A new calculation, reported in the January 25, 2008 issue of
Physical Review Letters, confirms the six-quark theory of
particle-anti-particle asymmetry. This is the first complete
calculation of this phenomenon to employ a highly accurate description
of the quarks that adds a fifth dimension beyond those of space and
This result allows recent experiments studying the decays of
bottom quarks to be compared with earlier, strange quark experiments.
This comparison agrees with the predictions of the Standard Model of
particle physics and implies that the particle-anti-particle
asymmetries (technically known as "CP-symmetry violation") seen in
these two different decay processes have a common origin.
This research was carried by physicists from the U.S.
Department of Energy's Brookhaven National Laboratory (BNL),
Columbia University, the University of Connecticut, Edinburgh
University, University of Southampton, and the RIKEN BNL Research
Center (RBRC) using powerful, massively parallel supercomputers
specially constructed to perform these calculations and capable of tens
of trillions of arithmetic operations per second. The work was funded
by the Particle Physics and Astronomy Research Council in the UK (now
the Science & Technology Facilities Council), the RIKEN
Laboratory in Japan, and the Office of High Energy Physics within the
U.S. Department of Energy's Office of Science.
Earth, our solar system, our galaxy - and likely the entire
visible universe - are made of matter, not anti-matter. While it is
easy to create anti-matter in the particle collisions that take place
in large particle accelerators, the anti-particles produced there
immediately annihilate with matching particles in the surrounding
normal material, disappearing into a burst of light and other particles
whose energy quickly dissipates.
Could we distinguish a mirror universe made of anti-matter
instead of matter, in which research workers made of anti-matter could
create fleeting examples of matter in their anti-matter accelerators?
If there were a perfect symmetry between our "matter" universe and one
composed of anti-matter, what determines which type of universe we
In a Nobel Prize-winning experiment performed in 1964 at
Brookhaven Lab, small differences were discovered between the laws
obeyed by particles and anti-particles. These clearly distinguish a
matter universe from an anti-matter universe.
Accommodating such a matter-anti-matter asymmetry into a
fundamental theory is not easy. A theory made from only two pairs of
fundamental quarks, the so-called up-down pair and the charmed-strange
pair cannot easily allow such matter-anti-matter differences. Only when
a third pair of quarks, the top-bottom pair, are included does the
theory support this particle anti-particle asymmetry. This connection
between the number of types of quarks and matter-anti-matter asymmetry
was discovered by Kobayashi and Maskawa, who made a compelling case for
the existence of the then-undiscovered top quark on this basis. The
resulting theory, with the now-known three quark pairs, offers a very
beautiful explanation for matter-anti-matter asymmetry. Is it correct?
Since the six-quark theory supports only a single type of
matter-anti-matter asymmetry, every signature for such an asymmetry
must be connected to every other. Thus, the asymmetry seen in the
decays of mesons containing bottom quarks can be related to the
matter-anti-matter asymmetry seen in the decay of mesons containing
strange quarks. However, to accurately link the recent bottom quark
experiments carried out at the B-Factories at SLAC (Stanford, CA) and
at KEK (Japan) with the 1964 Brookhaven experiment, one must have a
quantitative understanding of the quarks that appear in tightly bound
combinations that make up the particles being studied.
Fortunately, the calculation of such decays is now possible
using very powerful supercomputers and a computational treatment of the
quarks known as lattice QCD. (QCD stands for quantum chromodynamics,
the theory of the strong interaction between quarks and gluons -
indirectly seen particles that act to hold the quarks together. The
term lattice refers to the grid of points in space-time used as a
framework for the numerical calculation.)
The actual phenomenon calculated is a surprising oscillation
between a K meson (made up of a strange quark and an anti-down quark)
and its anti-particle, which occurs roughly 5 billion times per second.
Unfortunately, the aspect of this oscillation that distinguishes
particles and anti-particles is very subtle and would not be present at
all if the mass of the down quark, which is already very small, were
zero. Since there are many other, much larger possible sources of such
oscillations, a very delicate calculation is required which treats the
light down quark accurately and can distinguish between the correct and
the incorrect oscillation mechanisms.
A formulation sufficiently accurate to perform this
calculation correctly was invented in the early 1990s. In this approach
normal spin-1/2 particles, such as electrons and quarks, are allowed to
move in four, not three, spatial dimensions so that space-time acquires
a fifth spatial dimension. In contrast to the standard space-time
dimensions, which are presumed to extend to infinity, this fifth
dimension is bounded, ending in two four-dimensional boundaries,
similar to the two-dimensional top and bottom of a three dimensional
cardboard box. When spin-1/2 particles travel into this fifth
dimension, they behave as very massive particles - so heavy that they
would not have been seen in experiments to date. However, when they
move along the two boundaries, these particles appear physical. The
particles on one boundary spin in a right-handed sense and those on the
other carry a left-handed spin. The spin-1/2 particles realized using
this new approach are called domain wall fermions, and this method
provides just the accurate description of the quarks that is needed for
the oscillation calculation described above to be reliably carried out.
The calculation reported here builds upon earlier, pioneering,
lattice QCD studies of this phenomenon carried out over the past 20
years in Europe, Japan, the U.S. and the UK. However, it is only with
this five-dimensional domain wall fermion method, made practical by the
current massively parallel supercomputers, that it has become possible
to accurately incorporate the subtleties implied by the very small
quark masses and to reach a level of accuracy comparable to the current
The result suggests that the six-quark theory correctly
describes the matter-anti-matter asymmetry seen in the decays of both
the bottom and strange mesons. If the strange and bottom experiments
are combined with the less demanding theory for the bottom meson
system, the oscillation amplitude for the strange mesons (a quantity
call BK) can be determined to be 0.78 with an error of 0.09. The result
of this new calculation gives an entirely consistent value of 0.72 for
this same quantity with an error of 0.04.
Of course, there are still many important questions that need
to be answered. Calculations of even greater numerical accuracy can
reduce the errors and permit an even more challenging comparison
between theory and experiment. Of great interest is the possibility
that this difference between matter and anti-matter explains why we are
made of matter instead of anti-matter. Perhaps as our universe cooled
after the Big Bang, this difference between particles and
anti-particles pushed the cooling universe in the "matter direction,"
causing us to ultimately be made of matter not anti-matter?
Unfortunately, even though