Lepton number

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. 

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... 

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... 

The symbol ve indicates the antiparticle of the electron neutrino.) In this equation, the number of leptons on the left is zero, so the number of leptons on the right must also be zero. This equivalence can only be true if we assign a lepton number L of 1 to the electron (by convention) and L = — 1 to the ve (being an antiparticle). Consider the reaction... 

Here L = — 1 on both sides of the equation where we assign lepton numbers of +1 for every lepton and — 1 for every antilepton (e+ is an antilepton). By contrast, the... 

Solution On the left-hand side of the equation we assume that we have a 24Na nuclide (with 11 electrons) and a single positron, which is an antilepton. The conservation rules imply that the mass number of the product will be 24, the atomic number will be Z= 11 + 1, the 11 electrons will carry over, and an antilepton has to be created to conserve lepton number. Thus,... 

These reactions, called inverse (3 decay, were obtained by adding the antiparticle of the electron in the normal (3 decay equation to both sides of the reaction. When we did this we also canceled (or annihilated) the antiparticle/particle pair. Notice that other neutrino-induced reactions such as ve + n —> p+ + e do not conserve lepton number because an antilepton, ve, is converted into a lepton, e. Proving that this reaction does not take place, for example, would show that there is a difference between neutrinos and antineutrinos. One difficulty with studying these reactions is that the cross sections are extremely small, of order 10-19 bams, compared to typical nuclear reaction cross sections, of order 1 barn (10—24 cm2). 

In the second study, Ray Davis and co-workers, irradiated a large volume of liquid CC14 with antineutrinos from a reactor. The putative reaction, ve + 37C1 —> 37 Ar + e, could be detected by periodic purging of the liquid, collection of the noble gas, and then detection of the induced activity (37Ar is unstable, of course). The reaction was not observed to occur. Thus, they concluded that the reactor emits antineutrinos and that lepton number is conserved in the reactions. 

Beyond atomic spectroscopy muonium renders the possibility to search directly and sensitively for yet unknown interactions between the two charged leptons from two different generations. Among the mysteries observed for leptons are the apparently conserved lepton numbers. As a matter of fact, several distinctively different lepton number conservation schemes appear to hold, some of which are additive and some are multiplicative, parity-like. Some of them distinguish between lepton families and others don t [46,47,48,49,50]. No local gauge invariance has been revealed yet which would be associated with any of these empirically established laws. Since there is common believe [51] that any discrete conserved quantity is connected to a local gauge invariance, a breakdown of lepton number conservation is widely expected, particularly in the framework of many speculative models. 

The new leptogenesis scenario is very interesting due to its possible connection to the neutrino sector and lepton number violation. 

In the case of the p-p reaction, if the tunnelling operation is successful, an unstable nuclide consisting of 2 protons is created. What can happen next is that either the inverse reaction occurs (one proton escapes from the nucleus) or else one proton quickly releases a positron to remove excess electric charge, and a neutrino to conserve momentum and lepton number, and becomes a neutron thus forming a deuterium nucleus. 

Lepton Family number (LF), Lepton number (L), or Baryon number (B) violating modes... 

S = 1.6 794 common usage, LF means lepton family violation and not lepton number ... 

In all reactions the lepton number must be conserved the total number of leptons minus antileptons on each side of a decay or reaction process must be the same. A similar law is valid for the quarks. In the reaction above several quantum numbers are obeyed (i) the charge is the same on both side, (ii) the lepton number is zero on both sides (none = electron minus anti-neutrino), (iii) the quark number is conserved. The elementary reactions in Figure 10.4 can all be described in terms of lepton and quark transformations. 

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