**ABSTRACT
**

Experiment E832, Kaons at the Tevatron (KTeV), is a new fixed target experiment at the Fermi National Accelerator Laboratory (Fermilab) which will begin to run in August 1996. This experiment will focus on the observation of direct CP violation in the neutral kaon meson. CPT symmetry is an exact symmetry in nearly all quantum field theories. The current experiment will determine if there is a direct CP violating component in the kaon system, or if CP violation occurs only indirectly through the mixing of kaon eigenstates. Direct CP violation is predicted by the Standard Model. The observation of direct CP violation would therefore have significant implications in particle physics.

The current experiment is an upgrade of a previous Fermilab experiment, E731, which obtained results which were consistent with no direct CP violation. E832 hopes to reduce the systematic and statistical errors of the previous by a factor of 10 through an improved detection mechanism and better understanding of sources of error.

This paper describes E832 including the goals,
apparatus, and relevant physics of the experiment.

**INTRODUCTION
**

Particle physics contends that every particle has a corresponding antiparticle with identical mass but opposite electric charge. Apparently however, the universe is composed almost exclusively of matter. Some asymmetry between matter and antimatter must necessarily account for the contradiction, but as of yet this asymmetry is not understood. A slight variance in the production of matter and antimatter at the time of the Big Bang could explain such a discrepancy. Therefore, understanding the exact nature of this asymmetry, if one exists, is imperative in the struggle to comprehend the nature of the universe.

This paper begins with an overview of the
physics relevant to the KTeV experiment. Included in this overview
is a discussion of the CPT Theorem and two of its parameters parity
and charge conjugation, and a discussion on CP symmetry. Also
included in this overview is discussion on the kaon meson, indirect
CP violation, and direct CP violation. Next is a description of
the design and method of the KTeV experiment.

**THE PHYSICS
**

**CPT Theorem
**

The CPT Theorem is one of the most basic precepts of particle physics. It deals with the three independent parameters C (charge conjugation), P (space reversal or parity), and T (time reversal). The CPT Theorem states that the combined operation of time reversal, charge conjugation, and space reversal in any order is an exact symmetry of any interaction and that under the three transformations all physical laws must be invariant. To elaborate, if each particle is replaced with its corresponding antiparticle, and the space coordinate and time are reversed, the physical laws are unchanged (Sachs).

The CPT Theorem is rigorously mathematical,
and its validity is based on the assumption that the physical
laws of the universe may be mathematically described. According
to the logic of the theorem, CPT may be invariant if each of the
independent parameters C, P, and T is invariant. If one of the
parameters is not conserved then there must also be some compensating
violation in one of the other parameters in order for the theorem
to be sound.

**Parity
**

Space reversal or parity invariance is the
symmetry of an object and its reflection in a mirror, or invariance
of the interchange left right (Frauenfelder and Henley). The
parity operation, P, changes the sign of any polar vector:

Until 1956 most physicist regarded the law
of parity invariance as self-evident. This followed from the belief
that none of the fundamental interactionsógravity, electromagnetism,
the strong interactions, and the weak interactionsódifferentiated
between mirror images. In 1956 Lee and Yang showed theoretically
that there could be parity nonconservation in the weak interaction.
They proposed an experiment which was later carried out by Wu
et al. In the experiment, radioactive^{ 60}Co was placed
in a magnetic field and the nuclei were aligned so that their
spins pointed in the direction of the field. Wu found that more
particles were emitted in the direction opposite to the field
than in the direction along the field (Sachs). Reflected in a
mirror, the ^{ 60}Co nuclei spin in the opposite direction,
so the field is also the opposite direction. However in the mirror,
the particles are preferentially emitted in the same direction,
and parity is therefore violated.

The CPT Theorem is sound both theoretically
and experimentally. Therefore, if the theorem is correct, a violation
in one of the parameters must be accompanied by a compensating
violation of another parameter.

**Charge Conjugation
**

Charge conjugation changes each particle
into its corresponding antiparticle of opposite electric charge.
Physicists also assumed that the motion of particles was invariant
under charge conjugation until evidence of parity violation was
shown. Evidence of charge conjugation nonconservation in the weak
interactions may be found in the neutrinos. All neutrinos are
left-handed (helicity of -1, m_{s}=-) and all antineutrinos
are right-handed (helicity of +1, m_{s}=+). Applying charge
conjugation to a left-handed neutrino yields a left-handed antineutrino,
which does not exist. Therefore, charge conjugation is violated
in the weak interactions.

**CP Symmetry
**

CP is the result of carrying out the charge
conjugation operation on the mirror image of an object. Physicists
observed that parity violation always seemed to be accompanied
by a compensating charge conjugation violation. A form of symmetry
is restored through the combination of the two operations of space
reversal and charge conjugation. Through CP, the laws of motions
were apparently unchanged. For the pion decay:

where the neutrino is always left-handed,
parity reversal leads to:

with a right-handed neutrino, which is not
found in nature. The operation of charge conjugation on the initial
reaction yields:

a pion decays into a left-handed antineutrino,
which is also not found in nature. By combing the operations of
space reversal and charge conjugation the initial reaction becomes:

with a right-handed antineutrino. Symmetry
is seemingly restored. The existence of this invariance is the
focus of Fermilab experiment E832, Kaons at the Tevatron. This
experiment will probe the possibility of the existence of direct
CP violation in the neutral kaon.

**Kaons and CP Conservation
**

The neutral K meson is a mixture of K^{0
}and its antiparticle K^{0}.

K^{0} = down-antistrange ( ) K^{0}
= antidown-strange ( )

Charge conjugation changes K^{0} into
K^{0 }and vise versa .

Space reversal has the following effect on
K^{0}:

Therefore, the combined effect of charge conjugation
and space reversal is the following:

If CP is conserved, then the eigenstates of
CP are the physical eigenstates:

hence

Therefore if CP is conserved, K_{1 }can
only decay into a CP = +1 state and K_{2 }can only decay
into a CP = -1 state. K^{0} usually decays into a two-pion
configuration with P = +1 and C = +1, or a three-pion configuration
with P = -1 and C = +1. A pion has a CP state = -1, hence:

Therefore, if CP is conserved the following
decays will occur:

But the following will not occur (if CP is
conserved):

**Indirect CP Violation
**

The energy released from a 2 decay is greater
than the energy released from a 3 decay, therefore the 2 decay
is much faster.

K_{2 }lifetime = 5.2*10^{-8}
sec

For a K^{0 }beam of composition:

most of the K_{1 }will decay after
a few centimeters, and several meters from the kaon source there
should be a pure K_{2} beam. Therefore, near the source
there should be predominately 2 events, but far from the source
there should only be K_{2 decays.}

A pure K_{2} beam is obtained at
some point which is a certain length from the kaon production
source. CP is violated if 2 events are observed after this point.
In 1964 Cronin and Fitch observed about one K_{2 }^{+-}
event for every 500 decays at the end of a 57 meter kaon beam.
These CP violating events had a branching ratio of 2*10^{-3}
and accounted for .2 percent of the total decays.

The equation:

defines K_{1} and K_{2} to
be eigenstates of CP. The Cronin and Fitch experiment showed that
the long-lived kaon cannot be an eigenstate of CP because CP is
violated. If CP is violated, the physical kaon eigenstates are
linear combinations of K_{1} and K_{2}:

where is a measure of the deviation from
perfect CP symmetry, somewhere at the 10^{-3} level.

CP invariance violation acts to spontaneously
mix a very small part of K_{2} into the K_{1}
to form a physical linear combination called K_{S} (S
for short-lived). In the same manner, a very small part of K_{1}
is mixed into the K_{2} to form another physical linear
combination called K_{L} (L for short-lived). K_{S}
and K_{L} form separate components of the neutral kaon
beam.

The K_{1} CP eigenstate is CP even,
while the K_{2} CP eigenstate is CP odd. K_{S}
decays to the CP even states ^{+-} or ^{00} via
its K_{1} component. K_{L} decays to the CP odd
states ^{0+-} or ^{000 }via its K_{2}
component about 34% of the time. About .2% of the time K_{L}
decays to the CP even states ^{+-} or ^{00}. Indirect
CP violation is a result of the very small CP even K_{1}
component of K_{L} decaying into a CP even pion mode.

**Direct CP Violation
**

For the neutral kaon system, direct CP violation
occurs if the CP odd K_{2} component of K_{L}
decays into a CP even pion mode:

The extent of direct CP violation is either zero (if direct CP violation does not exist) or some real number (if direct CP violation does exist). Experiment Na 31 at CERN found evidence of direct CP violation with a three sigma standard deviation from zero. Experiment E731 at Fermilab found an answer consistent with zero, which suggests that there is no evidence for the existence of direct CP violation.

The direct decay of the K_{2} meson
into two pions differs from the direct decay of the K_{1}
meson into two pions such that the two decays can be distinguished.
The K_{1} meson is twice as likely to decay into the ^{+-}
state as it is into the ^{00} state. As a result of isospin
arguments, this ratio is the opposite for the K_{2} meson.
K_{2 }is twice as likely to decay into the ^{00}
state as it is into the ^{+-} state. In the absence of
direct CP violation, K_{L} will decay to two pions only
via its small CP even K_{1} element. Therefore, the ratio
of ^{+-} to ^{00} will be 2 to 1. If, however,
there is some level of direct CP violation, K_{L} will
also decay to two pions via its CP odd K_{2} element,
which exhibits a 1 to 2 ratio of ^{+-} to ^{00}.
Therefore, if direct CP violation occurs, the 2 to 1 ratio will
be modified to an extent dependent upon the level of CP violation
(Adair).

^{+-}:^{00} 2:1 (direct
CP violation)

**THE EXPERIMENT
**

Figure 1 shows a plan view of the KTeV experiment.
Two neutral kaon beams enter the experimental hall from the Fermilab
Tevatron. The beams travel in a vacuum. Virtually all of the K_{S}
mesons have decayed before the beams reach the regenerator, so
that two pure K_{L} beams remain when they reach the regenerator.
When a K_{L} beam passes through dense matter, it may
scatter incoherently into charged fragments, or coherently regenerate
forward into a K_{L} beam with a K_{S} component.
In the experiment, one of the two K_{L} beams passes through
a dense block of matter called the regenerator. Here, some portion
of the K_{L} mesons, indicated as , are transformed into
K_{S} mesons. Therefore, one of the kaon beams is described
as pure K_{L}, and the other is described as K_{L }+
K_{S}.

At its most basic level the purpose of the
experimental apparatus is to detect the charged and neutral kaon
decay particles so that the ^{+-} and ^{00} ratios
may be ascertained. Charged particle detection is relatively straightforward.
The kaon beams pass through a large magnet which deflects the
charged decay particles dependent upon their charge and momentum.
Four drift chambers detect the trajectories of the particles as
they pass through the spectrometer. From this information the
momentum of charged particles, and hence the kaon, may be obtained.
The kaon decay position is found by extrapolating the charged
particle trajectories to a common point.

Neutral particle detection is more difficult than charged particle detection because the neutral decay particles are not effected by the magnetic field of the magnet. Neutral particle detection occurs in the CsI calorimeter. The calorimeter is composed of 3100 blocks of CsI crystals which are stacked according to Figure 2. The array contains 2232 small crystals (2.5 cm * 2.5 cm * 50 cm) and 868 large crystals (5.0 cm * 5.0 cm * 50 cm) stacked in a square surface. The small crystals are placed closer to the beam holes because they provide greater resolution than the larger crystals in the area of high decay density.

The neutral pions which result from kaon
decay undergo further decay. Each neutral pion decays to two photons,
such that a K_{s }^{00} decay yields a total
of four photons and a K_{L }^{000} decay yields
a total of six photons. In order to determine the kaon momentum,
the energies and positions of the photons and a which make up
the final kaon decay state must be determined. The determination
of energies and positions of these photons allow the accurate
determination of the kaon decay position.

**CONCLUSION
**

It is hoped that the Fermilab Kaons at the Tevatron experiment will improve measurements of direct CP violation by at least one order of magnitude. Because of systematic and statistical error, a measurement of zero would still leave open the possibility that CP violation exists at a level very close to zero. However, a measurement which is three standard deviations or more from zero will give the experimenters a high confidence level that direct CP violation has been observed. The possibility of observed direct CP violation could have broad implications with regard to the CPT Theorem and the universe.

As was previously stated, in order for the CPT Theorem to hold, a violation in one of the parameters must accompanied by a compensating violation of another parameter. If CP is violated, the time parameter must also be violated so that CPT may be conserved. Theorists have found very strong proofs of the validity of the CPT Theorem, and experimentalists have also discovered a wealth of information which supports the theorem. Therefore, if the direct CP violation is observed the time reversal nonconservation is implied.

Physicist believe that time reversal is independently symmetric. One problem is that all particles are eigenstates of parity, and some are eigenstates of charge conjugation, but no particles are eigenstates of time reversal. Therefore, experiments which independently test the symmetry of time reversal are difficult because they are susceptible to errors and because any asymmetry would be very small.

The discovery of direct CP asymmetry would
provide physicists with greater insight of the nature of the universe.
If the symmetry between matter and antimatter were perfect, the
universe would be composed equally of matter and antimatter, which
would interact and annihilate each other, releasing energy. Observation
reveals that the universe is composed almost exclusively of matter,
with a very small antimatter composition. CP violation could explain
this asymmetry in the universe and give scientists greater insight
into the nature of the universe.

**REFERENCES
**

Adair, Robert K. *Scientific American*.
"A Flaw in the Universal Mirror."

Frauenfelder, Hans and Ernest M. Henley. *Subatomic
Particles*. Englewood Cliffs, New Jersey: 1974. Prentice-Hall,
Inc.

Gibbons, Lawrence K.* A Precise Measurement
of the CP-Violation Parameter Re('/) and Other Kaon Decay Parameters*.
August 1993.

Greenhalgh, John Field. *A Study of Photons
from decays of the K _{L}^{0}*. January 1981.

Karlsson, Magnus. *CPT Symmetry of Neutral
Kaons: An Experimental Test*. August 1990.

Sachs, Robert G. *Science*. "Time
Reversal." Vol. 176. 12 May 1972.

**ACKNOWLEDGMENTS
**

I would like to thank Mrs. Dianne Engram and Dr. Jim Davenport for providing me with the opportunity to participate in the Summer Internships in Science and Technology program at the Fermi National Accelerator Laboratory. The time that I have spent at Fermilab has been educational, exciting, and fun. I would like to thank my supervisor Dr. Vivian OíDell for all of her support and assistance. I would also like to thank my ìsurrogate supervisorî Dr. Juliana Whitmore for her knowledge and advice, and for guiding me all summer long.