CP Violation and Anti-matter

Contents

Matter Antimatter Asymmetry
Kaon Decay
Standard Model and CP Violation
B Meson Decay
Leptogenesis

Matter Antimatter Asymmetry

There are strong evidences that the universe is made of matter with very few antimatter. It is believed that particles and antiparticles were equally numerous in the early universe, but the former came to dominate as the universe cooled. It is observed that only a small asymmetry is required in the early universe, as today we have only one leftover proton for 109 photons (assuming the photons were created by the annihilation of particles and antiparticles).

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Kaon Decay

CP Operation Elementary Particles As shown in Figure 01, charge conjugation (C) reverses the sign of quantum numbers such as electric charge, changing a particle to its antiparticle. Parity (P) reverses the arrow on all vectors associated with the object. The laws of classical mechanics and electromagnetism are invariant under either of these operations, as is the strong interaction of the Standard Model. These symmetries,

Figure 01 CP Violation
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Figure 02 Elementary Part-icles [view large image]

 however, are broken in the weak interaction. For many years, it appeared that the combined operation (CP) were invariant even for weak interactions until it was shown to be otherwise in 1964.
The neutral K meson Ko (a particle that contains a strange quark and a light quark as shown in Figure 02) manifests itself in two modes with respect to the weak interaction. In Figure 03 one mode is labelled Kshort with shorter half-life, a CP state of +1 and decays into two charged pions (also with CP=+1); the other is Klong with longer half-life, a CP state of -1 and
K Meson Decay decay into three neutral pions (also with CP=-1). The 1964 experiment by Cronin and Fitch looked for the decay products of Klong. They observed a few decays of the Klong turning into pairs of oppositely charged pions: about 1 out of a total of 500 decays. This kind of decay arrives at a final CP state that is different from the initial CP state and proves that CP symmetry was not preserved exactly by the weak interaction.

Figure 03 Ko Meson Decays
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Standard Model and CP Violation

According to the Standard Model, CP violation occurs in the weak interaction, more specifically when quarks undergo weak interactions and turn into quarks with different electric charge. All of the possible transitions of this type can be represented by a matrix of numbers, known as the CKM matrix (there are only four independent parameters in the matrix).

The weak interaction is the only one in which a quark can change into another type (flavor) of quark or a lepton into another type of lepton. In this transformation, a quark is allowed only to change charge by a unit amount e (the charge of the electron). Because quarks and leptons can change flavor by weak interactions, only the lightest quarks and leptons are included in the stable matter of the world around us - all heavier ones decay to one or another of the lighter ones. If we look at all the ways in which one quark can turn into another quark with a charge change of e, that's just all quarks with charge +2/3e (u, c, or t) paired with quarks with charge -1/3e (d, s, or b). That's nine possible pairings. Each of these pairings has its own weak charge associated with it, which is related to a physical constant which we call a "coupling constant" which contains real and imaginary parts - it is a complex number. The set of coupling constants can be represented by the 3x3 CKM matrix (Figure 04):
CKM Matrix In contrast with electric charge, which seems to come in a well-defined universal unit, each of these nine coupling constants is different. The triumph of the Standard Model is that it predicts a set of relationships between the nine elements of the CKM matrix and it predicts that they include properties that result in CP violation. The CP violation is related to the fact that the matrix elements include imaginary numbers. If we look at enough decays that involve the different matrix elements, we can see whether the relationships are true (there are only four independent parameters in the matrix).

Figure 04 CKM Matrix
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The CKM matrix has a property known as unitarity due to the physical properties it represents. Mathematically, this defines a set of equations that the matrix elements must satisfy. One of such equations is:

VudVub*/VcdVcb* + 1 + VtdVtb*/VcdVcb* = 0

Complex numbers can be represented as points on a two-dimensional plane, or equivalently as vectors in a plane. Each term in the above equation is complex and can be drawn as a vector in the plane. Arranging the three vectors head-to-tail gives the sum. Since the sum is zero, the three vectors should form a closed polygon, that is, a triangle. Since one leg of the triangle is just 1.0, it lies on the x-axis and has a length of 1. The triangle is then defined by a single point on the plane at the apex. This is known as a unitarity triangle as shown in Figure 05. Currently, physicists are measuring the angle = arg(VtdVtb*/VcdVcb*), i.e., the polar angle of the complex number VtdVtb*/VcdVcb*, to determine the degree of CP-violation in Bo decay. The different modes of decay are also indicated in the diagram; D is the D meson containing a charm quark and a light quark.

Unitarity Triangle

Figure 05 Unitarity Triangle

We need to know all of the elements in the matrix, both their real and imaginary parts, to test the relationships predicted by the Standard Model. To measure the imaginary parts, we need to measure CP violation in many meson decays. For K meson decays the elements we can look at are mostly in the second column of the matrix. With B meson (a particle that contains a heavy bottom quark and a light quark) decays we can look in the third row and the third column. With the combination of both, we cover nearly all of the matrix and should be able to check all of the matrix relationships. Some decays are predicted to display CP violation, others are not. The fact that these coupling constants have to be determined by experimental measurements is considered to be a shortcoming of the Standard Model. A more fundamental theory is needed to explain the origin of these constants.

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B Meson Decay

Modern CP-violation experiments are designed to study decays of B mesons into those final states that have a definite CP number. These heavier particles can spontaneously decay into matter and antimatter fragments in a greater number of ways than lighter particles, increasing the odds of finding something unexpected. The experimental challenge comes from the fact that B meson decays to CP eigenstates such as have very small branching ratios and in general low efficiencies for complete reconstruction of the final state. It is therefore necessary to produce a very large sample of B mesons to perform a CP measurement. At the High Energy Accelerator Research Organization (KEK) in Japan and the Stanford Linear Accelerator Center (SLAC) in California, accelerators have been designed to produce a plentiful supply of B mesons, through specially tuned electron - positron collisions. At each facility is a detector (Belle in Japan, and BaBar in California) to pick up and study
B Meson the decays of the many millions of B mesons created - hence these facilities are known as "B factories". Figure 06 shows the BaBar detector and the particle tracks from the B meson decay. The latest measurements yield a value of sine(2) = 0.78 0.08, which is exactly that needed to explain the magnitude of CP violation seen in the Cronin-Fitch experiment. However, these measurements also predict a value of one leftover proton to 1018 photons (resulting from the annihilation of particles and antiparticles). It is in disagreement with observation by many orders of magnitude.

Figure 06 B Meson Decay
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Leptogenesis

Leptogenesis The disagreement with observation is now supported by three years of B meson decay data. It seems that the Standard model alone is not able to explain the phenomenon of matter-antimatter asymmetry. A new theory called leptogenesis (Figure 07) suggests that an exceptionally heavy but unstable breed of neutrino existed in the very early universe. These heavy neutrinos decayed to the second generation of neutrinos and anti-neutrinos with a bias toward the neutrinos. They then changed their masses, becoming protons/neutrons and antiprotons/antineutrons, and leading to the imbalance between matter and antimatter at the dawn of time.

Figure 07 Leptogenesis
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NDB An experiment to look for neutrinoless double-beta decay (NDB, see Figure 08) is running since 1990 at the Gran Sasso laboratory near Rome. The claim for discovery is still in dispute. But the findings could confirm the neutrinos' changing behaviour (flip-floping between antineutrino and neutrino as shown in the lower diagram of Figure 08), and the existence of an extremely heavy form of neutrino at high temperatures (such as in the aftermath of the big bang).

Figure 08 NDB Decay
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