We propose a new search strategy for quark partners which decay
into a boosted Higgs and a light quark. As an example, we consider
phenomenologically viable right handed up-type quark partners of mass

Article funded by SCOAP3

310$\,GeV) is very mild as the experimental searches were not designed to search for Higgs bosons arising from composite light quark partner decays. The main focus of this paper is to design a dedicated search for singlet partners of light quarks, and study the potential of such searches to discover the quark partners at the Run II of the LHC. For the purpose of illustration, we study right-handed up-type quark partners, which are QCD pair-produced and decay dominantly into a Higgs boson and an up-type quark. We design the analysis in an effective theory framework, such that --- although being motivated by composite quark partner searches --- our results can be applied to any heavy vector-like quark model in which the vector-like quark has a decay channel into a Higgs and a light quark. We focus on the potential of LHC Run II to probe light quark partners of mass $\sim 1 \TeV$, where the decays of light quark partners typically result in boosted Higgs bosons. In order to increase the signal rate, we consider only the decays of the Higgs boson to a $b\bar{b}$ pair. Seemingly complicated, such final states are particularly interesting, as traditional event reconstruction techniques fail. Due to the large degree of collimation of Higgs decay products, methods of Higgs tagging via ``jet substructure'' need to be employed~\cite{Butterworth-ml-2008iy}. In addition, the boosted di-Higgs event topology accompanied by two light jets offers a myriad of handles on large SM backgrounds. As we will show in the following sections, a combination of kinematic constraints of pair produced heavy particles, boosted Higgs tagging and double $b$-tagging is able to achieve a signal to background ratio $S/B > 1$ for light quark partner masses of 1\,TeV. The same analysis shows that signal significance of $\sim 7 \sigma$ can be achieved with $35 \fb^{-1}$ of integrated luminosity, sufficient to claim a discovery. \looseness=-1 For the purpose of boosted Higgs tagging, we use the Template Overlap Method (TOM)~\cite{Almeida-ml-2011aa,Almeida-ml-2010pa, Backovic-ml-2012jj, Backovic-ml-2013bga}. We propose a new form of overlap analysis which utilizes both Higgs template tagging and top template tagging in order to optimize the rejection of SM backgrounds while maintaining sufficient signal efficiency. The ``multi-dimensional'' TOM tagger compares the likelihood that a boosted jet is a Higgs to the likelihood that a boosted jet is a top quark, whereby a Higgs tag assumes that a jet is sufficiently Higgs like and not top like. Furthermore, we find that requiring at least one $b$-tag in each of the Higgs tagged jets significantly improves signal purity, especially with respect to large multi-jet backgrounds. We organized the paper in three sections. Section~\ref{sec:model} summarizes the theoretical framework of MCHM with partially composite RH up-type quark partners and introduces the effective model of the light up-type quark partners. In section~\ref{sec:model} we also discuss the diagonalization of mass matrices, calculation of the couplings in the mass eigenbasis and other relevant parameters which enter the effective parametrization used throughout the paper. Section~\ref{sec:results} deals with a phenomenological study of LHC Run II searches for up-type quark partners. We propose and discuss in detail a set of observables which can be used to efficiently detect and measure the partners at $1 \TeV$ mass scales, as well as present results on $S/B$ and signal significance using our cutflow proposal. We conclude in section~\ref{sec:conclusions}. A brief discussion of models in which the quark partner is not dominantly RH can be found in the appendix. ]]>

800 \GeV$ established by CMS~\cite{Chatrchyan-ml-2013wfa}. \item The singlet top partner $\tilde{T}\equiv \tilde{U}_3$ (as well as the the charge 2/3 partners in $Q^U_3$ multiplet) has decay channels into $tZ$, $th$, and $Wb$. CMS established a lower bound on the mass of a charge 2/3 partner of 687~-~782\,GeV~\cite{Chatrchyan-ml-2013uxa}, with the strongest bound applying if $\tilde{T}\rightarrow tZ$ is the dominating decay. The analogous ATLAS bounds are $\sim$~350~-~810\,GeV~\cite{Aad-ml-2014efa}. \item 3rd family charge -1/3 partners can decay into $bZ$, $bh$, and $Wt$. CMS constrained their mass to lie above 582~-~785\,GeV, again depending on the branching ratios~\cite{CMS-ml-2013una,CMS-ml-2012hfa}.\footnote{Again, the bounds are strongest when the branching ratio into $Zb$ is large. However, a recent CMS study~\cite{CMS-ml-2014bfa} focussed on the the all-hadronic channel $pp\rightarrow B\bar{B}\rightarrow hbh\bar{b}\rightarrow b\bar{b} b b \bar{b}\bar{b}$ and showed that limits are improved when making use of jet-substructure techniques. Assuming 100 \% branching ratio of $B\rightarrow hb$,~\cite{CMS-ml-2014bfa} obtained a lower bound on the mass of 846\,GeV.} The current ATLAS lower mass bound on the charge $-1/3$ partners is $\sim$~350~-~800\,GeV~\cite{Aad-ml-2014efa}. \item Bounds on partners in the multiplets $Q^U_{1,2}$ have been studied in detail in ref.~\cite{Delaunay-ml-2013pwa}, where a bound of $\left(M^U_{4}\right)_{1,2} > 530 \GeV$ for QCD pair produced partners was established, which also applies to partners in the $Q^D_{1,2}$ multiplets. These bounds on light quark partners are weaker than the bounds on 3rd generation quark partners. Third generation partners decay into electroweak gauge bosons (or a Higgs) and a third generation quark, leading to final states which can be efficiently ``tagged'' at the LHC and hence allow to reduce or eliminate the numerous SM backgrounds. On the other hand, partners of light quarks decay into light quark flavors which are significantly more difficult to distinguish from the SM background channels. \item So far, the most unconstrained partners are the light quark singlet partners $\tilde{U}_{1,2}$ and $\tilde{D}_{1,2}$. The dominant decay mode into $ h j$, leads to a (potentially large) di-Higgs signature which has not been searched for at LHC run I.\footnote{ATLAS~\cite{Aad-ml-2014xxy,ATLAS-ml-2014xxx} and CMS~\cite{CMS-ml-2014eub,CMS-ml-2013eua} published results on di-Higgs signals which result from the decay of a heavy resonance (KK-graviton or, respectively, a heavy Higgs), but these searches do not apply to the di-Higgs signal considered here, as the sum of the invariant mass of the decay products does not form a resonance in our case.} The only constraint we are aware of has been obtained in ref.~\cite{Flacke-ml-2013fya}, where the absence of $h\rightarrow \gamma\gamma$ decays with high $p^{\gamma\gamma}_T$ has been used to establish a bound of $M_1 > 310$\,GeV. \end{itemize} In this article, we study the discovery reach for the weakest constrained and therefore potentially lightest quark partner at LHC run II: a light-quark $\SO(4)$ singlet partner. Focussing on the singlet partner, the model defined in eq.~(\ref{eq:defgenmod}) can be simplified. For simplicity, we take the limit $M_4 \gg M_1$, and discuss the model for the up-partner only. Note that the phenomenology of $d,s,c$ partners is analogous.\footnote{In this article we focus on parameter independent bounds which arise from QCD pair production of quark partners. For (parameter dependent) single production, the quark flavor affects the production cross section (\cf~\cite{Flacke-ml-2013fya}).} Under these simplifying assumptions, the Lagrangian of the up-quark sector following from eq.~(\ref{eq:defgenmod}) is~\cite{Flacke-ml-2013fya} \beq \begin{split} \mathcal{L}&= i \bar{\tilde U}\slashed{D}\tilde U -M_1\bar{\tilde{U}}\tilde{U} + i\ \bar{q}_L\,\slashed{D}q_L +i\ \bar{u}_R\,\slashed{D}u_R\\ &\quad -\left[-\frac{y_L}{\sqrt{2}} f \bar{u}_L \sin\left(\frac{h+\langle h\rangle}{f}\right) \tilde{U}_R + y_R f\bar{\tilde{U}}_L \cos\left(\frac{h+\langle h\rangle}{f}\right) u_R+\mbox{h.c.}\right].\label{pcLag1}\ \end{split} \eeq Expanding around the vacuum expectation value $ \langle h \rangle$ yields the effective quark mass terms \beq \mathcal{L}_m=-(\bar{u}_L, \bar{\tilde{U}}_L) M_u \left(\begin{array}{c} u_R\\ \tilde{U}_R \end{array}\right)+ \mbox{h.c.} \mbox{\hspace{8pt} with \hspace{8pt}} M_u= \left( \begin{array}{cc} 0& -\frac{y_L}{\sqrt{2}}f \sin \epsilon\\ y_R f \cos\epsilon & M_1 \end{array} \right) \equiv \left( \begin{array}{cc} 0& m_L\\ m_R & M_1 \end{array} \right). \eeq Note that the effective mass terms $m_L$ and $m_R$ arise from the left- and right-handed pre-Yukawa mass terms which have inherently different symmetry properties. The $y_L$ coupling links a fundamental fourplet to a composite $\SO(4)$ singlet while the $y_R$ coupling links a fundamental singlet to a composite fourplet. Therefore, $y_L$ and $y_R$ are independent parameters which are not required to be of the same order of magnitude by naturalness. For simplicity, we choose $y_R \gg y_L$ here, and discuss consequences of the opposite limit $y_R \lesssim y_L$ in appendix~\ref{app:yLlyR}. For $y_R \geq y_L$, the mixing mass terms have a hierarchy $m_R \gg m_L$. The eigenvalues of the squared mass matrix are \bea M^2_{u_l}&=&\frac{m_L^2m_R^2}{M^2_1+m_L^2+m_R^2}\left[1+\mathcal{O}\left(\frac{m_L^2 m_R^2}{\left(M_1^2+m_L^2+m_R^2\right)^2}\right)\right]\approx \frac{m_L^2m_R^2}{M^2_{U_h}}\label{Mul}\, ,\\ M^2_{U_h}&=&\left(M_1^2+m_L^2+m_R^2\right)\left[1+\mathcal{O}\left(\frac{m_L^2 m_R^2}{\left(M_1^2+m_L^2+m_R^2\right)^2}\right)\right]\approx \left(M_1^2+m_R^2\right), \eea where the lighter eigenvalue $M_{u_l}$ is to be identified with $m_u$, implying $|m_Lm_R|/M_1^2\ll 1$. The bi-unitary transformation which diagonalizes the mass matrix is a rotation by $\varphi_{L,R}$ on the left- and right-handed up-quarks where \beq \tan{\varphi_{R}}\approx \frac{m_{R}}{M_1}\gg \tan{\varphi_{L}}\approx \frac{m_{L}}{M_1}\,. \label{eqmixangles} \eeq The couplings of the mass eigenstates to the $Z$ bosons follow from rewriting \beq \mathcal{L}_Z = (\bar{u}_L , \bar{\tilde{U}}_L) \left[ \frac{g}{2 c_w}\left( \begin{array}{cc} 1 & 0 \\ 0 & 0 \end{array} \right)-\frac{2 g}{3}\frac{s^2_w}{c_w}\cdot \mathbbm{1}\right] \slashed{Z} \left(\begin{array}{c} u_L\\ \tilde{U}_L \end{array} \right) - \frac{2 g}{3}\frac{s^2_w}{c_w}(\bar{u}_R, \bar{\tilde{U}}_R)\slashed{Z}\cdot \mathbbm{1}\left(\begin{array}{c} u_R\\ \tilde{U}_R \end{array} \right), \label{ZLag} \eeq \looseness=-1 in the mass eigenbasis $(u_l,U_h)$. Note that the couplings arising from the $\U(1)_X$ gauge couplings are universal. A rotation into the mass eigenbasis of these terms does not induce any ``mixed'' interactions of the $Z$ to $u_l$ and $U_h$ and leaves the $Z$ couplings to right-handed light quarks unaltered. Mixing in the left-handed sector induces non-universality of the light quark couplings to the $Z$, but the correction to the left-handed coupling is of order $\sin^2\varphi_L \sim m^2_L/M^2_1 \ll m_u/M_1\sim \mathcal{O}(10^{-6})$, such that corrections to the hadronic width of the $Z$ are negligible.\footnote{For $d,s,c$ partners, the analogous corrections are $\ll$ $10^{-6}, 10^{-4}, 10^{-3}$ such that no bounds apply as long as $y_R\geq y_L$.} The ``mixed'' coupling of the $Z$ to $u_l$ and $U_h$ in the left-handed sector is \beq g^{L}_{U_h u_l Z} = g \frac{\cos \varphi_L\sin \varphi_L}{2 c_w}\approx \frac{g}{2 c_w}\frac{m_L}{M_1}\,.\label{Zeff} \eeq \looseness=-1 Analogous to the neutral current, the mass mixing in the left-handed sector also induces negligible corrections to the $Wud$ vertex and a ``mixed'' coupling between the $W$, $U_h$, and $d$: \beq g^{L}_{U_h d_l W} = \frac{g}{\sqrt{2}} \sin \varphi_L\approx \frac{g}{\sqrt{2}}\frac{m_L}{M_1}\,.\label{Weff} \eeq The Higgs couplings to the quark mass eigenstates follow from expanding eq.~(\ref{pcLag1}) to first order in $\epsilon$ and subsequent rotation into the mass eigenbasis. In the gauge eigenbasis the Yukawa terms read \beq \mathcal{L}_{\rm Yuk} = -\frac{\lambda_L}{\sqrt{2}} h \bar{\tilde{U}}_R u_L-\frac{\lambda_R}{\sqrt{2}} h \bar{\tilde{U}}_L u_R+\mbox{h.c.} \,, \eeq with \beq \lambda_L = -y_L \cos(\epsilon) \,\,\,\, \lambda_R = - \sqrt{2} y_R \sin(\epsilon)\,. \eeq Rotating into the mass eigenbasis, the mixing Yukawa interactions \beq \mathcal{L}_{\rm Yuk,mix} = -\frac{\lambda^{\rm mix}_L}{\sqrt{2}} h \bar{U}_{h,R} u_{l,L}-\frac{\lambda^{\rm mix}_R}{\sqrt{2}} h \bar{U}_{h,L} u_{l,R}+\mbox{h.c.} \,, \eeq are \beq \lambda^{\rm mix}_L = -y_L \cos(\epsilon) \cos\varphi_L \cos\varphi_R\,, \,\,\,\, \lambda^{\rm mix}_R = - \sqrt{2} y_R \sin(\epsilon) \cos\varphi_L \cos\varphi_R\,. \label{lambdapceff} \eeq In the regime $y_L\ll y_R$ considered here, the mixing couplings to $h,W,Z$ which are proportional to $y_L$ can be neglected, and the model is described by the simple effective action \beq \mathcal{L}_{\rm eff}=\mathcal{L}_{\rm SM}+\bar{U}_h\left(i\slashed{\partial}+ e \frac{2}{3}\slashed{A} -g\frac{2}{3}\frac{s^2_w}{c_w}\slashed{Z}+ g_3 \slashed{G} \right)U_h - M_{U_h}\bar{U}_hU_h -\left[\frac{\lambda^{\rm mix}_{R}}{\sqrt{2}}h\bar{U}_{h,L}u_{l,R}+\mbox{h.c.}\right]\,. \label{Lpceff} \eeq The Lagrangian in eq.~\eqref{Lpceff} and the definition of the effective coupling of eq.~\eqref{lambdapceff} is valid for up-type quark partners. The analogous calculation for down-type partners yields the same Lagrangian with the charge factors $2/3$ being replaced by $-1/3$ as directly follows from the $\U(1)_X$ charge assignments. The phenomenology of this model is particularly simple: \begin{itemize} \item The partner state $U_h$ carries color charge and can therefore be produced via QCD pair production.\footnote{For a large value of $\lambda^{\rm mix}_R\gtrsim g_s$ and depending on the partner quark flavor, additional production channels exist which have been discussed in ref.~\cite{Flacke-ml-2013fya}, however here, we focus on the parameter independent QCD pair production.} \item The dominant decay channel for the quark partner is $U_h\rightarrow u h$.\footnote{Decays into $Z u$ and $W d$ are suppressed in the regime $y_L \ll y_R$ which is described by the effective Lagrangian eq.~(\ref{Lpceff}). The decays are only present in the regime $y_L \gtrsim y_R$ with branching ratios $\Gamma_{U_h\rightarrow h u} : \Gamma_{U_h\rightarrow Z u} : \Gamma_{U_h\rightarrow W d}$ of $1:1:2$ in the limit $y_L \gg y_R$. For a detailed discussion \cf appendix~\ref{app:yLlyR}.} \end{itemize} This model hence predicts $p p \rightarrow U_h \bar{U}_h \rightarrow h h j j$ as a distinct signature at the LHC. In the following sections, we will explore the prospects for discovery of such signals at the LHC Run II, with the focus on partner masses of $\sim 1 \TeV$. In our model, the dominant branching ratio to $U_h \rightarrow uh$ is a consequence of the fact that the quark partner is an $\SU(2)$ singlet, where we assumed $y_R \gg y_L$. A dominant $uh$ branching ratio can also be achieved in model implementations where $U_h$ is a part of an $\SU(2)$ doublet, in the limit of $y_L \gg y_R$. Conversely, the regions of parameter space where $y_R \ll y_L$ (in the case of \SU(2) singlet) and $y_R \gg y_L$ (in the case of \SU(2) doublet) would result in significant branching ratios to other final state such as $Zj$ and $Wj$. Note that most of our proposal for $U_h$ searches (with the exception of our $b$-tagging strategy which would have to be modified) in the following sections can be applied to $Zj$ and $Wj$ final states as well, as the final state kinematics are most affected by the mass of $U_h$, and to a lesser degree by the structure of the $U_h \rightarrow Xj$ vertex, where $X = h, W, Z$. ]]>

15$\,GeV,~$| \eta |< 5$. Next, we shower the events with \verb|PYTHIA 6|~\cite{Sjostrand-ml-2006za} using the MLM-matching scheme~\cite{Artoisenet-ml-2010cn} with \verb|xqcut|~$> 20$\,GeV and \verb|qcut|~$> 30$\,GeV. We match the multi-jet events up to four jets, while the $t\bar{t}$ and $b\bar{b}$ samples are matched up to two extra jets. We cluster all showered events with the \verb|fastjet|~\cite{Cacciari-ml-2011ma} implementation of the anti-$k_T$ algorithm~\cite{Cacciari-ml-2008gp}. In order to perform the analysis with a manageable number of events in the background channels (i.e.\ $\sim 10^6 $), we impose a generator level cut on $H_T$, a scalar sum of all final state parton transverse momenta. The motivation for the generator level $H_T$ cut comes from the fact that pair produced light quark partner events contain two objects of mass $\sim 1 $\,TeV, implying that the signal will be characterized by $H_T$ of roughly 2\,TeV. In order to avoid possible biases on the background data by increasing the $H_T$ cut too much, we hence require $ H_T > 1.6$\,TeV on all generated backgrounds. We summarize the cross sections for the signal parameter point of $M_{Uh} = 1 \TeV$ and the most dominant backgrounds in table~\ref{tab:HT1600}. For completeness, we show the $U_h$ pair production cross section as function of $M_{Uh}$ in figure~\ref{fig:Partonic2}, where we assume ${\rm Br}(U_h \rightarrow hu) = 1$ and the branching ratio of Higgs to a pair of $b$ quarks is included. Notice that the total production cross section for partner masses above 1.3\,TeV goes into the sub-femtobarn region which will be challenging to probe at the Run II of the LHC with $35 \fb^{-1}$ of integrated luminosity. A closer look at the numerical values of the signal and background cross sections suggests that a total improvement in $S/B$ of $\mathcal{O} (10^5)$ is desired to reach $S/B \sim 1$. For that purpose, we will introduce a new cut scheme in section~\ref{sec:cutflow}, which exploits the characteristic topology and kinematic features of the signal events. \begin{figure} \centering \includegraphics[scale=0.5]{Xsection_MUh.pdf} \includegraphics[scale=0.5]{SigmaRatio_HTcut3_New.pdf} ]]>

15$\,GeV, $|\eta| < 5$ and $H_T > 0$\,GeV. Right: signal and background cross sections as a function of $H_T$ cut. The plot is normalized to NLO as in table~\ref{tab:HT1600}.]]>

1600$\,GeV), at 14\,TeV LHC. We normalize the ``$t \bar{t}$ +0,1,2 jets'' to the NNLO + NNLL result of ref.~\cite{Czakon-ml-2013goa}, while for the rest of the backgrounds we use a conservative estimate for the NLO K-factor of 2.0.]]>

0.4, \,\,\,\,\, Ov_3^t <0.4 \,. \end{equation} As we will show in the following sections, the combined requirement on $Ov_2^h$ and $Ov_3^t$ is very efficient at removing the $t\bar{t}$ fake rate. For the purpose of this analysis, we generate 17 sets of both two body Higgs and three body top templates at fixed $p_T$, starting from $p_T = 425 \GeV$ in steps of $50 \GeV$, while we use a template resolution parameter $\sigma = p_T /3$ and scale the template subcones according to the rule of ref.~\cite{Backovic-ml-2012jj}. ]]>

300$\,GeV, $| \eta |< 2.5$ \\ \cline{3-3} & & Declare the two highest $p_T$ fat jets \\ & & satisfying $Ov_{2}^h > 0.4$ and $Ov_{3}^t < 0.4$\\ & & to be Higgs candidate jets. \\ & & At least 1$b$-tag on both Higgs candidate jets. \\ \cline{3-3} & & Select the two highest $p_T$ light jets ($r=0.4$) \\ & & with $p_T > 25 \GeV$ to be the $u$ quark candidates. \\ \cline{2-3} & \multirow{4}{*}{Complex Cuts} & $|\Delta_{h} | < 0.1$ \\ & & $| \Delta_{U_h} | < 0.1$ \\ & & $m_{U_{h1,2}} > 800$\,GeV \\ \hline \end{tabular} ]]>

300 \GeV, \,\,\,\,\,\,\, |y^{R=0.7}| < 2.5\,. \end{equation} The requirement on the presence of four fat jets pre-selects signal event candidates, as we expect two pairs of boosted Higgs-light jets to appear in the final state.\footnote{Selecting 4 $R=0.7$ fat jets also simplifies the TOM jet substructure analysis. } In order to determine which of the four jets are the Higgs candidates, we select the two highest $p_T$ fat jets which satisfy the TOM requirement of \begin{equation} Ov_2^h > 0.4, \,\,\,\,\,\,\,\, Ov_3^t < 0.4 \,, \label{eq:tom_reqs} \end{equation} of section~\ref{sec:TOM}. The requirement on peak template overlap is designed to select the two Higgs candidate jets in the event, while ensuring that the jets are not fake tops. If less than two fat jets pass the overlap requirement, the event is rejected. The overlap selections in eq.~\eqref{eq:tom_reqs} deserve more attention. Figure~\ref{fig:Overlaps2d} illustrates how utilizing multi-dimensional TOM analysis (i.e.\ $Ov_2^h$ and $Ov_3^t$) can help in reducing the background contamination of signal events. If we consider only $Ov_2^h$ (dashed line), a significant fraction of $t\bar{t}$ would pass any reasonable overlap cut. However, in a two dimensional distribution, it is clear that many of the $t\bar{t}$ events which obtain a high $Ov_2^h$ also obtain a high $Ov_3^t$ score. Contrary to $t\bar{t}$ events, the signal events almost never get tagged with a high $Ov_3^t$ score, as it is difficult for a proper Higgs fat jet to fake a top. Hence, an upper cut on $Ov_3^t$ (solid line) efficiently eliminates a significant fraction of $t\bar{t}$ events, at a minor cost of signal efficiency. Note that the peak at $Ov_2^h \approx Ov_3^h \approx 0$ in the signal distributions corresponds to events where the hardest/second hardest fat jet is likely a light jet. \begin{figure} \centering \includegraphics[width=0.49\textwidth]{mh_hard1_BeforeOv.pdf} \includegraphics[width=0.49\textwidth]{mh_Higgs1_AfterOv.pdf}\\ \includegraphics[width=0.49\textwidth]{mh_hard2_BeforeOv.pdf} \includegraphics[width=0.49\textwidth]{mh_Higgs2_AfterOv.pdf} ]]>

25 \GeV, \,\,\,\,\, |y^{r=0.4}| < 2.5, \,\,\,\,\,\, \Delta R_{uh} > 1.1\,, \end{equation} where $\Delta R_{uh}$ stands for the plain distance in $\eta, \phi$ between the $r=0.4$ jet (i.e.\ the up type quark) and each of the Higgs candidate fat jets. We declare these jets to be the $u$ quark candidates. Since we expect two Higgs fat jets in the final state, a comparison between the masses of the two hardest fat jets which pass the overlap criteria provides a useful handle on the background channels. In order to exploit this feature, we construct a mass asymmetry \begin{equation} \Delta_{h} \equiv \frac{m_{h1} - m_{h2}}{m_{h1} + m_{h2}}\,, \end{equation} where $m_{h_{1,2}}$ are the masses of the two Higgs candidate jets. Figure~\ref{fig:MassPlotsDeltas} (left panel) shows the distribution of $\Delta_{h}$ for signal events and relevant backgrounds. Even after the overlap selections, the background distributions are significantly wider than the signal. Hence, in order to further suppress the background channels, we impose a cut of \begin{equation} |\Delta_{h}| < 0.1\,. \end{equation} \begin{figure} \centering \includegraphics[width=0.49\textwidth]{Delta_mh_Ex.pdf} \includegraphics[width=0.49\textwidth]{Delta_mU_Ex.pdf} ]]>

1.1.$ A correct Higgs-light jet pair then minimizes the value of \begin{equation} \Delta_{U_h} = \mathrm{min} \left[ |m^{U_h}_{11} -m^{U_h}_{22}|, |m^{U_h}_{12} - m^{U_h}_{21}|\right]\,. \end{equation} \begin{figure} \includegraphics[width=0.49\textwidth]{m_Uh1.pdf} \includegraphics[width=0.49\textwidth]{m_Uh2.pdf} ]]>

800, 1000 \GeV, \end{equation} for the benchmark values of $M_{U_h} = 1, 1.2 \TeV$ respectively, where we construct the mass of $U_{h1}$ and $U_{h2}$ from Higgs-light jet pairs which minimize $\Delta U_h$. ]]>

800$\,GeV & 0.50 & 3.6 $\times 10^{-1}$ & 1.6 & 67.0 & 7.3 $ \times 10^{-3}$ & 3.6 $ \times 10^{-1}$ \\ \hline $b$-tag & 0.34 & 4.4 $\times 10^{-2}$ & 1.1 $\times 10^{-2}$ & 1.5 $\times 10^{-2}$ & \textbf{4.8} & \textbf{7.5} \\ \hline \end{tabular} ]]>

1$\,TeV & 0.22\phantom{0} & 1.9 $ \times 10^{-1}$ & 1.0 & 45.0 & 4.8 $ \times 10^{-3}$ & 1.9 $ \times 10^{-1}$ \\ \hline $b$-tag & 0.134 & 2.2 $ \times 10^{-2}$ & 8.5 $ \times 10^{-3}$ & 1.2 $ \times 10^{-2}$ & \textbf{3.1} & \textbf{3.8} \\ \hline \end{tabular} ]]>

1$ with signal significance of $\sim 7 \sigma$ at $35 \fb^{-1}$, assuming light quark partners of $ M_{U_h} =1 \TeV.$ The significance we obtain is sufficient to claim a discovery of $1 \TeV$ light quark partners. In addition, we find that probing masses higher than $1 \TeV$ will require more luminosity and will be challenging at Run II of the LHC. However, even with $35 \fb^{-1}$ signal significance of more than $3\sigma$ is achievable for $M_{U_h} = 1.2 \TeV$, enough to rule out the model point. Requiring that there exist four fat jets with $p_T >300 \GeV$ in an event, together with our boosted Higgs tagging procedure result in an improvement of $S/B$ by roughly a factor of 70-100 at $\sim 20\%$ signal efficiency relative to the pre-selection cuts. Additional cuts on mass asymmetries improve $S/B$ by roughly of factor a 3 in total. \begin{figure} \centering \includegraphics[width=0.49\textwidth]{bTable_signal.pdf} \includegraphics[width=0.49\textwidth]{bTable_ttbar.pdf}\\ \includegraphics[width=0.49\textwidth]{bTable_bbbar.pdf} \includegraphics[width=0.49\textwidth]{bTable_multi.pdf} ]]>

1$ and $S/\sqrt{B}\sim 7$ is possible for quark partners of mass $1\TeV$ with $35 \fb^{-1}$ of integrated luminosity. Our results show that the LHC Run II could achieve sufficient sensitivity to light quark partners of mass $1 \TeV$ to claim discovery. Probing masses higher than $1 \TeV$ using our proposed cut-scheme will be difficult at Run II of the LHC, yet with $35 \fb^{-1}$ we find that a signal significance of more than $3\sigma$ is achievable for $M_{U_h} = 1.2 \TeV$, sufficient to rule out the model point. The event selection procedure we propose begins by requiring the presence of four fat jets (i.e.\ $R=0.7$), two of which are tagged as Higgs candidates. We perform Higgs tagging by considering a combination of the Higgs two body peak overlap, $Ov_2^h$, and the top three body overlap $Ov_3^t$, where we require a \emph{lower} cut on $Ov_2^h$ and an \emph{upper} cut on $Ov_3^t$. The two-dimensional overlap analysis allows us to suppress the QCD backgrounds, including $t\bar{t}$, to a much better degree compared to the analysis utilizing only $Ov_2^h$. In addition to jet substructure tagging, we also require the two Higgs candidate jets to be $b$-tagged, as well as that the mass difference between the Higgs jets is small. Kinematics of heavy pair produced quark partners offer an additional handle on the background channels, and we require that the mass difference between the reconstructed $U_h$ partners also be small. The greatest improvement in the signal significance comes from $b$-tagging, as requiring two Higgs fat jets to be $b$-tagged diminishes the enormous multi-jet background. Our study represents a ``proof of principle'' that successful searches for TeV scale light quark partners decaying to $hj$ are possible at the Run II of the LHC. Further work is necessary to study the effects of pileup contamination on the results of the analysis. Yet, it is likely pileup effects will be manageable, even at $\sim 50$ interactions per bunch crossing. The TOM analysis of boosted jets is weakly susceptible to pileup at 50 interactions per bunch crossing~\cite{Backovic-ml-2013bga}, as long as the fat jet $p_T$ is corrected so that the appropriate template bin is used in the analysis. Alternatively, many issues with determining the jet $p_T$ in a high pileup environment could be bypassed by analyzing each jet with template sets at a range of transverse momenta. Effects of pileup on jet mass do not represent an issue for our event selection proposal, as the combination of $Ov_2^h$ and $Ov_3^t$ selections serves as an excellent intrinsic mass filter. Furthermore, recent experimental studies of ref.~\cite{Capeans-ml-1291633} suggest that effects of pileup on $b$-tagging at LHC Run II will be under control. Future analyses using our event selection could also benefit from a detailed detector simulation. ]]>