We investigate Higgs-boson pair production at the LHC when the final
state system arises from decays of vector-like quarks coupling to the Higgs
boson and the Standard Model quarks. Our phenomenological study includes
next-to-leading-order QCD corrections, which are important to guarantee accurate
predictions, and focuses on a detailed analysis of a di-Higgs signal in the four

Article funded by SCOAP3

945$\,GeV constraint. For masses above this limit, the most stringent and sole constraint arises from searches for singly-produced $B$ quarks subsequently decaying into a $Wq$ system that is produced by $u\bar{u}$ annihilation. The reason is twofold. First, the corresponding CMS search is charge-sensitive and specifically targets the presence of $W^-$ bosons in the final state. Next, the other relevant single VLQ production option giving rise to $W^-$ bosons involves an $\bar{X}$ resonance. The latter can only be produced via $\bar{u} \bar{u}$ annihilation that is suppressed by the parton densities, which renders the search ineffective. This motivates the development of a future search for $W^+q$ VLQ decays, which could benefit from a parton-density-enhanced $u u$ initial state. Making use of the results of ref.~\cite{CMS-ml-2016pul} and eq.~\eqref{eq:kapbr}, we derive a bound on the $\kappa^B_R$ coupling that depends on the $B$ quark mass (left panel of figure~\ref{fig:m1}). In the right panel of figure~\ref{fig:m1}, we re-express the results, via the mixing angle $\varphi_R$, in terms of the $T$ coupling to the Higgs boson and the $T$-quark mass. The red area indicates the bounds derived from VLQ pair production, and the blue region reflects the single-VLQ production constraints. Further constraints could however arise from EW precision tests~\cite{Cacciapaglia-ml-2015ixa}. \begin{figure} \centering \includegraphics[width=0.49\textwidth]{figs/kapBvsMB.pdf} \hfill \includegraphics[width=0.49\textwidth]{figs/kapTvsMT.pdf} ]]>

20~{\rm GeV} \qquad \text{and} \qquad |\eta^j|< 2.5 \,. \label{eq:AK4PtEta} \ee \looseness=-1 Jets are potentially tagged as $b$-jets with an efficiency extracted from the maps provided in ref.~\cite{Chatrchyan-ml-2012jua} and we additionally constrain the transverse momentum of all $b$-tagged jets to fulfil \be p_T^b > 40~{\rm GeV}\; ~\mbox{(ATLAS)} \qquad\text{or}\qquad p_T^b > 30~{\rm GeV}\; ~\mbox{(CMS)} \ee in our ATLAS-like and CMS-like analysis, respectively. In both our resolved analyses, we select events that contain at least four resolved $b$-tagged jets, \be N(b) \geq 4 \,. \ee The four leading $b$-jets are then combined into two pairs of jets for which the angular distance in the transverse plane obeys \be \Delta R (b,b) < 1.5\,, \label{eq:DRbbCMS} \ee each pair of $b$-jets being assumed to originate from the decay of a Higgs boson. \looseness=-1 In the CMS-like analysis, we follow the \emph{medium-mass region} selection~\cite{CMS-ml-2016tlj} that has been designed to optimally probe resonantly produced di-Higgs systems where the resonance mass lies between 400\,GeV and 1200\,GeV\@. Denoting by $M_{h_1}$ and $M_{h_2}$ the invariant masses of the two reconstructed Higgs boson candidates, we select events for which these masses satisfy \be \chi_{\rm CMS}^2 = \bigg( \frac{M_{h1}-\bar M_h}{\sigma_h}\bigg)^2 + \bigg( \frac{M_{h2}-\bar M_h}{\sigma_h} \bigg)^2 < 1 \,, \label{eq:chi2CMS}\ee where $\bar M_h$ is the average mean of the $M_{h_1}$ and $M_{h_2}$ distributions and is equal to 115\,GeV\@. We moreover choose a width $\sigma_h=23$\,GeV, as stemming from the CMS procedure for increasing the analysis sensitivity in the medium-mass region. In contrast, our ATLAS-like analysis includes first a selection on the transverse momentum, pseudorapidity and invariant mass of the reconstructed Higgs bosons. The transverse momentum of the leading reconstructed Higgs-boson candidate $p_T(h_1)$ is constrained to~fulfil \be p_T(h_1) > \left\{ \begin{array} {l l} 200~{\rm GeV} \qquad & \text{for}~m_{4j} < 600~{\rm GeV} \,,\\ 0.65\ m_{4j} - 190~{\rm GeV} \qquad & \text{for}~m_{4j} \in [600, 910]~{\rm GeV} \,,\\ 400~{\rm GeV} \qquad & \text{for}~m_{4j} > 910~{\rm GeV} \,, \end{array}\right. \ee where $m_{4j}$ is the invariant mass of the system made of the two reconstructed Higgs bosons (or equivalently of the four leading $b$-jets), while the transverse momentum of the subleading Higgs-boson candidate $p_T(h_2)$ must obey \be p_T(h_2) > \left\{ \begin{array} {l l} 150~{\rm GeV} \qquad & \text{for}~m_{4j} < 520~{\rm GeV} \,,\\ 0.23\ m_{4j} + 30~{\rm GeV} \qquad & \text{for}~m_{4j} \in [520, 990]~{\rm GeV} \,,\\ 260~{\rm GeV} \qquad & \text{for}~m_{4j} > 990~{\rm GeV} \,. \end{array}\right. \ee Moreover, the two reconstructed Higgs bosons are required to be not too separated in pseudorapidity, \be |\Delta\eta(h_1, h_2)| < \left\{ \begin{array} {l l} 1 \qquad & \text{for}~m_{4j} < 820~{\rm GeV} \,,\\ 0.0016\ m_{4j} - 0.28 \qquad & \text{for}~m_{4j} > 820~{\rm GeV} \,. \end{array}\right. \ee A final selection is imposed on the two masses of the reconstructed Higgs bosons $M_{h_1}$ and~$M_{h_2}$, \be \chi_{\rm ATLAS}^2 = \bigg( \frac{M_{h_1}-\bar M'_h}{0.1\ M_{h_1}}\bigg)^2 + \bigg( \frac{M_{h_2}-\bar M_h}{0.1\ M_{h_2}} \bigg)^2 < 2.56 \,, \label{eq:ATLASresolved}\ee with $\bar M'_h = 124$\,GeV. ]]>

200~{\rm GeV} \qquad\text{and}\qquad |\Delta\eta(h_1, h_2)| < 1.3\,. \label{eq:CMSDeta} \ee The final discriminant variable in the CMS-like boosted analysis is the reduced mass \be m_{\rm red} = m_{4j} - \Big(M_{h_1}-M_h\Big) - \Big(M_{h_2}-M_h\Big) \label{eq:mred}\ee with $M_h = 125$\,GeV and $m_{4j}$ abusively denoting the invariant mass of the di-Higgs system (for having consistent notations with the previous section). The reduced mass $m_{\rm red}$ is further imposed to be greater than 1\,TeV. \looseness=-1 For the ATLAS-like analysis, the `fat jet' $J_{h}^A$ (with $A$ standing for ATLAS) is defined by once again using the anti-$k_t$ jet algorithm but with this time a distance parameter set to \be R = 1.0\,. \ee While CMS uses boosted jet algorithms based on particle-flow tracks~\cite{Khachatryan-ml-2014vla,CMS-PAS-PFT-09-001}, the ATLAS collaboration reconstructs its fat jets (also called large-$R$ jets~\cite{ATLAS-CONF-2014-018}) from the information extracted from the topological clusters of the hadronic calorimeter. In our ATLAS-like boosted analysis, large-$R$ jets are clustered within the {\sc FastJet} version embedded into \de\, and then trimmed~\cite{Krohn-ml-2009th}, before we apply constraints on the invariant mass ($m^{J_{h}^A}$), pseudorapidity and transverse momentum of the two leading fat jets, \be m^{J_{h}^A} > 50~{\rm GeV}\,,\qquad |\eta(J_{h}^A)| < 2 \qquad\text{and}\qquad p_T(J_{h}^A)| > 250~{\rm GeV}. \ee The signal region is defined by imposing extra constraints on the two leading fat jets that are identified as the two reconstructed Higgs bosons $h_1$ and $h_2$, \beq p_T(h_1) > 350~{\rm GeV}\,, \quad p_T(h_2) > 250~{\rm GeV} \, \quad \text{and}\quad |\Delta\eta(h_1, h_2)| < 1.7 \,, \eeq and by enforcing the $\chi^2_{\rm ATLAS}$ variable defined in eq.~\eqref{eq:ATLASresolved} to fullfil \beq \chi^2_{\text{ ATLAS}} < 2.56\,. \eeq After these selection, we derive the invariant mass of the reconstructed Higgs bosons pair $m_{2J}$ that is used in the ATLAS analysis, to characterise the signal. ]]>

800$\,GeV, the single VLQ production channel leads to efficiencies that are higher than for pair production. The inclusion of this channel is therefore useful to assess the LHC sensitivity to VLQ models by means of di-Higgs probes more accurately. A stronger reach can hence be expected, as already suggested by the results shown in figure~\ref{fig:CX2D}. \begin{figure} \centering \includegraphics[width=0.475\textwidth]{figs/catlas.pdf} \hfill \includegraphics[width=0.49\textwidth]{figs/c1_CMSrecast_resolved.pdf} ]]>