Journal of the Physical Society of Japan Vol. 76, No. 11, November, 2007, 111009 SPECIAL TOPICS #2007 The Physical Society of Japan Frontiers of Elementary Particle Physics, the Standard Model and Beyond Muon Physics: A Pillar of the Standard Model à Bradley Lee ROBERTS Department of Physics, Boston University, Boston, MA 02215, U.S.A. (Received April 8, 2007; accepted April 18, 2007; published November 12, 2007) Since its discovery in the 1930s, the muon has played an important role in our quest to understand the sub-atomic theory of matter. The muon was the first second-generation standard-model particle to be discovered, and its decay has provided information on the (Vector–Axial Vector) structure of the weak interaction, the strength of the weak interaction, GF, and the conservation of lepton number (flavor) in muon decay. The muon’s anomalous magnetic moment has played an important role in restricting theories of physics beyond the standard standard model, where at present there is a 3:4 difference between the experiment and standard-model theory. Its capture on the atomic nucleus has provided valuable information on the modification of the weak current by the strong interaction which is complementary to that obtained from nuclear decay. KEYWORDS: muon, weak decay, muon capture, magnetic moment, lepton flavor violation DOI: 10.1143/JPSJ.76.111009 provided information on nuclear root-mean-square charge 1. Introduction radii. The Lamb shift in muonic hydrogen, ÁE2PÀ2S, which The muon was first observed in a Wilson cloud chamber is being measured at at the Paul Scherrer Insitut (PSI), is 1) 7) 2 3 by Kunze in 1933, where it was reported to be ‘‘a particle given by f209:974ð6Þ5:226Rp þ 0:036Rpg meV, where 2) of uncertain nature’’. In 1936 Anderson and Neddermeyer Rp is the proton rms charge radius. This experiment should reported the presence of ‘‘particles less massive than protons provide a precise measurement of Rp. The weak nuclear but more penetrating than electrons’’ in cosmic rays, which capture, called ordinary muon capture (OMC), of the muon was confirmed in 1937 by Street and Stevenson,3) Nishina, on the atomic nucleus following the cascade to the 1S 4) À Tekeuchi, and Ichimiya, and by Crussard and Leprince- ground state, þ Z N ! ZÀ1N þ , is the analog to Ringuet.5) The Yukawa theory of the nuclear force had the weak capture of a K-shell electron by the nucleus, and predicted such a particle, but this ‘‘mesotron’’ as it was provides information on the modification of the weak called, interacted too weakly with matter to be the carrier interaction by hadronic matter. of the strong force. Today we understand that the muon is The muon mass of 106 MeV restricts the muon to decay a second generation lepton, with a mass about 207 times into the electron, neutrinos, and photons. Thus muon decay the electron’s. Like the electron, the muon obeys quantum is a purely leptonic process, and the dominant decay mode is À À electrodynamics (QED), and can interact with other particles ! e þ þ e. This three-body decay tells us that the through the electromagnetic and weak forces. Unlike the individual lepton number, electron and muon, is conserved electron which appears to be stable, the muon decays separately, and that the two flavors (kinds) of neutrinos are through the weak force. distinct particles.10) Here the À and eÀ are ‘‘particles’’ and The muon lifetime of 2.2 ms permits one to make precision the þ and eþ are the antiparticles. In the 1950s, it became measurements of its properties, and to use it as a tool to possible to make pions, and thus muons, in the laboratory. study the semileptonic weak interaction, nuclear properties, The energetically favorable decay þ ! e was searched as well as magnetic properties of condensed matter systems. for and not found8) to a relative branching ratio of The high precision to which the muonium (þeÀ atom) <2  10À5. Also searched for was the neutrinoless capture hyperfine structure can be measured and calculated makes of a À on an atomic nucleus,9) À þ N ! eÀ þ N , which it a significant input parameter in the determination of was not found at the level of 5  10À4. Such processes are fundamental constants.6) In this review, I will focus on the said to ‘‘violate lepton flavor’’, and continue to be the object role of the muon in particle physics. of present and planned studies reaching to sensitivities of A beam of negative muons can be brought to rest in 10À14 and 10À16, respectively. matter, where hydrogen-like atoms are formed, with a The muon, like the electron, is a spin 1=2 lepton, with a nuclear charge of Z. The Bohr radius for a hydrogen-like magnetic moment given by atom is inversely proportional to the orbiting particle’s mass q qh g À 2 2 2 s (rn ¼½n hc=½mc Z ), so that for the lowest quantum s ¼ gs s; ¼ð1 þ aÞ ; a ; ð1Þ 2m 2m 2 numbers of high-Z muonic atoms, the muon is well inside of the atomic electron cloud, with the Bohr radius of the 1S where the muon charge q ¼e, and gs, the spin g-factor is atomic state well inside the nucleus. The 2P ! 1S x-ray slightly greater than the Dirac value of 2. The middle energies are shifted because of the modification of the equation above is useful from a theoretical point of view, as Coulomb potential inside the nucleus, and these x rays have it separates the magnetic moment into two pieces: the Dirac moment which is unity in units of the appropriate magneton, ÃE-mail: [email protected] eh=2m, and is predicted by the Dirac equation; and the 111009-1 J. Phys. Soc. Jpn., Vol. 76, No. 11 SPECIAL TOPICS B. L. ROBERTS anomalous (Pauli) moment, where the dimensionless quan- νμ νμ νμ tity a is referred to as the anomaly. The muon anomaly, like the electron’s, arises from radiative corrections that are G G + ν + F F discussed below. μ W e μ ν + ν e μ e When the muon was discovered, it was an unexpected surprise. Looking at this from our 21st century perspective, γ + + + it is easy to forget how we reached what is now called the e e e ‘‘standard model’’ of subatomic physics, which incorporates (a) (b) (c) three generations of leptons, e, , and and their neutrinos; three generations of quarks; the electro-weak gauge bosons, Fig. 1. (Color online) Muon decay in (a) the standard model; (b) the Fermi theory; (c) radiative corrections to the Fermi theory. , W, and Z; and the gluons that carry the strong force. When this author joined the field as a graduate student in the mid 1960s, none of this was clear. Quarks were viewed by many as a mathematical device, not as constituent particles. While the Fermi theory is nonrenormalizeable, the QED Even after quarks were inferred from deep inelastic electron radiative corrections are finite to first order in GF, and to scattering off the proton, we only knew of the existence all orders in the fine-structure constant . This gives the 14) of three of them. While the V–A structure of the weak relationship between GF and the muon lifetime, , interaction was first inferred from nuclear decay, the study 1 G2 m5 of muon decay has provided a useful laboratory in which to ¼ F ð1 þ ÁqÞ; ð3Þ 3 study the purely leptonic weak interaction, to search for 192 physics beyond the standard model, such as additional terms where Áq is the sum of phase space, and QED and hadronic in the interaction besides the standard-model V–A structure, radiative corrections. More properly one should write G as well as looking for standard model forbidden decays like since new physics contributions could make G different for ! e . For many years, the experimental value of the the three leptons.16) muon’s anomalous magnetic moment has served to constrain The MuLan experiment at PSI has recently reported a physics beyond the standard model, and continues that new measurement of the muon lifetime 2.197 013(21)(11) ms role today. (Æ11 ppm),17) to be compared with the previous world average 2.197 03(4) ms (19 ppm).18) The new world 2. Muon Decay and GF average muon lifetime of 2.197 019(21) ms gives, assuming À À The muon decay ! e e is purely leptonic. Since only standard-model physics in muon decay, GF ¼ À5 2 m MW , muon decay can be described by a local four- 1:166 371ð6Þ10 GeV (5 ppm). This experiment should fermion (contact) interaction. While nonrenormalizeable, eventually reach a precision of 1 ppm on . at low energies it provides an excellent approximation to the full electroweak theory. The weak Lagrangian is written 3. Nuclear Muon Capture as a current–current interaction, where the leptonic current is The weak capture of a muon on a proton has much in of the (V–A) form, u ð1 À 5Þu. common with nuclear decay. As for other low-energy Michel11) first wrote down a parameterization of muon weak processes, the interaction can be described as a decay, defining five parameters, , , , , and h, which are current–current interaction with the (V–A) leptonic current combinations of the different possible couplings allowed by given by u ð1 À 5Þu. Because the strong interaction Lorentz invariance in muon decay. The standard model has can induce additional couplings,19) the hadronic current is clear predictions for these parameters and they have been more complicated.