Introduction to Supersymmetry
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Introduction to Supersymmetry
20th century physics has seen two major paradigm shifts in the way we
understand Mother Nature. One is quantum mechanics, and the other is
relativity. The marriage between the two, called quantum field theory,
conceived an enfant terrible, namely anti-matter. As a result, the number of
elementary particles doubled. We believe that 21st century physics is aimed
at yet another level of marriage, this time between quantum mechanics and
general relativity, Einstein's theory of gravity. The couple has not been
getting along very well, resulting in mathematical inconsistencies,
meaningless infinities, and negative probabilities. The key to success may
be in supersymmetry, which doubles the number of particles once more.
Why was anti-matter needed? One reason was to solve a crisis in the 19th
century physics of classical electromagnetism. An electron is, to the best
of our knowledge, a point particle. Namely, it has no size, yet an electric
charge. A charged particle inevitably produces an electric potential around
it, and it also feels the potential created by itself. This leads to an
infinite "self-energy" of the electron. In other words, it takes substantial
energy to "pack" all the charge of an electron into small size.
On the other hand, Einstein's famous equation says that mass of a particle
determines the energy of the particle at rest. For an electron, its rest
energy is known to be 0.511 MeV. For this given amount of energy, it cannot
afford to "pack" itself into a size smaller than the size of a nucleus.
Classical theory of electromagnetism is not a consistent theory below this
distance. However, it is known that the electron is at least ten thousand
times smaller than that.
What saved the crisis was the existence of anti-matter, positron. In quantum
mechanics, it is possible to "borrow" energy within the time interval
allowed by the uncertainty principle. Once there exists anti-matter, which
can annihilate matter or be created with matter, what we consider to be an
empty vacuum undergoes a fluctuation to produce a pair of electron and
positron together with photon, annihilating back to vacuum within the time
interval allowed by the uncertainty principle (a). In addition to the effect
of the electric potential on itself (b), the electron can annihilate with a
positron in the fluctuation, leaving the electon originally in the
fluctuation to materialize as a real electron (c). It turns out, these two
contributions to the energy of the electron almost nearly cancel with each
other. The small size of the electron was made consistent with
electromagnetism thanks to quantum mechanics and the existence of
anti-matter.
Currently the Standard Model of particle physics is facing a similar crisis.
We know that our Universe is filled with a mysterious condensate of Higgs
boson, which disturbs matter particles and forces, not letting them go far
and hence making them massive. For example, the carrier of the weak force, W
boson, bumps on the Higgs condensate all the time, and the force has become
short-ranged, extending only over a thoughsandth of the size of nuclei. All
masses of known elementary particles must have come from the Higgs boson.
However, the mass of the Higgs boson receives a large contribution from its
interaction with itself making it impossible for us to study physics at
smaller distances. Because the gravity is believed to be unified with other
forces at an extremely small distance called Planck length , the marriage
between quantum mechanics and gravity appears a remote dream.
Supersymmetry is an idea that history repeats itself to solve similar
problems. For every particle, there is a superpartner whose spin differs by
1/2. By doubling the number of particles again, there is similar
cancellation between the process with ordinary particles only and another
process with their superpartners. Then the Standard Model can describe
physics down to the Planck length, making the marriage a realistic hope. In
fact, it is a necessary ingredient in the only available candidate for
quantum theory of gravity, string theory.
Supersymmetry actually makes the unification of three other forces, strong,
weak, and electromagnetic, also a reality. In (a), in the Standard Model
without supersymmetry, the strengths of three forces change as a function of
energies, and become closer to each other at very high energies. Together
with supersymmetry (Minimal Supersymmetric Standard Model or MSSM), however,
they become equal within a percent-level accuracy.
Where are superpartners? It is a realistic hope that coming accelerator
experiments will find them, possibly Tevatron collider at Fermilab,
Illinois, or the Large Hadron Collider at CERN, Geneva, Switzerland in this
decade.
It is amusing that superpartners may actually be everywhere without us
noticing. Our galaxy is known to be full of Dark Matter, weakly interacting
particles whose gravitational pull binds the galaxy together despite its
fast rotation. The picture (a) shows the measurement of Doppler shift in
21cm line that allows us to determine the rotational speed of other
galaxies. The rotational speed is much faster than what the gravitional pull
by stars would allow (b). One of the best candidates for Dark Matter is the
lightest supersymmetric particle.
Even though supersymmetry solves many problems in particle physics, it also
poses new problems.
a.. What makes superpartners heavier than ordinary particles? This is the
problem of supersymmetry breaking.
b.. Why are superpartners so well hidden in rare phenomena? Arbitrary mass
spectrum of superpartners actually would cause too large effects in rare
processes that change flavor of particles. There must be some special reason
why such effects are well hidden.
c.. How do we discover superpartners experimentally? How do we extract
information on the mechanism of supersymmetry breaking?
d.. How does supersymmetry impact cosmology? Is the lightest
supersymmetric partner the Dark Matter? How do we prove it?
We are working on these problems.
Our group had made substantial contributions to the theoretical study of
supersymmetry. It was Bruno Zumino, together with Julius Wess, who
discovered the possibility of supersymmetry in four-dimensional spacetime
back in 1973. Until early 1980's, however, it was more of a mathematical
curiosity than a serious possibility for the realistic theory of nature.
Lawrence Hall, together with Joe Lykken and Steven Weinberg, laid the
foundation of relatistic supersymmetric phenomenology. Mary K Gaillard made
it possible to systematically study quantum effects in supersymmetric theory
of gravity, supergravity. Hitoshi Murayama, together with Gian Giudice and
two former Berkeley postdocs, Markus Luty and Riccardo Rattazzi, found
subtle quantum contributions to masses of superpartners, independently with
two other former Berkeley postdocs, Lisa Randall and Raman Sundrum.
This home page is based on the introduction in Supersymmetry Phenomenology
by Hitoshi Murayama.
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