Muonium - Physics of a Most Fundamental Atom Klaus P

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Muonium - Physics of a most Fundamental Atom Klaus P. Jungmanna aKernfysisch Versneller Instituut, Rijksuniversiteit Groningen, Zernikelaan 25, NL-9747 AA Groningen

The hydrogen-like muonium atom (M=µ+e−) oﬀers possiblitites to measure fundamental constants most precisely and to search sensitively for new physics. All experiments on muonium at the presenetly most intense muon sources are statistics limited. New and intense muon sources are indispensable for improved measurements.

1. Introduction troscopy experiments are a microwave measurement of the Zeeman splitting in the ground state The dominant interaction within the M atom hyperfine structure ∆νHFS and a two-photon [1,2] is electromagnetic. In the framework of 2 2 laser excitation of the 1 S1/2-2 S1/2 transition. bound state Quantum Electrodynamics (QED) Both energy intervals can be calculated to very the electromagnetic part of the binding can high precision, which allows to extract fundamen- be calculated to sufficiently high accuracy for tal constants. modern high precision spectroscopy experiments. There are also contributions from weak interactions arising through Z0-boson exchange and 2. Hyperfine structure from strong interactions owing to vacuum po- The most recent experiment at LAMPF had a larization loops containing hadrons. The cor- krypton gas target inside of a microwave cavity responding energy level shifts can be obtained at typically atmospheric density and in a homo- to the required level of precision using standard geneous magnetic field of 1.7 T [3]. Microwave theory. Precision experiments in M can provide transitions between the two energetically highest sensitive tests of the Standard Model of particle respectively two lowest Zeeman sublevels of the physics. Sensitive searches for new, yet unknown n=1 state at the frequencies ν12 and ν34 involve forces in nature become possible. Parameters in a muon spin flip. Due to parity violation in the speculative theories can be restricted. In partic- weak interaction muon decay process the e+ from ular, such speculations which try to expand the µ+ decays are preferentially emitted in the µ+ Standard Model in order to gain deeper insights spin direction. This allows a detection of the spin into some of its not well understood features, i.e. flips through a change in the spatial distribution where the standard theory gives well a full de- of the decay e+. The experiment has utilized the scription, but lacks a satisfactory explanation of technique of ”Old Muonium”, which allowed to the observed facts. In addition, fundamental con- reduce the line width of the signals below half of stants like the muon mass mµ, its magnetic mo- the ”natural” line width ∆νnat = 1/(2πτµ) [4], ment µµ and magnetic anomaly aµ and the fine where τµ = 2.2µs is the muon lifetime. structure constant α can be measured precisely The magnetic moment was measured to 120 by M spectroscopy. ppb, which translates into a muon-electron mass Recent precision experiments in M include ratio µµ/me of the same accuracy. The zero-field spectroscopy of electromagnetic transitions in the hyperfine splitting is determined to 12 ppb and atom and a search for muonium-antimuonium agrees well with the theoretical prediction which (M-M) conversion. All these experiments involve is known to 120 ppb [5]. For the M hyperfine M atoms in the ground state where they can structure the comparison between theory and ex- be produced with highest efficiency. The spec- periment is possible with almost two orders of 2 magnitude higher precision than for natural hy- electron mass ratio can be extracted from this to drogen because of the not sufficiently known pro- 0.8 ppm. Alternatively the measurement can be ton charge and magnetism distributions. The interpreted as a test of the charge quantization achieved – some six orders of magnitude higher in the first two lepton generations which results −9 – experimental precision in hydrogen maser ex- as qm+ /qe− + 1 = −1.1(2.1) · 10 . This is the periments can unfortunately not be exploited for best verification of charge equality in the first two a better understanding of fundamental interac- generations. The existence of one single universal tions. Most of the corrections to the Fermi HFS unit of charge is solely an experimental fact. No splitting in M arise from QED. This allows for underlying symmetry could yet be identified. the most precise determination of the fine structure constant α from a bound state. Among the 4. Muonium-Antimuonium Conversion non-QED contributions is the strong interaction through vacuum polarization loops with hadrons In addition to the indirect searches for signa- (56 ppb) and a parity conserving axial vector- tures of new physics in the muon magnetic anom- axial vector weak interaction (-14 ppb). aly and in electromagnetic interactions within the It should be noted that µµ is an essential in- M atom the bound state offers also the possibility put into the muon g-2 measurement. Future g-2 to search more directly for predictions of specula- experiments might be limited by this quantity un- tive models. The process of (M-M) onversion vio- less some improved number will be determined in lates additive lepton family number conservation. a future high precision experiment. It would be an analogy to the well known K0-K0 Recently, generic extensions of the Standard and B0-B0 oscillations. M-M conversion appears Model, in which both Lorentz invariance and naturally in many theories beyond the Standard CPT invariance are not assumed, have attracted Model. The interaction could be mediated, e.g., widespread attention in physics. Diurnal varia- by a doubly charged Higgs boson ∆++, Majorana tions of the ratio (ν12 − ν34)/(ν12 + ν34) are pre- neutrinos, a neutral scalar, a supersymmetric τ- dicted. An upper limit could be set from a re- sneutrino, or a doubly charged bileptonic gauge analysis of the LAMPF data at 2 · 10−23 GeV for boson. the Lorentz and CPT violating parameter. In At PSI an experiment was designed to exploit a a specific model by Kostelecky and co-workers powerful new signature, which requires the coin- a dimensionless figure of merit for CPT tests is cident identification of both particles forming the sought by normalizing this parameter to the par- anti-atom in its decay [11]. Thermal M atoms ticle mass. In this framework ∆νHFS provides a in vacuum from a SiO2 powder target, are ob- significantly better test of CPT invariance than served for decays. (Vacuum is indispensable, as in electron g-2 and the neutral Kaon oscillations[6]. a gas or in condensed matter the conversion would be significantly suppressed.) Energetic electrons − 3. 1s-2s interval from the decay of the µ in the atom can be identified in a magnetic spectrometer. The positron Doppler-free excitation of the 1s-2s transition in the atomic shell of M is left behind after the has been achieved in pioneering experiments at decay with 13.5 eV average kinetic energy. It KEK [7] and at RAL [8]. In all these experiments has been post-accelerated and guided in a mag- two counter-propagating pulsed laser beams at netic transport system onto a position sensitive 244 nm wavelength were employed to excite the micro-channel plate detector (MCP). Annihila- n=2 state. The successful transitions were then tion radiation can be observed in a segmented detected by photo-ionization with a third photon pure CsI calorimeter around it. The decay vertex from the same laser field through the released µ+. can be reconstructed. The measurements were The RAL experiment [9] yields ∆ν1s2s(exp) performed during a period of 6 months in total to 4 ppb in good agreement with a theoretical over 4 years during which 5.7·1010 M atoms were value which is known to 0.6 ppb[10]. The muon- in the interaction region. One event fell within 3 a 99% confidence interval of all relevant distribu- source. There the ’Old Muonium’ technique could tions. The expected background due to accidental be benefitially employed, because the conversion coincidences is 1.7(2) events. Depending on the progresses with time squared and beam related interaction details one has to account for a sup- background falls off exponentially with time. pression of the conversion in the 0.1 T magnetic field in the spectrometer. This amounts maxi- REFERENCES mally to a factor of about 3 for V±A type interactions. The upper limit on the conversion prob- 1. V.W. Hughes and G. zu Putlitz, in: Quantum ability is 8.2 · 10−11 (90% C.L.). The coupling Electrodynamics, ed. T. Kinoshita (World Sci- constant is bound to below 3.0 · 10−3 G , where entific, 1990) p. 822 F 2. K. Jungmann, nucl-ex/0404013 (2004) GF is the Fermi coupling constant. This new result, which exceeds limits from pre- 3. W. 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