Theory implementation

The leading order Alpgen Monte Carlo program have been used to generate $W\to e\nu$ + n parton events samples for n = 1,2,3 and 4. The parton kinematic were fixed by the following cuts:

• parton:
  • $p_T\ge 8$ GeV
  • $\vert\eta\vert\le 3$
  • $\Delta R \ge 0.2$, where $\Delta R = \sqrt{\Delta \eta^2+\Delta\phi^2}$
• leptons:
  • $p_T\ge 1$ GeV
  • $\vert\eta\vert\le 5$

The parton density functions were set to CTEQ5L (these functions are extracted by a one loop calculation assuming 5 quark flavours). The strong coupling constant $\alpha_s$ was fixed to 0.127 at the $Z^0$ mass and a one-loop evolution expression was used to extract $\alpha_s$ at the $q^2$ of the process.

The electroweak parameters used in the calculation are reported in the following table.

Table: Electroweak generation parameters

parameter	$M_W$	$M_Z$	$G_F$
value	80.41 GeV	91.188 GeV	1.16639 $\times 10^{-5}~\mathrm{GeV}^{-2}$

The main limitation of a leading order calculation is the dependence on the renormalization scale choice of the process. To compare the results obtained in this analysis 4 different $q^2$ scales have been used: $(2\cdot M_W)^2$, $(M_W/2)^2$, $M_W^2+\Sigma (p^{jets}_T)^2$ and $<(p^{jets}_T)^2>$.

Parton level events were then processed by the Herwig Monte Carlo shower program to add initial and final state radiation and to fragment partons into hadrons. These events were finally passed through full Geant detector simulation and were reconstructed with the same offline code used for data.

The final events were required to have not more than one parton associated to a reconstructed jet.