Muon Number Conservation Research Articles

Search for the decay μ+ → e +e +e −

A search for the decay μ + → e +e +e −, which violates the conservation of muon number, was done at the πE3 channel of the Swiss Institute for Nuclear Research (SIN). The experiment used a large-solid-angle magnetic spectrometer (SINDRUM), equipped with cylindrical multiwire proportional chambers and a scintillator hodoscope. A total of 7.3 × 10 12 μ + were stopped in an 11 mg/cm 2 foam target. Accidental background was reduced by requiring e +e +e − events to be prompt and to have a good vertex. The remaining 7443 events are compatible both in number and momentum distribution with the decay μ + → e + e + e −ν e ν μ , if one assumes the standard electroweak theory. No candidate for the decay μ + → e +e +e − was found. Taking into account the overall acceptance for this decay of (13.8 ± 0.5)% a new upper limit for the branching ratio B μ → 3 e = μ(μ + → e + e + e −)/μ(μ + → e +ν e ν μ) < 2.4 × 10 −12 (90% confidence) is derived.

Higgs-meson production in muon-number-violating processes

We calculate cross sections for coherent production of Higgs mesons in the Coulomb field of a heavy nucleus in processes which violate conservation of muon number. Depending on the specific model for muon-number violation and on the mass of the Higgs meson, such processes could be observable at Fermilab.

Muon-number-nonconservation effects in a gauge theory withV + Acurrents and heavy neutral leptons

Since in gauge theories eigenstates of weak interactions are in general not mass eigenstates, we would not expect flavor conservation. In particular this should also hold for the flavors: muon numbers and electron numbers, etc. The apparent conservation of muon number in the standard $V \ensuremath{-} A$ theory should be interpreted as reflecting the fact that neutrino masses (if not identically zero) are almost degenerate when viewed on the normal mass scale. In theories containing $V + A$ currents, the right-handed muon and electrons are expected to couple to intermixing leptons in the GeV range. In such theories muon-number-violation effects will be dramatically larger. However, when constructing new models of leptons one should be mindful that flavor-changing neutral-current processes such as $\ensuremath{\mu}\ensuremath{\rightarrow}e\ensuremath{\gamma}$ and $\ensuremath{\mu}\ensuremath{\rightarrow}\mathrm{ee}\overline{e}$ are suppressed experimentally. This indicates the need for a leptonic Glashow-Iliopoulos-Maiani cancellation mechanism. We have proposed a way to incorporate these features in an ${\mathrm{SU}}_{2}$ \ifmmode\times\else\texttimes\fi{} ${\mathrm{U}}_{1}$ gauge theory. Basically it involves the addition to the standard Weinberg-Salam theory of right-handed doublets with the electron and muon coupled to orthogonal heavy neutrinos. This leads to an electronic neutral current which is purely vector and its attendant suppression of parity-violation effects in high-$Z$ atoms. Muon-number-nonconservation effects involving only familiar particles are higher-order weak processes and are naturally of the order $G_{F}^{}{}_{}{}^{2}$. In this paper we give details of our calculations of $\ensuremath{\mu}\ensuremath{\rightarrow}e\ensuremath{\gamma}$, $\ensuremath{\mu}\ensuremath{\rightarrow}\mathrm{ee}\overline{e}$, ${K}_{L}\ensuremath{\rightarrow}e\overline{\ensuremath{\mu}}$, $K\ensuremath{\rightarrow}\ensuremath{\pi} e\ensuremath{\mu}$, and $\ensuremath{\mu}e$ conversion in a nucleus, etc. In order to have a natural theory, we have incorporated recent suggestions made by Bjorken, Lane, and Weinberg about the Higgs structure for such a model. This modification increases the rate for $\ensuremath{\mu}\ensuremath{\rightarrow}e\ensuremath{\gamma}$ by a factor of 25 but does not materially affect other processes. For a heavy-lepton mass-difference and mixing-angle combination of $sin\ensuremath{\varphi}cos\ensuremath{\varphi}[m{({N}_{1})}^{2}\ensuremath{-}m{({N}_{2})}^{2}]\ensuremath{\simeq}1$ ${\mathrm{GeV}}^{2}$, the branching ratio for $\ensuremath{\mu}\ensuremath{\rightarrow}e\ensuremath{\gamma}$ is 4 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}10}$, that for $\ensuremath{\mu}\ensuremath{\rightarrow}\mathrm{ee}\overline{e}$ is around ${10}^{\ensuremath{-}11}$; the $\ensuremath{\mu}e$ conversion rate can be as large as ${10}^{\ensuremath{-}9}$ when compared to the ordinary muon capture in the nucleus. If there is a quark $b$ coupled to the $u$ quark through the $V + A$ current, this conversion rate will be decreased by a factor of 30. The rates for the muon-number-nonconserving $K$ decay are more sensitive to the relative lepton masses. For example the branching ratio of ${K}_{L}\ensuremath{\rightarrow}e\overline{\ensuremath{\mu}}$ is about ${10}^{\ensuremath{-}10}$ for $\frac{m({N}_{1})}{m({N}_{2})}\ensuremath{\simeq}4$, and a 1.8-GeV charmed quark.

Muon number non-conserving processes in gauge theories of weak interactions

We discuss muon number non-conserving processes in two models of weak and electromagnetic interactions. In the first model there are six leptons with purely left-handed weak currents, while the second model has been recently proposed by Cheng and Li. In particular we study the process μ + nucleus → e + nucleus and find that in some cases, including the first model, it offers a more sensitive probe of muon number conservation than the decay μ → e γ. We also improve the existing calculations of other decays in that, for the first model, our results are exact in the mass of the heavy neutral lepton while for the Cheng-Li model we go beyond the leading logarithmic approximation for gm → 3e.

Spontaneous Breakdown of Muon-Number Conservation and Off-Diagonal Neutral Currents

We suggest that the conservation of muon number is associated with a local gauge principle and that small nonconservation effects develop from the spontaneous breakdown of the gauge symmetry. Experimental consequences of the scheme, stemming from the spontaneous genesis of off-diagonal neutral currents, are discussed in detail.

Heavy leptons, lepton mixing, and nonconservation of lepton-type number

Introducing a new weak doublet of heavy leptons, one is led to a mixing of the various lepton states with respect to the weak interaction and subsequently to the violation of electron and muon number conservation (e.g., the decay μ→e γ). The new charged lepton can only decay via such a mixing and is therefore relatively long-lived ( τ>10 −11 sec). It can be produced singly in ν μ nucleus scattering at high energies. Various other phenomenological consequences are discussed.

Mechanism for Nonconservation of Muon Number

We consider the possibility that muon-number conservation is not a fundamental symmetry of nature. In simple SU(2) \ensuremath{\bigotimes} U(1) gauge theories with several scalar boson doublets, muon number will still atuomatically be conserved by the intermediate-vector-boson interactions, but not by effects of virtual scalar bosons. The branching ratio for $\ensuremath{\mu}\ensuremath{\rightarrow}e+\ensuremath{\gamma}$ is estimated to be of order ${(\frac{\ensuremath{\alpha}}{\ensuremath{\pi}})}^{3}$. Other $\ensuremath{\mu}\ensuremath{-}e$ transition processes are also discussed.

Trimuon production by neutrinos and SU(8) L × U(1) gauge model

A gauge model of weak interactions is proposed to naturally incorporate copious production of charged heavy leptons leading to trimuon events in high energy neutrino reactions and a small violation of muon number conservation.

Testing the Muon-Number Conservation Law inν¯μ+e−Interactions at High Energies

We propose to test the validity of the multiplicative muon-number conservation law by comparing the quasielectric reactions nu-bar/sub mu/+e/sup -/..--> mu../sup -/+nu-bar/sub e/ and ..nu../sub mu/+e/sup -/..--> mu../sup -/+..nu../sub e/ at approximately-greater-than400 GeV. We note that the measured electron spectrum in muon decay places strong constraints on the effective Lagrangian for the nu-bar/sub mu/-induced process. (AIP)

Nonconservation of muon number and CP noninvariance

Based upon a possible quark-lepton symmetry, we suggest that the conservation of muon number may be violated by a matrix element of the order of the Fermi constant times the CP-violating parameter times the squared electric charge. We urge a renewed experimental search for the decay μ ± → e ±e +e − with a branching ratio of about 4 × 10 −9.

Sum Rules on Neutral Current Interactions Based on a Baryon-Lepton Symmetry Model

Sum rules. and inequalities are presented for neutrino reactions of neutral current inter­ action which satisfies baryon-lepton symmetry. According to the symmetry which was first discovered in charged weak current, neutral current with l.dSI=1 is automatically forbidden as a consequence of muon number conservation in leptonic neutral current. Assumptions on leptonic neutral current are (i) ,a-number conservation, (ii) e-,a universality and (iii) the general combination of V and A types. New triangle relations and sum rules are presented for neutrino-electron scattering cross sections. Several inequalities are also derived for cross sections which combine neutrino-electron with inclusive neutrino scattering.

High energy electronic neutrino ( ve) and antineutrino ( [formula omitted]) interactions

The total cross-sections for v e ( v e ) -nucleon scattering have been measured. A test has been made of the muon number conservation law. A limit of 2.4 GeV is found the mass of the “Georgi-Glashow type” heavy lepton

Search for Muonium-Antimuonium Conversion

We have searched for the conversion of muonium to antimuonium, which would be allowed by a multiplicative muon number conservation law. The results are consistent with zero conversion rate, and set an upper limit to the magnitude of the weak-interaction coupling constant for the process of 5800 times the vector coupling constant of beta decay.

III. The neutrino programme at the C. E. R. N. proton synchrotron

An obvious experiment that arises from the previous neutrino studies (Block et al . 1964; C. E. R. N. 1965; Myatt 1965) is to investigate neutrino interactions on free protons in a propane bubble chamber. A new neutrino beam sufficiently intense to achieve this aim is being constructed at C. E. R. N. A schematic layout of the installation is shown in figure 1. The bubble chamber programme which will start early 1967, will investigate N* formation in neutrino proton interactions (C. E. R. N. 1966) and will extend the scope of the previous studies of neutrino-nucleon interactions. A spark chamber installation (Hahn, Gerber, Hofer &amp; Krienen 1965) will be operated simultaneously with the bubble chamber for a new test of muon number conservation. The event rate of muons identified in the spark chambers and whose sign has been deter­mined in their passage through the bubble chamber, will be compared with that expected from detailed estimation of the neutrino flux (W. Venus, private communication). A violation of muon number conservation to the extent of a few μ + per thousand μ - produced by v μ should be detectable.