Electroweak radiative corrections to muon capture

Electroweak radiative corrections to muon capture on nuclei are computed and found to be sizable. They enhance the capture rates for hydrogen and helium by 2.8% and 3.0%, respectively. As a result, the value of the induced pseudoscalar coupling, g(P)(exp), extracted from a recent hydrogen 1S singlet capture experiment is increased by about 21% to g(P)(exp)=7.3+/-1.2 and brought into good agreement with the prediction of chiral perturbation theory, g(P)(theory)=8.2+/-0.2. Implications for helium capture rate predictions are also discussed.     

Effect of correlations on nuclear muon capture

The process μ⁻+¹²C→¹²B+v _μ is studied using the modified Hartree Fock wavefunction obtained with the unitary-model-operator-approach starting from the realistic hardcore nucleon-nucleon interaction, with the aim of testing the wavefunctions and obtaining a numerical value for the induced pseudoscalar coupling constant (g _P ). These observables, namely, the partial capture rate to the¹²B(1⁺; g.s), its recoil nuclear polarisation and the total capture rate, which exhaust the available experimental data in the above process have been calculated and compared with the other theoretical and experimental results. As far as the partial capture rate is concerned the use of the unitary-model operator approach wave functions for¹²C withb=2.09 fm and Cohen-Kurath wave function for¹²B(1⁺; g.s) reduces the pure shell model capture rate by about 30%. The effect of strong configuration mixing in the ground state of¹²C in taken into account by introducing a scale factor ξ similar to the ‘amplitude reduction factor’ of Donnelly and Walecka. With this ξ the agreement with the experiment both for the partial capture rate and the beta decay ‘ft’ value is found to be satisfactory. The¹²B(1⁺; g.s) recoil polarisation is found to be insensitive to the use of the unitary-model-operator-approach wave functions. When compared with the experimental data, we obtaing _P =(14.9±1.9)g _A . The total capture rate is found to be sensitive to the use of the unitary-modeloperator-approach wave functions which contain the effect of nucleon-nucleon short range correlations and we obtain a satisfactory agreement with the experiment for¹⁶O and¹²C, thereby revealing the importance of the effect of such correlations in the total capture rate studies.     

Effect of meson exchange corrections on allowed muon capture

Corrections to the impulse approximation calculation of the γ?ν angular correlation coefficient and recoil nuclear polarization in allowed muon capture transitions, arising from meson exchange effects, are studied and the value for the induced pseudoscalar coupling consistent with both observables is found to be (13.3 + 3)_gA, to a large extent free from nuclear wave function uncertainties.     

Cascade process in muon capture and gamma-neutrino angular correlations

A nuclear cascade process resulting from muon capture and subsequent deexcitation by gamma emission is considered. Possible observable quantities such as the final nuclear polarization and the gamma-neutrino angular correlation coefficients are investigated. It is shown that the nuclear transition with the spin sequence 0 → J_I → 0 is very favorable for study since the angular correlation coefficients in this case are not affected by the uncertainties in the gamma decay matrix elements. For a more restricted transition with J_I = 1, there exist some simple relations connecting the asymmetry coefficient of the recoil nucleus emitting the gamma ray and the gamma-neutrino angular correlation coefficients. These relations are shown to be independent of both the nuclear structure and the muon capture coupling constants. Numerical results are presented for the nuclear transition

${}^{16}\text{O}\text{(0}{}^{\mathrm{+}}\text{, g.s.)}\textcolor{red}{}{}^{16}\text{N}\text{(1}{}^{\mathrm{?}}\text{, 392}\text{KeV}\text{)}\textcolor{red}{}{}^{16}\text{N}\text{(0}{}^{\mathrm{?}}\text{, 120}\text{KeV}\text{).}$

     

Hard meson corrections to the amplitude for radiative muon capture and the elementary particle method

Hard meson corrections to the amplitude of radiative muon capture on the proton are derived within the framework of vector meson dominance in the tree approximation. The weak form factors are mediated by π, ρ and A₁ mesons which may radiate. The model reproduces the terms in the amplitude of lower order in the momentum transfers as derived from low-energy theorems and determines higher-order terms which are otherwise ambiguous or undetermined. Arguments are given why a similar approach to radiative muon capture in nuclei in an elementary particle method is expected to fail.     

Hard meson corrections to the amplitude for radiative muon capture and the elementary particle method

Hard meson corrections to the amplitude of radiative muon capture on the proton are derived within the framework of vector meson dominance in the tree approximation. The weak form factors are mediated by π, ρ and A₁ mesons which may radiate. The model reproduces the terms in the amplitude of lower order in the momentum transfers as derived from low-energy theorems and determines higher-order terms which are otherwise ambiguous or undetermined. Arguments are given why a similar approach to radiative muon capture in nuclei in an elementary particle method is expected to fail.     

Quantum corrections to liquid correlations

Sudarshan's semi-classical treatment of correlation functions is applied to the study of quantum corrections to the Van Hove function. In its generalised form, it enables one to choose the best correlation function for a given potential. Higher-order correlations are also sketched briefly and the details are similar to those considered by Oppenheim and Bloom.     

Quantum corrections to liquid correlations

Sudarshan's semi-classical treatment of correlation functions is applied to the study of quantum corrections to the Van Hove function. In its generalised form, it enables one to choose the best correlation function for a given potential. Higher-order correlations are also sketched briefly and the details are similar to those considered by Oppenheim and Bloom.     

First-order radiative corrections to polarized muon decay spectrum

The first-order QED corrections to the polarized muon decay spectrum are considered. The exact dependence on electron and muon masses is kept. Numerical results are presented.     

Second-order eikonal corrections for

The first-order eikonal approximation is frequently adopted in interpreting the results of A(e,e^′p) measurements. Glauber calculations, for example, typically adopt the first-order eikonal approximation. We present an extension of the relativistic eikonal approach to A(e,e^′p) which accounts for second-order eikonal corrections. The numerical calculations are performed within the relativistic optical model eikonal approximation. The nuclear transparency results indicate that the effect of the second-order eikonal corrections is rather modest, even at Q²≈0.2 (GeV/c)². The same applies to polarization observables, left–right asymmetries, and differential cross sections at low missing momenta. At high missing momenta, however, the second-order eikonal corrections are significant and bring the calculations in closer agreement with the data and/or the exact results from models adopting partial-wave expansions.     

Gamma-rays following muon capture

The energy and intensity of γ-rays following capture of muons by Si, Ti, Mn, Fe, Co, Ni, Y, Ag and Au were measured with a Ge(Li) detector. In most cases it was possible to identify the final nucleus from the energy of the γ-ray observed. In general, this showed that one or more neutrons were emitted in the initial stages of de-excitation. In the case of capture by Fe and Ni the evidence pointed to a mode of de-excitation by the emission of a proton and a neutron and in Ti by γ-rays alone. In these measurements it was possible to account for as much as 60% of the muons captured in Co, less in the other elements, and only 15 % in Si.     

Hadronic loop corrections to the muon anomalous magnetic moment

The dominant theoretical uncertainties in both the anomalous magnetic moment of the muon and the value of the electromagnetic coupling at the Z scale, M(Z), arise from their hadronic contributions. Since these will ultimately dominate the experimental errors, we study the correlation between them, as well as with other fundamental parameters. To this end we present analytical formulas for the QCD contribution from higher energies and from heavy quarks. Including these correlations affects the Higgs boson mass extracted from precision data.     

Radiative muon capture in medium-heavy nuclei

Radiative muon capture in nuclei is thoroughly investigated in view of its sensitivity to the pseudoscalar coupling constant g_P. In the photon energy domain of interest (k ? 60 MeV) the effective one-body hamiltonian in use is shown essentially to hold true, with minor corrections due to the muon propagator in the nuclear field and to the two-step process. The closure approximation is avoided by appropriately integrating the response function calculated in the Fermi gas model, in the energy-momentum transfer plane.Theoretical predictions in medium-heavy nuclei of the high-energy photon spectrum, of photon polarization, and of muon-spin photon angular correlation are given for various values of the pseudoscalar coupling constant.     

Negative muon capture in3He

We compute the partial capture rate of negative muons in³He by following the analysis of Peterson to include the relativistic corrections and the exchange effects, for various values of theg _p /g _A ratio. We also calculate the total capture rate. The ground state of³He is assumed to be spherical. The radial dependence of the ground state wave function is taken to be (a) one parameter Irving function, (b) a modified three-parameter Irving function and (c) a function having ‘soft-core’, whose parameters have been fixed in a variational calculation of the binding energy of the triton using a non-local momentum-dependent potential involvingp ² terms. The calculated values of the capture rates are compared with the experimental data to find a value for theg _p /g _A ratio.     

Radiative muon capture on nuclei

Radiative muon capture rates of stopped meons, spectra, circular polarisation, and asymmetries of emitted -quanta in¹⁶O and⁴⁰Ca are analysed using the shell-model nuclear wave functions. Calculated characteristics show considerable sensitivity to the value of induced pseudoscalar coupling constantg _p. Where possible we compare the theoretical results with the preliminary experimental data.Dedicated to the 25th anniversary of the Joint Institute for Nuclear Research.On leave of absence fromthe Institute of Nuclear Physics, Czechosl. Acad. Sci., 250 68 e, Czechoslovakia.     

Radiative muon capture on hydrogen

The radiative capture of negative muons by protons can be used to measure the weak induced pseudoscalar form factor. Brief arguments why this method is preferable to ordinary muon capture are given followed by a discussion of the experimental difficulties. The solution to these problems as attempted by experiment #452 at TRIUMF is presented together with preliminary results from the first run in August 1990. An outlook on the expected final precision and the experimental schedule is also given. Talk presented by W. Bertl at the Symposium “The Future of Muon Physics” in Heidelberg, Germany, May 7–9, 1991     

Virtual and soft pair corrections to polarized muon decay spectrum

Radiative corrections to the muon decay spectrum due to soft and virtual electron-positron pairs are calculated within the next-to-next-to-leading approximation. The effect is relevant for modern precision experiments on the decay spectrum.