Weak Interaction Contribution

2 Higher Order Radiative Corrections to the Finite Size Effect 

One can consider also higher order radiative corrections to the finite size effect. Such contribution originating from very small distances and enhanced by the large logarithm ln(l/(mro)) (ro here is the radius of the nucleus) was obtained in [50, 51, 55]. Its relative magnitude with respect to the leading finite size contribution is a Za) and it is universal for S and P state. 

There exist also nonuniversal corrections of order a Za) both for S and P states. These corrections originate from large distances and are enhanced by large infrared logarithms n Za) squared. Radiative corrections for S states are enhanced by the large logarithm n Za) squared, and are like the technically similar purely radiative correction to the Lamb shift of order a Za) m considered above. The coefficient before this logarithm squared can be easily obtained. 

Due to smallness even of the leading order finite size effect it is hard to imagine that these nice results would find any phenomenological applications for light atoms, and we do not reproduce their calculation here. 

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The weak interaction contribution to the Lamb shift is generated by the Z-boson exchange in Fig. 6.7, which may be described by the effective local low-energy Hamiltonian... 

The weak interaction contribution to hyperfine splitting is due to Z-boson exchange between the electron and muon in Fig. 6.7. Due to the large mass of the Z-boson this exchange is effectively described by the local four-fermion interaction Hamiltonian... 

The weak interaction contribution to HFS was calculated many years ago [53, 54], and even radiative corrections to the leading term were discussed in the literature [55, 56, 57]. However, this weak contribution to HFS was cited in the later literature with different signs [9, 19]. This happened probably because the weak correction was of purely academic interest for early researchers. The discrepancy in sign was subjected to scrutiny in a number of works [20, 58, 59] which all produced the result in agreement with [54]... 

The weak interaction contribution to hyperfine splitting in hydrogen is easily obtained by generalization of the muonium result in (10.38)... 

Another reason to improve the HFS theory is provided by the perspective of reducing the experimental uncertainty of hyperfine splitting below the weak interaction contribution in (10.38). In such a case, muonium could become the first atom where a shift of atomic energy levels due to weak interaction would be observed [85]. 

The Standard Model prediction of ae may be written as the sum of electromagnetic, hadronic, and weak interaction contributions ... 

In order to enhance the sensitivity of to the weak effect and beyond, it is important to sharpen the QED and hadronic contributions as much as possible. Improvement of the a4 term of aM by an order of magnitude is in progress and will be completed within a few months. Some a5 terms will also be improved or newly evaluated in the near future. This puts the QED part of in a very good shape. Of course the hadronic contribution must be improved further to give the weak interaction contribution to aM a very stringent test. 

Theoretical computation to about 0.1 kHz or 20 ppb appears realistic. We might remark that weak interaction contributions to iv are predicted11 at the level of 16 ppb. 

The principles of double-helix formation between two strands of DNA apply to many other biochemical processes. Many weak interactions contribute to the overall energetics of the process, some favorably and some... 

The theoretical value of the anomaly is given as a sum of a QED contribution, a weak interaction contribution, and a hadronic contribution... 

We know from the standard model of elementary particle physics [116] that there is a tiny weak interaction contribution to every Coulomb interaction. For ordinary matter, where particle interconversion can be ignored, weak interactions due to exchange of neutral Z vector bosons are involved. Unlike the Coulomb interaction, the (neutral and charged variants of) weak interactions do not conserve parity. This leads, in consequence, to a very small energy difference between mirror-image molecules (enantiomers), which in turn might prove to be of importance for the development of a homochiral biochemistry on our planet [117]. 

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