Physics Beyond the Standard Model

Where Does Mass Come From?

•  The electroweak “gauge” theory only has conserved currents for its weak charges if the W’s and Z are massless, like the photon is. It also helps if quarks and leptons are massless in the Energy.

•  To maintain this, but yet have physical masses, we fill the vacuum with some sludge. A particle’s 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.

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 W’s 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 particle’s 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.

•  .

Increasingly General Theories

• Grand Unified Theories of electroweak and strong interactions

• Supersymmetry • Superstring Theories – 10 dimensions

with gravity • Superstring Unification to M Theory

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 the cloud is penetrated.

•  Electromagnetic coupling α1 increases with energy from 1/137 to 1/40 at 1017 GeV Unification Scale

•  Strong coupling α3 decreases from ~1 to 1/40 •  Weak coupling to W’s is α2. •  So couplings come together at unification scale

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) νe e- anti-νe e+ •  Recently, neutrino oscillations and mass were

found, adding the anti-νe. •  In the GUT, there are vector bosons that take

fundamental particles into another in the multiplet.

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.

Particle Supersymmetry

•  In a Grand Unified Theory, all quarks and leptons are in a generation are united into one family.

•  The GUT gauge bosons transform one quark or lepton to another, such a gluon changing one color quark into another.

•  Another 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.

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 •  The Next Linear Collider (NLC) will be needed to

map out the sparticles and Higgs interactions in detail.

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 W’s and Z’s would have spin ½

Winos and Zinos (after Wess and Zumino) •  Spin 0 Higgs would have spin ½ Higgsinos •  In a supergravity theory, spin 2 gravitons

have spin 3/2 gravitino look-alikes.

Why Supersymmetry (SUSY)?

•  It’s 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) Higgs’s 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.

Evolution of Gauge Couplings (reciprocals)

Standard Model Supersymmetry

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.

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.

Pictures of John Schwarz and Ed Witten

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).

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 Schwarz’s wife. •  “The Elegant Universe” by Brian Greene, http://www.pbs.org/wgbh/nova/elegant

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

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.

Speculative Models of Extra Dimensions

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

Gravity

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.

Brane with attached string and graviton in extra

dimension

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/ rn+2 for n extra dimensions, at r < 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.

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.

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.