The influence of pairing correlations on the isospin symmetry breaking corrections of superallowed Fermi beta decays

Within the framework of quasi-particle random phase approximation, the isospin breaking correction of superallowed 0⁺ → 0⁺ beta decay and unitarity of Cabibbo-Kobayashi-Maskawa mixing matrix have been investigated. The broken isotopic symmetry of nuclear part of Hamiltonian has been restored by Pyatov’s method. The isospin symmetry breaking correction with pairing correlations has been compared with the previous results without pairing. The effect of pairing interactions has been examined for nine superallowed Fermi beta decays; their parent nuclei are ²⁶Al, ³⁴Cl, ³⁸K, ⁴²Sc, ⁴⁶V, ⁵⁰Mn, ⁵⁴Co, ⁶²Ga, ⁷⁴Rb.     

Renormalization scheme dependence of electroweak radiative corrections

We compare two renormalization schemes of the electroweak standard model: the on-shell scheme withe, M _W ,M _Z ,M _H , and the fermion masses {m _f } as free parameters, and an intermediate scheme where theW boson self energy is renormalized atq ²=0 instead ofq ²=M _W ². TheM _W ?M _Z interdependence, and the differentiale ⁺ e ^?→μ ⁺ μ ^? cross section including polarized beams are calculated in both schemes to one-loop order. We find striking differences between the forward-backward asymmetries and the polarization asymmetries near theZ resonance after inclusion of weak and QED corrections.     

The isospin mixing and the superallowed Fermi beta decay

In the present work, the isospin admixtures in the nuclear ground states of the parent nuclei and isospin structure of the isobar analog resonance (IAR) states have been investigated by studying the 0^?+???0^?+? superallowed Fermi ?? decays using Pyatov??s restoration method. Within the random phase approximation (RPA), in this method, the effect of isospin breaking due to the Coulomb forces has been evaluated, taking into account the effect of pairing correlations between nucleons.     

Considerations concerning the radiative corrections to muon decay in the Fermi and Standard theories

The FAC, PMS, and BLM optimization methods are applied to the QED corrections to the muon lifetime in the Fermi V-A theory. The FAC and PMS scales are close to m_e, while the BLM scale nearly coincides with the geometric average √m_em_μ. The optimized expressions are employed to estimate the third order coefficient in the (m_μ) expansion and the theoretical error of the perturbative series. Using arguments based on effective field theory and a simple examination of Feynman diagrams, it is shown that, if contributions of (m_μ²/M_W²) are neglected, the corrections to muon decay in the SM factorize into the QED correction of the Fermi V-A theory and the electroweak amplitude g²/(1 − Δr), both of which are strictly scale-independent. We use the results to clarify how the QED corrections to muon decay and the Fermi constant G_F should be used in the SM, and what is the natural choice of scales if running couplings are employed.     

Microscopic calculations of isospin-breaking corrections to superallowed beta decay

The superallowed β-decay rates that provide stringent constraints on physics beyond the standard model of particle physics are affected by nuclear structure effects through isospin-breaking corrections. The self-consistent isospin- and angular-momentum-projected nuclear density functional theory is used for the first time to compute those corrections for a number of Fermi transitions in nuclei from A=10 to A=74. The resulting leading element of the Cabibbo-Kobayashi-Maskawa matrix, |V(ud)|=0.97447(23), agrees well with the recent result of Towner and Hardy [Phys. Rev. C 77, 025501 (2008)].     

Self-energy radiative corrections in hydrogen-like systems

The one-photon self-energy radiative level shift of an electron in a Coulomb field is examined. An expression for the level shift which is suitable for direct numerical evaluation, for Z in the range 10–110, is obtained. It is based on the known Coulomb radial Green's functions and not on a power series expansion in Zα. In the following paper, the numerical evaluation of the level shift for the $\text{1S}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ state is described.     

Experimental validation of the largest calculated isospin-symmetry-breaking effect in a superallowed Fermi decay

A precision measurement of the γ yields following the β decay of (32)Cl has determined its isobaric-analogue branch to be (22.47(-0.18)(+0.21))%. Since it is an almost pure-Fermi decay, we can also determine the amount of isospin-symmetry breaking in this superallowed transition. We find a very large value, δ(C) = 5.3(9)%, in agreement with a shell-model calculation. This result sets a benchmark for isospin-symmetry-breaking calculations and lends support for similarly calculated, yet smaller, corrections that are currently applied to 0+ → 0 + transitions for tests of the standard model.     

Electromagnetic radiative corrections in parity-violating electron-proton scattering

QED radiative corrections have been calculated for leptonic and hadronic variables in parity-violating elastic ep scattering. For the first time, the calculation of the asymmetry in the elastic radiative tail is performed without the peaking-approximation assumption in hadronic variables configuration. This method has been validated in a comparison with the PVA4 data. It has been also used to evaluate the radiative corrections to the parity-violating asymmetry measured in the G⁰ experiment. The results obtained are here presented.     

One-loop leading logarithms in electroweak radiative corrections

We discuss the evaluation of the collinear single-logarithmic contributions to virtual electroweak corrections at high energies. More precisely, we prove the factorization of the mass singularities originating from loop diagrams involving collinear virtual gauge bosons coupled to external legs. We discuss, in particular, processes involving external longitudinal gauge bosons, which are treated using the Goldstone-boson equivalence theorem. The proof of factorization is performed within the 't Hooft–Feynman gauge at one-loop order and applies to arbitrary electroweak processes that are not mass-suppressed at high energies. As basic ingredients we use Ward identities for Green functions with arbitrary external particles involving a gauge boson collinear to one of these. The Ward identities are derived from the BRS invariance of the spontaneously broken electroweak gauge theory. Received: 4 May 2001 / Published online: 6 July 2001     

One-loop leading logarithms in electroweak radiative corrections

We present results for the complete one-loop electroweak logarithmic corrections for general processes at high energies and fixed angles. Our results are applicable to arbitrary matrix elements that are not mass suppressed. We give explicit results for 4-fermion processes and gauge-boson pair production in annihilation. Received: 20 October 2000 / Published online: 23 January 2001     

Self-energy and vertex radiative corrections in LQG

We consider the elementary radiative-correction terms in loop quantum gravity. These are a two-vertex “elementary bubble” and a five-vertex “ball”; they correspond to the one-loop self-energy and the one-loop vertex correction of ordinary quantum field theory. We compute their naive degree of (infrared) divergence.     

The radiative return at small angles: virtual corrections

Virtual corrections for electron-positron annihilation into one real and one off-shell photon of invariant mass are evaluated. Special attention is paid to those configurations where the real photon is collinear with the beam direction. This calculation is an important ingredient of a Monte Carlo program, which simulates events with tagged photons from initial-state radiation, including NLO corrections. Received: 24 April 2002 / Published online: 12 July 2002     

The angular dependence of X-ray dispersion corrections

The angular dependence of X-ray dispersion corrections is discussed. It is pointed out that angular dependence of the dispersion corrections is not simply a function of the ratio sin/ contrary to numerical data reported in the International Tables for X-ray Crystallography (1983), several books on X-ray diffraction, and other publications.Hönl [1] showed correctly that the dispersion corrections depend on the Bragg angle and X-ray wavelength independently, and this result is supported by experimental investigation of the Borrmann effect using single crystals of silicon and germanium.It is shown how Hönl's method for calculating the angular dependence of dispersion corrections by means of hydrogen-like eigenfunctions can be generalized to more accurate one electron wave functions which are now available in the form of numerical data.     

The beta-decay of 8He

A many-level, many-channel R-matrix formula is used to fit the measured ⁸He β-decay data, including the half-life, branching ratios and delayed neutron and triton energy spectra. Satisfactory fits are found with contributions from four 1⁺ levels of ⁸Li, at 0.98, 3.08, 5.15 and 9.06 MeV. The 32 reduced width amplitudes are taken from a shell-model calculation, with only two requiring adjustment. Gamow-Teller matrix elements obtained from the fits are in reasonable agreement with shell-model values.