Charged current scaling functions

For CC reactions the relevant term in the Lagrangian for the hadron to absorb a W is h W which according to (9.3.10) and (9.2.1) describes the quark transitions at the hadronic vertex, shown in Fig. 16.8 (a) 

Similarly the above term in the Lagrangian generates the antiquark transitions shown in Fig. 16.8 (6). 

The transitions do not all have the same strength and are controlled by the elements of the KM matrix introduced in Section 9.2 and whose determination is studied in Chapter 18. From the form of /i+ one has the following couplings for the quark and antiquark transitions  

In writing down the contributions to the scaling functions we have to compute matrix elements of these couplings. Then in comparing an antiquark matrix element with that of the analogous quark matrix element 

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In NC reactions initiated by a charged lepton, as discussed in Section 15.5, it becomes necessary to take into account interference between 7 and exchange when cannot be neglected compared with M. The cross-section formula (15.5.10) requires the scaling functions F y,Ff discussed already and the interference scaling functions F defined in terms of the currents in (15.5.11). 

For electrolyses involving time scales shorter than about 500 /is, the diffusion layer is of the same order as S, and the absorbance is sensitive to the evolving concentration profile of R (6, 46, 47). The resulting optical transients can be useful for characterizing rather fast electrochemical processes, which are otherwise complicated severely by nonfaradaic contributions to current and charge functions. Theoretical absorbance transients can be computed from (17.1.13), once the diffusion-kinetic equations defining the concentration profile of R have been solved, either analytically or by numeric methods such as digital simulation. 

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