text:
\section{Introduction}

The weakly interacting massive particles (WIMPs), which appear in many theories beyond the Standard Model (SM), remain to be one of the most attractive candidates for cold dark matter (DM) to explain the observed energy budget in the universe. The relic abundance of dark matter particles is set by their annihilation cross section $\sigma \propto g_{\rm eff}^4/M_{\rm DM}^2$ in the early universe \cite{Lee:1977ua,Goldberg:1983nd}
\begin{equation}
\Omega_{DM} h^2 = 0.11 \times \left(\frac{2.2 \times 10^{-26}~{\rm cm}^3/{\rm s}}{\langle \sigma v \rangle_{{\rm freeze}}}\right) .
\label{eq:relic}
\end{equation}
To avoid over-closure of the universe, today's relic abundance $\Omega_{DM} h^2 \sim 0.1$ translates to a limit on the dark matter mass as
\begin{equation}
M_{\rm DM} < 1.8~{\rm TeV} \left(\frac{g^2_{\rm eff}}{0.3}\right) .
\end{equation}
The electroweak coupling strength and the TeV mass scale naturally appear, leading to the notion of the ``WIMP miracle''. This strongly motives the search for the WIMP dark matter in the underground laboratories \cite{CDEX,XENON1T,XENON1T1512,PICO-2L,PICO-60,LUX-SD,LUX-SI,PandaX-II-SI,PandaX-II-SD,LZ-CDR,1509-08767},
in collider experiments \cite{CMSmonojetPublished,ATLASmonojet}, as well as indirect detections via gamma rays, positrons and neutrinos \cite{AMS02-Ele1,AMS02-Ele2,AMS02-Ele3,IC79-2016,SuperK,ANTARES-SUN-DM,FermiLAT-6yr-Gamma,Conrad:2014tla}.

With the impressive improvement of sensitivities in the underground experiments \cite{PandaX-II-SI,PandaX-II-SD,LUX-SI,LUX-SD} for the dark matter direct detection, the null results have put stringent limits on the dark matter-nucleon scattering cross sections, excluding much of the parameter region for many WIMP dark matter models and thus challenging the WIMP miracle paradigm. On the other hand, the WIMP DM interactions with the SM particles and the mass spectra may be rather subtle. The annihilation cross section that governs the relic abundance and the dark matter-nucleon scattering cross section that controls the direct detection may not be from the same set of diagrams. It is therefore prudent to explore scenarios with suppressed dark matter-nucleon scattering cross sections.

Supersymmetry (SUSY) remains to be the strongest contender for theories beyond the SM. One of the desirable features for SUSY is the existence of a WIMP dark matter candidate, the lightest supersymmetric particle (LSP), typically the neutralino ($\chi_1^0$). It has been realized recently that there are regions in the SUSY parameter space where the direct detection cross section is highly suppressed due to subtle cancelations of the couplings. These regions are dubbed as the  ``blind spots'' \cite{blindspots} for the DM direct detection.
It has been shown \cite{blindspots} that the DM coupling to the $Z$-boson $Z\chi_1^0\chi_1^0$
can be almost zero and thus the spin-dependent (SD) scattering amplitude will be vanishingly small. Analogously, the DM coupling to the Higgs boson $h\chi_1^0\chi_1^0$
can be almost zero, leading to the spin-independent (SI) scattering amplitude to be vanishingly small. These would be very unfortunate scenarios as far as the DM direct detections are concerned. One would wish to seek for other possible means to search for the WIMP dark matter in those parameter regions.

In this paper, we carry out comprehensive analyses for the DM searches under the blind-spot scenarios in MSSM. In particular, we explore the complementary coverage for the theory parameters among the different searching schemes for the direct detections, the indirect detections with astro-physical means, as well as the collider searches for SUSY signals \cite{1405-6716,1409-6322,1412-5952,1501-06357,1508-01173,1509-05076,1509-05771}.

We find that the SI scattering blind spots may be rescued by SD scattering searches in the future direct detection experiments. The neutrino detections from IceCube and SuperK could approach the sensitivity on the SD scattering cross section for certain blind spots, while the detection of gamma rays from Fermi-LAT may not reach the desirable sensitivity for searching for the DM blind-spot regions.
Furthermore, the SUSY searches at the LHC, in particular the future upgrade to higher luminosities (HL-LHC), will substantially extend the coverage for the blind-spot scenarios to large parameter regions.
The dark matter blind spots thus may be unblinded with the collective efforts in future DM searches.

This paper is organized as follows. In Sec.~\ref{sec:BS}, we define the blind spots for the spin-independent and spin-dependent scatterings in DM searches. We further study the constraints from the relic abundance for those scenarios in Sec.~\ref{sec:RD}. We discuss the DM direct detection via the spin-dependent scattering, and quantify the DM indirect searches at the Fermi-LAT from gamma rays and at the neutrino experiments in Sec.~\ref{sec:search}. Before presenting our collider studies at the LHC, we first examine the existing bounds on the SUSY parameters in Sec.~\ref{sec:LEP}. Our main results for the collider coverage are presented in Sec.~\ref{sec:collider}. We summarize our results in Sec.~\ref{sec:conclusion}.

\section{Blind Spots}
\label{sec:BS}

Direct detections of the SUSY WIMP dark matter ($\chi_1^0$) in the underground laboratories usually go through two classes of scattering diagrams via the Higgs and $Z$-boson exchanges,
as shown in Fig.~\ref{fig:feynDD}. The WIMP scattering cross section sensitively depends on the couplings of $h\chi_1^0\chi_1^0$ and $Z\chi_1^0\chi_1^0$, which are governed by the components of the $\chi_1^0$ admixture.
It is sometimes informative to think about the limiting cases, that for large $|M_1|$, $|M_2|$, $|\mu|\gg m_Z$, the lightest neutralino $\chi_1^0$ is bino-like, wino-like or Higgsino-like, with mass being approximately $M_1$, $M_2$, $\pm \mu$, whichever one is the smallest, respectively.
Furthermore, the neutralino LSP-nucleus scattering via the axial-vector interaction $Z\chi_1^0\chi_1^0$ couples to the spin of the nucleus (spin-dependent, SD)
and that via the scalar interaction $h\chi_1^0\chi_1^0$ is independent of the spin (spin-independent, SI).
The scattering cross section off a heavy nuclear target of an atomic number $A$ for the SI interactions will be proportional to $A^2$ due to the coherent effect of the nucleons.
DM direct detections are thus more sensitive to the SI interactions due to this enhancement. On the other hand, the SD interactions may still be significant because of the stronger gauge interactions via the $Z$ exchange.

\begin{figure}[tb]
\centering
\begin{fmffile}{SI}
\begin{fmfgraph*}(150,100)
\fmfleft{i1,i2}
\fmfright{o1,o2}
\fmf{fermion,label=$\tilde{\chi}_1^0$,label.side=left}{i2,v2}
\fmf{fermion,label=$\tilde{\chi}_1^0$,label.side=left}{v2,o2}
\fmf{dashes,label=$h$}{v1,v2}
\fmf{fermion,label=$q$,label.side=right}{i1,v1}
\fmf{fermion,label=$q$,label.side=right}{v1,o1}
\end{fmfgraph*}
\end{fmffile}
\begin{fmffile}{SD}
\begin{fmfgraph*}(150,100)
\fmfleft{i1,i2}
\fmfright{o1,o2}
\fmf{fermion,label=$\tilde{\chi}_1^0$,label.side=left}{i2,v2}
\fmf{fermion,label=$\tilde{\chi}_1^0$,label.side=left}{v2,o2}
\fmf{boson,label=$Z$}{v1,v2}
\fmf{fermion,label=$q$,label.side=right}{i1,v1}
\fmf{fermion,label=$q$,label.side=right}{v1,o1}
\end{fmfgraph*}
\end{fmffile}
\caption{Feynman diagrams for direct detection of SUSY neutralino LSP dark matter.}
\label{fig:feynDD}
\end{figure}

\subsection{SI blind spots}

\begin{table}[tb]
\centering
\begin{tabular}{|c|c|c|}
\hline
$m_{\chi_1^0}$ & condition & signs \\
\hline
$M_1 (<M_2, |\mu|)$ & $M_1+\mu\sin2\beta=0$ & $\text{sign}(M_1/\mu)=-1$ \\
\hline
$M_2 (<M_1, |\mu|)$ & $M_2+\mu\sin2\beta=0$ & $\text{sign}(M_2/\mu)=-1$ \\
\hline
$|\mu| ( < M_1, M_2)$ & $\tan\beta=1$ & $\text{sign}(M_{1,2}/\mu)=-1$ \\
\hline
$M_{1,2} (< |\mu|)$ & $M_1=M_2,\quad |\mu|>|{M_{1,2}}/{\sin2\beta}|$ & $\text{sign}(M_{1,2}/\mu)=-1$ \\
\hline
\end{tabular}
\caption{\label{tab:SIBS}The SI blind-spot mass relations.  }
\end{table}

The spin-independent (SI) blind spots correspond to a vanishing $h\chi_1^0\chi_1^0$ coupling.
Using the low-energy Higgs theorem, we obtain the following condition on the theory parameters \cite{blindspots}:
\begin{equation}
(m_{\chi_1^0}+\mu\sin2\beta)\left(m_{\chi_1^0}-\frac{1}{2}(M_1+M_2+ (M_1-M_2) \cos2\theta_{\text{W}})\right)=0.
\label{eq:SI_condition}
\end{equation}
From this relation, we can extract the tree level blind-spot conditions as given in Table~\ref{tab:SIBS}. The first three conditions are obtained by requiring the first bracket in Eq.~(\ref{eq:SI_condition}) to be zero. In this case, the LSP mass is exactly equal to the mass
of a pure gaugino or Higgsino state ($M_1$, $M_2$ or $|\mu|$) as listed in the first column of Table~\ref{tab:SIBS}. The last condition is obtained by requiring the second bracket to be zero. In this case the neutralino mass is equal to the gaugino mass parameters $m_{\chi_1^0}=M_1=M_2$. The additional condition on $|\mu|$ guarantees that the neutralino state with mass $M_1=M_2$ is the lightest neutralino and therefore the LSP.

Two remarks are now in order. First, we note that loop corrections to the LSP mass will slightly shift the exact location of the blind spots, but will not affect their existence.
Second, if there is BSM new physics that has significant couplings to the LSP and the SM quarks, then the additional contributions could change the above blind-spot conditions. Examples include  the heavy Higgs boson \cite{blindspotsHeavyH}, light squark \cite{blindspotsStops}, and the singlet scalar in NMSSM \cite{blindspotsNMSSM}. We will not discuss those cases further.

\subsection{SD blind spots}
\label{sec:bs}

\begin{table}[tb]
\centering
\begin{tabular}{|c|c|c|}
\hline
$m_\chi$ & condition & signs \\
\hline
$M_{1,2}$ & $M_1=M_2,\quad |\mu|>|{M_{1,2}}/{\sin2\beta}| $ & $\text{Sign}({M_{1,2}/\mu})=-1$ \\
\hline
-- & $\tan\beta=1$ & -- \\
\hline
\end{tabular}
\caption{\label{tab:SDBS}
The SD blind-spot mass relations.}
\end{table}

The spin-dependent (SD) blind spots correspond to vanishing $Z\chi_1^0\chi_1^0$ coupling.  For a pure Higgsino LSP, $\chi_{1,2}^0=\frac{1}{\sqrt{2}}(\tilde{H}_u^0\pm \tilde{H}_d^0)$, the only non-zero coupling is $Z\chi_1^0\chi_2^0$, with vanishing $Z\chi_1^0\chi_1^0$ and $Z\chi_2^0\chi_2^0$ couplings.  Pure bino or a pure wino states have no interaction with $Z$-boson. For a mixed LSP state, the $Z\chi_1^0\chi_1^0$ coupling must come from the Higgsino component in $\chi_1^0$. For $\tan\beta=1$ with restored symmetry of $u\leftrightarrow d$, the LSP $\chi_1^0$ also has vanishing coupling with $Z$-boson as in the case of a pure states \cite{blindspots}.

We have identified the following
mass relation, corresponding to a vanishing Higgsino component in the LSP $-$ a photino-like LSP,
which also leads to a SD blind spot:
\begin{equation}
M_1=M_2,\quad |\mu|>\left|\frac{M_{1,2}}{\sin2\beta}\right| ,\quad \text{Sign}(\frac{M_{1,2}}{\mu})=-1.
\label{eq:mostb}
\end{equation}
Such a case has not been pointed out in the existing blind-spot studies~\cite{blindspots}. In fact,
this is the same condition of a vanishing $h \chi_1^0 \chi_1^0$ coupling as in the last line of Table \ref{tab:SIBS}. Thus this region is both SD blind spots and SI blind spots $-$ it is the ``most blind'' of all!
We note that, Eq.~(\ref{eq:mostb}) with Sign$(M_{1,2}/{\mu})=+1$ would also lead to a SD blind spot. However in this case, $M_{1,2}$ will be smaller than $M_Z/2$, and we will not study it further because of the conflict with the collider bounds on the chargino/neutralino masses.
The SD blind-spot conditions under our consideration are listed in Table~\ref{tab:SDBS}.

In our analyses below, we choose the following benchmark cases which correspond to SI and/or SD blind-spot regions:
\begin{description}
\item[Case A (SI Blind Spots):] $M_1+\mu\sin2\beta=0,\ m_{\chi_1^0}=M_1$ with $M_2$ decoupled, sign$(\frac{M_1}{\mu})=-1$.
\item[Case B (SI Blind Spots):] $M_2+\mu\sin2\beta=0,\ m_{\chi_1^0}=M_2$ with $M_1$ decoupled, sign$(\frac{M_2}{\mu})=-1$.
\item[Case C (SI and SD Blind Spots):] $M_1=M_2,\ |\mu|>|\frac{M_{1,2}}{\sin2\beta}|$, sign$(\frac{M_{1,2}}{\mu})=-1$.
\end{description}
For each case, we use SuSpect~\cite{suspect} to generate the corresponding parameter points.

For our collider analyses, we focus on Cases A and B in details.  The collider phenomenology of Case C  would be similar to those of Case A and B given the nearly degenerate LSP and NLSPs made of bino and winos, with heavier Higgsino states. For the DM relic density and indirect constraints, we also study Case C.

In fact, there is a condition that would lead to another blind spot both for SI and SD, namely
$\tan\beta=1$, as already listed in Tables~\ref{tab:SIBS} and \ref{tab:SDBS}.
We will not discuss this scenario any further since this value of $\tan\beta$ is disfavored given the observed Higgs mass and because the phenomenological features are similar to the usual electroweakino LSP studies, with no characteristic mass scale for the NLSP states.

\section{Dark Matter Relic Density}
\label{sec:RD}

Today's relic density of DM from global fits to a variety of observations is~\cite{PlanckXIII}
\begin{equation}
\Omega_{DM} h^2 \approx 0.1184\pm 0.0012.
\label{eq:relicb}
\end{equation}
The relic density for light wino and Higgsino are always under-abundant due to the relatively large ${\rm SU(2)}_L$ coupling, while the relic density in the bino case is mostly over-abundant due to the suppressed annihilation cross section.

Case A of the blind-spot region with the bino-like LSP is generically disfavored by relic density analysis, except for the $Z$-pole region of $M_1\sim m_Z/2$ with small $|\mu|$, or $M_1\sim |\mu|$
with small $\tan\beta$ and considerable amount of bino-Higgsino mixing, as shown by the various contours labelled by the relic density values normalized to the observed value in the left panel of Fig.~\ref{fig:Relic_CaseA}. We calculate the relic density and the direct/indirect detection cross section by the package micrOMEGAs~\cite{micromegas1305,micromegas1005,micromegas0803,micromegas0607}.
In the right panel, we show the normalized relic density as a function of the dark matter mass parameter $M_1$, which clearly indicates the viable region near the $Z$-pole. Lower values of $|\mu |$ are more favorable.

\begin{figure}[tb]
\centering
\includegraphics[width=0.49\textwidth]{./Figures/CaseA_Relic_step10_zrange_1024-eps-converted-to.pdf}
\includegraphics[width=0.49\textwidth]{./Figures/CaseA_Relic_at_diff_mu_1024-eps-converted-to.pdf}
\caption{Case A: dark matter relic density normalized to the observed value. Left panel: contour plot in the $M_1-\mu$ plane for various values of the relics. Right panel: as a function of $M_1$ for $\mu = -100$ and $-200$ GeV.
The values of  $\tan\beta$ are fixed by the blind-spot relation
$M_1+\mu \sin2 \beta=0$ for both plots.  They are also indicated by the dashed lines on the left-panel.
}
\label{fig:Relic_CaseA}
\end{figure}

A possible situation to allow a large viable parameter space for Case A is to introduce co-annihilation for the LSP \cite{Ellis:1999mm,Han:2013gba}. In the left panel of Fig.~\ref{fig:Relic_CaseA_stau}, we present the normalized relic density for Case A with $M_{\tilde\tau_R}=M_1$ allowing the co-annihilation of the right-handed stau with the bino-like LSP. The observed relic density can be achieved in most of the $M_1$ versus $-\mu$ parameter space. The right panel of Fig.~\ref{fig:Relic_CaseA_stau} shows the effect of the
$\delta M=M_{\tilde\tau_R}-M_1$ on the relic density. Only when the stau is nearly degenerate with LSP with $\delta M < 3$ GeV, the effect of stau co-annihilation is strong enough to suppress the relic density to achieve the observed value. Since such a nearly degenerate right-hand stau would hardly affect our further results on electroweakino sector,  we will always include such stau to accommodate acceptable relic density for Case A for any further study.

However, in the wino-like LSP or Higgsino-like LSP case, the relic density is acceptably under-abundant. In Fig.~\ref{fig:Relic_CaseBC}, we show the relic density compared to observed value for Case B in $M_2$ versus $(-\mu)$ plane (left panel) and for Case C with $\mu=-8$ TeV and $\tan\beta = 8$ (right panel). For Case B,  the relic density in almost all the parameter region is acceptably under-abundant, only when the mass of the wino-like LSP is heavier than about 1.5 TeV, the relic density will achieve the observed value. For Case C as shown in the right panel of Fig.~\ref{fig:Relic_CaseBC}, the situation is similar to Case B. Since the wino annihilation dominates in this case, the relic density does not sensitively depend on the value of $\mu$ and $\tan\beta$.

In the rest of the paper, whenever the relic density is concerned, we will adopt the value in Eq.~(\ref{eq:relicb}) for Case A, and will use the predicted results of the under-abundant relic densities for Cases B and C.

\begin{figure}[tb]
\centering
\includegraphics[width=0.49\textwidth]{./Figures/CaseA_Relic_stauR_1024-eps-converted-to.pdf}
\includegraphics[width=0.49\textwidth]{./Figures/CaseA_Relic_M1vsdmstau_0-100_1024-eps-converted-to.pdf}
\caption{Case A: dark matter relic density normalized to the observed value. Left panel: contour plot in the $M_1-\mu$ plane for various values of the relics and $\tan\beta$, including the co-annihilation effect with stau:  $M_{\tilde\tau_R}=M_1$. Right panel: contour plot in the $M_1$ versus $\delta M = M_{\tilde{\tau}_R}-M_{1}$ plane for $\mu = -400$ GeV. }
\label{fig:Relic_CaseA_stau}
\end{figure}

\begin{figure}[tb]
\centering
\includegraphics[width=0.49\textwidth]{./Figures/CaseB_Relic_step10_zrange_1024-eps-converted-to.pdf}
\includegraphics[width=0.49\textwidth]{./Figures/CaseC_Relic_1024-eps-converted-to.pdf}
\caption{Dark matter relic density normalized to the observed value. Left panel for Case B, in the $M_2 - \mu$ plane  for various values of the relics.
Right panel for Case C, versus $M_{1,2}$ for $\mu = -8$ TeV and $\tan\beta = 8$.
\label{fig:Relic_CaseBC} }
\end{figure}

\section{Dark Matter Direct and Indirect Detections}
\label{sec:search}

There have been considerable efforts in searching for DM particles in the underground
experiments \cite{PICO-2L,PICO-60,LUX-SD,LUX-SI,PandaX-II-SI,PandaX-II-SD,LZ-CDR}.
Since our Case A and Case B parameter regions are only SI-blind but have unsuppressed SD  cross sections, direct detection experiments aiming at constraining spin-dependent dark matter-nucleon scattering cross section~\cite{PICO-2L,PICO-60,LUX-SD,PandaX-II-SD,LZ-CDR} could provide important information for the theory parameter space.

The indirect detection of dark matter aims mainly at three kinds of detectable objects: gamma rays, charged-particle cosmic ray and neutrinos, from the relic DM annihilations. Constraints from indirect detection via gamma rays and charged-particle cosmic ray can be translated into upper bounds on the thermal averaged annihilation cross section for different dark matter annihilation channels.\footnote{This only works for an $s$-wave. For velocity dependent thermal averaged annihilation cross section, the indirect detection only constraints $\langle\sigma{v} \rangle_{\rm today}$, not $\langle\sigma{v} \rangle_{\rm freeze\ out}$.} Since limits from the charged-particle cosmic ray depend heavily on the propagation model,  we only  consider the constraints from gamma-ray detection~\cite{FermiLAT-6yr-Gamma}.  Furthermore, indirect dark matter detection via neutrino coming from the Sun can be used to put upper limits on the spin-dependent dark matter-proton scattering cross section~\cite{IC79-2016,SuperK,ANTARES-SUN-DM} under the equilibrium assumption.

\subsection{Dark matter direct detection via SD scattering}

The DM search sensitivity has been improved substantially over the years \cite{1509-08767}. By design, the blind-spot scenarios are the most difficult situations for the direct detection. However, our Cases A and B are blind spots only for SI scattering, with unsuppressed cross sections for SD scattering.
The spin-dependent DM-neutron scattering cross section $\sigma_{SD, \chi n}$ versus the LSP mass are presented in Fig.~\ref{fig:SigmaSDn} for Case A (left panel) and Case B (right panel).
Note that, when calculating the cross section involving dark matter, we have properly treated the relic density for each case as stated at the end of Sec.~\ref{sec:RD}.
The constraints obtained from the direct detection are also shown there for LUX (upper solid curves), PandaX II (middle solid curves) and the LZ perspective (bottom dotted curves).
From these figures, we find that LUX just reached the sensitivity near $M_1\sim 100$ GeV in Case A, and is still nearly one order of magnitude away in Case B.
The bounds report by the PandaX II experiment \cite{PandaX-II-SD} can exclude a region in the parameter space up to $-\mu\approx 250$ GeV in Case A, but remains insensitivity in Case B.
The projected reach of the future DM direct detection experiment LZ \cite{LZ-CDR} for spin-dependent scattering is expected to cover parts of the blind-spot parameter regions with up to 700 GeV on $M_1$ for Case A and on $M_2$ for Case B as seen by the dotted curves.

On the other hand, the spin-dependent DM-proton scattering cross section $\sigma_{SD, \chi p}$ is known to be somewhat smaller than that for DM-neutron scattering, and is shown in Fig.~\ref{fig:SigmaSDp} for Case A (left panel) and Case B (right panel). The constraints obtained from the current direct detection experiments are not quite sensitive enough yet as shown by the solid curves in the figure. The future projection for the LZ experiment may be able to cover up to $M_1\sim 400$ GeV in Case A, and 100 GeV in Case B, as seen by the dotted curves.
\begin{figure}
\centering
\includegraphics[width=0.49\textwidth]{./Figures/CaseA_SD_n_1024-eps-converted-to.pdf}
\includegraphics[width=0.49\textwidth]{./Figures/CaseB_SD_n_1024-eps-converted-to.pdf}
\caption{
Spin-dependent DM-neutron scattering cross section: left panel for Case A and right panel for Case B.
The $90\%$ CL. limits from LUX, PandaX II, and the LZ projection are also shown.
The color code indicates the $\mu$ values as labeled on the right-handed vertical axis.}
\label{fig:SigmaSDn}
\end{figure}

\begin{figure}
\centering
\includegraphics[width=0.49\textwidth]{./Figures/CaseA_SD_p_1024-eps-converted-to.pdf}
\includegraphics[width=0.49\textwidth]{./Figures/CaseB_SD_p_1024-eps-converted-to.pdf}
\caption{
Spin-dependent DM-proton scattering cross section: left panel for Case A and right panel for Case B.
The $90\%$ CL. limits from LUX, PandaX II, PICO, and the LZ projection are also shown.
The color code indicates the $\mu$ values as labeled on the right-handed vertical axis.
}
\label{fig:SigmaSDp}
\end{figure}

\subsection{Neutrino detection}

The spin-dependent DM-proton scattering cross section $\sigma_{SD, \chi p}$ can also be constrained by indirect searches for neutrino signals coming from the Sun, assuming equilibrium of DM capture and annihilation.
We present the theoretical prediction for the scaled\footnote{While the SD $\chi$-$p$ scattering cross section does not depend on the dark matter annihilation modes, the experimental limits of the indirect detection via neutrinos do. Since it is difficult to show the experimental limits for each parameter point, we choose to present the experimental limits assuming the observed DM relic density and 100\% annihilation fraction into a certain channel, while scaling the $\chi$-$p$ scattering cross section  for each parameter point with the corresponding DM relic density and the annihilation fraction into a particular final state.} scattering cross section $\sigma_{SD, \chi p}$ versus the LSP mass together with bounds from several neutrino telescope experiments in Fig.~\ref{fig:SigmaSDpCaseA} for Case A and Fig.~\ref{fig:SigmaSDpCaseB} for Case B, respectively.
Two DM annihilation channels to $WW$ and $\tau\tau$ are shown on the left and right panels, respectively.  We see from Fig.~\ref{fig:SigmaSDpCaseA} that the bounds from SuperK and IceCube are reaching the low mass region for the Case A blind-spot scenario. In Case B, the IceCube bounds on the $WW$ mode impose the most stringent limits. However, these bounds are still about an order of magnitude away from
the relevant blind-spot parameter space as shown in the left panel of Fig.~\ref{fig:SigmaSDpCaseB}.\footnote{In Ref.~\cite{1501-06357},
the authors pointed out
that models where the dark matter is dominantly a wino-like neutralino are strongly excluded by IceCube, and that the wino relic density close to the thermally produced value satisfies the IceCube bound. This conclusion is consistent with what we found here for Case B, where the DM is typically under-abundant.
}
For both Case A and Case B, we have combined all contributing channels to compare with the IceCube-79 String results \cite{IC79-2016}, and find that our parameter space is still beyond the current reach, except for a small $M_1$ and $|\mu|$ region as already seen in Fig.~\ref{fig:SigmaSDpCaseA}.

The observational aspects for Case C are more difficult since it is both a SD and a SI blind spots. In addition to the absence of the DM direct detection signals, the indirect detection via neutrinos is also difficult given the negligible SD interactions.

\begin{figure}
\centering
\includegraphics[width=0.49\textwidth]{./Figures/CaseA_SD_WW_IceCube_1024-eps-converted-to.pdf}
\includegraphics[width=0.49\textwidth]{./Figures/CaseA_SD_tautau_IceCube_1024-eps-converted-to.pdf}
\caption{Case A: Scaled spin-dependent DM-proton scattering cross section for DM annihilation channels: left panel $WW$ mode and right panel $\tau\tau$ mode. Experimental sensitivities from IceCube, SuperK and ANTARES are shown. The color code indicates the $\mu$ values as labeled on the right-handed vertical axis.}
\label{fig:SigmaSDpCaseA}
\end{figure}

\begin{figure}
\centering
\includegraphics[width=0.49\textwidth]{./Figures/CaseB_SD_WW_IceCube_1024-eps-converted-to.pdf}
\includegraphics[width=0.49\textwidth]{./Figures/CaseB_SD_tautau_IceCube_1024-eps-converted-to.pdf}
\caption{Case B: Scaled spin-dependent DM-proton scattering cross section for DM annihilation channels: left panel $WW$ mode and right panel $\tau\tau$ mode. Experimental sensitivities from IceCube, SuperK and ANTARES are shown.
The color code indicates the $\mu$ values as labeled on the right-handed vertical axis.  }
\label{fig:SigmaSDpCaseB}
\end{figure}

\subsection{Gamma-ray detection}

Gamma rays can be produced in dark matter annihilation through radiation, hadronization, or direct pair production, with different spectrum for different annihilation channels.
The theoretical prediction (colored regions) for the velocity-averaged cross section $\langle \sigma v \rangle$ are presented on the left panels in Figs.~\ref{fig:FermiGamma_CaseA}, \ref{fig:FermiGamma_CaseB} and \ref{fig:FermiGamma_CaseC} for Cases A, B and C, respectively, for the most sensitive channel $W^+W^-$.
The limits based on the gamma-ray observation from the Fermi-LAT results~\cite{FermiLAT-6yr-Gamma} are  shown by the solid black curves
in all the three figures.
We see that the sensitivity from the $W^+W^-$ channel is still not reaching the theoretical parameter regions for the blind-spot scenarios.\footnote{Ref.~\cite{Agrawal:2014oha} mentioned that the Galactic center gamma-ray excess can be explained by a thermal-relic neutralino of the MSSM annihilating into $WW, ZZ, hh, t \bar t$ and the DM blind spots could be a viable region of MSSM parameter space. However, the blind-spot scenarios considered in this paper do not provide sufficient annihilation to explain this excess since the $Z$-coupling from bino-Higgsino mixing is small for bino-like DM, and  the wino-like DM is typically under-abundant.}

\begin{figure}[tb]
\centering
\includegraphics[width=0.49\textwidth]{./Figures/CaseA_FermiGamma_WW_scaled_1024-eps-converted-to.pdf}
\includegraphics[width=0.49\textwidth]{./Figures/CaseA_FermiGamma_Combine_1024-eps-converted-to.pdf}
\caption{Case A:
Left panel shows the predicted cross section $\langle\sigma v\rangle$ versus the DM mass (colored regions) and the limits from Fermi-LAT gamma-ray observation for the $W^+W^-$ channel (the black curve).
The color code indicates the $\mu$ values.  Right panel shows the normalized multiple channel cross section by the color code in the $M_1-\mu$ plane.}
\label{fig:FermiGamma_CaseA}
\end{figure}

\begin{figure}[tb]
\centering
\includegraphics[width=0.49\textwidth]{./Figures/CaseB_FermiGamma_WW_scaled_1024-eps-converted-to.pdf}
\includegraphics[width=0.49\textwidth]{./Figures/CaseB_FermiGamma_Combine_1024-eps-converted-to.pdf}
\caption{Case B:
Left panel shows the predicted cross section $\langle\sigma v\rangle$ versus the DM mass (colored regions) and the limits from Fermi-LAT gamma-ray observation for the $W^+W^-$ channel (the black curve).
The color code indicates the $\mu$ values.  Right panel shows the normalized multiple channel cross section by the color code in the $M_2-\mu$ plane.}
\label{fig:FermiGamma_CaseB}
\end{figure}

\begin{figure}[tb]
\centering
\includegraphics[width=0.49\textwidth]{./Figures/CaseC_FermiGamma_WW_scaled_1024-eps-converted-to.pdf}
\includegraphics[width=0.49\textwidth]{./Figures/CaseC_FermiGamma_Combine_1024-eps-converted-to.pdf}
\caption{
Case C:
Left panel shows the limits from Fermi-LAT gamma-ray observation shown by the black (upper) curve and the predicted $\langle\sigma v\rangle$   for the $W^+W^-$ channel by the red (lower) curve.
Right panel shows the normalized multiple channel cross section versus  $M_{1,2}$. }
\label{fig:FermiGamma_CaseC}
\end{figure}

The above results are based on the assumption that the gamma-ray events in the Fermi-LAT experiment is 100\% from the $W^+W^-$. The similar assumption was also applied to the analyses for the other channels such as  $b\bar b,\ u\bar u$, as well as $\tau\tau$. A more accurate treatment would be to add those individual channels with appropriate efficiency factors and the corresponding relic abundance to account for the observed inclusive gamma-ray events.
For a channel labelled by $i$, denote the total efficiency by $A^{i}$ including the detector efficiency, the cosmic related factors and so on. Then the 95\% upper limit on the average cross section for this channel $\langle\sigma v\rangle_{95\%}^{i}$ satisfies:
\begin{eqnarray}
\langle\sigma v\rangle_{95\%}^{i}\times A^{i}\times \Omega_{obs}^2 = N_{obs}^{95\%},
\label{equ:FermiLAT-channel}
\end{eqnarray}
where $N_{obs}^{95\%}$ is the 95\% upper limit on the events from DM annihilation based on the observed events. The experiments will determine the efficiencies for each channel $A^i$. If we want to combine all the contributing channels, then the cross sections should satisfy
\begin{eqnarray}
N_{obs}^{95\%} \geq \sum_{i} \langle\sigma v\rangle^i\times A^{i}\times \Omega_{theo}^2
= N_{obs}^{95\%}\times\sum_{i} \frac{\langle\sigma v\rangle^i}{\langle\sigma v\rangle_{95\%}^i}\times\frac{\Omega_{theo}^2}{\Omega_{obs}^2} \ .
\label{equ:FermiLAT-combine1}
\end{eqnarray}
This leads to an important relaltion we will use:
\begin{eqnarray}
\sum_{i}\frac{\langle\sigma v\rangle^i}{\langle\sigma v\rangle_{95\%}^i}\times\frac{\Omega_{theo}^2}{\Omega_{obs}^2} \leq 1 ,
\label{equ:FermiLAT-combine2}
\end{eqnarray}
which we call the ``normalized multiple channel cross section''.   Regions with the normalized multiple channel cross section well below 1 are much more difficult to be probed by Fermi-LAT gamma-ray observation, while regions with the normalized multiple channel cross section   close to 1 might be covered by the next generation experiments.

Improving the above $W^+W^-$ channel results, we present on the right panels in Figs.~\ref{fig:FermiGamma_CaseA}, \ref{fig:FermiGamma_CaseB} and \ref{fig:FermiGamma_CaseC} for Cases A, B and C, respectively, the normalized multiple channel cross section.
For Case A, the channel combination improves the observability somewhat, but the current results from Fermi-LAT are still about one to two orders of magnitude weak to provide any relevant bound even for the low mass region of $M_1$, as seen in Fig.~\ref{fig:FermiGamma_CaseA}.
For Case B, the relic density is far below the observation when the wino is light, so the relic density scaling governs the outcome. With the $WW$ channel dominant, the blind-spot region is at least two orders of magnitude below the sensitivity of the gamma-ray experiments, as seen in Fig.~\ref{fig:FermiGamma_CaseB}.\footnote{Ref.~\cite{Fan:2013faa} showed that wino dark matter has been strongly constrained by the Fermi-LAT and HESS data.   However, these bounds do not apply to the blind-spot scenario in Case B since the wino is typically under-abundant, which weakens the constraints.}
For Case C, the $WW$ channel is also dominant but still at least two orders of magnitude below the current sensitivity, as seen in
Fig.~\ref{fig:FermiGamma_CaseC}, for $\mu = -8$ TeV and $\tan\beta = 8$. The dependence on $\mu$ and $\tan\beta$ is very weak.

\section{Current Bounds from LEP}
\label{sec:LEP}

\subsection{$Z$ invisible width}
\label{sec_EW}

Electroweak precision measurements at the $Z$-pole provide significant bounds on the SUSY mass parameters.
If the neutralino is light enough, $m_Z> 2m_{\chi_1^0}$, it can be produced via the decay of a $Z$-boson. Such decays are strongly constrained by the measurements at LEP I.   The invisible decay width of $Z$ is constrained  to be $\Gamma_{inv}= 497.4 \pm 2.5$ MeV \cite{LEP-Zpeak},
which can be translated to
an upper limit of non-SM contributions to the invisible decay width of the $Z$-boson
\begin{equation}
\Gamma_{inv}^{BSM} < 3.1\ {\rm MeV\ at}\ 95\% \ {\rm confidence\ level\ (CL)}.
\label{eq_51}
\end{equation}
 This is a conservative bound before the Higgs discovery.
A stronger bound can be obtained using ZFitter \cite{Bardin:aa} with the measured Higgs mass $m_h=125$ GeV. We find the $Z$-boson invisible decay width to be $\Gamma_{inv}^{SM}= 501.7 \pm 0.2$ MeV, which sets a stronger upper bound on the BSM contributions to be
\begin{equation}
\Gamma_{inv}^{BSM} < 1.1\ {\rm MeV\ at}\ 95\% \ {\rm CL}.
\label{eq_52}
\end{equation}

\begin{figure}[tb]
\centering
\includegraphics[width=0.32\textwidth]{./Figures/CaseA_ZinvExclusion_0-300_1024-eps-converted-to.pdf}
\includegraphics[width=0.32\textwidth]{./Figures/CaseB_ZinvExclusion_0-300_1024-eps-converted-to.pdf}
\includegraphics[width=0.32\textwidth]{./Figures/CaseC_ZinvExclusion_tb5_1024-eps-converted-to.pdf}
\caption{$Z$-boson invisible decay width to neutralinos for Cases A (left), B (middle), and C (right). The two middle thick (red) contours indicate the exclusion bounds imposed by Eqs.~(\ref{eq_51}) and (\ref{eq_52}).
}
\label{fig:Zinv}
\end{figure}

In Fig.~\ref{fig:Zinv}, we show the calculated partial decay width of the $Z$-boson into a pair of neutralinos $\Gamma(Z\to \chi_1^0\chi_1^0)$, as well as
$\Gamma(Z\to \chi_1^0\chi_2^0,\  \chi_2^0\chi_2^0)$ when appropriate, in the SUSY mass parameter space for Cases A (left), B (middle), and C (right). The two middle thick (red) contours indicate the exclusion bounds imposed by Eqs.~(\ref{eq_51}) and (\ref{eq_52}).
For a bino-like LSP as in Case A, the coupling of the $Z$ is proportional to the bino-Higgsino mixing $N_{13,14}$: $g_{Z \chi_1^0\chi_1^0} \sim N_{13}^2-N_{14}^2$ \cite{HABER198575}. At large Higgsino masses $|\mu|$, the mixing becomes small and therefore the coupling becomes highly
 suppressed \cite{Djouadi:aa}:\footnote{In the last step we used the blind-spot relation from Table \ref{tab:SIBS}. }
\begin{equation}
g^2_{Z \chi_1^0\chi_1^0}  = \frac{s_W^2 m_Z^4 \cos(2\beta)^2}{(\mu^2 - M_1^2)^2} = \frac{s_W^2 m_Z^4}{\mu^2 (\mu^2 - M_1^2)}.
\label{equ:gzxx}
\end{equation}
The decay width $\Gamma(Z\to \chi_1^0\chi_1^0)$ is sufficiently suppressed at large Higgsino masses and thus the LEP bound is weaker as seen in Fig.~\ref{fig:Zinv} (left). The constraints are stronger for the wino-like LSP (Case B) since the wino-Higgsino mixing is enhanced by a factor ${c_W^2}/{s_W^2}$ compared to the bino-Higgsino mixing as seen in Fig.~\ref{fig:Zinv} (middle). The constraints in Case C are similar to those in Case B but with a cut-off induced by the blind-spot relation as shown by the gray dash line in Fig.~\ref{fig:Zinv} (right).  We can see that the electroweak precision measurements exclude parameter regions
\begin{equation}
\begin{aligned}
M_1 \lesssim\ &43 {\rm\ GeV \ \  and \ \ } |\mu|\lesssim 110-150 \text{ GeV \ \ for a bino-like LSP (Case A), and}\\
M_2 \lesssim\ &43 {\rm\ GeV \ \ and \ \   } |\mu|\lesssim 200-270 \text{ GeV \ \  for a wino-like  LSP (Case B), and}\\
M_{1,2} \lesssim\ &43 {\rm \ GeV \ \ and \ \ } |\mu|\lesssim 220-290 \text{ GeV \ \ for a bino-wino mixing LSP (Case C, }\tan\beta = 5\text{).}
\nonumber
\end{aligned}
\end{equation}

\subsection{LEP2 chargino searches}
\label{sec:LEP2}

Some of the strongest bounds on the blind-spot parameter space come from chargino searches at LEP \cite{LEP-Chargino1}. The DELPHI collaboration performed a search for charginos with a sufficient mass splitting to the lightest neutralino produced in pair production by looking for events with missing transverse momentum  in association with jets or leptons \cite{Abdallah:2003xe}. Using the data set up to 209 GeV, this search led to a mass bound
\begin{equation}
{\rm DELPHI:}\quad m_{\chi_1^\pm} > 102\ {\rm  GeV\  for}\ \Delta m = m_{\chi_1^\pm}-m_{\chi_1^0}>5\ {\rm GeV}.
\end{equation}
Complementary to the above analysis, the ALEPH collaboration performed a dedicated study to analyze the case of small mass splitting, taking into account both standard chargino searches with energetic leptons and jet as well as signatures with an ISR photon balanced by missing energy \cite{LEP-ALEPH}. This analysis found
\begin{equation}
{\rm ALEPH:}\quad m_{\chi_1^\pm} > 93\ {\rm  GeV\  for}\ \Delta m = m_{\chi_1^\pm}-m_{\chi_1^0} < 5\ {\rm GeV}.
\end{equation}
We will take those results into account in the LHC searches in the next section.

\section{Dark Matter Searches at the LHC}
\label{sec:collider}

We now consider the searches for DM at the LHC in the blind-spot scenarios in the hope to cover the parameter space that would be difficult for the direct and indirect  dark matter searches.
 The most common signature for the DM search at colliders would be the missing transverse momentum (customarily called the ``missing energy'') carried away by the DM particles escaping from detection.

The SUSY signatures are essentially governed by the mass different between the produced particles (mostly the chargino NLSP) and the decay final state (the neutralino LSP) $\Delta m = m_{\chi^\pm} - m_{\chi^0}$.
In general, four different search strategies are considered:

\begin{enumerate}
	\item \textbf{Charged Track:} If the mass difference $\Delta m < m_\pi$ is small, the chargino is long-lived which leads to a charged track like a muon. The sensitivity for identifying charged tracks in collider experiments is very high. LEP searches \cite{LEP-ALEPH,collaboration:aa} for chargino pair production $e^+e^- \to \chi^+\chi^-$  excludes such particles up to $m_{\chi^\pm_1}<102$ GeV.   Searches at the LHC  for long-lived charged particles exclude the production cross section of relatively stable charginos  to be above 4 fb at 8 TeV using 20 fb$^{-1}$  data  (ATLAS) \cite{ATLAS:2014fka} or about 1 fb at 13 TeV using 13 fb$^{-1}$ data (CMS)  \cite{CMS:2016ybj}.     However, in MSSM, loop corrections to the chargino and neutralino mass typically induce a mass splitting of a few hundred MeV.    The charginos usually decay before traveling too far.  Therefore charged track searches for long-lived particles do not apply in our cases.
	\item \textbf{Disappearing Track:} For intermediate mass differences $m_\pi < \Delta m< {\rm a\ few\ GeV}$, the chargino decays inside detector with soft decay products after travelling some distance from the interaction point. This results in a disappearing track signature which we will discuss in Sec.~\ref{sec:disap}.
	\item \textbf{Electroweakino Searches:} If the mass difference is large $\Delta m >$ few GeV, the chargino promptly decays inside the detector with energetic decay products, leading to observable leptons or jets plus missing energy. These searches will be discussed in Sec.~\ref{sec:EWsearch}.
	\item \textbf{Monojet/monophoton Searches:}  If we only consider the pair production of the neutralino LSP (or with its degenerate charged partners), mono-jet or mono-photon searches have been a standard channel for dark matter searches at colliders.  These searches will be discussed in Sec.~\ref{sec:monojet}.
\end{enumerate}

\subsection{Disappearing track searches}
\label{sec:disap}

Both Case B and Case C contain regions of parameter space with small enough wino-Higgsino mixing that permits a disappearing track (DT) signal. ATLAS and CMS performed a search for disappearing tracks using the 8 TeV data with 20 ${\rm fb}^{-1}$ integrated luminosity \cite{ATLAS-Disappearing_Track,CMS-Disappearing}.   We further projected the reach for 14 TeV with 300 or 3000 fb$^{-1}$  integrated luminosity by scaling the 8 TeV result with parton
 luminosity \cite{collider-reach}. We show the results altogether in Fig.~\ref{fig:DT14TeV} for the 95\% CL exclusion from disappearing track searches.
Results for Case B are shown in the left panel in the $M_2-\mu$ plane, for ATLAS at 8 TeV with 20 fb$^{-1}$ (lower solid curve) and for 14 TeV at 300 (middle dotted curve) and 3000 (upper dash-dotted curve) fb$^{-1}$, respectively.
The vertical column with the corresponding color code labels the mass difference $\Delta m = m_{\chi^\pm} - m_{\chi^0}$, including two-loop corrections \cite{twoloopdeltam}.   $M_2$ less than about 250 GeV, 600 GeV, and 1100 GeV can be excluded at 95\% CL at  large $|\mu|$ case under three different luminosities, respectively.

\begin{figure}[tb]
\centering
\includegraphics[width=0.49\textwidth]{./Figures/CaseB_DisappearingTrack.pdf}
\includegraphics[width=0.49\textwidth]{./Figures/summary_DT_C.pdf}
\caption{
95\% CL exclusion from disappearing track searches at the LHC.
Left panel for Case B in the $M_2-\mu$ plane:
ATLAS at 8 TeV with 20 fb$^{-1}$ (solid curve) and the projection for 14 TeV at 300 (dashed curve) and 3000 (dash-dotted curve) fb$^{-1}$, respectively. Mass difference $\Delta m$ is shown by  the corresponding color code.
Right panel for Case C in the $\tan\beta-M_{1,2}$ plane:
ATLAS at 8 TeV with 20 fb$^{-1}$ (far left black region) and the projection for 14 TeV at 300 (middle red region) and 3000 (right blue region) fb$^{-1}$, with three different values of $\mu$, respectively.   The solid and dotted gray lines in the upper-right corner indicate the upper limit on $M_{1,2}$: $M_{1,2}/\sin(2\beta)= |\mu|$ for a given value of $|\mu|$.
\label{fig:DT14TeV}
}
\end{figure}

Results for Case C are shown in the right panel of Fig.~\ref{fig:DT14TeV} in the $\tan\beta-M_{1,2}$ plane, again for ATLAS at 8 TeV with 20 fb$^{-1}$ (far left black region) and for 14 TeV at 300 (middle red region) and 3000 (right light-blue region) fb$^{-1}$, with three different values of $-\mu=8,\ 14$ and 25 TeV, respectively, for illustration. The coverage region is on the left-side of the curves.   Note that the blind-spot requirement $|\mu|>{M_2}/{\sin2\beta}$ ensures the neutralino to be lighter than the chargino. This relation imposes an upper bound for the blind-spot parameter space on $\tan\beta$ for given $M_{1,2}$ and $\mu$ as indicated by the gray lines in the right panel of Fig. \ref{fig:DT14TeV}.
We see the wide coverage for the mass parameters: the larger $|\mu|$ is, the better coverage because of the weaker mixing and thus a more efficient disappearing track search.  The coverage also gets better for large values of $\tan\beta$. While the LSP mass is fixed by the blind-spot relation at tree level, $m_{\chi^0_1}=M_{1,2}$, the chargino mass at tree level is given by
\begin{equation}
m_{\chi_1^+}^2 \approx m_{\chi_1^0}^2 +\frac{2 m_W^2 M_2}{\mu^2} \left(|\mu|\sin2\beta -M_2\right).
\end{equation}
For larger $\tan\beta$, the mass splitting between the chargino and neutralino state becomes smaller

\begin{equation}
\Delta m^2 \approx \frac{2m_W^2 M_2}{|\mu |} \left( {2 \over \tan\beta} - {M_2\over |\mu|} \right),
\end{equation}
and therefore the sensitivity for disappearing track searches increases at large $\tan\beta$.

We would like to emphasize the significance of the coverage of the blind-spot parameter space for  Case C by the LHC searches, since it is the ``most blind'' scenario with vanishingly weak SI and SD scattering signal, and thus hopeless for DM direct and indirect detections, as pointed out earlier.

\subsection{Electroweakino searches}
\label{sec:EWsearch}

In the previous section, we have discussed the case in which the NLSP is almost mass-degenerate with the LSP.
Once the mass splitting is sufficiently large, typically more than a couple of GeV, the heavy electroweakino (EW) will promptly decay into the LSP and a  (virtual) $W,\ Z$ or Higgs-boson.

The mass spectrum and the decay patterns of Case A is illustrated in Fig.~\ref{fig:spectrum} (left panel). The LSP is a bino-like neutralino while the NLSPs are Higgsino-like neutralinos and chargino. The wino-like states are decoupled and are assumed not contribute to the collider phenomenology. The main NLSP production channels are
\begin{equation}
q\bar q\to \chi_{2}^0 \chi_{3}^0,\ \ \chi_{2,3}^0 \chi_1^\pm\ \ {\rm and}\ \  \chi_1^+ \chi_1^-.
\end{equation}
The heavy gaugino decays in Case A include
\begin{equation}
\chi_{2,3}^0 \to Z\chi_1^0,\ \  h\chi_1^0 \ \ {\rm and}\ \ \chi_1^\pm \to  W^\pm \chi_1^0.
\end{equation}
We therefore expect to observe the signatures
\begin{equation}
W^+ W^- + \ensuremath{\slashed{E}_T},\ WZ+\ensuremath{\slashed{E}_T},\ Wh+\ensuremath{\slashed{E}_T},\ ZZ+\ensuremath{\slashed{E}_T},\ \  Zh+\ensuremath{\slashed{E}_T}\ \ {\rm  and}\ \  hh+\ensuremath{\slashed{E}_T}.
\label{eq:casea}
\end{equation}
Note that introducing a right-handed stau to achieve correct relic density will not affect the results of the collider search, as the decay rate of Higgsino-like NLSP into stau is negligible.

The center panel of Fig.~\ref{fig:spectrum} shows the mass spectrum and the decay patterns for Case B with a wino LSP. The mass difference among the wino triplet is very small and therefore the decay products of the wino-like chargino state will be too soft to be appreciable.
Hence, the three wino-triplet states can be treated as LSPs. The Higgsino-like neutralinos and chargino form the NLSP states while the bino-like states is decoupled. The main NLSP production channels are
\begin{equation}
 q\bar q \to \chi_{2}^0 \chi_{3}^0,\ \ \chi_{2,3}^0 \chi_2^\pm\ \ {\rm and}\ \ \chi_2^+ \chi_2^-.
 \end{equation}
 The heavy gaugino decays in Case B include
\begin{equation}
\chi_{2,3}^0 \rightarrow Z\chi_1^0,\  h\chi_1^0, \  W^\pm\chi_1^\mp\  {\rm and}\  \chi_2^\pm \rightarrow W^\pm\chi_1^0,\ Z\chi_1^\pm,\ h\chi_1^\pm.
\end{equation}
Comparing with Case A in Eq.~(\ref{eq:casea}), we therefore have the additional final state
\begin{equation}
W^\pm W^\pm+\ensuremath{\slashed{E}_T} ,
\end{equation}
coming from the process $\chi_{2}^0 \chi_{3}^0 \to W^\pm W^\pm \chi_1^\mp \chi_1^\mp$ or  $\chi_{2,3}^0 \chi_{2}^\pm \to W^\pm W^\pm \chi_1^\mp \chi_1^0$.  This provides a very clean same-sign dilepton final state with very low SM backgrounds.

In Case C as seen in Fig.~\ref{fig:spectrum} (right panel), the mass spectrum of the bino-wino-like states is compressed ($M_1=M_2$) and therefore these states can be treated as (nearly degenerate) LSPs. The Higgsino-like neutralinos and chargino form the NLSP states. If the Higgsino mass is decoupled, no NLSP would be produced and therefore direct electroweakino searches would not provide any
 constraint \cite{EWK}. For smaller Higgsino masses within the reach of LHC,  all the final states will be similar to those in Case B and they could be observed as well.  In the discussion of the collider reaches below, we focus on Case A and Case B only.  We will comment on Case C at the end of this section.

\begin{figure}[tb]
\centering
\includegraphics[width=1\textwidth]{./Figures/MassSpectrum.pdf}
\caption{Electroweakino mass spectrum for Case A (left), Case B (center) and Case C (right). Possible decay channels into a $Z$-boson (blue), Higgs-boson (red) and $W$-boson (green) are indicated.
}
\label{fig:spectrum}
\end{figure}

In Fig.~\ref{fig:proCS_AB}, we present the production cross section contours of the dominant channels with gauge boson final states ($ZW^\pm ,\ W^\pm W^\mp ,\ W^\pm W^\pm$ and $ZZ$), for Case A in the $M_1-\mu$ plane and Case B in the $M_2-\mu$ plane, respectively. These cross sections take into account all possible NLSP pair productions $\chi\chi$ with their decays to gauge bosons including the decay branching fractions. We see that cross sections may reach the level of 1 fb for  the NLSP mass parameter $|\mu| \sim 800$ GeV.

\begin{figure}
\centering
\includegraphics[width=0.49\textwidth]{./Figures/CaseA_CS_all-eps-converted-to.pdf}
\includegraphics[width=0.49\textwidth]{./Figures/CaseB_CS_all-eps-converted-to.pdf}
\caption{Cross section contours for Higgsino-like NLSPs  pair production with subsequent decays to the corresponding gauge-boson final states,
$ZW^\pm$ (solid curves),
$W^\pm W^\mp$ (dashed),
$W^\pm W^\pm$ (dash-dotted), and
$ZZ$ (dotted), at 14 TeV LHC for Case A in the $M_1-\mu$ plane (left), and Case B in the $M_2-\mu$ plane (right).
}
\label{fig:proCS_AB}
\end{figure}

Both ATLAS and CMS performed direct electroweakino searches using NLSP pair production. Current experiment limits of several combined channels are shown in Table \ref{tab:ExpResCombined}, for $m_{\ensuremath{\chi^0_1}}=0$ with strong assumptions that $m_{\ensuremath{\chi^\pm_1}}=m_{\ensuremath{\chi^0_2}}$, and the NLSP decays to $\ensuremath{\chi^0_1}$ with $100\%$ branching fraction. The results in Table \ref{tab:ExpResCombined} are meant to be a general guidance for the current situation.  However,   they cannot be easily translated to the blind-spot scenarios because of the hidden information such as the values of $\tan\beta$.
The best sensitivity is obtained in the $WZ$-channel, considering both the $3\ell$ and $2\ell 2j$ final state. The CMS limits for the combined channel ($2\ell,\ 3\ell$) are slightly weaker than the  ATLAS limits due to a $2\sigma$ deviation in the CMS observed data from the expected results.   We apply the CMS bounds from \cite{CMS-SUS-13-006} to the blind-spot scenarios Case A and Case B. The corresponding limits can be seen in Fig. \ref{fig:ElectroweakinoSummary} as dark gray shaded region.

\begin{table}[tb]
\centering
\resizebox{\textwidth}{!}{
\begin{tabular}{|c|c|r l |}
\toprule[1pt]
Production and Decay &  Search Channel & \multicolumn{2}{c|}{95\% CL Exclusion Region}  \\
\midrule[1pt]
$pp\to\ensuremath{\chi^0_2}\ensuremath{\chi^\pm_1} \to ZW^\pm \ensuremath{\chi^0_1} \ensuremath{\chi^0_1}$
& $2\ell+2j+\ensuremath{\slashed{E}_T}$
& ATLAS \cite{1403-5294}:&$100<m_{\ensuremath{\chi^0_2},\ensuremath{\chi^\pm_1}}<420\text{ GeV}$ \\
& $3\ell+\ensuremath{\slashed{E}_T}$
& CMS \cite{CMS-SUS-13-006}:&$100<m_{\ensuremath{\chi^0_2},\ensuremath{\chi^\pm_1}}<270\text{ GeV}$ \\
\midrule[1pt]
$pp\to\ensuremath{\chi^0_2}\ensuremath{\chi^\pm_1} \to hW^\pm \ensuremath{\chi^0_1} \ensuremath{\chi^0_1}$
& $\ell+b\bar{b}+\ensuremath{\slashed{E}_T}$, $\ell+\gamma\gamma +\ensuremath{\slashed{E}_T}$
& ATLAS \cite{1501-07110}:&$125<m_{\ensuremath{\chi^0_2},\ensuremath{\chi^\pm_1}}<272\text{ GeV}$ \\
& $\ell^\pm\ell^\pm+\ensuremath{\slashed{E}_T}$, $3\ell+\ensuremath{\slashed{E}_T}$
& CMS \cite{CMS-SUS-14-002,CMS-SUS-13-006}:&$130<m_{\ensuremath{\chi^0_2},\ensuremath{\chi^\pm_1}}<215\text{ GeV}$ \\
\bottomrule[1pt]
\end{tabular}
}
\caption{Current combined exclusion regions on the electroweakinos at the 8 TeV LHC, assuming $m_{\ensuremath{\chi^0_1}}=0,\ m_{\ensuremath{\chi^\pm_1}}=m_{\ensuremath{\chi^0_2}}$, and the NLSP decays to $\ensuremath{\chi^0_1}$ with $100\%$ branching fraction.}
\label{tab:ExpResCombined}
\end{table}

There have already been many studies analyzing the reach of electroweakino searches in the context of MSSM at the LHC \cite{Bino-Higgsino1,Bino-Higgsino2,Bino-Higgsino3,Wino-Higgsino1,Wino-Higgsino2,Wino-Higgsino3,1310-4274,1511-05386}.   Those results cannot be directly translated into bounds on the blind-spot parameter space described by the parameter relations given in Table \ref{tab:SIBS}.
In the following we estimate the reach for electroweakino searches at 14 TeV LHC for the blind-spot regions by performing a detailed collider study.
We use Madgraph 5/MadEvent v1.5.11 \cite{Alwall:2011aa} to generate signal events in the relevant mass parameter plane. Each signal sample consists 250,000 events and contains up to 1 additional jet. These events are passed to Pythia 6.4 \cite{Sjostrand:2006aa} to simulate initial and final state radiation, showering and hadronization. The events are further passed through Delphes 3.1 \cite{Ovyn:2009aa,Favereau:2013aa} with the Snowmass combined LHC detector card \cite{Anderson:2013aa} to simulate detector effects.
We use the backgrounds generated for the Snowmass Energy Frontier Simulations \cite{Anderson:2013aa} without pile-up. We include the main backgrounds with two or more leptons in the final state: $VV$ (boson pair), $VVV$ (triple boson), $t \bar t$ (top pair) and $t\bar tV$ (top pair plus boson) production.
To simulate the trigger, we require the events to pass one of the three selections:
\begin{equation}
{\rm either}\ p_{T,\ell}>30\ {\rm GeV};\quad {\rm or\ two\ leptons}\ p_{T,\ell_1}, p_{T,\ell_2} >20,\ 10\ {\rm  GeV};\quad {\rm or}\  \ensuremath{\slashed{E}_T} > 100\ {\rm GeV}.
\end{equation}
In this section, we do not consider a situation containing a compressed spectrum. The trigger efficiencies are high for the lepton selections.

We separate these events into different signal regions which are discussed below. Each signal region has a set of observables. These will be passed to a Boosted Decision Tree (BDT) which is implemented in the Root package TMVA \cite{Hoecker:aa}.\footnote{For each benchmark point we train a set of 1000 randomized BDT with a maximal depth of 3.} Using HistFactory \cite{Cranmer:2012sba}, RooFit \cite{Verkerke:2003ir} and RooStats \cite{Moneta:2010pm}, the resulting BDT distribution is used to perform a hypothesis test yielding the significance. We assume a 10\% systematic error on the background cross sections.
Although this is a rather conservative choice, our conclusions would not change much if we vary this value since the observability is dominated by the statistics.

For all signal regions, we include the following variables as input for the BDT: lepton transverse momentum $p_{T,\ell_i}$ for all leptons $\ell_i$,  missing energy  $\ensuremath{\slashed{E}_T}$ and the scalar sum of hadronic transverse momentum $H_{T}$. We distinguish different signal regions based on lepton content of the final states:
\begin{itemize}
\item \textbf{Same-Sign Dilepton ($W^\pm W^\pm + \ensuremath{\slashed{E}_T}$):} This signal region consists of events with two same-sign leptons. This mainly targets the processes $\chi_{2}^0\ \chi_{3}^0 \to W^\pm W^\pm \chi_1^\mp \chi_1^\mp$ and $\chi_{2,3}^0 \chi_{2}^\pm \to W^\pm W^\pm \chi_1^\mp \chi_1^0$  (Case B) which have a same-sign dilepton plus missing energy final state. The dominating backgrounds are vector boson-pair, top-pair and top-pair vector boson associate production with leptonic decays. We use the following variables as additional input for the BDT:
\begin{itemize}
\item $R_{\ell\ell}$, $p_{T,\ell\ell}, m_{\ell\ell}$: separation, transverse momentum and invariant mass of the two leptons.
\end{itemize}

\item \textbf{Opposite-Sign Dilepton ($W^\pm W^\mp + \ensuremath{\slashed{E}_T}$):} This signal region consists of events with two opposite-sign leptons. However, this channel suffers from large $tt$, $WW$ and mono-$Z$ backgrounds and therefore is insensitive in most parts of the parameter space.

\item \textbf{Trilepton ($W^\pm Z + \ensuremath{\slashed{E}_T}$):} This signal region consists of events with three leptons. This mainly targets the processes like $\chi_{1,2}^\pm\ \chi^0_{2,3} \to W^\pm Z \chi_1^0 \chi_1^0$ which has a tri-lepton plus missing energy final state.   We require at least one opposite-sign, same flavor lepton pair which will be identified as $Z$ originated. The dominating backgrounds are $WZ$ production with sub-leading contributions from triple vector boson and top-pair vector boson associate production.  We use the following variables as additional input for the BDT:
\begin{itemize}
\item $\Delta R_Z$, $p_{T,Z}, m_{Z}$: separation, transverse momentum and invariant mass of the two leptons which are considered to be $Z$ originated.
\item $M_T$, $\Delta R_{Zl}$, $m_{Z,\ell}$: transverse mass of the $W$-originated lepton, separation and invariant mass of the $Z$-candidate and the third lepton.
\end{itemize}

\item \textbf{Four Leptons ($ZZ + \ensuremath{\slashed{E}_T}$):} This signal region consists of events with four leptons. This mainly targets the processes like $\chi^0_2\ \chi^0_{3} \to Z Z \chi_1^0 \chi_1^0$ which has a four-lepton plus missing energy final state. We require   two opposite-sign, same flavor lepton pairs which will be assumed to be $Z$ originated. The dominating backgrounds are $ZZ$, triple vector boson and top-pair vector boson associate production. We use the following variables as additional input for the BDT:
\begin{itemize}
\item $\Delta R_{Z_i}$, $p_{T,Z_i}, m_{Z_i} \ (i=1,2)$: separation, transverse momentum and invariant mass of the two leptons which are considered to be $Z$ originated .
\item $\Delta \phi_{ZZ}$, $\Delta R_{ZZ}$, $m_{ZZ}$: angular separation, separation and invariant mass of the two $Z$-candidates.
\end{itemize}

\end{itemize}
For each signal region we independently perform an analysis for final states with one and two lepton flavors, and combine the results afterwards. While the identification of the $Z$-candidate is straightforward in the case of a two lepton-flavor final state, we choose the opposite-sign lepton pair closest to the $Z$ mass in the one lepton flavor final state case. We do not include a search strategy targeting the decay channels with $h$ in the final states due to large backgrounds.

\begin{figure}[tb]
\centering
\includegraphics[width=0.49\textwidth]{Figures/summary_A_300.pdf}
\includegraphics[width=0.49\textwidth]{Figures/summary_B_300.pdf}
\caption{Estimated 95\% CL. exclusion reach for eletroweakino searches for Case A (left) and Case B (right). The colored regions show the same-sign di-lepton (orange), tri-lepton (green) and four-lepton (blue) channel as well as their combination (yellow). The combined 5$\sigma$ discovery reach is indicated by the thick solid line next to the hatched region.
Existing constraints from Electroweak Precision Measurements, LEP~\cite{Abdallah:2003xe,LEP-ALEPH} and LHC~\cite{CMS-SUS-13-006} are shown in gray shaded regions. }
\label{fig:ElectroweakinoSummary}
\end{figure}

The results of our analysis are shown in Fig.~\ref{fig:ElectroweakinoSummary}. The LEP limits from electroweak precision measurement and chargino searches, as discussed in Sec.~\ref{sec:LEP2}, are shown as light gray shaded area in Fig.~\ref{fig:ElectroweakinoSummary}. While chargino searches exclude $M_2 \approx m_{\chi^+_1} \lesssim 100$ GeV for Case B, only   a small region with $-\mu\lesssim 100$ GeV is excluded in Case A.
Bounds from current LHC searches at 8 TeV \cite{CMS-SUS-13-006} are shown as dark gray shaded area and exceed the LEP  bounds only in Case A for $-\mu=140$ GeV and $M_1 = 70$ GeV.
We consider 14 TeV LHC at an integrated luminosity of 300 fb$^{-1}$ and take into account a 10\% systematic error on the background cross sections.
The colored region shows the estimated 95\% CL exclusion reach for the same-sign dilepton channel (orange region with dashed line in the right panel), tri-lepton channel (green region with dotted line), four lepton channel (blue region with dash-dotted line) and a combination of all channels (yellow region with solid line). We can see that the three lepton channel (green) provide the best reach in Case A. A similar reach is obtained by the same-sign dilepton channel (orange) in Case B.
The combined reach in Case B is therefore about 100 GeV better than either the trilepton channel or the same-sign dilepton channel.   The reach in the four lepton final channel (blue) is limited due to the smaller $\chi\chi\to ZZ+\ensuremath{\slashed{E}_T}$ cross section (see Fig.~\ref{fig:proCS_AB}) and the small branching fraction $Z \to \ell \bar\ell$.
The thick solid line with next to the hatched area encloses the estimated 5$\sigma$ discovery reach for 14 TeV LHC with integrated luminosity of 300 fb$^{-1}$.  At the 14 TeV LHC with 300 ${\rm fb}^{-1}$ luminosity, the 95\% CL reach with the combination of all channels in $|\mu|$ is about 700 GeV for both  Case A  and Case B.    The 5$\sigma$ discovery reach is about 500 GeV for both cases.

We do not perform a detailed collider study for electroweakino searches for Case C. The NLSP production rates vanish for a decoupled Higgsino masses when  the NLSPs are out of the LHC reach. If the Higgsino is   within the reach of LHC, then the collider phenomenology will be similar to that of Case B. In the most optimistic case, in which the Higgsino has the lightest possible mass allowed by the blind-spot relation, $\mu + M_2\sin2\beta=0$, the reach is expected to be very similar to Case B.   Thus we do not further study the collider phenomenology of Case C in detail.

\subsection{Mono-jet searches}
\label{sec:monojet}

While the production of only an LSP pair is unobservable at colliders, the LSP pair production in association with a hard ISR jet (or photon) provides a clean and distinctive signature in dark matter searches. The main SM background to this mono-jet final state comes from $Z+$jet production in which the $Z$-boson decays into neutrinos. The rate for this process is small and hence making searches for such events with large missing transverse momentum balanced by an energetic jet (or photon) a promising tool for neutralino LSP at colliders.

If the LSP is bino-like, its coupling to the $Z$-boson is proportional to the bino-Higgsino mixing,  which quickly decreases at large Higgsino masses (see discussion in Sec.~\ref{sec_EW}). Therefore the LSP pair production rate is strongly suppressed and no limit based on mono-jet searches can be obtained in Case A.

Both ATLAS \cite{ATLASmonojet} and CMS \cite{CMSmonojetPublished} have performed a monojet search at 8 TeV LHC using 20.3 fb$^{-1}$ and 19.7 fb$^{-1}$ integrated luminosity respectively. For Case B, using the same cuts used by ATLAS and the upper limit set by ATLAS \cite{ATLASmonojet},   the current exclusion bounds are rather weak.  Only the region where LSP mass is less than about 100 GeV have been excluded by current 8 TeV results.   These limits have a similar reach as the mono-photon search at LEP.

To estimate the collider reach and expected bounds at 14 TeV LHC, we perform a MC analysis.\footnote{More details about the methodology can be found in Sec.~\ref{sec:EWsearch}.}  As signal we consider the pair production of both wino-like states generated with up to two additional jets. We use the backgrounds generated by the Snowmass Energy Frontier Simulations \cite{Anderson:2013aa} without pile-up. We consider the main backgrounds including large missing energy: $W/Z$ + jets and vector boson pair production.

For jet identification, we use the anti-$k_t$ jet algorithm with $R=0.4$ to find jets with $p_T>30$ GeV and $|\eta_j|<4.5$. Similar to the CMS 8 TeV analyses \cite{CMSmonojetPublished}, we require events to either pass the missing energy trigger $\ensuremath{\slashed{E}_T}>120$ GeV, or the MET+Jet trigger with $\ensuremath{\slashed{E}_T}>105$ GeV and a leading jet with $p_T>80$ GeV and $|\eta|<2.6$. Events with more than two jets are rejected. Events with leptons ($e,\mu,\tau$), photons and tagged jets ($b,\tau$) are vetoed. Following the analysis in \cite{Wino-Higgsino2} we assume a systematic error of $1-2\%$ on the background cross section.
Two signal regions are defined based on the number of jets: 1 jet + $\ensuremath{\slashed{E}_T}$ and 2 jets + $\ensuremath{\slashed{E}_T}$. As input for the BDT we use $\ensuremath{\slashed{E}_T}$, $H_T$, the jets transverse momentum and rapidity $p_{T,j}$ and $\eta_{j}$ as well as the angular separation between jet and missing energy or the two jets,  $\Delta \phi (\ensuremath{\slashed{E}_T},j) $ and $\Delta \phi (j,j)$.

We find that typically the $W/Z$+jets backgrounds dominate while the sub-leading vector boson pair background has a similar cross section as the signal. The mass reach is shown in Fig.~\ref{fig:MonojetSummary}.  Both the one and two jet channels contribute about equally. Combining both channels, we obtain a 95\% CL exclusion reach of
$100-210$  GeV ($130-280$ GeV) at 14 TeV LHC with 300 (3000) fb$^{-1}$ assuming a systematic error on the background cross section of $1\%-5\%$, as indicated by the wide bands in Fig.~\ref{fig:MonojetSummary} (the left panel).   Increasing the systematic error from 1\% to $5\%$ would lower the mass coverage by almost 100 GeV or more.
These limits are in agreement with the results found for a pure wino LSP in \cite{Wino-Higgsino2}. The mono-jet search limits for Case C is very similar to that of Case B.

\begin{figure}[tb]
\centering
\includegraphics[width=0.49\textwidth]{Figures/summary_monojet.pdf}
\includegraphics[width=0.49\textwidth]{Figures/summary_barchart.pdf}
\caption{Left:
Mass reach in the monojet channel with 1-jet and 2-jets events at 14 TeV LHC with  300 fb$^{-1}$  (green) and 3000 fb$^{-1}$  (yellow) integrated luminosity.  The bands are generated by varying the background systematics  from $1\%$ (dashed far-right curves), $2\%$ (solid middle  curves), to $5\%$ (dotted far-left curves).
Right: Exclusion and discover reach at 14 TeV LHC assuming 1\% systematic uncertainty on the background cross section.}
\label{fig:MonojetSummary}
\end{figure}

 A scenario similar to our Case C, with $M_1 \approx M_2$ and decoupled $\mu$ resulting in a compressed spectrum, has been studied in the literature \cite{Schwaller:2013baa} using signatures of  large missing energy and soft leptons.  At 95\% CL, the reach is $M_1\approx M_2 > 150-200$ GeV at LHC with 300 fb$^{-1}$ luminosity assuming a systematic error of 1\% on the background cross section. Ref.~\cite{vbf-tao} proposed a search for VBF production of bino-wino LSP pairs with two forward jets.  At 14 TeV LHC with 300 fb$^{-1}$ luminosity,  a 95\% CL reach of $M_1=M_2> 200$ GeV for $\tan\beta=5$ can be obtained. However, given that $S/B\sim 2-3$\%, the results heavily depends on effective control of the systematic errors.

\section{Summary and Conclusions}
\label{sec:conclusion}

In this paper, we carried out comprehensive analyses for the dark matter (DM) searches under the
 blind-sport scenarios in MSSM. We first summarized all the theoretical conditions for blind spots, and listed  three distinctive situations (Cases A, B, C) at the end of Sec.~\ref{sec:BS}. We identified a new blind-spot condition for both spin-independent (SI) and spin-dependent (SD)  scattering (Case C) that was not studied in the literature \cite{blindspots}. We then quantified the requirements of acceptable DM relic abundance for the blind-spot scenarios as shown in Sec.~\ref{sec:RD}. We found that Case A was disfavored by the relic density considerations because of the bino nature of the DM candidate with a low annihilation rate, as seen in Fig.~\ref{fig:Relic_CaseA}. However, including co-annihilation effects with a light slepton could help to enhance the annihilation cross section and render the relic density at an acceptable level, as shown in Fig.~\ref{fig:Relic_CaseA_stau}.
Cases B and C can readily provide an acceptable relic density since winos are typically under-abundant as long as they are not too heavy, as seen in Fig.~\ref{fig:Relic_CaseBC}.
Co-annihilation could also help to extend to heavier winos by enhancing the annihilation cross section and thus to yield a desirable relic density.
Note that including light slepton, e.g. $\tilde{\tau}_R$, will not have notable effects in the DM direct and indirect detections, as well as collider searches for the gauginos.

We set out to explore the complementary coverage for the blind spots in the MSSM theory parameters, for the projection of the future underground DM direct searches, the indirect searches from the relic DM annihilation into photons and neutrinos, and for collider DM searches including the current bounds from the existing LEP and LHC results, as well as the future LHC upgrade to higher luminosities (HL-LHC). We found that
\begin{itemize}
\item
The SI blind spots for Cases A and B may be rescued by the SD direct detections, as seen in Figs.~\ref{fig:SigmaSDn} and \ref{fig:SigmaSDp}, with $\chi$-$n$ scattering more promising than that of $\chi$-$p$ scattering.
\item
The neutrino detections from IceCube and SuperK are approaching the sensitivity on the SD scattering cross section for the blind-spot region for Case A in the best $WW$ channel and the next $\tau\tau$ channel, as seen in Fig.~\ref{fig:SigmaSDpCaseA}, but still about an order of magnitude away for Case B, as in seen Fig.~\ref{fig:SigmaSDpCaseB}.
\item
The detection of gamma-rays from Fermi-LAT may not reach the desirable sensitivity for searching for the DM blind-spot regions, as shown in Figs.~\ref{fig:FermiGamma_CaseA}, \ref{fig:FermiGamma_CaseB} and \ref{fig:FermiGamma_CaseC}.
\item
The $Z$-invisible decay searches at LEP1 already excluded the small-mass region for $m^{}_{\text{DM}}<45$ GeV as discussed in Sec.~\ref{sec_EW} and in Fig.~\ref{fig:Zinv}.
The chargino searches at LEP2 also imposed some bounds as seen in Sec.~\ref{sec:LEP2}.
\item
The Disappearing Track (DT) search of winos at the LHC experiments are particularly sensitive to the large values of $|\mu|$ and $\tan\beta$ when the mixing with Higgsinos are small. The projected $95\%$ CL  sensitivity at the 14 TeV LHC could reach $M_{2}\sim 600\ (1100)$ GeV with 300 fb$^{-1}$ (3000 fb$^{-1}$) for Case B, and $M_{1,2}\sim 1\ (2)$ TeV with 300 fb$^{-1}$ (3000 fb$^{-1}$) for Case C,
as shown in the two panels of Fig.~\ref{fig:DT14TeV}, respectively.
\item
Cross sections for the electroweakino (EW) pair production and decay to $WW/WZ/ZZ$ channels at the 14 TeV LHC are plotted in Fig.~\ref{fig:proCS_AB}. The SUSY search sensitivity with 300 fb$^{-1}$ may  cover the blind-spot regions of Case A
up to $M_{1}\sim 300$ GeV (400 GeV) for $5\sigma$ ($95\%$ CL),
and Case B
up to $M_{2}\sim 260$ GeV (380 GeV) for $5\sigma$ ($95\%$ CL),
and $|\mu| \sim 500$ GeV (700 GeV) for $5\sigma$ ($95\%$ CL),
as shown in Fig.~\ref{fig:ElectroweakinoSummary}.   With 3000 ${\rm fb}^{-1}$ luminosity, the reach in $|\mu|$ is about 150 GeV better.
\item
The searches of mono-jet signal at the 14 LHC with 300 fb$^{-1}$ luminosity  may reach a sensitivity to cover the blind-spot regions of Case B up to $M_{2}\sim 130$ GeV (210 GeV) for $5\sigma$ ($95\%$ CL) as shown in Fig.~\ref{fig:MonojetSummary}. The coverage can be improved by about $30\%$ in the mass reach with 3000 fb$^{-1}$.
\end{itemize}

\begin{figure}[tb]
\centering
\includegraphics[width=0.49\textwidth]{Figures/summary_A.pdf}
\includegraphics[width=0.49\textwidth]{Figures/summary_B.pdf}
\caption{Summary plot for the blind-spot reach including the current bounds from LEP and LHC, future DM search projection, and 95\% CL exclusion reach at the 300 ${\rm fb}^{-1}$ 14 TeV LHC and the HL-LHC.
Left panel for Case A in the $M_1-\mu$ plane and right panel for Case B in the $M_2-\mu$ plane. ``DT'' denotes the disappearing track search. }
\label{fig:Summary}
\end{figure}

\begin{table}[tbh]
\centering
\begin{tabular}{|c|c|c|c|}
\hline
Blind spots in Sec.~\ref{sec:bs}/Searches: & Direct detection & Indirect detection & LHC searches \\ \hline
Case A (SI) & yes (SD) & maybe (SD) & yes (EW) \\ \hline
Case B (SI) & yes (SD) & maybe not (SD) & yes (DT, EW, jets) \\ \hline
Case C (SI  $\&$ SD) & no & no & yes (DT, EW, jets) \\ \hline
\end{tabular}
\caption{
Blind spots as defined in Sec.~\ref{sec:bs} and their search sensitivities in various means as discussed in the text. Notations and details can be also found in this summary section. }
\label{tab:sum}
\end{table}

\noindent
Our results are summarized in Fig.~\ref{fig:Summary} for Cases A and B and tabulated in Table  \ref{tab:sum}, where we see the complementarity for the blind-spot coverage, including the current bounds from LEP and LHC, future DM search via the SD scattering, and collider reach at the 14 TeV LHC and the HL-LHC extension for the SUSY blind-spot parameters.
Proper treatments of the DM relic densities have been taken into account, as stated at the end of Sec.~\ref{sec:RD}.

In conclusion,
 the SUSY WIMP dark matter would be difficult to discover in the blind-spot regions via the leading direct detection means via the SI scattering, as well as via the indirect detections with gamma rays.
We point out that the SI scattering blind spots \cite{blindspots} may be rescued by SD scattering searches in the future direct detection experiments. The neutrino detections from IceCube and SuperK are approaching the sensitivity on the SD scattering cross section for the blind-spot Case A.
Furthermore, the SUSY searches at the LHC will substantially extend the coverage for all the three blind-spot scenarios to large parameter regions, in particular including the ``most blind'' scenario Case C.
After all, the dark matter blind spots may be unblinded with the collective efforts in future DM searches.
In the optimistic situation with a discovery for the SUSY signals at the LHC, it is of ultimate important to determine the parameters both for the masses and couplings to check against the DM properties as well as the blind-spot relations. Only with those achievements of a fully consistency check, can one reach the conclusion for the identification of the SUSY dark matter.

\acknowledgments
We would like to thank Xerxes Tata for discussions.
The work of TH is supported in part by the Department of Energy under Grant No.~DE-FG02-95ER40896, and in part by PITT PACC.  The work of FK is supported by NSF under Grant PHY-1620638. FK also acknowledges support from the Fermilab Graduate Student Research Program in Theoretical Physics operated by Fermi Research Alliance, LLC under Contract No.~DE-AC02-07CH11359 with the United States Department of Energy. The work of SS is supported by the Department of Energy under Grant DE-FG02-13ER41976/de-sc0009913, and partly by the National Science Foundation of China (NSFC) under Grant No.~11428511.   The work of YW is supported by Chinese Scholarship Council.  We would also like to thank the Aspen Center for Physics for hospitality, where part of the work was completed. The Aspen Center for Physics is supported by the NSF under Grant No.~PHYS-1066293.

\bibliographystyle{JHEP}

redpajama_set_name: RedPajamaArXiv


text:
One in fifty people in the UK have declared LGBT status. We think that's wrong.
Category: Blogger's Corner, Industry News, community, bisexual, gay, transgender, lesbian, jobseekers, environment, believe, significant, national statistics
Recent data says one in 50 people in the UK (1.7%) identified as lesbian, gay or bisexual in 2016. The Office of National Statistics (ONS) says that's a significant increase from their previous figures. We believe that's actually just a shadow of the LGBT (lesbian, gay, bisexual and transgender) community in the UK.
We created VERCIDA to be the service of choice for jobseekers looking to work in diverse environments. And the information we gather from our users suggests a much higher disclosure rate of LGBT status - around 5.34%. As an organisation, that's great - we're truly championing a comfortable environment that allows people to bring their whole self to work. On the flip side, it suggests for every person out and self-declaring, there are two that are not.
How big is the UK's LGBT community?
The LGBT charity Stonewall agrees with us - suggesting the community is actually between 5% and 7%. Others have put it as high as one in 10. The shortfall between the estimate and the statistical data is down to people being reluctant to come out, the rights group says. The problem, they say, is that people can be honest with an anonymous survey but struggle harder to be open with family and colleagues.
That's because it can be a hostile environment for LGBT employees. Half of trans employees are so worried about workplace discrimination they have hidden the details of their sexuality, said a Stonewall survey earlier this year. More disturbingly, one in eight have been physically attacked by colleagues or customers. That's a shocking figure. That figure must change.
At VERCIDA, we believe supportive environments are incredibly important to helping people achieve their potential. We assist our users to find people and environments that allow them to be open, honest and successful. Like Stonewall, we think there needs to be better recognition of the discrimination and anti-LGBT abuse that still exists. And better solutions for smashing down and removing those barriers. We're proud to be using technology to tackle those challenges.
The data from the ONS showed more men (2.3%) identified as LGB than women (1.6%), and persons of mixed race or multiple ethnic groups were most likely to identify as LGB (4.3%.) London has the largest LGB community in the UK (at 2.7%). That's being put down to the city's young and diverse population. And high social acceptability of sexual identities which mean people are more likely to explore their own sexuality.
Tags: clicking on links loads other articles with the selected tagpotential achieve supportive Discrimination workplace colleagues struggle anonymous organisation disclosure information environment jobseekers community believe significant national statistics transgender lesbian gay bisexual LGBT
VERCIDA
Dependency (Parenting & Carers)
Diversity Diaries 3: The Fearful Fool
In this addition to our Diversity Diaries series we will be taking a look at fear and diving into its relationship with prejudice. CHAPTER FOUR: THE FEARFUL FOOL Lack of understanding, ignorance...
Stonewall CEO Ruth Hunt, why the charity is going trans inclusive?
The charity, which previously only lobbied only on gay, lesbian and bisexual issues in England and Wales, announced on Monday that it would now also include trans issues in its brief. Explaining the...
Diversity Diaries 5: Cultivating Community
At VERCIDA we discuss many communities with a passionate ethos of supporting every individual, from any community, in finding a role they can be happy in, in an inclusive company that will support the...
Neurodiversity with Alexander Chocolate: Alex's Story
At VERCIDA, we celebrate all types of diversity with a firm belief that opening the door to diversity is not only necessary in creating a fair working culture for all, but that it is also good for bus...

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Very gently lived in home built in 2017! For those looking for a fixer upper, there's nothing to see here! This home is REALLY ready to move into with all the beautiful finish details of a Meritage Home. Large stainless refrigerator remains. Completely foam, Energy Star home that will save $$$ on utility bills! LARGE Master Suite with very generous sitting area,a true owner's retreat! Great loft space for hanging out. Large open family/kitchen area. Be ready to call this HOME! I DID say MERITAGE, right?!
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text:
Q: Tensorflow: cross index slicing of a tensor I have two tensors of the following shape:
tensor1 => shape(10, 99, 106)
tensor2 => shape(10, 99)

The tensor2 contains values ranging from 0 - 105 That I wish to use to slice the last dimension of the tensor1 and obtain tensor3 of the shape
tensor3 => shape(10, 99, 99)

I have tried using:
tensor4 = tf.gather(tensor1, tensor2)
# this causes tensor4 to be of shape (10, 99, 99, 106)

Also, using
tensor4 = tf.gather_nd(tensor1, tensor2)
# gives the error: last dimension of tensor2 (which is 99) must be
# less than the rank of the tensor1 (which is 3).

What I am looking for something that resembles the numpy's cross_indexing for this.

A: You can use tf.map_fn:
 tensor3 = tf.map_fn(lambda u: tf.gather(u[0],u[1],axis=1),[tensor1,tensor2],dtype=tensor1.dtype)

You can think of this line as a loop that runs over the first dimensions of tensor1 and tensor2, and for each index i in the their first dimension it applies tf.gather on tensor1[i,:,:] and tensor2[i,:].

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			Ode to a tragic lover:   March 5th 2009

When I think about you I feel happiness-

				Its like a light on, to show me your face

				for a moment I am suspended

				This is not the way I suspected it would go

				For me it did seem you would- burst through the door

				or was it a dream?

				When I close my eyes and fall

				your not here to sleep

				Running fingers through your hair

				 feeling the texture of defeat

				you swore the ring you'd wear and would keep

				I needed you to take your shoes off

				and walk into the lake

				when the fires came I called your name

				 but I missed you

				Now I leisure, smoke, my days

				you're the ashes blow away-

				All you are is ashes when I die

				as I exhale your memories one last time.


text:
Opening Arctic Waters to Drilling Is Trump Priority, Key Senator Says
The Polar Pioneer drilling rig, pictured in Dutch Harbor while contracted to Shell to drill an exploratory well in the Chukchi Sea. Photo: Shell Alaska
By Jennifer A. Dlouhy and Catherine Traywick
(Bloomberg) — Senator Lisa Murkowski said President Donald Trump is interested in opening up new coastal waters for oil and gas drilling and reversing Obama-era policies that restrict energy development in Alaska.
Both Trump and Interior Secretary Ryan Zinke are weighing ways to expand opportunities to drill in Arctic waters though the changes could take years to accomplish administratively, Murkowski said in an interview on the sidelines of the CERAWeek conference in Houston.
"It's fair to say we are looking at how we might be able to — how the administration might be able to — allow for opportunities within this important area, offshore Alaska," Murkowski said.
Murkowski, who heads the Senate Energy and Natural Resources Committee, joined her fellow Republican senator from Alaska, Dan Sullivan, in a meeting with Trump and Zinke earlier this week to discuss the issue. Trump "clearly understood the impact of taking off-line" oil and gas development in the Chukchi and Beaufort seas north of Alaska, Murkowski said.
"What was very clear was a recognition that what Alaska has to offer is considerable, important and we need to be working to undo much of what the Obama administration did in terms of locking up these resources," Murkowski said of her talks with Trump.
Wildlife Refuge Drilling
Among her targets: making it easier to develop parcels in the National Petroleum Reserve-Alaska, a 23-million-acre (9.3 million hectare) region set aside 94 years ago because of its oil and gas potential, and allowing the activity in part of the Arctic National Wildlife Refuge (ANWR).
Any decision to open up ANWR would fall to Congress, where Murkowski and Sullivan are pushing legislation that would allow oil and gas development in as much as 2,000 acres of the refuge.
The president can set some changes into motion immediately by directing the Interior Department to rewrite a plan for selling offshore oil and gas leases over the next five years and add auctions of tracts in the Arctic and Atlantic oceans that the Obama administration left out. But wedging those sales back into the plan would require environmental analysis and public comment periods — perhaps consuming a year for the Arctic and even longer for parcels along the U.S. East Coast.
The Trump administration also is weighing how to undo an executive order that President Barack Obama used to withdraw almost all U.S. Arctic waters and underwater canyons in the Atlantic Ocean from future oil and gas leasing. Environmentalists say it would be unprecedented for any president to rescind such a designation, and the reversal would almost certainly be challenged in court.
'Legal Scrutiny'
"You would have opponents lining up, so it must be done in a way that can survive legal challenge," Murkowski said. Although an executive order reversing Obama's decision would be the cleanest option, she said such action isn't imminent because Zinke still needs to assemble a legal team to help craft an approach capable of withstanding legal scrutiny.
"What that requires is a good solid legal team that is walking you through the steps of the process, and right now the secretary is without a team," Murkowski said. "I know for a fact that has been a level of frustration for Secretary Zinke. He is itching to go and is very frustrated by the fact that he doesn't have his folks in place."
Trump has repeatedly pledged to expand U.S. energy development and remove "obstacles" holding back exploration of America's "vast untapped domestic energy reserves."
Obscure 1953 Provision
Most federal decisions over offshore oil and gas development happen in five-year increments, through the government's schedule for selling leases. But Obama aimed to set permanent policy in 2016 when he invoked an obscure provision in a 1953 law to withdraw U.S. waters from future oil and gas leasing. The provision previously had mostly been used to permanently protect coral reefs, walrus feeding grounds, and marine sanctuaries.
Any move by Trump to undo Obama's protections is sure to draw a legal challenge, but it could take years before a lawsuit is ready to be filed, and there is scant legal precedent on the matter.
Presidents have modified decisions from predecessors to indefinitely withdraw areas from drilling, but have never rescinded them altogether. The statute doesn't include a provision for reversal. And a legal opinion from the U.S. attorney general in 1938 on similar designations under a different law said they "do not imply a power to undo."
Whether the oil industry really wants the territory is an open question.
Shell Gives Up
While the U.S. Arctic is estimated to hold 27 billion barrels of oil and 132 trillion cubic feet of natural gas, energy companies have struggled to tap those resources in harsh conditions at the top of the globe. Exploration costs are high in remote Arctic waters, where work is confined to just a few months each year and there is sparse infrastructure to support the activity.
Oil major Royal Dutch Shell Plc spent more than seven years and roughly $8 billion trying to find a large stash of crude in the Chukchi Sea, which lies between Alaska and Siberia, but it ended the quest in 2015 after a test well yielded disappointing results.
Industry leaders say Arctic crude is needed to meet the world's energy needs and help keep oil flowing through the 40-year-old Trans-Alaska Pipeline System. The activity also may support the development of infrastructure that could help buttress U.S. security as climate change and melting sea ice opens up new shipping routes in the Arctic Ocean.
Still, there are signs that Alaska's oil prospects may be looking up. The Spanish oil company Repsol SA on Thursday announced a 1.2 billion-barrel discovery on Alaska's North Slope, the biggest U.S. onshore oil find in three decades. That follows a 2016 announcement by closely held Caelus Energy Corp. claiming to have found at least 2 billion barrels of recoverable oil far beneath Smith Bay, in northwestern Alaska.


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You made your orchestral debut at the age of 11 with the Seattle Symphony and your father, Gerard Schwarz, conducting. He is also conducting your performance with the QSO. How often do you have the opportunity to perform together?
I am very lucky to have the chance to perform with my father frequently. I jump at any chance to perform with him! So far we have performed eight different concertos together (two were world premieres) and this is our first Elgar. We have made two recordings as well-- one for Naxos and the other for public television in the US. This season we will perform seven more times together, including my first Don Quixote of Strauss.
Do you feel more at ease performing under your father's direction compared to another conductor?
This has evolved over the past few years. At first I was more nervous to play with him than any other conductor. He is very demanding and I felt much pressure to play to his standards. Now I am much more at ease playing with him than any other conductor. As I play with more and more different styles of conducting, I have grown to appreciate what I used to take for granted-- his innate chamber music and listening qualities from the podium. He is so natural and instinctive, I can mould phrases in the moment without any fear of losing my colleagues in the orchestra. It is a true gift to work with him.
What is your favourite part of Elgar's Cello Concerto?
My favourite part of the Elgar Concerto is the long, introspective coda to the last movement. For me it is a mournful statement that references the recitative quality that pervades the whole concerto. It both brings back the great slow movement theme, and then finally the opening of the first movement to close the piece. It leaves me with the sense of having come full circle.
What type of cello do you play?
I play an English cello made in 1790 by Benjamin Banks. It is a beautiful instrument of a dark cherry varnish, made in Salisbury. The bow I play is of the French maker Marcel Lapierre made in the 1970s.
Why did you initially choose to play the cello rather than another instrument?
I started on the piano to establish a basis of harmony and counterpoint. Then I wanted to learn the double bass. Knowing the physical and musical limitations of the bass, my parents urged me to consider the cello. Though I always thought I would eventually switch, I am very grateful to have been nudged in that direction!
Will you and your father have time for a holiday while you are in Australia?
Unfortunately not. This is my first time in Australia and nothing would make me happier than to see the great beauty of the country. I will be coming to Australia from Mexico where I am playing the Dvorak Concerto. After Australia I must get back to New York City to prepare for a performance of the Haydn C Major Concerto in Toledo, OH.


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Here's where things get weird. I got up early, it was still dark, and just as I turned on the light in the study a mouse leaped off my desk and beat it under the closet door. I was still convinced I was dealing with a hacker, but then noticed that though I hadn't touched my computer, it wasn't asleep. Staring at me on the screen was a long note.
i know this is farfetched but well, Sir, i really am a mouse but i used to be a person. did you ever read archy and mehitabel? these things can happen. at least i'm a mammal not a cockroach.
just call me racy h. that h is a mouse thing, pretentious if you ask me but they all do it. all i know is that i was living a fine life just like you - well i ate better than you do, Sir. honest, cheetos? - and then i died and now i'm a mouse. there's lots of us around you know. that cat who lives across the road? used to be horace greeley. i'm not making that up. nice guy but i keep my distance. there's a barred owl nearby, total chatterbox at 3 in the morning as i'm sure you know, fredda, was some talk-radio host. we do not get along she says it's just her luck to have been reincarnated in vermont instead of some right-thinking place like idaho, i think she's baiting me but i keep my thoughts to myself because owls and mice, we have a history.
Anyway, thank you for your computer. it's not easy typing, fine for you people with fingers but with tiny little mouse legs? these keys are harder to press than you think, and it's hard to stretch more than two keys so don't expect many capital letters from me tho i'm trying to expand my repertoire and i might get d pretty soon and maybe l tho who knows. it feels good to be writing again. expression is the need of my soul, that's what archy said and it is. you can't eat words, but you can be sustained by them.
Up next... "Mice out of hand? Sez you!"
Want to get caught up? Here's Post #1, "Sir, i don't want my neck snapped"


text:
Sandeep Sharma: Accidental death, say police. Not so, say family and colleagues
By freespeechcollective on November 1, 2018 • ( 2 Comments )
The shocking footage of a dumper truck swerving sharply to mow down journalist Sandeep Sharma in Madhya Pradesh went viral and the protests that followed forced the state's Chief Minister to announce a CBI inquiry. But barely seven months later, Sharma's death is a mere statistic in the record of road accidents, not a murder, not by a ruthless sand mafia and definitely not by the police officer who had allegedly threatened him and against whom Sharma had complained .
Name: Sandeep Sharma
Date of death: March 26, 2018
Brief synopsis: Sandeep Sharma, 35, was run over by a dumper truck in Bhind in Madhya Pradesh when he was riding his bike. He died on the spot. The dumper truck driver fled from the spot.
Sharma was employed with News World channel and had done a report on the nexus between the police and the sand mining mafia in Chambal region, Madhya Pradesh, in October 2017. He and his colleague, Vikas Purohit, had received several threats to their lives. They had even written to then Bhind superintendent of police Prashant Khare on Nov 3, 2017, citing threats from a sub-divisional police officer, Indra Veer Singh Bhadouria, and the sand mining mafia in the area.
Police Investigation: A Special Investigative Team (SIT) was formed immediately after his death. Preliminary reports said that police were checking the CCTV footage and recording statements of eyewitnesses to determine whether the death was accidental or a suspected murder. The CCTV footage accessed by police clearly showed the dumper following the Sharma for a distance before hitting him and running over him.
Police arrested the dumper truck driver Ranbir Yadav the same day and the truck owner, Bhaskar Sharma, the next day. Both are out on bail. The case is being heard in the Motor Accidents Tribunal in Bhind.
Madhya Pradesh chief minister, Shivraj Singh had ordered a Central Bureau of Investigation (CBI) investigation on March 27, 2018. However, the CBI said that since the SIT had investigated the case and maintained that it was an accident, there was nothing more to investigate.
Purohit, Sharma's colleague and eye-witness to his death, was following on his own bike just behind Sharma and saw the dumper truck deliberately swerve into him. He gave his statement to the police but they still maintain it was an accident. He expressed helplessness at the situation and said he had to leave Bhind and has sought work in a news channel in Bhopal.
The officer, Indra Veer Singh Bhadouria, remained in his post and no action was taken against him. However, three months after Sharma's death, he was transferred to Bhopal on a complaint of corruption, filed by a local congress politician.
Meanwhile, Sharma's aged parents, his wife and two children, rattled by the killing, shifted to Bhopal. In 2004, they had already lost their first son, a solider, in Jammu. Now, they survive on the produce of the agricultural land they have in Bhind.
Purohit felt that the administration should have taken more stringent steps to follow up on the complaint both of them had filed on Nov 3, 2017. "Both of us worked together. We have been following up on the sand mining for so many months and were filing many stories. This is a huge robbery. At least six police officers have died, aside from a number of citizens. But the local administration and the higher-ups in the police force do nothing. The [illegal] sand mining is continuing and destroying the Chambal river," he said.
Status of case: Hearings are currently on in the Motor Accidents Claims Tribunal regarding the 'accident' and compensation to be awarded to the survivors. The family did get a one-time compensation of Rs 500,000 from the state government but have not accepted it on principle.
Categories: Impunity Indicator
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Pingback: A Free Speech Impunity Indicator: Tracking justice, demanding accountability – FreeSpeechCollective
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