The articles range from the forefront of formal theory treating the physics of extra dimensions to details of particle detectors. Although special emphasis is placed on the physics of kaons, charmed and beauty particles, top quarks, and neutrinos, the articles also dealing with electroweak physics, quantum chromodynamics, supersymmetry, and dynamical electroweak symmetry breaking. Violations of fundamental symmetries such as time reversal invariance are discussed in the context of neutral kaons, beauty particles, electric dipole moments, and parity violation in atoms.
The constraints are plotted on the r , h plane in Fig. The allowed region is larger than that favored by many other analyses . The following ratio of ratios then can differ from unity:. In a standard convention , tree amplitudes contain no weak phases, since they involve the CKM elements V ud and V us.
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The top quark in the loop gives rise to a weak phase through the CKM element V td. Others see articles in  permit slightly higher values. The error in the average includes a scale factor  of 1. Additional uncertainties are associated with m c  and V cb.
CP Violation: Past, Present, and Future
More data are expected from the final analysis of this experiment, as well as from a future version with improved sensitivity. The direct contribution probes the parameter h. A CP- or T-violating angular asymmetry in this process has recently been reported [47, 48]. One also looks forward to a rich set of effects in decays of particles containing b quarks, particularly B mesons. We now describe the experiments and the effects they are expected to see.
By July , these detectors had accumulated about 14 and 6 fb - 1 of data at the energy of the U 4 S resonance, which decays almost exclusively to B [52, 53]. Thus, instead of mass eigenstates like K L , two main types of B decays are of interest: decays to CP eigenstates, and "self-tagging" decays. Both have their advantages and disadvantages. In this case one measures sin2 b with negligible corrections. In decays to CP eigenstates, one must determine the flavor of the decaying B at time of production.
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The weak phase changes sign under CP-conjugation, while the strong phase does not. The rate asymmetry is then. The two amplitudes must have different weak and strong phases in order for a rate asymmetry to be observable. The CKM theory predicts the weak phases, but no reliable estimates of strong phases exist.
We shall note some ways to avoid this problem. The interference between direct and mixing terms in B decays to CP eigenstates modulates the exponential decay see, e. D m is the mass splitting, and l 0 expresses the interference of decay and mixing amplitudes.
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The time integral of the modulation term is. This asymmetry arises from the phase 2 b characterizing the two powers of V td in the B 0 - 0 mixing amplitude. The tagging methods are of two main types. In "opposite-side" methods, since strong interactions produce b and in pairs, one learns the initial flavor of a decaying B from the "other" b -containing hadron produced in association with it. Electron-positron collisions provide B mesons in pairs at the c.
It then becomes necessary to distinguish the vertices of the decaying and tagging B 's from one another when studying CP eigenstates. In symmetric collisions the U 4 S is produced at rest and the proper path length of a decaying B is only about 30 m m. BaBar also used two neural net methods. The samples reported by the summer of [52, 53] are shown in Table III. There is no contradiction yet! New results are due to be presented in February of The tree amplitude [ Fig. The penguin amplitude [ Fig. The relative weak phase between the tree and penguin amplitudes thus is non-zero, and direct CP violation can arise if the relative strong phase d T - d P also is non-zero.
One proposal see the first of Refs. However, they can be calculated , so that measurements of the rates for these processes can yield useful information on g. A necessary condition for the observability of direct CP asymmetries based on the interference of two amplitudes, one weaker than the other, is that one must be able to detect processes at the level of the absolute square of the weaker amplitude . Then the rate asymmetry in Eq. Then 2.
The statistical error in is based on the total number of events. Then the significance of the asymmetry in number of standard deviations is. Thus aside from the factor of 2 one must be able to see the square of the weaker amplitude at a significant level in order to see a significant asymmetry due to A 1 - A 2 interference. In searching for direct CP asymmetries one thus considers B decays with at least two amplitudes having an expected weak phase difference, with a large enough rate that the smaller amplitude alone would be detectable, and with a good chance for a strong phase difference.
Many branching ratios for charmless B decays are one to several parts in 10 5. Thus when sensitivities to branching ratios of a few parts in 10 7 are reached, searches for direct CP asymmetries will take on great significance. A fit to these and other processes in the second of Refs. Each of these channels has particular advantages. The proposal of Ref. The sum of R and R s allows one to determine r. Using R , r , and A 0 , one can solve for both d and g.
Recent upper limits on CP-violating asymmetries in B decays to light-quark systems , defined as. The dominant decay modes of the neutral charmed mesons D 0 and are to states of negative and positive strangeness, respectively, and not to CP eigenstates. Thus D 0 - mixing induced by shared final states is expected to be small. Short-distance contributions to mixing also are expected to be small. If any rate difference is expected, it would be in the direction favoring a slightly greater rate for the CP-even mass eigenstate.
CP violation in the charm sector is expected to be small in the Standard Model.
It is also easy to look for, since D mesons are easier to produce than B mesons and the Standard Model background is low. No evidence for mixing is found by the Fermilab E Collaboration . No CP-violating asymmetries have been seen in charmed meson decays at the level of several percent [80, 82].
The cqq states are providing unique insights into baryon spectroscopy [83, 84, 85], while the c states [86, 87], are important sources of information about the corresponding b states, useful for "same-side" tagging of neutral B mesons. Future CP studies involve a broad program of experiments with kaons, charmed and B mesons, and neutrinos. Charmed mesons: While great strides have been taken in the measurement of mass and lifetime differences for CP eigenstates of the neutral charmed mesons D 0 , [78, 79], it would be worth while to follow up present hints of nonzero effects.
Both electron-positron colliders and hadronic experiments devoted to future B studies may also have more to say about mixing, lifetime differences, and CP violation for charmed mesons. It will be able to probe charmless B decays down to branching ratios of 10 - 6.enter
Flavor Physics for the Millennium Tasi 2000
Other final states of great interest at this level include VP and VV , where P , V denote light pseudoscalar and vector mesons. This decay is expected to have a branching ratio of only a few parts in 10 8 if rescattering is unimportant, but could be enhanced by more than an order of magnitude in the presence of rescattering from other channels. The moving center-of-mass facilitates both flavor tagging and improvement of signal with respect to background.
Hadronic reactions at high energies will produce copious b 's incorporated into nonstrange, strange, and charmed mesons, and baryons.
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A measurement of the strange- B mixing parameter D m s is likely to be made soon. The width difference expected between the CP-even and CP-odd eigenstates of the B s system [54, 55] should be visible in the next round of experiments. Neutrino studies: The magnitudes and phases in the CKM matrix are connected with the quark masses themselves, whose pattern we will not understand until we have mapped out a similar pattern for the leptons.
Our knowledge of the Cabibbo-Kobayashi-Maskawa is likely to improve over the next few years [95, 96]. The narrow range of r , h increases the chance that any non-standard physics will show up as a contradiction among various measurements, most likely by providing additional contributions to B 0 - 0 mixing  but possibly directly affecting decays . The number of baryons in the Universe is much larger than the corresponding number of antibaryons. Sakharov proposed  three requirements for this preponderance of matter over antimatter: 1 an epoch in which the Universe was not in thermal equilibrium, 2 an interaction violating baryon number, and 3 CP and C violation.
The observed baryon asymmetry is not explained directly by the CP violation in the CKM matrix; the effects are too small, requiring some new physics. Two examples are the following:. Neutrino masses at the sub-eV level can signal large right-handed neutrino Majorana masses, exceeding 10 11 GeV . Lepton number L , violated by such masses, can be reprocessed into baryon number B by B - L conserving interactions at the electroweak scale . New CP-violating interactions must exist at the high mass scale if lepton number is to be generated there. These interactions could be related to CKM phases .
If this alternative is correct, it will be important to understand the leptonic analogue of the CKM matrix! Progress in "tagging" neutral B 's and rich information from measurements of many B decay rates will round out the picture. If B decays do not provide a consistent set of CKM phases in the next few years, we will re-examine other proposed sources of CP violation.
Most of these, in contrast to the CKM theory, predict neutron and electron dipole moments very close to their present experimental upper limits. If, however, the CKM picture remains self-consistent, we should ask about the origin of the CKM phases and the associated quark and lepton masses.