Physics Beyond the Physics Beyond the Standard ModelStandard Model

Summary by Dennis SilvermanSummary by Dennis Silverman

Physics and AstronomyPhysics and Astronomy

UC IrvineUC Irvine

Where Does Mass Come From?Where Does Mass Come From?

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

To maintain this, but yet have physical masses, To maintain this, but yet have physical masses, we fill the vacuum with some sludge. A we fill the vacuum with some sludge. A particle’s mass is then proportional to the particle’s mass is then proportional to the amount each particle couples to this sludge. amount each particle couples to this sludge.

The sludge is the everywhere constant vacuum The sludge is the everywhere constant vacuum value of the neutral Higgs. value of the neutral Higgs.

The Higgs Fields in the SMThe Higgs Fields in the SM

Three extra Higgs fields, Three extra Higgs fields, HH++, H, H--, anti-H, anti-H00 make up make up the extra component of the extra component of the W and Z spins the W and Z spins needed to make them needed to make them massive.massive.

The W’s have a mass of The W’s have a mass of 81 GeV, and the Z of 90 81 GeV, and the Z of 90 GeV.GeV.

The HThe H00 has a constant has a constant vacuum density, and can vacuum density, and can also make a physical also make a physical particle.particle.

H

H

H

H 0

0,

How to Find the Higgs How to Find the Higgs

The Higgs vacuum value is uniform, neutral, appears the The Higgs vacuum value is uniform, neutral, appears the same at all velocities, and undetectable – except for the same at all velocities, and undetectable – except for the fact that it gives mass to everything.fact that it gives mass to everything.

A particle’s mass is proportional to its coupling to the A particle’s mass is proportional to its coupling to the Higgs and therefore to its vacuum density.Higgs and therefore to its vacuum density.

The excitations of the Higgs is a real particle, predicted The excitations of the Higgs is a real particle, predicted to be at about 115-130 GeV.to be at about 115-130 GeV.

This should show up in the LHC in some rare decays.This should show up in the LHC in some rare decays. It would have shown up at the Fermilab Tevatron, except It would have shown up at the Fermilab Tevatron, except

that the intensity has not met expectations.that the intensity has not met expectations.

Increasingly General TheoriesIncreasingly General Theories

Grand Unified Theories of electroweak Grand Unified Theories of electroweak and strong interactionsand strong interactions

SupersymmetrySupersymmetry Superstring Theories – 10 dimensions with Superstring Theories – 10 dimensions with

gravitygravity Superstring Unification to M TheorySuperstring Unification to M Theory

Running Coupling ConstantsRunning Coupling Constants

Charged particles have virtual quantum allowed clouds Charged particles have virtual quantum allowed clouds around them of photons and electron-positron pairs.around them of photons and electron-positron pairs.

Colored particles have virtual gluons and q-anti-q pairs.Colored particles have virtual gluons and q-anti-q pairs. So the total coupling at long distance or “charge”, is So the total coupling at long distance or “charge”, is

different from the coupling at short distance, where the different from the coupling at short distance, where the the cloud is penetrated.the cloud is penetrated.

Electromagnetic coupling Electromagnetic coupling 11 = e = e22//c increases with energy c increases with energy from 1/137 to 1/40 at 10from 1/137 to 1/40 at 101717 GeV Unification Scale GeV Unification Scale

Strong coupling Strong coupling 33 = g = g22//c decreases from c decreases from ~1 to 1/40~1 to 1/40 Weak coupling to W’s is Weak coupling to W’s is 2.2.

So couplings come together at unification scaleSo couplings come together at unification scale

Running Gluonic Couplingg3g3

3 = (g3)2 /c

Running CouplingsRunning Couplings

Fundamental Particles for UnificationFundamental Particles for Unification

Unification means that at a GUT scale, where masses can Unification means that at a GUT scale, where masses can be ignored, all fundamental particles appear in the same be ignored, all fundamental particles appear in the same multiplet.multiplet.

This allows their charges to be the same or given fractions This allows their charges to be the same or given fractions of each other, and accounts for the proton and electron of each other, and accounts for the proton and electron charge being equal.charge being equal.

The particles from the SM to include for the first generation The particles from the SM to include for the first generation are the 16 (left handed):are the 16 (left handed):

uur r uug g uub b ddr r ddgg d dbb anti-(u anti-(ur r uug g uub b ddr r ddgg d dbb)) ee e e-- anti- anti-ee e e++

Recently, neutrino oscillations and mass were found, Recently, neutrino oscillations and mass were found, adding the anti-adding the anti-e.e.

In the GUT, there are vector bosons that take fundamental In the GUT, there are vector bosons that take fundamental particles into another in the multiplet.particles into another in the multiplet.

Sequence of GUTSSequence of GUTS Standard Model of electroweak doublets for quarks and Standard Model of electroweak doublets for quarks and

leptons plus photon (SU(2)xU(1)) and three colors leptons plus photon (SU(2)xU(1)) and three colors (xSU(3)). It has (xSU(3)). It has , W, W±±,, Z, and 8 gluons as bosons. Z, and 8 gluons as bosons.

Combine 3 colors and electroweak doublet (SU(5)) – Combine 3 colors and electroweak doublet (SU(5)) – ruled out as causes proton decay at level not seen – has ruled out as causes proton decay at level not seen – has 5 + 10 fundamental particles. It has 24 bosons.5 + 10 fundamental particles. It has 24 bosons.

Add extra neutrino mode for massive neutrinos – 16 Add extra neutrino mode for massive neutrinos – 16 fundamental (SO(10))fundamental (SO(10))

There are 45 gauge bosons in SO(10).There are 45 gauge bosons in SO(10). 27 fundamentals (E6), including singlet quarks and 27 fundamentals (E6), including singlet quarks and

neutrinos.neutrinos. E7, E8 (heterotic string)E7, E8 (heterotic string) Three generations of each fundamental multipletThree generations of each fundamental multiplet

A Bit of History of UnificationA Bit of History of Unification Electricity unified with magnetism (M. Faraday and J. C. Electricity unified with magnetism (M. Faraday and J. C.

Maxwell).Maxwell). Relativity and General Relativity (A. Einstein).Relativity and General Relativity (A. Einstein). Quantum Mechanics (Planck, Bohr, Schrodinger and Quantum Mechanics (Planck, Bohr, Schrodinger and

Heisenberg).Heisenberg). Relativistic quantum mechanics (P. Dirac).Relativistic quantum mechanics (P. Dirac). Quantum Electrodynamics (R. Feynman, Tomonaga, Quantum Electrodynamics (R. Feynman, Tomonaga,

Schwinger).Schwinger). Quarks and Quantum Chromodynamics (Nemann, M. Quarks and Quantum Chromodynamics (Nemann, M.

Gell-Mann and G. Zweig).Gell-Mann and G. Zweig). Unification of Electromagnetism with Weak Interactions to Unification of Electromagnetism with Weak Interactions to

form Electroweak theory (S. Weinberg, A. Salam).form Electroweak theory (S. Weinberg, A. Salam). Grand Unified TheoriesGrand Unified Theories SupersymmetrySupersymmetry Superstring Theory of Everything including gravity.Superstring Theory of Everything including gravity.

Proton DecayProton Decay In a GUT there are X and Y gauge bosons that In a GUT there are X and Y gauge bosons that

can transform a quark into an antiquark, and a can transform a quark into an antiquark, and a quark into a lepton, since they are in the same quark into a lepton, since they are in the same multiplet.multiplet.

This allow protons in quarks to decay into a This allow protons in quarks to decay into a lighter pi or K meson and a lepton.lighter pi or K meson and a lepton.

Don’t worry, the lower limit on the lifetime is 10Don’t worry, the lower limit on the lifetime is 103434 years, far longer than the age of the universe of years, far longer than the age of the universe of 10101010 years. years.

It takes a detector the size of Super-K to see a It takes a detector the size of Super-K to see a few proton decays a year in these theories.few proton decays a year in these theories.

Proton DecayProton Decay

ug

ub

dr

e+

dr

anti-danti-r

P

Xanti-r

Particle SpinParticle Spin

Orbital angular momentum is quantized to Orbital angular momentum is quantized to integer units of Planck’s constant over 2integer units of Planck’s constant over 2: :

= h/2= h/2.. Quarks and leptons have half a unit of Quarks and leptons have half a unit of

angular momentum as spin, or are spin 1/2 angular momentum as spin, or are spin 1/2 particles, also called fermions.particles, also called fermions.

Photons and W’s and Z are spin 1 particles, Photons and W’s and Z are spin 1 particles, also called bosons.also called bosons.

Gravitons have spin 2, and are bosons.Gravitons have spin 2, and are bosons.

Particle SupersymmetryParticle Supersymmetry In a Grand Unified Theory, all quarks and leptons are in In a Grand Unified Theory, all quarks and leptons are in

a generation are united into one family.a generation are united into one family. The GUT gauge bosons transform one quark or lepton to The GUT gauge bosons transform one quark or lepton to

another, such a gluon changing one color quark into another, such a gluon changing one color quark into another.another.

A grander symmetry would be to transform all gauge A grander symmetry would be to transform all gauge bosons to fermions with the same charges, and vice bosons to fermions with the same charges, and vice versa.versa.

Thus for every spin ½ fermion there would be a spin 0 Thus for every spin ½ fermion there would be a spin 0 boson with the same charges and flavor, and to every boson with the same charges and flavor, and to every gauge boson, there would be a like charged and coupled gauge boson, there would be a like charged and coupled spin ½ fermion. spin ½ fermion.

These look-alikes, except for spin, are called sparticles.These look-alikes, except for spin, are called sparticles.

Conserved SupersymmetryConserved Supersymmetry

If supersymmetryness is conserved, sparticles can only If supersymmetryness is conserved, sparticles can only be created or destroyed in pairsbe created or destroyed in pairs

Sparticles would then decay to the ordinary particles plus Sparticles would then decay to the ordinary particles plus another sparticle,another sparticle,

until they reach the lightest supersymmetric particle until they reach the lightest supersymmetric particle (LSP)(LSP)

The LSP should be neutral and is a leading dark matter The LSP should be neutral and is a leading dark matter candidatecandidate

They should have masses about 1 TeVThey should have masses about 1 TeV They should be produced in pairs at the LHC in 2007They should be produced in pairs at the LHC in 2007 The Next Linear Collider (NLC) will be needed to map The Next Linear Collider (NLC) will be needed to map

out the sparticles and Higgs interactions in detail.out the sparticles and Higgs interactions in detail.

Sparticle NamesSparticle Names

Thus with quarks there would be spin 0 squarksThus with quarks there would be spin 0 squarks Leptons would have spin 0 sleptons (selectron Leptons would have spin 0 sleptons (selectron

and sneutrino)and sneutrino) The photon also would have a spin ½ photinoThe photon also would have a spin ½ photino The W’s and Z’s would have spin ½ Winos and The W’s and Z’s would have spin ½ Winos and

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

spin 3/2 gravitino look-alikes.spin 3/2 gravitino look-alikes.

Why Supersymmetry (SUSY)?Why Supersymmetry (SUSY)?

It’s believers think it is a beautiful symmetry between It’s believers think it is a beautiful symmetry between fermions and bosons, and should be a part of nature.fermions and bosons, and should be a part of nature.

If the sparticles are at about 1 TeV, then the running If the sparticles are at about 1 TeV, then the running coupling constants actually do meet at a GUT scale of coupling constants actually do meet at a GUT scale of 10101717 GeV. GeV.

GUT scale (mass) Higgs’s would normally couple to the GUT scale (mass) Higgs’s would normally couple to the light SM Higgs and bring its mass up to the GUT scale. light SM Higgs and bring its mass up to the GUT scale.

Adding sparticles to particles cancel this coupling to Adding sparticles to particles cancel this coupling to leave the SM Higgs light, solving the so-called Heirarchy leave the SM Higgs light, solving the so-called Heirarchy problem.problem.

String Theory requires SUSY, again for similar String Theory requires SUSY, again for similar cancellations.cancellations.

Minimal SUSY Standard ModelMinimal SUSY Standard Model

The MSSM has two Higgs doublets, as opposed The MSSM has two Higgs doublets, as opposed to the one in the standard model.to the one in the standard model.

The doublets also have distinct anti-Higgs.The doublets also have distinct anti-Higgs. Thus there are 8 Higgs particles.Thus there are 8 Higgs particles. Three are “eaten” to make the WThree are “eaten” to make the W±± and Z and Z

massive.massive. One makes the neutral mass generating Higgs.One makes the neutral mass generating Higgs. Four more are observable, of which two are Four more are observable, of which two are

charged.charged.

Evolution of Gauge Couplings (reciprocals) Evolution of Gauge Couplings (reciprocals)

Standard Model Supersymmetry

Meeting of the Running Couplings Meeting of the Running Couplings (reciprocals) in MSSM(reciprocals) in MSSM

What is String Theory?What is String Theory? It is the theory that elementary particles are really strings It is the theory that elementary particles are really strings

with tension, that obey relativity and quantum with tension, that obey relativity and quantum mechanics.mechanics.

By dispersing the particle away from a point, it avoids By dispersing the particle away from a point, it avoids infinities in the treatment of gravity or gravitons by infinities in the treatment of gravity or gravitons by pointlike particles.pointlike particles.

The string size is close to the Planck size of 10The string size is close to the Planck size of 10-32-32 cm, cm, which is the smallest size where gravity becomes strong.which is the smallest size where gravity becomes strong.

To avoid “anomaly” infinities requires supersymmetry To avoid “anomaly” infinities requires supersymmetry and 10 dimensions (1 time and 9 space dimensions).and 10 dimensions (1 time and 9 space dimensions).

String theory then provides a quantum theory of gravity.String theory then provides a quantum theory of gravity. Andre Neveu, John Schwarz, Michael Green and Pierre Andre Neveu, John Schwarz, Michael Green and Pierre

Ramond were founders.Ramond were founders.

Pictures of John Schwarz and Ed Pictures of John Schwarz and Ed WittenWitten

Types of Superstring TheoriesTypes of Superstring Theories There are five superstring theories.There are five superstring theories. There is one open superstring theory with left (L) There is one open superstring theory with left (L)

moving waves (SO(32)).moving waves (SO(32)). There are two closed superstring theories:There are two closed superstring theories:

Type IIA: L-R parity symmetricType IIA: L-R parity symmetric Type IIB: L only, parity violatingType IIB: L only, parity violating

There are two heterotic string theories of a There are two heterotic string theories of a product of a string theory in 26 dim (with L product of a string theory in 26 dim (with L moving waves) x a superstring in 10 dim (with R moving waves) x a superstring in 10 dim (with R moving waves).moving waves). (SO(32)) and (E8 x E8).(SO(32)) and (E8 x E8).

Unification of Superstring TheoriesUnification of Superstring Theories

Recently, in the second string revolution, it was Recently, in the second string revolution, it was discovered that there are transformations discovered that there are transformations between all five superstring theories. (Ed Witten)between all five superstring theories. (Ed Witten)

This means they are all views of a larger theory This means they are all views of a larger theory which is not well understood, but is called M which is not well understood, but is called M theory. It may be in 11 dimensions. theory. It may be in 11 dimensions.

For further information, see For further information, see http://http://superstringtheory.comsuperstringtheory.com//, run by Patricia , run by Patricia

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

Towards Verification of Towards Verification of Superstring TheorySuperstring Theory

Since superstring theory included the three Since superstring theory included the three unified forces of GUTS and gravity, it has been unified forces of GUTS and gravity, it has been called the Theory of Everything.called the Theory of Everything.

It has not been possible to “solve” superstring It has not been possible to “solve” superstring theory to find a unique physical model.theory to find a unique physical model.

There are a half-million ways to topologically There are a half-million ways to topologically “compactify” the extra six dimensions to very “compactify” the extra six dimensions to very short distances, and leave the four dimensional short distances, and leave the four dimensional world that we live in.world that we live in.

So many GUTS and breakup paths of GUTS to So many GUTS and breakup paths of GUTS to the SM are still possiblethe SM are still possible

Verification of Superstring TheoryVerification of Superstring Theory

The masses of sparticles are not well predicted.The masses of sparticles are not well predicted. If they are in the TeV range, they will appear in the LHC. If they are in the TeV range, they will appear in the LHC. Once they are found, the NLC e+ e- collider will more Once they are found, the NLC e+ e- collider will more

precisely determine their properties.precisely determine their properties. The convergence of the running coupling strengths at a The convergence of the running coupling strengths at a

GUT scale is more successful with SUSY particles than GUT scale is more successful with SUSY particles than in the SM.in the SM.

If SUSY is found, it will be considered a success of string If SUSY is found, it will be considered a success of string theory. If not found, it could spell its demise.theory. If not found, it could spell its demise.

The lightest neutral SUSY particle (LSP) could be dark The lightest neutral SUSY particle (LSP) could be dark matter, and there are experiments to directly detect matter, and there are experiments to directly detect them, but they will take a while to reach large enough them, but they will take a while to reach large enough scale.scale.

How do strings scatter?How do strings scatter?

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

Speculative Models of Extra Speculative Models of Extra DimensionsDimensions

Large Extra Dimensions and BranesLarge Extra Dimensions and Branes Early Unification with a Strong GravityEarly Unification with a Strong Gravity

Brane SolutionsBrane Solutions

String Theories have membrane solutionsString Theories have membrane solutions The most used is that all our 4 dimensional The most used is that all our 4 dimensional

world is a membrane in the 10 dimensional world is a membrane in the 10 dimensional world.world.

Open string ends are attached to the membrane. Open string ends are attached to the membrane.

Quarks, leptons and interacting bosons for Quarks, leptons and interacting bosons for strong and electroweak particles are confined to strong and electroweak particles are confined to the brane. the brane.

But gravitons as closed strings can leave the But gravitons as closed strings can leave the brane and spread out in the extra dimensions.brane and spread out in the extra dimensions.

Brane with attached stringBrane with attached stringand graviton in extra dimensionand graviton in extra dimension

Large Extra Dimension ModelsLarge Extra Dimension Models By experimental limits, extra dimensions could still be as By experimental limits, extra dimensions could still be as

large as 0.1 millimeter, and this will be tested by gravity, large as 0.1 millimeter, and this will be tested by gravity, which behaves as F which behaves as F ~ M~ M11 M M22/ r/ rn+2n+2 for n extra dimensions, for n extra dimensions, at r < R.at r < R.

In these, gravity could become strong at 1 TeV and unify In these, gravity could become strong at 1 TeV and unify with the other forces there. (Nima Arkani-Hamed, with the other forces there. (Nima Arkani-Hamed, Dimopoulos and Dvali)Dimopoulos and Dvali)

The extra dimension could be curled up with 1 TeV The extra dimension could be curled up with 1 TeV excitations, or at the String or Planck Scale.excitations, or at the String or Planck Scale.

The former would show up in experiment at Fermilab or The former would show up in experiment at Fermilab or the LHC as invisible missing energy disappearing into the LHC as invisible missing energy disappearing into the extra dimensions in excitations there, or as one the extra dimensions in excitations there, or as one micro black hole a second being produced.micro black hole a second being produced.

Plane Extra DimensionPlane Extra Dimension

The extra dimension could be between two flat branes, The extra dimension could be between two flat branes, one of which is physical, and one of which has gravity one of which is physical, and one of which has gravity (unphysical brane).(unphysical brane).

The gravity field exponentially decreases from the The gravity field exponentially decreases from the unphysical to the physical brane.unphysical to the physical brane.

Thus gravity appears weak to us on the physical brane, Thus gravity appears weak to us on the physical brane, but is strong on the unphysical brane.but is strong on the unphysical brane.

Called the Randall-Sundrum model.Called the Randall-Sundrum model. The extra dimension models so far do not give GUT The extra dimension models so far do not give GUT

theories, spoiling the supersymmetry triumph of theories, spoiling the supersymmetry triumph of explaining the convergence of coupling constants at the explaining the convergence of coupling constants at the GUT scale.GUT scale.

Relevance of Particle PhysicsRelevance of Particle Physics We are closer to accounting for some leftover matter, We are closer to accounting for some leftover matter,

possibly requiring three generations of quarks and leptons.possibly requiring three generations of quarks and leptons. We may someday account for inflation and dark matter We may someday account for inflation and dark matter

(SUSY?) and dark energy.(SUSY?) and dark energy. We understand how the Sun shines through weak We understand how the Sun shines through weak

interactions.interactions. We understand how color forces and quarks form We understand how color forces and quarks form

nucleons.nucleons. We may soon find how a Higgs gives mass to everything”.We may soon find how a Higgs gives mass to everything”. There may be Grand Unification to keep charges of There may be Grand Unification to keep charges of

everything the same and allow particle changing everything the same and allow particle changing interactions.interactions.

We may have found a way to have gravity that is consistent We may have found a way to have gravity that is consistent with quantum mechanics.with quantum mechanics.