Associated production of a top quark and a charged Higgs boson

We compute the inclusive and differential cross sections for the associated production of a top quark along with a charged Higgs boson at hadron colliders to next-to-leading order (NLO) in perturbative quantum chromodynamics (QCD) and in supersymmetric QCD. For small Higgs boson masses we include top-quark pair production diagrams with subsequent top-quark decay into a bottom quark and a charged Higgs boson. We compare the NLO differential cross sections obtained in the bottom parton picture with those for the gluon-initiated production process and find good agreement. The effects of supersymmetric loop contributions are explored. Only the corrections to the Yukawa coupling are sizable in the potential discovery region at the CERN Large Hadron Collider (LHC). All expressions and numerical results are fully differential, permitting selections on the momenta of both the top quark and the charged Higgs boson.

Figure 1

The leading-order Feynman diagrams for the production process $gb\to t{H}^{-}$. We indicate how the bottom partons are created through gluon splitting.

Figure 2

Cross section dependence on the cutoff parameters ${\delta }_c$ and ${\delta }_s$ at the LHC energy. Left: The soft cutoff ${\delta }_s$ is fixed to different values. Right: two-dimensional logarithmic dependence on both cutoff parameters.

Figure 3

The scale variation of the cross sections at the LHC for $m_H=250\mathrm{GeV}$ and $\tan \beta =30$. The central values are ${\mu }_R^0=M/2$ and ${\mu }_F^0=M/5$. The four panels show the leading-order cross section, the complete NLO cross section, the $gb$ induced NLO cross section and the $gg$ induced contribution to the NLO cross section.

Figure 4

Left: The $t{H}^{-}$ inclusive cross section at the LHC as a function of $\tan \beta$. The solid curve is the NLO result, with the scale variations around the central scale $\mu /{\mu }_0=1/4-4$ indicated by the thinner solid curves. Also shown are the leading-order result with a running bottom-quark Yukawa coupling (dashed curve) as well as a pole-mass Yukawa coupling (dotted curve). Right: The total cross section at the LHC as a function of the charged Higgs boson mass as the solid curve. The NLO and LO cross sections are shown as the dashed upper and lower curves, respectively. The dotted curves show the cross sections for $pp\to t{\overline{t}}^{*}+X$ with a subsequent decay $\overline{t}\to \overline{b}{H}^{-}$ in the Breit-Wigner approximation $({\sigma }_{\mathrm{BW}})$ and that including the complete set of off-shell diagrams $({\sigma }_{\mathrm{off}\mathrm{\text{−}}\mathrm{shell}})$.

Figure 5

The cross section for the Tevatron ($2\mathrm{TeV}$) as a function of the charged Higgs boson mass. We also show the cross sections for $pp\to t{\overline{t}}^{*}+X$ with a subsequent decay ${\overline{t}}^{*}\to \overline{b}{H}^{-}$ in the Breit-Wigner approximation and including the complete set of off-shell diagrams.

Figure 6

The kinematic distributions for the heavy final-state particles at the LHC: transverse momentum and rapidity of the charged Higgs boson (left) and the top quark (right) for the process $gb\to t{H}^{-}$. The dashed curve shows the leading-order distribution with the central choice of scales. The solid and the dotted curves represent the NLO results for three choices of the bottom quark and the gluon factorization scale ${\mu }_F=M/5$, ${\mu }_F=20\mathrm{GeV}$ and ${\mu }_F=10\mathrm{GeV}$. The bottom row shows the distribution of the invariant mass of the top quark and the Higgs boson pair from the LO and NLO calculations, plus a rescaled NLO distribution (the last panel). The scaling factor involves the gluon parton densities at the different factorization scales.

Figure 7

The kinematic distributions for the final state at the LHC: the top-quark transverse momentum and the invariant mass of the top quark and the Higgs boson pair. We compare the NLO result for the process $gb\to t{H}^{-}$ with the process $pp\to \overline{b}t{H}^{-}+X$. Apart from the complete set of diagrams with the physical bottom-quark mass, we show the purely $q\overline{q}$ induced process and the complete set of diagrams with a mathematical cutoff instead of the physical bottom-quark mass $m_b\to 0.46\mathrm{GeV}$.

Figure 8

LO and NLO $p_T$ distribution of the Higgs boson, with cuts $p_{T,t}>50\mathrm{GeV}$ or $p_{T,t}>100\mathrm{GeV}$ on the transverse momentum of the top quark. The Higgs boson mass is $m_H=250\mathrm{GeV}$, and $\tan \beta =30$.

Figure 9

Left: Normalized distributions in $\Sigma p_T$ (defined in the text) for the NLO process $gb\to t{H}^{-}$, for $m_H=250\mathrm{GeV}$ and $500\mathrm{GeV}$. Right: A two-dimensional plot of the correlation between $\Sigma p_T$ and $\Delta \varphi$, for $m_H=250\mathrm{GeV}$ and $\tan \beta =30$.

Figure 10

The supersymmetric contributions to the NLO cross section for $gb\to t{H}^{-}$, with the dotted curve showing the resummed ${\Delta }_b$ contribution and the solid curve showing the combination of the resummed ${\Delta }_b$ and non-${\Delta }_b$ contributions. The supersymmetric parameters are described in Table . The central value of $\mu$ in SPS4 is noted in the plot; the central value of $\tan \beta$ in SPS5 is at the lower end of the plot, $\tan \beta =5$. All parameters and masses except for $\mu$ and $\tan \beta$ are kept constant. The curves denoted ${\sigma }_{2\mathrm{HDM}}$ show NLO QCD cross sections without SUSY contributions.

Figure 11

The supersymmetric contributions to the NLO prediction for the cross section $gb\to t{H}^{-}$. The supersymmetric parameter points are the scenarios A and C, picked from Ref. 37. All parameters and masses except for $\mu$ are kept constant. The gluino mass in both scenarios is $1\mathrm{TeV}$; the lighter top-squark and bottom-squark masses are $0.5\mathrm{TeV}$ for scenario A (left-hand side) and $1\mathrm{TeV}$ for scenario C (right-hand side). The top-squark mass difference is $100\mathrm{GeV}$ and the bottom-squark mass difference $150\mathrm{GeV}$. In contrast to Ref. 37 we resum only the SUSY-QCD corrections. The curves denoted ${\sigma }_{2\mathrm{HDM}}$ show NLO QCD cross sections without SUSY contributions.