Probing the Pseudoscalar portal to Dark Matter via $\bar{b} b Z( \rightarrow \ell\ell) + E_{T} \hspace{-8mm}/\hspace{4mm}$: From the LHC to the Galactic Centre Excess

TL;DR

This paper introduces a novel LHC search strategy for Dark Matter involving a pseudoscalar portal, which can explore new parameter space and potentially explain the Galactic Centre gamma-ray excess.

Contribution

It proposes a new collider search channel for Dark Matter via a pseudoscalar portal, extending the reach beyond existing methods and linking collider results to astrophysical observations.

Findings

The proposed search can probe previously inaccessible parameter space.

It offers a method to test the Dark Matter origin of the Galactic Centre excess.

The search is effective with LHC Run 2 data.

Abstract

We propose a new search for Dark Matter at the LHC, characteristic of scenarios beyond the Standard Model with a pseudoscalar portal between the visible and dark sectors. This search, leading to a $\bar{b} b Z( \rightarrow \ell\ell) + E_{T} \hspace{-4mm}/\hspace{2mm}$ final state, reaches large regions of parameter space not probed by Dark Matter searches via multi-jet $+ E_{T} \hspace{-4mm}/\hspace{2mm}$, searches for new scalars and flavour bounds. We show that this search could be used to test the Dark Matter origin of the gamma ray Galactic Centre excess with LHC Run 2 data.

Figures

Equations

$$V_{\mathrm{dark}}=\frac{m_{a_0}^2}{2}{a}_0^2+m_{\chi }\bar{\chi }\chi +y_{\chi }{a}_0\bar{\chi }i{\gamma }^5\chi .$$

$$V_{\mathrm{portal}}=i\kappa a_0{H}_1^{†}{H}_2+h.c.$$

$$⟨\sigma \mathrm{v}⟩$$

$$\times \sum _f{N}_C\frac{m_f^2}{v^2}\sqrt{1-\frac{m_f^2}{m_a^2}}.$$

$$\mathrm{Br}\left(B_s\to {\mu }^{+}{\mu }^{-}\right)\simeq \mathrm{Br}{\left(B_s\to {\mu }^{+}{\mu }^{-}\right)}_{\mathrm{SM}}$$

$$\times \left({\left|1+x_B{\tan }^2\beta \frac{f(x_t,x_a,r)}{4Y(x_t)}\right|}^2+{\left|x_B{\tan }^2\beta \frac{g(r)}{4Y(x_t)}\right|}^2\right),$$

$$f\left(x_t,x_a,r\right)=g(r)$$

$$Y(x)$$

$$m_{T2}^2\equiv \underset{\overrightarrow{k_T}+\overrightarrow{q_T}=/\overrightarrow{p_T}}{\min }\left\{\max \left[m_T^2(\overrightarrow{p_T^{{\ell }^{+}}},\overrightarrow{k_T}),m_T^2(\overrightarrow{p_T^{{\ell }^{-}}},\overrightarrow{q_T})\right]\right\}$$

Full text

††preprint: KCL-PH-TH/2017-28

I. Introduction

The nature of dark matter (DM) is an unsolved mystery at the interface of particle physics and cosmology. One widely studied DM candidate is the Weakly-Interacting-Massive-Particle (WIMP), whose relic abundance is obtained via thermal freeze-out in the early Universe with a mass in the range $\mathrm{GeV}-\mathrm{TeV}$ (see Bertone:2004pz for a review).

There is an ongoing multi-pronged experimental effort to search for WIMP DM via its interactions with Standard Model particles: indirectly by measuring the energetic particles produced by DM annihilations in space and directly by measuring the scattering of ambient DM from nuclei. The observed gamma ray excess in the Fermi-LAT space telescope observations of the Milky Way Galactic Centre TheFermi-LAT:2015kwa may be interpreted as the existence of weak-scale DM annihilating into $\bar{b}b$ pairs Goodenough:2009gk ; Hooper:2010mq ; Hooper:2011ti ; Abazajian:2012pn (see Karwin:2016tsw for a recent exhaustive analysis of the excess and its DM interpretation). While arguably there is some tension between the DM interpretation of the gamma ray excess at the Galactic Centre and the non-observation of emission due to DM annihilation in dwarf spheroidal galaxies Ahnen:2016qkx 111However we are also aware that the errors on the astrophysical J-factors used in Ahnen:2016qkx are somewhat small and allowing more freedom in the fit and adding a systematic error representing the possibility of triaxiality in the halos could reduce this disagreement somewhat Bonnivard:2015xpq ., the self-annihilation cross section needed to explain the excess can be consistent with that required to generate the observed relic abundance through thermal freeze-out in the early Universe $\langle\sigma\mathrm{v}\rangle\simeq 3\times 10^{-26}{\rm cm}^{3}/{\rm s}$. At the same time, current limits on the spin-independent DM interaction cross section with nuclei by the Large-Underground-Xenon (LUX) Akerib:2016vxi and PandaX Tan:2016zwf experiments strongly constrain DM masses in the range $10-100$ GeV. A compelling DM interpretation of the gamma ray Galactic Centre excess (GCE) in combination with the non-observation of a signal in DM direct detection experiments is via the existence of a pseudoscalar mediator between the visible and DM sectors Boehm:2014hva ; Izaguirre:2014vva ; Ipek:2014gua , which yields spin-dependent DM-nucleon interactions, for which experimental limits are much less stringent. Pseudoscalar mediated DM-nucleon interactions generally lie well below the reach of present DM direct detection experiments.

Direct and indirect probes of DM are complemented by searches at colliders, where pairs of DM particles could be produced. These escape the detector and manifest themselves as events possessing an imbalance in momentum conservation, via the presence of missing transverse momentum $\not{E}_{T}$ recoiling against a visible final state $X$. Searches for events with large $\not{E}_{T}$ are currently a major focus at the Large Hadron Collider (LHC) largely due to their connection to DM Morrissey:2009tf . In this work we present a new search avenue for DM at the LHC, characteristic of renormalizable, gauge invariant scenarios beyond the Standard Model with a pseudoscalar portal between the visible and dark sectors. The search is characterized by a $b\bar{b}\,Z\,\,(Z\to\ell\ell)+\not{E}_{T}$ final state. We show that this new DM search channel of a leptonically decaying $Z$ boson, two bottom quarks and missing transverse momentum will yield a powerful probe of the region of parameter space consistent with a DM interpretation of the GCE through LHC Run 2 data.

II. The Pseudoscalar Portal Into Dark Matter

We focus our analysis on scenarios with a pseudoscalar mediator between DM and the SM fermions. These can yield a compelling explanation of the GCE through DM annihilation into $b$-quarks (see e.g. Izaguirre:2014vva ; Ipek:2014gua ). For concreteness we consider DM to be a Dirac fermion $\chi$ with mass $m_{\chi}$, singlet under the SM gauge interactions and coupling to a real singlet pseudoscalar mediator $a_{0}$ via

[TABLE]

However, for the pseudoscalar to be able to mediate interactions between DM and the SM fermions, $SU(2)_{\mathrm{L}}\times U(1)_{\mathrm{Y}}$ gauge invariance requires the existence of new states beyond the SM in addition to the DM particle and the pseudoscalar mediator Nomura:2008ru ; Goncalves:2016iyg . A renormalizable and gauge invariant realization of the pseudoscalar portal between DM and the SM leads to the extension of the SM Higgs sector with a second Higgs doublet, as first noted in Nomura:2008ru . A theory with the required ingredients then naturally resembles a two Higgs doublet model (2HDM) Nomura:2008ru ; Goncalves:2016iyg ; No:2015xqa ; Bauer:2017ota . We note that this also yields a compelling explanation for the preferential coupling of the pseudoscalar mediator to third generation SM fermions ($b$-quarks and $\tau$-leptons), in relation to the GCE.

In the following we provide a brief review of the 2HDM aspects of relevance to us (for a general review of 2HDM theory and phenomenology, see e.g. Branco:2011iw ): The two Higgs doublets are $H_{j}=\left(\phi_{j}^{+},(v_{j}+h_{j}+i\,\eta_{j})/\sqrt{2}\right)^{T}$, with ($j=1,2$). $v_{j}$ are the vev of the doublets ($\sqrt{v^{2}_{1}+v^{2}_{2}}=v$ and $v_{2}/v_{1}\equiv\mathrm{tan}\beta$). We consider a 2HDM scalar potential with Charge-Parity (CP) conservation and a softly broken $\mathbb{Z}_{2}$ symmetry. The presence of this $\mathbb{Z}_{2}$ symmetry in the couplings of the doublets $H_{j}$ to fermions allows to forbid dangerous tree-level flavour changing neutral currents, by forcing each fermion type to couple to one doublet only Glashow:1976nt . In Type I 2HDM all fermions couple to $H_{2}$, while for Type II 2HDM up-type quarks couple to $H_{2}$ and down-type quarks and leptons couple to $H_{1}$. The scalar spectrum of the 2HDM contains a charged scalar $H^{\pm}=\mathrm{cos}\beta\,\phi_{2}^{\pm}-\mathrm{sin}\beta\,\phi_{1}^{\pm}$, a neutral CP-odd scalar $A_{0}=\mathrm{cos}\beta\,\eta_{2}-\mathrm{sin}\beta\,\eta_{1}$ and two neutral CP-even scalars $h=\mathrm{cos}\alpha\,h_{2}-\mathrm{sin}\alpha\,h_{1}$, $H_{0}=-\mathrm{sin}\alpha\,h_{2}-\mathrm{cos}\alpha\,h_{1}$. We identify $h$ with the 125 GeV Higgs state, which has SM-like properties when the mixing angle $\alpha$ in the neutral CP-even sector satisfies $\beta-\alpha=\pi/2$.

As we show now, the 2HDM allows for pseudoscalar mediated interactions between the visible sector and the DM candidate $\chi$ in (1). The portal between the visible and dark sectors occurs via

[TABLE]

which causes the would-be 2HDM state $A_{0}$ to mix with $a_{0}$, yielding two pseudoscalar mass eigenstates $a,A$: $a=c_{\theta}\,a_{0}-s_{\theta}\,A_{0}$, $A=c_{\theta}\,A_{0}+s_{\theta}\,a_{0}$, with $c_{\theta}\equiv\mathrm{cos}\theta$ and $s_{\theta}\equiv\mathrm{sin}\theta$. This mixing allows both $a$ and $A$ to couple simultaneously to DM and the SM fermions, providing the portal between visible and DM sectors. The coupling of $a$ $(A)$ to DM is given by $s_{\theta}\,y_{\chi}$ ($c_{\theta}\,y_{\chi}$). Regarding the pseudoscalar couplings to SM fermions, these are given by $g_{\mathrm{SM}}\times y_{f}/\sqrt{2}$ (with $y_{f}$ the Yukawa coupling of the fermion). We consider here a Type II 2HDM, for which the $g_{\mathrm{SM}}$ coupling of $a$ $(A)$ is given by $s_{\theta}\,\mathrm{tan}^{-1}\beta$ ($c_{\theta}\,\mathrm{tan}^{-1}\beta$) for up-type quarks and $s_{\theta}\,\mathrm{tan}\beta$ ($c_{\theta}\,\mathrm{tan}\beta$) for down-type quarks and charged leptons. To simplify the following discussion, we also restrict ourselves to $\beta-\alpha=\pi/2$ (the so-called alignment limit) where $h$ behaves exactly as the SM Higgs Gunion:2002zf . We note that for a Type II 2HDM, deviations from the alignment limit are strongly constrained by LHC Higgs measurements Aad:2015pla .

For the rest of this work, we consider the benchmark value $m_{\chi}=45$ GeV: For a pseudoscalar mediator, Karwin:2016tsw finds a preferred range $m_{\chi}\in[50,\,170]$ GeV if DM annihilates into $b$-quark pairs, and $m_{\chi}\in[10,\,20]$ GeV if it annihilates into leptons, concerning the GCE. In the present case, DM annihilates dominantly into $b$-quarks, with a small ($\sim 10\,\%$) annihilation component into $\tau$-leptons. We also consider the mediator $A$ (doublet-like) to be much heavier than $a$ (singlet-like). For $m_{\chi}<m_{a}\ll m_{A}$, DM annihilates to SM particles through $s$-channel $a$ exchange. The velocity averaged annihilation cross section for $\chi\bar{\chi}\to{\rm SM}$ in the nonrelativistic limit is

[TABLE]

with $\Gamma_{a}$ the decay width of $a$. The sum is over quarks ($N_{C}=3$) and charged leptons ($N_{C}=1$). Reproducing the observed DM relic density requires $\langle\sigma\mathrm{v}\rangle\simeq 3\times 10^{-26}{\rm cm}^{3}/{\rm s}$, which favours large values of $\mathrm{tan}\beta$ (particularly for not too large values of $y_{\chi}$).

Flavour constraints from $\bar{B}\to X_{s}\gamma$ decays yield a lower bound on $m_{H^{\pm}}$ in Type II 2HDM, given by $m_{H^{\pm}}>480$ GeV at 95% C.L. Misiak:2015xwa . In addition, electroweak precision observables strongly constrain the splitting between the charged scalar $H^{\pm}$ and either of the neutral states $H_{0}$, $A$ Grimus:2007if . Combined, these yield $m_{A},\,m_{H_{0}},\,m_{H^{\pm}}\gtrsim 500$ GeV. On the other hand $m_{A},\,m_{H_{0}},\,m_{H^{\pm}}$ may not be taken arbitrarily high if $s_{\theta}$ and/or $m_{a}$ are kept fixed due to unitarity constraints. For $m_{a}\sim 100$ GeV and $\theta=\pi/4$ the unitarity bounds on $m_{A},\,m_{H_{0}}$ are respectively $m_{A}\leq 1.4$ TeV, $m_{H_{0}}\leq 1$ TeV Goncalves:2016iyg . In the following we take as benchmarks $m_{H^{\pm}}=m_{H_{0}}=600$ GeV, $800$ GeV (and assume a somewhat larger $m_{A}$).

III. Experimental Constraints on the Dark Portal

The above pseudoscalar dark portal scenario is constrained in a variety of ways. Besides the aforementioned flavour bound $m_{H^{\pm}}>480$ GeV from $\bar{B}\to X_{s}\gamma$ decays, the existence of a light pseudoscalar $a$ coupling to SM fermions can be probed by its contributions to the decay $B_{s}\to\mu^{+}\mu^{-}$ Skiba:1992mg ; Logan:2000iv , which for $m_{a}\gg m_{B_{s}}\simeq 5.36$ GeV may be expressed as222We note the important $H^{\pm}$ contribution in the limit $s_{\theta}\to 0$ (see Logan:2000iv ) which was missed in Ipek:2014gua .

[TABLE]

with $x_{B}=m_{b}m_{B_{s}}/m_{W}^{2}$, $x_{t}=m_{t}^{2}/m_{W}^{2}$, $x_{a}=m_{a}^{2}/m_{A}^{2}$, $r=m_{H^{\pm}}^{2}/m_{t}^{2}$, $r_{t}=x_{t}\,r$, $g(r)=\log(r)/(r-1)$,

[TABLE]

and $Y(x)$ the Inami-Lim function,

[TABLE]

The average of the LHCb and CMS measurements of this mode from LHC 7 and 8 TeV data is $\mathrm{Br}\left(B_{s}\to\mu^{+}\mu^{-}\right)=\left(2.9\pm 0.7\right)\times 10^{-9}$ Aaij:2013aka ; Chatrchyan:2013bka ; CMSandLHCbCollaborations:2013pla which may be compared against the SM prediction $\left(3.65\pm 0.23\right)\times 10^{-9}$ Bobeth:2013uxa ; Buras:2013uqa .

For $m_{a}<m_{h}/2$ the presence of the decay $h\to aa$ yields stringent constraints on the model Ipek:2014gua , and consequently we only consider here the case $m_{a}>m_{h}/2$ for which non-standard Higgs decays are suppressed (note that for $m_{\chi}=45$ GeV the 3-body decay $h\to a\bar{\chi}\chi$ is also kinematically forbidden above $m_{a}=35$ GeV).

LHC searches for the states $H_{0}$, $A$ and $a$ decaying to $\tau^{+}\tau^{-}$ also place important constraints at large $\mathrm{tan}\beta$ ($a\to\bar{b}b$ has also been considered, see e.g. Kozaczuk:2015bea ). Focusing on $\phi=H_{0},\,a$, the latest CMS search for $\bar{b}b\phi\,(\phi\to\tau^{+}\tau^{-})$ with an integrated luminosity of 12.9 fb*-1* CMS:2016rjp yields limits on the parameter space for $m_{a}$, $m_{H_{0}}$, $s_{\theta}$, $\mathrm{tan}\beta$.

Finally, the pseudoscalar portal to DM can be probed at the LHC in the $\bar{t}t+\not{E}_{T}$ and $\bar{b}b+\not{E}_{T}$ channels (see Banerjee:2017wxi for a recent discussion), and in multi-jet $+\not{E}_{T}$ Buchmueller:2015eea . Using the results from CMS:2016uxr we find that $\bar{b}b+\not{E}_{T}$ searches at $\mathrm{tan}\beta\gg 1$ yield significantly weaker constraints that the ones discussed above (e.g. $B_{s}\to\mu^{+}\mu^{-}$). At the same time, $\bar{t}t+\not{E}_{T}$ searches are currently only sensitive to $\mathrm{tan}\beta<1$. For multi-jet $+\not{E}_{T}$ searches, using the analysis from Buchmueller:2015eea we find that these yield an important constraint at low $\mathrm{tan}\beta$, but still being subdominant to those from the searches discussed in the next Section.

IV. A New LHC Probe of Dark Matter

Remarkably, when $m_{H_{0}}\gg m_{a}$ the decay $H_{0}\to Za$ yields a new avenue to probe DM at the LHC. For $\mathrm{tan}\beta\gg 1$ as favoured by the GCE, a novel DM search channel presents itself: $pp\to b\bar{b}\,H_{0},\,H_{0}\to Z\,a$ $(Z\to\ell^{+}\ell^{-},\,a\to\bar{\chi}\chi)$. This topology for the final state $\bar{b}b\,\ell^{+}\ell^{-}+\not{E}_{T}$ has not yet been explored at the LHC, and we show here that this signature allows to probe a wide range of parameter space for pseudoscalar portal scenarios, in particular within the region consistent with a DM interpretation of the GCE.

In order to study the prospects for this signature at the LHC with $\sqrt{s}=13$ TeV c.o.m. energy, we require events with two oppositely charged electrons/muons in the invariant mass window $m_{\ell\ell}\in\left[76,106\right]$ GeV, with $p^{\ell}_{T}>20$ GeV and rapidity $|\eta^{\ell}|<2.5$. Our event selection further requires $|p_{T}^{\ell\ell}-\not{E}_{T}|/p_{T}^{\ell\ell}<0.5$ and a separation $\Delta R_{\ell\ell}>0.4$ between the same-flavor lepton pair. We also demand at least one $b$-tagged jet with333We note that a very low value of the chosen $p^{b}_{T}$ cut (for a very high value of $m_{H_{0}}$) could result in a breakdown of the perturbative expansion Degrande:2016aje for the $\bar{b}b$-associated production of $H_{0}$ (we thank Richard Ruiz for pointing out this issue to us). Using SusHi Harlander:2012pb We have estimated our $b\bar{b}H_{0}$ next-to-leading-order (NLO) $k$-factor to be $\sim 1.4$, close to the perturbative expansion validity limit, but arguably safe Degrande:2016aje . $p^{b}_{T}>30$ GeV.

The main SM backgrounds are $t\bar{t}$ and di-boson ($WZ$ and $ZZ$) + jets production444The $WW$ diboson background is strongly suppressed by the $m_{\ell\ell}$ selection in combination with a large amount of $\not{E}_{T}$. Other potential backgrounds become negligible when demanding a significant amount of $\not{E}_{T}$ in the event.. The requirement of one or more $b$-tagged jets acts as an effective suppressor of the latter, while the invariant mass window $m_{\ell\ell}$ helps diminish the $t\bar{t}$ background. In order to further reduce SM backgrounds we take advantage of the boosted configuration of the signal for $m_{H_{0}}\gg m_{a}+m_{Z}$, and demand the leading lepton in $p^{\ell}_{T}$ to satisfy $p^{\ell_{1}}_{T}>80$ GeV as well as $p^{\ell_{1}}_{T}+p^{\ell_{2}}_{T}>150$ GeV. Finally we use $\not{E}_{T}$ and the variable $m_{T2}$ Lester:1999tx to define our signal region. We calculate $m_{T2}$ using Lester:2014yga as

[TABLE]

where minimisation is over all possible vectors $\vec{k_{T}}$ and $\vec{q_{T}}$ that satisfy $\vec{k_{T}}+\vec{q_{T}}=\not{\vec{p_{T}}}$ (with $\left|\not{\vec{p_{T}}}\right|=\not{E}_{T}$). Our signal region is defined as555The $m_{T2}$ cut is chosen conservatively to ensure the background prediction is not dominated by the Monte Carlo statistical uncertainty. An analysis performed by the experimental collaborations would achieve better sensitivity through a stronger cut on $m_{T2}$. $\not{E}_{T}>110$ GeV, $m_{T2}>110$ GeV.

We generate our signal and background event samples at LO in MadGraph5$\_$MC@NLO Alwall:2014hca and perform showering in Pythia 8 Sjostrand:2014zea . For the $ZZ$ and $WZ$ backgrounds we include up to two additional jets in the final state, matched to parton shower. We replace a full detector simulation with a Gaussian smearing of the $p_{T}$ of final state paricles: We define jets, well isolated charged leptons and photons, and $\not{E}_{T}$ as the relevant final state objects. Jets are constructed with the FastJet package Cacciari:2011ma using the anti-$k_{T}$ algorithm Cacciari:2008gp with $R=0.4$, and are required to have $p_{T}>25$ GeV and $|\eta|<2.5$. We smear the $p_{T}$ of the visible particles and calculate both the truth $\not{E}_{T}$ and the reconstructed value calculated from the smeared visible objects. We then smear the difference between the truth and reconstructed $\not{E}_{T}$. The functions for the smearing of the visible objects and $\not{E}_{T}$, as well as the b-tagging efficiency and mistag rates, are chosen to match the ATLAS performance reported in Aad:2009wy for the leptons and $\not{E}_{T}$, Aad:2012ag for the jets and b-tag for the b-tagging. We derive the projected sensitivity of our search using the CLs method Read:2002hq , and assuming a conservative $20\%$ background systematic uncertainty added in quadrature to a $1/\sqrt{N}$ Monte Carlo uncertainty ($N$ the number of generated background Monte Carlo events in the signal region).

For a benchmark signal $m_{H_{0}}=600$ GeV, $m_{a}=150$ GeV, $\mathrm{tan}\beta=15$, $s_{\theta}=0.3$ the background and signal samples surviving event selection are shown in Figure 1 in the ($\not{E}_{T}$, $m_{T2}$) plane, highlighting the choice of signal region $\not{E}_{T},\,m_{T2}>110$ GeV as tailored for a clean signal extraction. In Figure 2 we show the 95% C.L. sensitivity of our proposed search (hatched region) with $300$ fb*-1* of integrated luminosity in the ($s_{\theta},\,\mathrm{tan}\beta$) plane for ($m_{H_{0}},\,m_{a}$) = ($600,\,150$) GeV (left) and ($800,\,150$) GeV (right), demanding $\langle\sigma\mathrm{v}\rangle\simeq 3\times 10^{-26}{\rm cm}^{3}/{\rm s}$ to fix $y_{\chi}$ in terms of $\mathrm{tan}\beta$ and $s_{\theta}$ in each case. We demand perturbativity $y_{\chi}<4\pi$, and show the lines $y_{\chi}=1$ (dotted grey) and $y_{\chi}=0.1$ (dot-dashed grey) for guidance.

The decay $H_{0}\to Za$ ($a\to\bar{\chi}\chi$) may be probed also by ATLAS/CMS mono-$Z$ searches in the $\ell^{+}\ell^{-}+\not{E}_{T}$ channel ATLAS-CONF-2016-056 ; CMS-PAS-EXO-16-038 , both for gluon-fusion (GF) production of $H_{0}$ and for $b\bar{b}$-associated production (if both $b$-jets are missed, since ATLAS-CONF-2016-056 ; CMS-PAS-EXO-16-038 impose jet/$b$-jet vetoes). We follow the LHC 13 TeV analysis selection of ATLAS ATLAS-CONF-2016-056 with $13.3\,\mathrm{fb}^{-1}$ to derive present 95% C.L. constraints on our signal in the ($s_{\theta}$, $\mathrm{tan}\beta$) plane, shown in Figure 2 for GF (yellow region) for $m_{H_{0}}=600$ GeV, $m_{a}=150$ GeV (Left) and $m_{H_{0}}=800$ GeV, $m_{a}=150$ GeV (Right). We also show the LHC projections to $300$ fb*-1* (dashed lines) using a naive $\sqrt{\mathcal{L}}$ increase in the signal cross section sensitivity (we note that even in this case, the ATLAS mono-$Z$ search from $b\bar{b}$-associated production is not sensitive enough to provide a constraint). In both cases, the coupling $y_{\chi}$ is fixed at each point to match the DM relic density. In addition, Figure 2 shows the present and projected to $300$ fb*-1* (when possible) constraints on the dark portal discussed in the previous section: the exclusion from CMS/LHCb 8 TeV $B_{s}\to\mu^{+}\mu^{-}$ measurements (red), the multi-jet $+\not{E}_{T}$ (black), and the $\bar{b}b$-associated production of $H_{0}\to\tau\tau$ (blue) and $a\to\tau\tau$ (brown). For the latter two, we use SusHi to obtain the NNLO $H_{0},\,a$ production cross section in association with $\bar{b}b$ at $13$ TeV LHC666We note that by performing the analysis of mono-$Z$ and our $\bar{b}bZ(\rightarrow\ell\ell)+\not{E}_{T}$ signature at LO, as compared to $H_{0},\,a\to\tau\tau$ at NNLO, we are being conservative by underestimating the constraining power of the former two signatures.. We note that $\bar{t}t+\not{E}_{T}$ and $\bar{b}b+\not{E}_{T}$ are not sensitive enough to provide a constraint in Figure 2.

As Figure 2 highlights, the ATLAS mono-$Z$ search will be able to probe the $\mathrm{tan}\beta\lesssim 5$ region (for GF production), while $B_{s}\to\mu^{+}\mu^{-}$ and the projected $H_{0}\to\tau\tau$ combined could strongly constrain the very high $\mathrm{tan}\beta$ region ($\mathrm{tan}\beta>10$ for $m_{H_{0}}=600$ GeV, $\mathrm{tan}\beta>20$ for $m_{H_{0}}=800$ GeV); meanwhile, the proposed search $pp\rightarrow\bar{b}b\,\ell^{+}\ell^{-}+\not{E_{T}}$ would yield access to the intermediate $\mathrm{tan}\beta$ region, probing also values of the mixing down to $s_{\theta}\sim 0.1$.

We note that in the above analysis, we have fixed $\Gamma_{H_{0}\to aa}=0$ (as can be done by an appropriate choice of the soft $\mathbb{Z}_{2}$ symmetry breaking term in the 2HDM scalar potential, see e.g. Bauer:2017ota ). A non-vanishing $\Gamma_{H_{0}\to aa}$ would weaken the constraints from mono-$Z$, our new signature $pp\rightarrow\bar{b}b\,\ell^{+}\ell^{-}+\not{E_{T}}$ and from $H_{0}\to\tau\tau$, but would at the same time yield new avenues to probe the pseudoscalar portal. We do not consider this scenario here for simplicity.

Finally, in Figure 3 we show the various constraints and projected sensitivities discussed above in the ($m_{a},\,s_{\theta}$) plane for a benchmark $m_{H^{\pm}}=m_{H_{0}}=600$ GeV, $\mathrm{tan}\beta=10$ and $y_{\chi}=1$, together with the $\langle\sigma\mathrm{v}\rangle=(2-4)\times 10^{-26}{\rm cm}^{3}/{\rm s}$ region where the observed DM relic density is obtained (green). This highlights the sensitivity of the proposed search to the parameter space region with the correct DM relic density (and favoured by the GCE excess) as compared to other experimental probes of the pseudoscalar portal to DM.

V. Conclusions

DM that interacts with the visible sector via a pseudoscalar mediator is an appealing scenario, naturally avoiding the limits from DM direct detection searches while generating a rich LHC phenomenology and yielding a possible explanation for the FERMI gamma ray Galactic Centre Excess. Generating a pseudoscalar coupling to SM fields in a consistent way implies the existence of additional BSM particles, as in theories with two Higgs doublets where the necessary coupling is naturally generated when the pseudoscalar mediator and that of the two-Higgs-doublet scenario mix. We have shown that such scenarios give rise to a new LHC DM search channel $\bar{b}bH_{0},H_{0}\rightarrow Za(Z\rightarrow\ell^{+}\ell^{-},a\rightarrow\bar{\chi}\chi)$. The final state with a leptonically decaying $Z$ boson, $b$-tagged jet(s) and large $\not{E_{t}}$ has not been explored yet at the LHC in the DM context.

We find that a large region of parameter space which gives the observed DM relic abundance (yielding at the same time an explanation for the Galactic Centre Excess) can be explored using the proposed search, showing in particular that it can reach a wide region of parameter space that cannot be probed by other means, notably $B_{s}\rightarrow\mu^{+}\mu^{-}$ decays, heavy Higgs ($H_{0}$) decays into tau-lepton pairs, and mono-$Z$ searches. This novel search can thus be very valuable in probing pseudoscalar portal DM scenarios at the LHC.

Acknowledgements

Acknowledgements.

J.M.N. thanks Seyda Ipek for a very insightful talk that inspired this project, as well as David Cerdeno and Richard Ruiz for useful discussions. P.T. and M.F. thank Bobby Acharya for helpful discussions. M.F., J.M.N. and P.T. are supported by the European Research Council under the European Union’s Horizon 2020 program (ERC Grant Agreement no.648680 DARKHORIZONS). The work of MF was supported partly by the STFC Grant ST/L000326/1.