Leptons

Tracing the historical development of quantum physics, the author describes the baffling and seemingly lawless world of leptons, hadrons, gluons and quarks and provides a lucid and exciting guide for the layman to the world of infinitesimal particles. 

Properties of Particles. From the research of the early part of the twentieth century, the existence of several types of particles was firmly estabhshed, and the properties were deterrnined. The particles that are involved in the decay of radioisotopes are given in Table 4. An additional type of conservation is that in all atomic and nuclear decays, the number of nucleons, ie, protons and neutrons, is conserved and the number of leptons, ie, electrons and neutrinos, is also conserved. 

There are four modes of radioactive decay that are common and that are exhibited by the decay of naturally occurring radionucHdes. These four are a-decay, j3 -decay, electron capture and j3 -decay, and isomeric or y-decay. In the first three of these, the atom is changed from one chemical element to another in the fourth, the atom is unchanged. In addition, there are three modes of decay that occur almost exclusively in synthetic radionucHdes. These are spontaneous fission, delayed-proton emission, and delayed-neutron emission. Lasdy, there are two exotic, and very long-Hved, decay modes. These are cluster emission and double P-decay. In all of these processes, the energy, spin and parity, nucleon number, and lepton number are conserved. Methods of measuring the associated radiations are discussed in Reference 2 specific methods for y-rays are discussed in Reference 1. 

Pauli proposed that two particles were emitted, and Fermi called the second one a neutrino, V. The complete process therefore is n — p -H e 9. Owing to the low probabiHty of its interacting with other particles, the neutrino was not observed until 1959. Before the j3 -decay takes place there are no free leptons, so the conservation of leptons requires that there be a net of 2ero leptons afterward. Therefore, the associated neutrino is designated an antineutrino, 9-, that is, the emitted electron (lepton) and antineutrino (antilepton) cancel and give a net of 2ero leptons. 

Electron Capture and /5" "-Decay. These processes are essentially the inverse of the j3 -decay in that the parent atom of Z andM transmutes into one of Z — 1 andM. This mode of decay can occur by the capture of an atomic electron by the nucleus, thereby converting a proton into a neutron. The loss of one lepton (the electron) requires the creation of another lepton (a neutrino) that carries off the excess energy, namely Q — — Z(e ), where the last term is the energy by which the electron was bound to the atom before it was captured. So the process is equivalent to... 

From the discussion on lepton conservation, it follows that the two emitted Ps would be accompanied by two antineutrinos. This case is denoted... 

L. Lederman (Batavia, Illinois), M. Schwartz (Mountain View, California) and J. Steinberger (Geneva) for the neutrino beam method and the demonstration of the doublet structure of the leptons through the discovery of the muon neutrino. 

M. L. Perl (Stanford) and F. Reines (Irvine, California) pioneering experimental contributions to lepton physics (discovery of the tau particle and detection of the neutrino, respectively). 

Second Quantized Description of a System of Noninteracting Spin Particles.—All the spin particles discovered thus far in nature have the property that particles and antiparticles are distinct from one another. In fact there operates in nature conservation laws (besides charge conservation) which prevent such a particle from turning into its antiparticle. These laws operate independently for light particles (leptons) and heavy particles (baryons). For the light fermions, i.e., the leptons neutrinos, muons, and electrons, the conservation law is that of leptons, requiring that the number of leptons minus the number of antileptons is conserved in any process. For the baryons (nucleons, A, E, and S hyperons) the conservation law is the... 

Conditional probability, 267 density function, 152 Condon, E. U., 404 Configuration space amplitude, 501 Heisenberg operator, 507 operators, 507, 514, 543 Conservation laws for light particles (leptons), 539 for heavy particles (baryons), 539 Continuous memoryless channels, 239 Contraction symbol for two time-labelled operators, 608 Control of flow, 265 Converse to coding theorem, 215 Convex downward function, 210 Convex upward function, 209 Cook, L. F 724... 

Table I presents the estimate of the electron EDM predicted by different particle physics models [8, 9]. As can be seen from this table, the value of the electron EDM in the SM is 10-12 orders of magnitude smaller than in the other models. This is due to the fact that the first nonvanishing contribution to this quantity arises from three-loop diagrams [30]. There are strong cancellations between diagrams at the one-loop as well as two-loop levels. It is indeed significant that the electron EDM is sensitive to a variety of extensions of the SM including supersymmetry (SUSY), multi-Higgs, left-right symmetry, lepton...

Lepton flavor-change, electron electric dipole moment, 242-243... 

Rekalo, M.P. (1978) Scattering of polarized leptons by hadrons and the anapole moment of leptons and... 

M. Altmann et al. Paper Contributed to the X International Symposium on Lepton and Photon Interactions at High Energies, 23rd-28th July 2001, Rome, Italy, astro-ph/0106314... 

The Km and Vj1iax of the Michaelis-Menten equation are actually made up of sums and products of little k s. You only have to look in most biochemistry texts to see a description of the derivation of the Michaelis-Menten equation in terms of little k s. The little k s are like quarks and leptons—you ve heard the names, but you re not quite sure what they are and even less sure about how they work. There s a section later (actually last) in the book if you haven t heard or can t remember about rate constants. 

For typical lepton energies of a few MeV, the de Broglie wavelength is of order 100 times the nuclear radius and when orbital angular momentum is zero, one can use the allowed approximation for their wave functions... 

It led to a prediction that the number of different sorts of neutrino (equivalent in standard particle physics to the number of families of quarks and leptons) is less than 4 and probably no more than 3. This prediction was subsequently confirmed (subject to slight reservations about differences between effective numbers of neutrino species in the laboratory and in the early Universe) by measurements of the width or lifetime of the Z° boson at CERN in 1990. 

Absence of electron or neutrino degeneracy, corresponding to lepton numbers Le, Lp, Lr that are zero or at least not large compared to B, where... 

Second, this decay allows to study the nature of p,ui and (ft— meson mixing. Note,that in references (Nasriddinov, 1994 Nasriddinov, 2001) the problems of 7r° — rj - and io — (ft mixings have been studied on the basis of this model as well and obtained reasonable results for the r-lepton decay probabilities. In this calculation, we used ui — 0-mixing... 

Note, that we studied (Nasriddinov, 1998) the t —> ir riuT decay of the r lepton in the framework of this method with taking into account the isotopic spin violation of chiral symmetry in the Oakes scheme.In this case the 7r° — rj - mixing Lagrangian has the form... 

Lepidolite, rubidium-bearing, 27 818 Lepirudin, 4 100, lOOt, 101 Leptin, 3 96-97 Lepton accelerator, 23 862 Leptons, 27 297, 298, 299 conservation of, 27 305 Leptophos, 4 358t Lercanidipine, 5 132-133... 

In order to study the effects of different TBF on neutron star structure, we have to calculate the composition and the EOS of cold, catalyzed matter. We require that the neutron star contains charge neutral matter consisting of neutrons, protons, and leptons (e, p ) in beta equilibrium. Using the various TBF discussed above, we compute the proton fraction and the EOS for charge neutral and beta-stable matter in the following standard way [23, 24] The Brueckner calculation yields the energy density of lepton/baryon matter as a function of the different partial densities,... 

Figure 12. Kepler period versus the rotational mass for purely hadronic stars as well as hybrid stars. The following core compositions are considered i) nucleons and leptons (dotted line) ii) nucleons, hyperons, and leptons (dashed line) in) hadrons, quarks, and leptons (solid line). The shaded area represents the current range of observed data.

This expectation is confirmed by analyzing the available data, and approximating the lepton component in ft equilibrated matter by an ideal gas. 

One of our main interests is to describe quark matter at the interior of a compact star since this is one of the possibilities to find color superconducting matter in nature. It is therefore important to consider electrically and color neutral2 matter in /3-equilibrium. In addition to the quarks we also allow for the presence of leptons, especially electrons muons. As we consider stars older than a few minutes, when neutrinos can freely leave the system, lepton number is not conserved. The conditions for charge neutrality read... 

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