Muon/electron

The dominant contribution to the uncertainty of this theoretical result is generated by the uncertainty of the muon-electron mass ratio in (12.4). 

The largest contribution to the uncertainty of the indirect mass ratio in (12.34) is supplied by the unknown theoretical contributions to hyperfine splitting. This sets a clear task for the theory to reduce the contribution of the theoretical uncertainty in the error bars in (12.34) to the level below two other contributions to the error bars. It is sufficient to this end to calculate all contributions to HFS which are larger than 10 Hz. This would lead to further reduction of the uncertainty of the indirect value of the muon-electron mass ratio. There is thus a real incentive for improvement of the theory of HFS to account for all corrections to HFS of order 10 Hz, created by the recent experimental and theoretical achievements. 

Weak Interactions were treated by Pais who, starting from Fermi s original theory, discussed the discovery by Lee and Yang,74 almost 5 years before, of the parity violation by weak interactions, its experimental confirmation,75 the muon-electron universality,76 the idea of an intermediate boson as a mediator of weak interaction, and the two-neutrinos question. 77... 

Here the first quoted uncertainty is due to the accuracy to which the muon-electron mass ratio mM/TOe is known, the second error is from the knowledge of a as obtained from electron g — 2 measurements [25], and the third value corresponds to estimates of uncalculated higher order terms. 

From these figures the muon/electron mass ratio is found to be... 

In an alternate interpretation the muon/electron charge ratio can be extracted. For hydrogen-like systems the leading order for the gross structure energy is proportional to (Z2a)a/n2 where Z is the nuclear charge in units of the... 

Secondly, one can assume for the form factor the existing experimental value 1 2 = (1.676 + 0.008) fm [3] (as seen by an electron probe), assume muon-electron universality, and then give a limit within which the QED vacuum polarization contribution is tested by these measurements. In doing this, one can see that such a QED correction is tested (at the momentum transfer implied by the experiment) to the level of 0.17% the result of this experiment represents to my knowledge one of the best direct tests, so far performed, of a vacuum polarization correction. 

Molecular dynamic information is obtained from a study of the variation of the muon spin relaxation rate with temperature. Reorientation depolarizes the muons by causing anisotropic or dipolar terms in the electron-muon hyperhne interaction to fluctuate. Peaks in the relaxation rate (analogous to 2i minima in NMR) occur when the reorientation rate matches the frequency of the dominant transition between the coupled muon-electron spin states. The correlation time, T, at each temperature can be obtained using the derivations of Cox and Sivia [14]. The measured relaxation rate X is given by the following expression ... 

Figure 7.4 Breit-Rabi energy level diagram for a muonium like (or a muoniated radical) system. is the muon-electron hyperflne constant and Ws is the total quantum number.

The muon-electron interaction is an ideal test of the point-like behavior of the two particles. Any deviation between the theoretical calculation and the measurement would be a sign for new types of interactions. A problem which is of high interest in the light of the gauge theories is the difference between muon and electron. Is there only the difference in mass or are there other differences What are the conservation laws, how well are they fullfilled, why do they exist ... 

In the following section new results on muonium spectroscopy are presented. Muonium (y e ) is a hydrogen-like atom consisting of two leptons. It provides an ideal system to determine muon properties and measure muon-electron interactions. is one of... 

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