once they are found, the NLC e e- collider will
  more precisely determine their properties.
• The convergence of the running coupling strengths
  at a GUT scale is more successful with SUSY
  particles than in the SM.
• If SUSY is found, it will be considered a success
  of string theory. If not found, it could spell
  its demise.
• The lightest neutral SUSY particle (LSP) could be
  dark matter, and there are experiments to
  directly detect them, but they will take a while
  to reach large enough scale.

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How do strings scatter?

• Via the pants diagram, where two strings merge
  to one, and then go back to two.

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Speculative Models of Extra Dimensions

• Large Extra Dimensions and Branes
• Early Unification with a Strong Gravity

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Brane Solutions

• String Theories have membrane solutions
• The most used is that all our 4 dimensional world
  is a membrane in the 10 dimensional world.
• Open string ends are attached to the membrane.
• Quarks, leptons and interacting bosons for strong
  and electroweak particles are confined to the
  brane.
• But gravitons as closed strings can leave the
  brane and spread out in the extra dimensions.

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Brane with attached stringand graviton in extra
dimension
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Large Extra Dimension Models

• By experimental limits, extra dimensions could
  still be as large as 0.1 millimeter, and this
  will be tested by gravity, which behaves as F
  M1 M2/ rn2 for n extra dimensions, at r lt R.
• In these, gravity could become strong at 1 TeV
  and unify with the other forces there. (Nima
  Arkani-Hamed, Dimopoulos and Dvali)
• The extra dimension could be curled up with 1 TeV
  excitations, or at the String or Planck Scale.
• The former would show up in experiment at
  Fermilab or the LHC as invisible missing energy
  disappearing into the extra dimensions in
  excitations there, or as one micro black hole a
  second being produced.

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Plane Extra Dimension

• The extra dimension could be between two flat
  branes, one of which is physical, and one of
  which has gravity (unphysical brane).
• The gravity field exponentially decreases from
  the unphysical to the physical brane.
• Thus gravity appears weak to us on the physical
  brane, but is strong on the unphysical brane.
• Called the Randall-Sundrum model.
• The extra dimension models so far do not give GUT
  theories, spoiling the supersymmetry triumph of
  explaining the convergence of coupling constants
  at the GUT scale.

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Relevance of Particle Physics

• We are closer to accounting for some leftover
  matter, possibly requiring three generations of
  quarks and leptons.
• We may someday account for inflation and dark
  matter (SUSY?) and dark energy.
• We understand how the Sun shines through weak
  interactions.
• We understand how color forces and quarks form
  nucleons.
• We may soon find how a Higgs gives mass to
  everything.
• There may be Grand Unification to keep charges of
  everything the same and allow particle changing
  interactions.
• We may have found a way to have gravity that is
  consistent with quantum mechanics.