In this chapter we will present the simplest calculations, the so-called tree-level calculations that do not yet require a deep knowledge of quantum field theory like renormalization and renormalization group. This step will give us leading formulas for the determination of various parameters of the SM like the Fermi constantand the parameters of the CKM matrix, which will be introduced and discussed in detail. These formulas will also give us a transparent picture of the leading decays ofmesons and leptons and will allow approximate determination of the parameters in question. Corrections to these leading expressions will be calculated or simply listed in later chapters. In this chapter we will also find out that in the case of meson decays some entries in the decay amplitudes cannot be calculated in perturbation theory. These are hadronicmatrix elements of quark currents and of four-quark operators. Their calculation will be done in other chapters.

This chapter presents the technology of quantum field theory at the one-loop level including general comments and results of two and higher loop calculationsthat we will need later on. The main goal here isthe presentation of the dimensional regularization and the development of the technologyfor one-loop calculations. The next goal isthe presentation of therenormalization and the renormalization group methods. While our presentation is rather general, we will show explicit results only in QCD and QED. The case of the renormalization of electroweak interactions willbe discussed briefly. One of the important results of this chapter will be the collection of integrals necessary not only to performthe renormalization of QED and QCD but also those that will be crucial for one-loop calculations at all stages of our expedition. We collected these integrals in an appendix.

This step deals exclusively with K-> pi pi decays and in particular with their two pillars: the so-called Delta I=1/2 rule and the ratio epsilon'/epsilon. We devote to it a separate chapter because the QCD analysis of both perturbative and nonperturbative contributions to these decays is very challenging. Morever, it appears that the SM has significant problems in explaining the data for epsilon'/epsilon,and presently it is not yet clear whether SM dynamics are fully responsible for the Delta I=1/2 rule. We present several analytical formulas forepsilon'/epsilon and its numerical value as a function of most important hadronic parameters that should allow us to monitor future progress in the evaluation of this ratio.

With all this knowledge we will show how aFlavor Expedition to the Zeptouniverse could in principle take place. Here we will address the question which of the processes considered in our book could give us best information about NP beyond the SM. In this context we will collect low-energy observables that could be useful for the search for NP, in particular beyond the reach of the LHC. Subsequently, with the goal to distinguish various NP models we will discuss DNA charts proposed already in a number of papers.

We will begin by presenting the general structure of gauge theories, stressing their symmetries and their breakdown. The structure of the Lagrangians in this chapter will be fundamental for the full book. We will encounter Lagrangians involvingspin-0, spin-1/2, and spin-1 fields. We will also collect literature in which further details can be found. But the information provided in this chapter should be sufficient for following the book.

This is one of the most important steps in our expedition. Here we will first discuss the concept of the operator product expansion (OPE) and the renormalization group equations for the Wilson coefficient functions of the operators present in the SM. In this part we will first concentrate our discussion on the simplest operators: current-current operators.We will calculate their coefficients including not only leading QCD effects(LO) but also nonleading ones (NLO). In more complicated cases we will indicate how such calculations should be done and present only the results for them.

Finally, we will be able to present a grand summary of weak decays, list open questions, andpresent a shoping list for the coming years.

We discuss here the choice of solid compounds and materials which best suit various types of applications, focusing mainly on the polarized targets. These materials include hydrogen-rich glassy hydrocarbons and simple cubic crystalline ammonia and lithium hydrides. The glassy hydrocarbons can doped by dissolved stable free radicals, while crystalline materials are doped by radiolytic paramagnetic radicals. The leading application of DNP up till now has been the scattering experiments in high-energy and nuclear physics. Other applications include measurements of slow neutron cross-sections, molecular physics using slow neutrons, nuclear magnetism and other solid-state physics experiments, and spin filters. The use of polarized solids in fusion and in magnetic resonance imaging has also been discussed. The material choice evidently depends strongly not only on the application but also on the goal of the experiment or process which is considered. More recently DNP has been used for the signal enhancement in NMR studies of complex chemical and biochemical molecules. In this context DNP and other enhancement techniques are called by the term “hyperpolarization”.

The principles of the continuous-wave (CW) NMR techniques is reviewed, as applied to the measurement of the nuclear polarization in polarized targets. The circuit theory of the series-tuned Q-meter is then described in detail in view of calculating precisely the CW NMR absorption signal and its integral, the signal-to-noise ratio, the probe coupling and sampling, and the signal saturation. Optimization of the series-tuned Q-meter circuit is discussed on the basis of the circuit theory. Improved Q-meter circuits will be reviewed, including the capacitively coupled Q-meter, the crossed-coil NMR circuit, and the introduction of quadrature mixer that enables the measurement of the real and imaginary parts of the RF signal simultaneously. Calibration and measurement of very small NMR signals then follows. We also treat the signal-to-noise issues, the electromagnetic interferences, and the NMR circuit drift issues.