on statistical basis which leg emits “first” (such an emission is the only one that matters as far as MC@NLO is concerned), the shower variables are related to the momenta given in eq. (\[Rproc\]) as follows: z&=&, \[shvz\]\
t\_i & = &(p\_i -k\_2)\^2, \[shvQ2\] with $i=1,2$ for the emissions from the parton coming from the left and from the right respectively. The branching generated with eqs. (\[shvz\]) and (\[shvQ2\]) is such that the Bjorken $x$’s associated with the initial-state partons of eq. (\[Rproc\]) (which we shall denote by ${z_1}$ and ${z_2}$) are [z\_1]{}=[\_1]{}/z,[z\_2]{}=[\_2]{}for an emission from leg 1, and [z\_1]{}=[\_1]{},[z\_2]{}=[\_2]{}/z for an emission from leg 2. In the branching, the c.m. energy of the Born-level subprocess is conserved (which, in the present case, is equivalent to the requirement that the virtuality of $V$ be a constant), and thus s=(p\_1+p\_2)\^2=[z\_1]{}[z\_2]{}S=s\_0/z. \[ss0z\] An easy way to achieve this is that of imposing that the Bjorken $x$’s of the Born-level subprocesses, ${\zeta_i}$, be separately conserved.

As shown in ref. [@Frixione:2002ik], the event-projection procedure can be formally determined by constructing two “observables” that are conserved in the branching process. According to what has been discussed above, a possible choice is: O\_1&=&[\_1]{}[\_2]{}S, \[Obs1\]\
O\_2&=&. \[Obs2\] 