Optimal truncation procedures in renormalization-group calculations

Renormalization or rescaling transformations generally produce more complicated interactions than are present in the initial Hamiltonian. After each rescaling it is necessary to truncate the Hamiltonian to make the next rescaling mathematically tractable. One is faced with the problem of choosing the coupling constants of the truncated Hamiltonian to obtain the best approximation. Following ideas of McMillan, we consider truncation procedures which give lower and upper bounds to the free energy. Conditions for optimal lower- and upper-bound truncations are derived. These optimal truncations are seen to yield exact results for the free energy in both the high- and low-temperature limits. Some of the problems inherent in all renormalization transformations that incorporate an optimal lower- or upper-bound truncation are discussed. Calculations for the twodimensional Ising model based on renormalization transformations which combine decimation and an optimal truncation are described. Even in the simplest approximation in which only nearest-neighbor interactions are retained the free energy is obtained to an accuracy of better than 1% for all temperatures if an optimal truncation rather than an ordinary truncation with no readjustment of the coupling constants is made. However, the simplest calculations involving optimal truncations are less successful in predicting derivatives of the free energy and critical exponents than the free energy itself.     

Study of spin resonance in Hg1−xCdxTe by four-photon mixing

Four-photon mixing is used to measure spin resonance of conduction electrons in Hg_1?xCd_xTe (x = 0.23). The magnetic tuning rate and the motionally narrowed linewidth are studied experimentally below and through the quantum limit and comparison is made with theory.     

Are there “prompt” like-sign dimuons?

From exposures of the CDHS detector at the CERN SPS we have obtained 367μ ⁺ μ ^? events in neutrino beams and 73μ ⁺ μ ⁺ events in an antineutrino beam. The magnitude of a prompt like-sign signal has been controversial in the past and moreover could not be explained by known production mechanisms. A critical discussion of the experimental situation is given. We have tried to reduce the systematic uncertainties of previous experiments and to get more information on the dependence of the signal with energy and the muon momentum cut-off. This experiment yields a signal of 2.8σ (2.4σ) of prompt like-sign dimuon events in the case of neutrinos (antineutrinos). The rate to charged current events is of the order of 10^?4 forp _μ<9GeV andE>100 GeV. The prompt signal has all the properties expected from the production and decay of charm-anticharm events. The magnitude, however, is substantially higher then the prediction of perturbative QCD but lower than some other experiments.