Physics Beyond the Standard Model Summary by Dennis Silverman Physics and Astronomy UC Irvine

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.

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. It would have shown up at the Fermilab Tevatron, except that the intensity has not met expectations.

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 1 = e2/c increases with energy from 1/137 to 1/40 at 1017 GeV Unification Scale Strong coupling 3 = g2/c decreases from ~1 to 1/40 Weak coupling to W’s is 2. So couplings come together at unification scale

Running Gluonic Coupling 3 = (g3)2 /c

Running Couplings

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+ Recently, neutrino oscillations and mass were found, adding the anti-e. In the GUT, there are vector bosons that take fundamental particles into another in the multiplet.

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 , 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

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.

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 allow protons in quarks to decay into a lighter pi or K meson and a lepton. Don’t 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.

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

Particle Spin Orbital angular momentum is quantized to integer units of Planck’s constant over 2:  = h/2. Quarks and leptons have half a unit of angular momentum as spin, or are spin 1/2 particles, also called fermions. Photons and W’s and Z are spin 1 particles, also called bosons. Gravitons have spin 2, and are bosons.

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. 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.

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.

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.

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.

Evolution of Gauge Couplings (reciprocals) Standard Model Supersymmetry

Meeting of the Running Couplings (reciprocals) in MSSM

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.

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

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.