NLO supersymmetric-QCD corrections to stop pair associated by $Z^0$ production at the LHC

We present the calculations of the production of $\widetilde{t_1}\overline{\widetilde{t_1}}{Z}^0$ in the minimal supersymmetric standard model at the Large Hadron Collider at center-of-mass energies of 7 and 14 TeV. We discuss the impact of the next-to-leading-order supersymmetric-QCD corrections on the cross sections of $\widetilde{t_1}\overline{\widetilde{t_1}}{Z}^0$ production and on the transverse-momentum distributions of the final stop quark. The uncertainties of the leading-order and supersymmetric-QCD corrected cross sections due to the renormalization/factorization scale are studied. Calculations demonstrate that the next-to-leading-order supersymmetric-QCD corrections improve the scale dependence of the leading-order cross sections and enhance significantly the transverse-momentum distributions.

Figure 1

The LO Feynman diagrams for the $q\overline{q}\to \widetilde{t_1}\overline{\widetilde{t_1}}{Z}^0$ and $gg\to \widetilde{t_1}\overline{\widetilde{t_1}}{Z}^0$ subprocesses.

Figure 2

A generic set of SUSY-QCD pentagon diagrams in the subprocesses $q\overline{q}\to \widetilde{t_1}\overline{\widetilde{t_1}}{Z}^0$.

Figure 3

A generic set of SUSY-QCD pentagon diagrams in the subprocesses $gg\to \widetilde{t_1}\overline{\widetilde{t_1}}{Z}^0$.

Figure 4

Dependence of ${\sigma }^{\mathrm{NLO}}$ ($pp\to \widetilde{t_1}\overline{\widetilde{t_1}}{Z}^0$) on the soft cutoff ${\delta }_s$ of the two-cutoff method, at 7 TeV, for $\mu =m_{\widetilde{t_1}}+\frac{M_{Z^0}}{2}$ and ${\delta }_c=10^{-4}$.

Figure 5

Dependence of ${\sigma }^{\mathrm{NLO}}$ ($pp\to \widetilde{t_1}\overline{\widetilde{t_1}}{Z}^0$) on the collinear cutoff ${\delta }_c$ of the two-cutoff method, at 7 TeV, for $\mu =m_{\widetilde{t_1}}+\frac{M_{Z^0}}{2}$ and ${\delta }_s=5\times 10^{-4}$.

Figure 6

Dependence of ${\sigma }^{\mathrm{NLO}}$ ($pp\to \widetilde{t_1}\overline{\widetilde{t_1}}{Z}^0$) on the soft cutoff ${\delta }_s$ of the two-cutoff method, at 14 TeV, for $\mu =m_{\widetilde{t_1}}+\frac{M_{Z^0}}{2}$ and ${\delta }_c=10^{-4}$.

Figure 7

Dependence of ${\sigma }^{\mathrm{NLO}}$ ($pp\to \widetilde{t_1}\overline{\widetilde{t_1}}{Z}^0$) on the collinear cutoff ${\delta }_c$ of the two-cutoff method, at 14 TeV, for $\mu =m_{\widetilde{t_1}}+\frac{M_{Z^0}}{2}$ and ${\delta }_s=5\times 10^{-4}$.

Figure 8

Scale dependence of the LO and NLO cross section at the 7 TeV LHC.

Figure 9

Scale dependence of the LO and NLO cross section at the 14 TeV LHC.

Figure 10

LO and NLO transverse-momentum distributions for stop at the 7 TeV LHC for $\mu ={\mu }_0$.

Figure 11

LO and NLO transverse-momentum distributions for stop at the 14 TeV LHC for $\mu ={\mu }_0$.