Fermi National Accelerator Laboratory

Kaons at the Tevatron

Direct CP Violation in the Kaon System

Halton A. Peters

Harvard University

Cambridge, Massachusetts

Supervisor: Dr. Vivian OíDell, Computing Division

May 28, 1996 August 4, 1996


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.


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.


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.


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:

x -x y -y (space reversal)

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 60Co 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 60Co 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, ms=-) and all antineutrinos are right-handed (helicity of +1, ms=+). 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:

+ + + L

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

+ + + R

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

- - + L

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:

- - + R

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 K0 and its antiparticle K0.

K0 = down-antistrange ( ) K0 = antidown-strange ( )

Charge conjugation changes K0 into K0 and vise versa .

C K0 = K0 C K0 = K0

Space reversal has the following effect on K0:

P K0 = -K0 P K0 = -K0

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

CP K0 = -K0 CP K0 = -K0

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

K10 = 2-[K0 - K0]

K20 = 2-[K0 + K0]


CP K10 = K10 CP K20 = -K20

Therefore if CP is conserved, K1 can only decay into a CP = +1 state and K2 can only decay into a CP = -1 state. K0 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:

CP state = (-1)(-1) = +1

CP state = (-1)(-1)(-1) = -1

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

K1 K2

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

K1 K2

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.

K1 lifetime = 0.89*10-10 sec

K2 lifetime = 5.2*10-8 sec

For a K0 beam of composition:

K0 = 2-[K1 + K2]

most of the K1 will decay after a few centimeters, and several meters from the kaon source there should be a pure K2 beam. Therefore, near the source there should be predominately 2 events, but far from the source there should only be K2 decays.

A pure K2 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 K2 +- 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:

CP K10 = K10 CP K20 = -K20

defines K1 and K2 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 K1 and K2:

KS0 = K10 + K20

KL0 = K20 + K10

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 K2 into the K1 to form a physical linear combination called KS (S for short-lived). In the same manner, a very small part of K1 is mixed into the K2 to form another physical linear combination called KL (L for short-lived). KS and KL form separate components of the neutral kaon beam.

The K1 CP eigenstate is CP even, while the K2 CP eigenstate is CP odd. KS decays to the CP even states +- or 00 via its K1 component. KL decays to the CP odd states 0+- or 000 via its K2 component about 34% of the time. About .2% of the time KL decays to the CP even states +- or 00. Indirect CP violation is a result of the very small CP even K1 component of KL decaying into a CP even pion mode.

Direct CP Violation

For the neutral kaon system, direct CP violation occurs if the CP odd K2 component of KL decays into a CP even pion mode:

K2 (direct CP violation 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 K2 meson into two pions differs from the direct decay of the K1 meson into two pions such that the two decays can be distinguished. The K1 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 K2 meson. K2 is twice as likely to decay into the 00 state as it is into the +- state. In the absence of direct CP violation, KL will decay to two pions only via its small CP even K1 element. Therefore, the ratio of +- to 00 will be 2 to 1. If, however, there is some level of direct CP violation, KL will also decay to two pions via its CP odd K2 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 (no direct CP violation)

+-:00 2:1 (direct CP violation)


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 KS mesons have decayed before the beams reach the regenerator, so that two pure KL beams remain when they reach the regenerator. When a KL beam passes through dense matter, it may scatter incoherently into charged fragments, or coherently regenerate forward into a KL beam with a KS component. In the experiment, one of the two KL beams passes through a dense block of matter called the regenerator. Here, some portion of the KL mesons, indicated as , are transformed into KS mesons. Therefore, one of the kaon beams is described as pure KL, and the other is described as KL + KS.

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 Ks 00 decay yields a total of four photons and a KL 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.


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.


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 KL0. 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.


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.