Muon Number Violation and some history
Muon Number Violation
(O. Shanker)
(contact: oshanker AT gmail DOT com)
Miscellaneous information about limits on muon number nonconservation.
"The weak interactions have shown a notorious disrespect for our ideas of what the symmetries of nature ought to be. The violation of parity and the even more startling violation of CP provide examples of this notoriety. In the field of flavour number the perversity of the weak interactions manifests itself from the opporsite direction, namely, nature presents physicists with a lot of symmetries which have no good reason for existing. For example, since the time the muon was found to behave like a heavy electron physicists have been debating over the question of why it exists. The symmetries of nature which account for its existence and the existence of other flavour numbers like electron number, strangeness, charm, etc. are still not completely understood and seem to be fortuitous symmetries."
(From "Present Status of Muon Number", TRIUMF preprint TRI-PP-81-10, 1981) .
The excerpt above may be descriptive of today's situation, even though it is nearly three decades old. Of course, today we know that neutrinos change their flavour, i.e., they oscillate from one flavour type to another. I will keep updating this page with information and links regarding the current limits on muon number violation. For introductory material, this site is a good place to start.
Physicists like to study symmetries. The weak interactions are special, in that we have symmetries which hold to a very high level, but which are violated ever so slightly. The only other situation which I can think of where such a small violation of an almost perfect symmetry occurs is for the forward-backward symmetry of the sequence of Riemann zeta values at Gram Points.
History of muon number
The idea of flavour numbers is in essence a description of the ultimate building blocks of nature. There is a close similarity between the basic elements of the ancient Greeks and Indians or the immutable chemical elements of Dalton and flavour numbers. However, the latter term is used only in relation to the modern concepts regarding the ultimate structure of matter. The discoveries at the end of the nineteenth century of the electron, of the transmutability of elements, etc. indicated that the basic building blocks of nature were far fewer than the ninety or so elements discovered till then. In the early decades of this century two fundamental building blocks, the proton and electron, were believed to be the constituents of all matter. With the realization that nuclear beta decay involved a new massless particle, the neutrino, a study of its nature was taken up. Racah (Nuovo Cimento 14, 322, 1937) and Pontecorvo ( Helv. Phys. Acta. Suppi. 1. 97, 1950) suggested experiments to see if the neutrino and its antiparticle were identical. The radiochemical experiments of Davis (Phys. Rev 97, 766, I955) established the separate existence of the neutrino and antineutrlno. it now seemed as if all interactions in nature conserved two quantities, baryon number and lepton number.
This simple situation did not last long and the discovery of the neutron, muon, pion and strange particles in the first half of this century showed that nature was more complex. Two new flavors, strangeness (Gell-Mann, I953; Nlshijima, i955) and muon number, were introduced within a short time of each other. The introduction of these new flavors was phenomenological, i.e., it merely served to explain the absence of certain particle reactions and did not lead to any new insights into the details of weak interactions. Since that time our understanding of flavour numbers and their conservation schemes has developed quite a lot, but we still do not understand why so many flavors exist in nature (in fact, many new flavors have been discovered since then). The brief historical sketch of the muon serves to illustrate the puzzlement that physicists felt, and still feel, about the existence of so many flavors.
The muon was discovered in cosmic rays by Anderson and Weddermeyer (I938) and by Street and Stevenson (i937l). At first it was confused with the particle predicted by Yukawa as mediating strong interactions. However, its stability in nuclear environments showed that it did not have a strong interaction with nucleons and hence could not be the particle predicted by Yukawa. In the forties it was established that the muon was very similar to the electron and seemed to differ from it only in mass. Hence physicists expected it to decay into the electron without accompanying neutrinos, in addition to its decay modes involving final state neutrinos. However, searches of increasing accuracy in the fifties and sixties for processes like u + ey, u+ -> e+e-e- and ue conversion failed to find them. The theoretical predictions for the rates of such processes were beset with problems of divergent integrals and artificial cutoffs because these decays proceeded in second order in the old non-renormalisabie models of weak interactions (current X current model or the old intermediate vector boson model with only one type of neutrino, reviewed in Frankel). These problems made it difficult to decide if the experimental upper limits suggested modifications in the theory of weak interactions. There seemed to be growing evidence for the existence of two types of neutrinos and for a new quantum number, muon number. This idea gained support with the introduction of intermediate vector boson theories of the weak interaction (Feinberg, I953; Schwinger, l957) Experimental tests for the new quantum number were discussed by Pontecorvo (I959): Schwartz (I960) and Lee and Yang. The need for introducing a new flavor was definitely established by the experiments of Danby at al. (1962), who showed that when neutrinos produced from the decay of plons into muons interacted with nuclei, they produced muons but not electrons. The rate for production of electrons and muons in these processes is unambiguously calculable even in the old models of weak interactions and a conflict between theory and experiment clearly emerged. Thus, it became necessary to introduce a new type of flavor.
The phenomenological nature of the old theories is well illustrated by the many different types of lepton number schemes that were proposed. The only way of choosing among them was to look for processes that were permitted in some schemes but not in others. The lepton number schemes did not predict rates for the exotic processes. The need to probe the validity of the different schemes was one reason for the experimental interest in lepton number violating processes in the seventies.
The motivation for possible violations of baryon number and lepton number is provided by Grand Unified theories. A pre-gauge theory review of muon number can be found in Frankel (Muon Physics, Vol II, Edited by V. W. Hughes and C. S. Wu, Academic press New York1974) and Pontecorvo, (Zh. Eksp. Teor. Fiz 53, 1717, I967 /Soviet Physics JETP 26, 984, 1968).
There has been a lot of buzz about possible non-standard Higgs bosons. Discovery of non-standard Higgs bosons would be interesting - however, just adding more Higgs doublets to the standard theory still leads to the absence of flavor violating neutral currents. The flavor changing effects in the quark sector come only from the charged currents, and in the lepton sector they are suppressed by the smallness of the neutrino masses.
Muon electron conversion
The June 2010 issue of "Symmetry" (A joint Fermilab/SLAC publication on the dimensions of particle physics) has an article on a planned experiment to measure the anomalous conversion of a muon to an electron in an Aluminium muonic atom. Recent articles on the experiment can be found at CERN Courier and at Fermilab’s Mu2e experiment. The experiment, Mu2e, will be done at Fermilab, with results expected in 2017.
Another muon to electron conversion experiment is COMET, proposed to be constructed at the Japan Proton Accelerator Research Complex.
The PRISM (Phase-Rotated Intense Slow Muon) experiment is proposed to increase the sensitivity to 10^-18, two orders of magnitude better than the Mu2e and COMET experiments. It uses a special type of accelerator, the fixed-field alternating-gradient (FFAG) accelerator.
Particle Data Group review of Leptoquarks: http://pdg.lbl.gov/2013/reviews/rpp2012-rev-leptoquark-quantum-numbers.pdf, http://pdg.lbl.gov/2011/reviews/rpp2011-rev-leptoquark-quantum-numbers.pdf, http://pdg.lbl.gov/2008/listings/s056.pdf and http://pdg.lbl.gov/2008/reviews/leptoquark_s056230.pdf
Links
International Scoping Study of future Neutrino Facility
http://www.fnal.gov/directorate/Longrange/Steering_Public/files/Flavor_molzon.ppt
Muon->electron Gamma
http://meg.web.psi.ch/index.html Ongoing Experiment
Muon->electron conversion on Nuclei
Mu2e: Layman's introduction to Muon-electron conversion experiment at Fermilab ( in Aluminium).
Philosophical transactions article on Muon to electron conversion
If you wish to see my other work, here are links to Machine Learning, Riemann Zeta zeros and to the dimension of complex networks.