Lepton number conservation

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. 

Violation of total lepton number conservation also implies violation of lepton family number conservation. 

From the point of view of field theory, muonium is the bound state of two point-like leptons, so it is an ideal system to study quantum mechanical effects. Several such experiments are described by Jungmann (2000) search for muonium-antimuonium conversion, which should be a violation of lepton number conservation precise measurement of spectroscopic transitions, which can be very well calculated and so provide a sensitive test of theories and direct tests of symmetry principles of field theory such as CPT invariance, which predicts the equivalent properties of particles and antiparticles. 

For many more limits testing lepton number conservation in r decays, see the 1992 edition of the Review of Particle Properties (Particle Data Group, 1992) see also Table 14.2. 

In these examples, the guiding principle is the principle of lepton number conservation. In any process, the total number of leptons and antileptons does not change the number before and after is conserved. Table I lists the assigned lepton numbers for each lepton family. The lepton number is positive for a lepton and negative for an antilepton. By applying the lepton numbers for the electron family, the principle of lepton conservation is exhibited in the three examples given. 

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. 

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... 

Like the leptons, there is a number conservation law for baryons. To each baryon, such as the neutron or proton, we assign a baryon number B = +1 while we assign B = — 1 to each antibaryon, such as the antiproton. Our rule is that the total baryon number must be conserved in any process. Consider the reaction... 

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. 

A potential M-M-conversion would violate additive lepton family number conservation and is discussed in many of the speculative theoretical approaches (see Fig. 10). It would be a full analogy in the sector of leptons to K°-K oscillations, which are well known and established in the quark sector of the standard model. 

The muon and the electron may be considered to belong to two different generations of leptons, which thus far appear to remain separate because of the independent conservation laws of muon number and of electron number. Any connection between the muon and the electron, such as a process which would violate muon number conservation, would be an important clue to the relationship... 

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. 

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. 

In keeping with the current interest in tests of conservation laws, we collect together a Table of experimental limits on all weak and electromagnetic decays, mass differences, and moments, and on a few reactions, whose observation would violate conservation laws. The Table is given only in the full Review of Particle Physics not in the Particle Physics Booklet. For the benefit of Booklet readers, we include the best limits from the Table in the following text. Limits in this text are for CL=90% unless otherwise specified. The Table is in two parts Discrete Space-Time Symmetries, i.e., C, P, T, CP, and CPT and Number Conservation Laws, i.e., lepton, baryon, hadronic flavor, and charge conservation. The references for these data can be found in the the Particle Listings in the Review. A discussion of these tests follows. 

Present experimental evidence and the standard electroweak theory are consistent with the absolute conservation of three separate lepton numbers electron number Le, muon number and tau number T,-. Searches for violations are of the following types ... 

Lepton family number conservation means separate conservation of each of L, L... 

Besides these strict conservation laws (energy, momentum, angular momentum, permutation of identical particles, charge, and baryon and lepton numbers), there are also some approximate laws. Two of these parity and charge conjugation, will be discussed below. They are rooted in these strict laws, but are valid only in some conditions. For example, in most experiments, not only the baryon number, but also the nirmber of nuclei of each kind, are conserved. Despite the importance of this law in chemical reaction equations, this does not represent any strict conservation law, as shown by radioactive transmutations of elements. 

Conservation of angular momentum Conservation of electric charge Conservation of baryon number Conservation of lepton number... 

Leptons, which include the electron, the neutrino, and the muon, have lepton number +1, and antileptons have lepton number —1 all other particles have lepton number 0. There is rigorous conservation of the lepton number in all reactions. 

P] A test of additive vs. multiplicative lepton family number conservation. 

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