unity which ensures that the total cross section is given by the LO result.

In the POWHEG approach, the inclusive differential cross section for the hardest emission is given by the QCD NLO differential cross section, that is d \^[[PO]{}]{}=|[B]{}(\_N) d\_N , \[eq:PO\] where $\bar{B}(\Phi_N) $ is defined by $$\begin{aligned}
  \bar{B}(\Phi_N) = B(\Phi_N) &+ \left[V(\Phi_N) + \int C(\Phi_N, \Phi_R) d\Phi_R\right]  \nonumber \\
&+ \int\left[R(\Phi_N, \Phi_R) d\Phi_R- C(\Phi_N, \Phi_R) d\Phi_R\right]. \label{eq:Bbar}\end{aligned}$$ The real-emission contribution, $R(\Phi_N, \Phi_R)$, corresponds to the radiation of an additional parton from the LO interaction and the virtual contribution, $V(\Phi_N)$, comes from the 1-loop correction to the LO process. $C(\Phi_N, \Phi_R)$ is a counter term with the same singular behaviour as the real and virtual contributions and is introduced to ensure the two square brackets in Eq. \[eq:Bbar\] are separately finite. The Sudakov form factor appearing in Eq. \[eq:PO\] is \^[PO]{}(p\_T) = ( - d\_R (p\_T (\_R ) -p\_T ) ). \[eq:POSudakov\] As with the conventional parton shower approach, the square bracket in Eq. \[eq:PO\] will integrate to unity and hence the total inclusive cross section will be given by the NLO result.

Typically, the counter term, $C(\Phi_N, \Phi_R)$, can be rewritten as a sum of dipole functions, 