10. FY06 Progress in Theoretical Physics
by Michael Peskin
Appendix B Self-Evaluation FY2006
Return to Table of
Contents
The research of the Theoretical Physics Group ranges
from the development of fundamental theories such as
M-theory, string theory, and higher dimensional theories
at very short distances to detailed calculations and
tests of theories directly relevant to high-energy
physics experiments at SLAC and elsewhere. This section
summarizes the current activities of the Theory Group
and a few of its important achievements in FY2006.
Physics at the International Linear Collider – The
Theory Group is intensively involved in all aspects of
physics related to the development of the
next-generation linear electron-positron collider (ILC).
Much of the work involves understanding how to use the
unique capabilities of the linear collider environment,
such as beam polarization, highly efficient heavy-quark
tagging, and the possibility of backward-scattered
photon beams, to test aspects of new physics at very
high energies that would otherwise be inaccessible. It
includes analyses of linear collider experiments on the
most familiar models of the next energy scale in
physics, including studies of the measurement of the
parameters of the spectrum of supersymmetric particles
of possible strong interactions coupling to the Higgs
sector and the top quark. It also includes exploration
of a wide variety of newly-proposed models, some of
which are discussed in later sections. Each phenomenon
has a specific experimental realization at the linear
collider, and we are making an effort to understand the
systematic picture of how these effects can be found and
distinguished.
Over the past year, we have made important progress
in two aspects of linear collider physics. First, we
have understood much more precisely than before how
measurements of the masses and cross sections of new
particles at the ILC will impact our understanding of
the particle physics origin of the dark matter that
makes up 80% of the mass in the universe. It has been
understood for some time that experiments at the ILC can
propose candidates for the origin of the dark matter.
The new studies make clear that the ILC can also measure
the properties of these particles sufficiently well to
provide microscopic predictions of the cosmic density of
these particles that can be directly compared to
astrophysical observations. The data from the ILC can
also be used to determine the cross sections of the dark
matter particles that are used in astrophysical
detection experiments. In this way, the combination of
ILC data with results from dark matter direct detection
experiments and from GLAST and other gamma ray
observatories can directly measure the distribution of
dark matter in the galaxy.
Second, we have understood with much greater clarity
how the measurements of cross sections and branching
fractions for new particles can resolve potential
ambiguities in the determination of the underlying
parameters of a model of new physics. These measurements
make essential use of the important capabilities of the
ILC for polarized beams and full-event reconstruction.
This analysis points to a capability for the ILC that
goes far beyond the discovery of new particles to the
clarification of physics at a very deep level.
Physics at Bottom Factories – The Theory Group is
intensively involved in all aspects of physics related
to the physics of B factories, and the BABAR
experimental programs in B physics and two-photon
collisions. Members of the group have devised new
methods for measuring the parameters of CP violation in
the Standard Model from analyzing detailed aspects of
specific rare B decay modes. We have also studied models
of CP violation beyond the Standard Model, and the
reactions involving ‘penguin’ diagrams that are expected
to probe for these effects most sensitively. In the past
year, we have been pleased to see methods developed in
our group for the characterization of B meson decays
using polarization of final-state vector bosons being
used to make high-precision measurements of the
fundamental CP-violating phases.
Development of Quantum Chromodynamics – Although
there is strong evidence that Quantum Chromodynamics (QCD)
is the fundamental theory of the strong interactions,
there is much room for improvement in the methods by
which QCD is applied to compute predictions for specific
processes. Members of the Theory Group have devised
improved computational methods for QCD both for
high-precision studies and for the extension of QCD
calculations to new regimes. These include the
development of ‘commensurate scale relations’ which aid
in removing scale and scheme ambiguities from QCD
calculations, and the development of renormalization
schemes that are analytic in the quark masses. In the
past year, these methods have been applied to define
gauge-invariant vertex functions for gluons and other
non-Abelian gauge bosons that seem to have powerful
applications both to QCD and to models of grand
unification. Members of the Theory Group have also been
pursuing insights into the strong-coupling region of QCD
from the gauge theory-gravity duality that has recently
been proposed in string theory. We have shown that
relatively simple hypotheses applied to five-dimension
theories of gravity lead to successful predictions for
the mass spectrum of mesons and baryons in the real
strong interactions. These theories also lead to
successful predictions for the form factors of mesons
and for the prediction of exclusive
large-momentum-transfer strong interaction processes.
Computational Perturbative Quantum Chromodynamics –
The most challenging aspect of improving methods
for QCD is that of devising methods for high-order
Feynman diagram calculations. Members of the Theory
Group have been devising methods to simplify the
computation of diagrams involving essentially massless
quarks and leptons participating in high-energy
collisions. In terms of technical difficulties of QCD
computations, the frontier now lies in the calculation
of two-loop or NNLO corrections, and in one-loop (NLO)
calculations with a large number of quarks and gluons in
the final state. These corrections are essential to
interpret the Tevatron and the eventual Large Hadron
Collider (LHC) data to the few-percent level, and to
understand the backgrounds to new physics signals at the
LHC. Over the past few years, members of the group have
taken a leading role in the community in developing
methods for the computation of QCD processes at NNLO.
More recently, the work of our group has mainly been
devoted to computing one-loop diagrams with many
final-state particles, making use of new computational
methods based on string theory in twistor space. In the
past year, members of our group have used these methods
to compute all one-loop QCD amplitudes contributing to
quark and gluon scattering processes involving up to 5
particles in the final state. These methods actually
compute infinite families of one-loop diagrams, so in
certain specific polarization states the answers are now
known for arbitrarily many final-state particles. These
methods seem to be extendable to reactions involving the
production of massive particles, including W, Z, and the
top quark. At the same time, these methods give new
insight into the computation of multiloop diagrams. In
the context of N=4 supersymmetric Yang-Mills theory, a
highly symmetric model that plays the role here of a
simplified model of QCD, members of our group have been
able to compute certain four-loop (NNNNLO) amplitudes.
The generalization of these calculations to QCD is now
being studied.
Superstring Theory and M-Theory – Members of the
Theory Group have been involved in studies of
superstring theory and its possible relevance to
elementary particle physics. Superstring theory may give
a context for the solution of the cosmological constant
problem, the question of why the observed cosmological
constant is tens of orders of magnitude smaller than
straightforward estimates in quantum field theory. Supersymmetry forces the cosmological constant to be
zero, but only if it is an exact symmetry of Nature, not
one that is spontaneously broken. It is a very important
question whether there is an intermediate solution in
which supersymmetry is broken but in such a way that the
theory still controls the magnitude of the cosmological
constant. A new direction of approach to this problem is
related to the fact that the observed universe seems to
contain a small positive cosmological constant. The
first solution of string theory with a positive
cosmological constant was constructed by members of our
group in 2003. Since then, we have been developing more
powerful methods for string model construction, and
these have revealed a wealth of new solutions to string
theory with positive cosmological constant. In the past
year, members of our group have made progress in this
program on several fronts. First, we have found new
geometrical methods that lead to new families of string
theory solutions. Second, we have been able to
demonstrate that certain solutions of string theory
which are known to be unstable resolve themselves into
new solutions with positive cosmological constant.
Third, we have understood better the possibility of
transitions between string solutions and computed rates
for the decay of one solution of a family into another.
This latter calculation has interesting similarities to
the analysis of black hole solutions in string theory.
Other studies in our group have clarified the
structure of black hole and other gravitational
solutions of string theory. Members of our group have
analyzed the effect of stringy corrections to the
equations of Einstein’s gravity in smoothing the
internal singular structure of black holes. These
corrections turn out to be important for precision
counting of black hole states and the microscopic
understanding of black hole entropy.
Models of New Particles associated with Electroweak
Symmetry Breaking – A central question in particle
physics for many years has been the nature of the Higgs
bosons or other particles that cause the spontaneous
breaking of electroweak symmetry. As we look forward now
to the start of physics at the LHC, it seems
particularly important to put all of the options for the
nature of the Higgs sector on the table. In the past
year, members of the Theory Group have opened several
new directions in this study. We have proposed models
with multiple Higgs bosons that, in different variants,
leads to theories in which Higgs bosons are especially
heavy and to theories in which Higgs bosons have new
types of associated partners. In the context of
supersymmetric models with grand unification, we have
proposed models in which the Higgs boson is composite.
In these models, the multiple possible bound states
provide the various levels of spontaneous symmetry
breaking that grand unification requires. We have
examined models in which the supersymmetric partners of
the Higgs bosons provide the cosmic dark matter, and we
have studied the implications of these models both for
dark matter searches and for the observation of new
particles at the LHC.
New Theoretical Methods – Other new theoretical
methods being developed by the Theory Group include:
applications of object-oriented programming techniques
to simulation problems in physics; new methods for
solving lattice Hamiltonian systems; light-cone Fock
state methods in non-perturbative QCD and non-perturbative
studies of QCD in light cone quantization.
Iterative renormalization-group-like methods for
diagonalizing the Hamiltonians of many-body systems have
been applied to 2-dimensional antiferromagnets. In the
past year, we have shown that these methods can produce
very accurate values of the ground state energy of these
systems in strong-coupling situations, and that these
methods can be used to analyze the complex phase
diagrams of these materials. |
SLAC National
Accelerator Laboratory, Menlo Park, CA