W production and decay in pp collisions

The main production mechanism and its subsequent decay say into can be visualized in the quark-parton model as in Fig. 5.3. Let /s be the CM energy of the pp collision. The cross-section s) to produce a of invariant mass /s will depend upon the elementary cross-section for ud — multiplied by the flux of u and d 

By definition this should equal the W production cross-section crvy(s) 

To obtain an estimate for the branching fraction we require the partial width r(W ud). As will be discussed in Chapter 9 quarks are assumed to couple to the W like the leptons (aside from the complication of Cabibbo mixing and its generalization, which we here ignore). To be precise we shall go through the calculation of r(W — in full detail 

The decay rate for in its rest frame is then given by 

The -function in (5.3.4) ensures energy-momentum conservation, so that K = p + q. Then remembering that = 0 we have 

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