Signatures of top flavour-changing dark matter

Journal of High Energy Physics, Mar 2016

We develop the phenomenology of scenarios in which a dark matter candidate interacts with a top quark through flavour-changing couplings, employing a simplified dark matter model with an s-channel vector-like mediator. We study in detail the top-charm flavour-changing interaction, by investigating the single top plus large missing energy signature at the LHC as well as constraints from the relic density and direct and indirect dark matter detection experiments. We present strategies to distinguish between the top-charm and top-up flavour-changing models by taking advantage of the lepton charge asymmetry as well as by using charm-tagging techniques on an extra jet. We also show the complementarity between the LHC and canonical dark matter experiments in exploring the viable parameter space of the models.

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Signatures of top flavour-changing dark matter

HJE Signatures of top avour-changing dark matter Jorgen D'Hondt 0 1 2 4 Alberto Mariotti 0 1 2 4 Kentarou Mawatari 0 1 2 3 4 Seth Moortgat 0 1 2 4 Pantelis Tziveloglou 0 1 2 4 Gerrit Van Onsem 0 1 2 4 International Solvay Institutes 0 1 2 0 Notkestr. 85, D-22607 Hamburg , Germany 1 53 Avenue des Martyrs , F-38026 Grenoble , France 2 Pleinlaan 2 , B-1050 Brussels , Belgium 3 Laboratoire de Physique Subatomique et de Cosmologie, Universite Grenoble-Alpes , CNRS/IN2P3 4 Theoretische Natuurkunde and IIHE/ELEM, Vrije Universiteit Brussel We develop the phenomenology of scenarios in which a dark matter candidate interacts with a top quark through avour-changing couplings, employing a simpli ed dark matter model with an s-channel vector-like mediator. We study in detail the top-charm avour-changing interaction, by investigating the single top plus large missing energy signature at the LHC as well as constraints from the relic density and direct and indirect dark matter detection experiments. We present strategies to distinguish between the top-charm Beyond Standard Model; Cosmology of Theories beyond the SM - and top-up avour-changing models by taking advantage of the lepton charge asymmetry as well as by using charm-tagging techniques on an extra jet. We also show the complementarity between the LHC and canonical dark matter experiments in exploring the viable parameter space of the models. 2.1 2.2 2.3 3.2 3.3 1 Introduction 2 Models 3 Complementarity between the LHC and non-collider experiments Conclusions and discussions 1 Introduction The description of dark matter (DM), whose abundant presence in the universe is supported by overwhelming observational evidence, is nowadays one of the main motivations for physics beyond the Standard Model (SM). The usual paradigm to realize the correct relic abundance of DM in the universe relies on a weak coupling between the SM particles and the DM candidate, the so-called weakly interacting massive particle (WIMP). This scenario implies that signatures of DM could be discovered in colliders and canonical DM experiments, such as direct and indirect detection experiments. Indeed, in the last years there has been intense activities in developing DM searches at the LHC and their possible interplay with underground and satellite DM experiments. Since the properties and the interaction of DM with SM particles are unknown, a current bottom-up approach is to employ simpli ed models of DM that capture the phenomenology of di erent types of theories beyond the SM. Simpli ed models typically consist of new DM species and mediator elds that connect the SM and the DM sectors. They are usually parametrised by the masses of the mediator and DM elds as well as the couplings of the mediator to the DM and the SM particles (see e.g. [1]). One interesting possibility among various types of simpli ed models is that the DM couplings can arise in Z0 models [2{4] and in the avoured DM paradigm [5{14], where the DM candidate belongs to a sector which is also responsible to explain the avour structure in the SM. Among the non-universal avour interactions, the couplings that involve third generation quarks are less constrained by low-energy experiments. Moreover, the top quark, being the heaviest of the SM particles, can be an interesting candidate to represent the portal through which DM couples to the SM sector. The LHC signatures and the DM constraints on such models are in general di erent from those of the usual WIMP models. Flavour non-universal yet diagonal DM models characterised by the four-fermion interaction between a DM pair and a top-quark pair have been studied in an e ective eld theory (EFT) approach [15{17] and searched for in a top-quark pair plus missing energy nal state at the LHC Run-I [18, 19]. Recently more studies in simpli ed models involving top quarks have been done [20{23]. It is interesting to extend these studies to a possibility of having a avour-changing coupling involving the top quarks. Inclusion of the top avour-changing interaction with DM opens a peculiar collider signature, the so-called monotop signature [3, 9, 24], already searched for by the ATLAS and CMS Collaborations [25, 26]. We note that in the past the top-up avour-changing coupling has been extensively studied [3, 4, 9, 24, 27{32], while the top-charm coupling has received less attention. Moreover, top avour-changing DM models are interesting also because they can account [33] for the excess of gamma rays originating in the centre of our galaxy [34{36], without any con ict with constraints from avour physics. We note that there has been recently some debate about the DM origin of this excess and several alternative explanations have been put forward (see e.g. [37{40] and references therein). Nevertheless it is interesting, during the analysis of our simpli ed model, to discuss the tantalizing possibility that this is indeed due to a DM signal. In this work, we study in detail the phenomenology of a simpli ed DM model with topcharm avour-changing interactions, highlighting the di erence from the top-up avourchanging case. We present the prospects for the LHC Run-II, concentrating on the leptonic single-top nal state. We also investigate the charge asymmetry of the lepton in the nal state and charm-tagging techniques to distinguish between the top-charm and top-up interaction models. Apart from the LHC DM searches, we discuss in detail the relic density, and indirect and direct detection constraints on the model. The interplay for DM searches between the LHC and non-collider experiments will reveal di erent features between the top-charm avour-changing interaction and the top-up one, furnishing another interesting manifestation of complementarity among di erent DM search experiments. The paper is organized as follows. In section 2 we introduce the simpli ed DM model involving the top avour-changing interaction, and classify the signatures depending on the model parameters. We also discuss the relation with the EFT approach. In section 3 we discuss signatures of our model at the LHC as well as in the relic density, direct and indirect detection experiments. Section 4 is devoted to our summary and discussion. { 2 { We start this section by describing simpli ed models for top avour-changing DM and discussing the possible signatures. Then, we give some remarks about the similarities and di erences of the signatures between the top-up and top-charm avour-changing models. Lastly, we introduce the corresponding EFT description to brie y mention the relation with the simpli ed model and its validity. 2.1 Simpli ed models Since the dynamics of DM are not known, simpli ed models have been proposed that extended by two new species, a DM particle and a particle that mediates the interaction between the DM and SM particles, called the \mediator". In this work we are interested in the phenomenological implications of the interactions of a fermionic Dirac DM ( ) with the quark sector through an s-channel vector-like mediator (Z0).1 The interaction Lagrangian is given by Lint = g Z0 + (giQj QiL QjL Z0 + giuj uiR ujR Z0 + gidj diR djR Z0 + h:c:) : (2.1) As mentioned in section 1, we are interested in avour-changing DM interactions in the up-quark sector, speci cally involving the top quark. If the interactions involve the SU(2)L doublets, large avour o -diagonal couplings in the left-handed sector would imply large avour violation also for the down sector, which are strongly constrained by avour physics, e.g. by Bd{Bd mixing [42]. Instead, avour-changing operators involving right-handed top quarks and up or charm quarks are phenomenologically viable. Therefore, we focus on studying the e ective avour-changing interaction with right-handed up-type quarks in the Lagrangian (2.1), i.e. Lint = g Z0 + (g13 uR tR Z0 + g23 cR tR Z0 + h:c:) : (2.2) Hereafter we omit the superscript `u' of the coupling parameters giuj . Note that if both the up and charm avour-changing operators are present we expect a relevant box diagram contribution to the D0{D0 mixing [43]. Hence in the following we consider one of these operators at a time. With the above simpli cation, the model has in total four parameters, i.e. two couplings and two masses: fg ; gi3; m ; mZ0 g with i = 1 or 2 : (2.3) space, which will be discussed below. We note here that, since we intend to focus on the experimental signatures of the top avour-changing DM model, we postpone to future investigation a detailed study of the possible UV completions. At the end of the paper we discuss the basic guidelines and the most relevant issues in constructing such complete theories, identifying possible parallel implications for low-energy phenomenology. 1An s-channel pseudo-scalar mediator case was studied recently in [41]. { 3 { monotop yes suppressed suppressed yes yes suppressed suppressed suppressed suppressed HJEP03(216) early universe determines its thermal relic density while late time annihilation in the centre of galaxies o ers a possibility to detect DM indirectly, via observation of its SM products. The annihilation channel is + ! Z0( ) ! t + q and t + q ; where q denotes an up quark or a charm quark. The annihilation is kinematically e cient for 2m > mt and is enhanced by threshold e ects for mZ0 2m . If mt > 2m , the annihilation is suppressed since it occurs via the o -shell top quark (and/or W boson). Therefore, DM would be overly produced in the early universe, inconsistent with the current observation of the relic abundance of DM. The relic density and the phenomenology of indirect detection experiments are detailed in section 3.2. DM-nucleus scattering. Another process that is potentially relevant for the phenomenology of our DM models is the elastic scattering + N ! + N ; of DM particles o nuclei of direct detection experiments. Detection of DM in this type of experiments is based on the observation of the nuclear recoil energy that the scattering releases. Di erent from usual avour-conserving DM models, the above interaction in our model occurs only through loop diagrams, and hence it is expected to be strongly suppressed. In section 3.2 we discuss further the direct detection phenomenology and calculate the one-loop process in our model. Top decay. If mt > 2m , top quarks can decay into a light quark (up or charm) plus a pair of DM through the on-shell or o -shell mediator: t ! q + Z0( ) ! q + + Z Γ ) 10-5 of DM as a function of the mediator mass. We assume a massless DM and take di erent values of the coupling parameters. The vertical grey line indicates mZ0 = mt. massless DM. For mZ0 < mt, where the top quark decays into the mediator on mass-shell, the width becomes too broad to be consistent with the current bound 1 . t . 4 GeV from Tevatron [44, 45]. We note that in this parameter region the width depends only on the coupling gi3 and the mediator mass. For mZ0 > mt, on the other hand, the anomalous decay arises through the o -shell mediator and hence is strongly suppressed as the mediator mass increases, unless the couplings are very large. In gure 2(left), we show the DM mass dependence with the coupling xed at (g ; gi3) = (3; 0:6). The anomalous decay becomes smaller when the DM becomes heavier due to the phase space suppression. As a reference, we mention the current limit on the top-quark avour-changing neutral current (FCNC) decay, although the analyses have not considered missing energy. The current most stringent limit is for the t ! Zq mode as B(t ! Zq) < 5 10 4 from the LHC Run-I data [46]. Mediator decay. The decay of the mediator depends strongly on the mass spectra and the values of the couplings. There are two decay modes, with partial widths given by (Z0 ! ) = (Z0 ! tq=tq) = gi23mZ0 g2 mZ0 s 12 4 1 1 4m2 m2Z0 mt2 m2Z0 1 + 2 1 m2 ! m2Z0 mt2 2m2Z0 ; mt4 2m4Z0 : (2.7) (2.8) and the branching ratio of the mediator decay into a pair of DM (bottom) as a function 10-5 of the mediator mass. For the massless DM ( gure 1), if mZ0 < mt, the mediator can only decay into a pair of DM. For mZ0 mt, on the other hand, the mediator dominantly decays into a top quark and a light quark if the two couplings are of similar size g gi3 due to the colour factor. For a large gi3 coupling the width becomes too large. Figure 2(right) shows that the branching ratio does not depend on the DM mass for mZ0 2m . We note that, even if Z0 is in the bottom of the mass spectrum, it decays via the o -shell top quark (and/or W boson), but its decay is strongly suppressed. Moreover, the loop-induced dijet decay channel can be relevant [4]. In this work, we are interested in the DM signature at the LHC, and hence we take g = 5 gi3 so that the branching ratio B(Z0 ! illustrative benchmark point, we take ) becomes more than 0.9. As our g = 3:0 and gi3 = 0:6 ; which can provide reasonable signal rate at the LHC as we will show below, still keeping the mediator width as Z0 =mZ0 . 1=4. Collider signatures. A distinctive collider signature in our model is a single top-quark production in association with large missing energy, the so-called monotop signature: p + p ! t + Z0( ) ! t + + ; where t denotes a top quark or a top anti-quark. The Feynman diagrams are shown in (2.9) (2.10) gure 3(top). point (2.9) at p Figure 4 shows the total cross sections of pp ! t (solid lines) for our benchmark s = 8 and 13 TeV as a function of the mediator mass, where we x the DM { 6 { g (gg) g q t Z0 g g g g q (qg) q (qg) q (qq) q q t q Z0 g g collisions at p Total cross sections for DM pair production in association with a top quark in pp s = 8 TeV (left) and 13 TeV (right) as a function of the mediator mass, where we assume the top-up (black) and top-charm (red) avour-changing DM model and x the DM mass at 30 GeV. For the processes with a (c-)jet, the kinematical cuts pjT > 25 GeV and j jj < 2:5 are imposed. t t Z0 Z0 t q Z0 g q g q q q 102 t q Z0 g g t t Z0 Z0 Z0 t q t q Z0 g g t q Z0 mass at 30 GeV and consider only mZ0 > mt to avoid the large top width. The cross section in the top-up model is larger than that in the top-charm one roughly by a factor of 10, (PDFs). The cross sections for both models increase by 3{5 times from p simply explained by the di erence between the up and charm parton distribution functions s = 8 TeV to 13 TeV. We note that the cross sections do not depend on the DM mass as long as the mediator is produced on-shell and the Z0 ! branching ratio is xed. In gure 4, we also show the cross sections for the monotop process in association with a jet by dashed lines, where we impose the transverse momentum p p pseudorapidity j j j < 2:5 as minimal cuts. As extra QCD jets often emerge at the energy scale of the LHC, we should take them into account for a reliable prediction, and indeed the cross sections are comparable with the ones without an additional jet, especially for the s = 13 TeV case. As shown in gure 3, in addition to the leading-order (LO) qg ! tZ0 process with a gluon emission, the gg and qq initial states contribute and enhance the production rate. We note that the steeper fall of the tj=c cross sections in the topjT > 25 GeV and the charm model for around mZ0 anomalous top decay, i.e. (tt) 200 GeV comes from the top-pair contribution with the B(t ! q ); see also gure 1(bottom-left). The extra jet contribution can not only enhance the signal but also give some hint to distinguish between the top-up and top-charm models. Although the charm-quark tagging is more di cult than the bottom-quark tagging, the technique is under development both in the ATLAS and CMS collaborations and promising for the LHC Run-II. Assuming an ideal 100 % c-tagging e ciency, the dotted lines in gure 4 present the cross sections for a single top plus a charm jet in association with missing transverse energy. The production cross section in the top-up model is not zero, but strongly suppressed, since this comes from the uc initial state only. For the top-charm model, on the other hand, the gg scattering can provide the charm nal state, and hence the production rate does not decrease so much even after identifying the jet as a charm jet. In this work, therefore, we take into account extra jets for the monotop signal by employing a matrix-element parton-shower (ME+PS) merging scheme [47] and investigate if we can get additional information on the models. It should be noted that if g . gi3, i.e. if the DM interaction with Z0 is subdominant, the dark sector is essentially decoupled and the model becomes a type of non-universal Z0 model, such as those intensively discussed in the context of the top forward-backward asymmetry reported by Tevatron [48, 49]. The t-channel Z0 produces top quarks in the forward region for qq ! tt [2]. Another distinctive signature in this scenario is same-sign tt pair production via qq or qq scattering with a t-channel Z0 [50, 51], searched for already in the LHC Run-I data [52, 53]. The diagrams in gure 3 also produce the same-sign top pair with jets if the Z0 dominantly decays into a top and a light quark. Note that if the new vector boson is not self-conjugate the model does not lead to the same-sign top signal [54]. 2.2 Top-up vs. top-charm interactions As mentioned in section 1, we focus primarily on the less explored top-charm DM model. Here, we list certain remarks related to the similarities and di erences of the top-up and avour-changing DM models, that will be discussed along the paper: indirect detection limits) is practically the same in the top-up and top-charm DM models. DM direct detection physics is a priori di erent in the two models, since the top-up DM model involves the interaction with a valence quark in nucleons. However we will demonstrate that both the top-up and top-charm models are beyond the reach of current and near future direct detection experiments. The contribution to the top width and the mediator width is once again practically HJEP03(216) the same in the top-up and top-charm DM models. At the LHC, the main di erence between the top-up and top-charm DM models lies in the monotop production cross section (if we assume g13 g23); see gure 4. In the monotop signature, as we will explore in section 3.1, the top-up and top-charm DM models can be distinguished by lepton charge asymmetry and by a charm-tagging technique on an extra jet. In conclusion, distinguishing between the top-up and top-charm models is very di cult in non-collider experiments, and may be challenging at the LHC. However, in this work we demonstrate that a combined approach can allow us in certain cases to select one of the two models as soon as a hint of new physics is discovered or enough luminosity at the LHC is collected. 2.3 E ective eld theory description Before turning to the detailed study of the phenomenology of the DM model, we introduce the corresponding EFT description to brie y mention the relation to the simpli ed model and its validity. The EFT Lagrangian corresponding to the simpli ed model in (2.2) is given by the following four-fermion contact interaction operators Lint EFT = 1 2 (c13 uR tR + c23 cR tR + h:c:) ; (2.11) where is the cuto scale. The EFT Lagrangian provides a valid description of the simpli ed model in the limit where the mediator is much heavier than the energy scale probed by the experiment. Therefore, for low-energy processes such as the DM annihilation in the late universe (relevant for indirect DM searches) and the elastic scattering of DM o nuclei (relevant for direct DM searches), the EFT Lagrangian provides an accurate description of the dynamics. However, if the energy reach is comparable or higher than the mediator mass such as at the LHC, the EFT approach does not o er a suitable framework for describing the DM interactions [55{60]. In order to give an idea of the region of the EFT parameter space that the LHC explores, let us rst show the branching ratio of t ! q (q = u or c) in the EFT description { 9 { 10-2 10-3 )χ10-4 [sp100 n o χχ+t χχ+t+j production in association with a top quark in pp collisions at p Left: branching ratio of the anomalous top decay as a function of the DM mass for di erent coupling parameters in the EFT description. Right: total cross sections for DM pair s = 8 TeV as a function of the DM mass, where we assume the top-up (black) and top-charm (red) avour-changing DM model in the EFT description. For the processes with a (c-)jet, the kinematical cuts pjT > 25 GeV and j jj < 2:5 are imposed. in gure 5(left), corresponding to the left-bottom panel in gures 1 and 2 for the simpli ed model. The partial width depends only on (ci3= 2)2 and m . For m mt=2 the decay channel is kinematically closed. For ci3= 2 = 10 5 the anomalous decay branching ratio can be of the order of 10 3 10 5. The cross sections are insensitive to the DM mass, except for the light DM case in the top-charm model, where the top-pair production contributes signi cantly. As we will discuss, the monotop searches at the LHC Run-I set an upper limit cross section of about O(1) pb [25, 26]. Hence the EFT parameter c23= 2 O(10 5) is the range that the LHC can explore in this model. By the tree-level matching relation between the EFT coe cient ci3 and the Z0 model parameters we can translate the value of the EFT parameter to the simpli ed model obtaining ci23 = g gi3 ; m2Z0 mZ0 > < 8>300 GeV 1 TeV >>:10 TeV with g g23 with g g23 with g g23 O(1) ; O(10) ; O(103) : (2.12) (2.13) For reasonable values of the couplings, the on-shell production of the mediator is within the LHC reach, which implies that the EFT is not valid. For the heavy Z0 case, on the other hand, the couplings extend beyond the perturbative regime. In the rest of the paper, we only consider the simpli ed model for the LHC phenomenology, while we mention the EFT approach in the relic density computation and in indirect DM experiments. 3 In this section we study the signatures of the top avour-changing DM model in detail. First, we discuss the monotop signal for the LHC Run-II. Then, we consider the limits from the non-collider DM experiments. Lastly, we combine the constraints from the collider and non-collider experiments to determine the viable parameter space of the model. In the following analyses we follow the strategy described in ref. [61] for new physics simulations. We have implemented the e ective Lagrangian (2.2) (as well as the EFT Lagrangian (2.11)) in FeynRules2 [62] to create the model les interfaced [63, 64] with MadGraph5 aMC@NLO [65] for the collider study as well as with MicroOMEGAs [66, 67] and MadDM [68, 69] for the non-collider study. 3.1 Monotop at the LHC As mentioned in section 1, the top-up avour-changing DM interaction has been studied in the monotop signature [3, 4, 9, 27{30] and searched for with the CMS detector for the hadronic top decays [26] and with the ATLAS detector for the leptonic top decays [25]. Let us rst estimate the constraints on the top-charm avour-changing DM interaction from the ATLAS-8TeV analysis [25]. The exotic vmet boson in the \non-resonant" model in [25] corresponds to the mediator Z0 in our model. They assume that only the top-up coupling is non-zero and the vmet boson decays into invisible particles with 100 % branching ratio. They put a bound of about 0.2 pb on the cross section times the leptonic top-decay branching ratio, (pp ! tvmet) B(t ! b` ), which is approximately independent on the vmet mass for mvmet > 400 GeV. This translates in an upper bound on the pp ! tvmet production cross section of about 1 pb. Although we take into account the visible Z0 decay, we choose the coupling in eq. (2.9) so that the invisible decay is dominant, and hence we directly apply the upper limit cross section of 1 pb for the pp ! t cross section in our model. Figure 4(left) indicates that the top-up DM model is bounded to have mZ0 & 800 GeV while the top-charm model is mZ0 & 400 GeV for our benchmark couplings. We note that the cross sections can be rescaled by varying the coupling gi3 and do not depend on the DM mass as long as the mediator is produced on-shell. In the following, we will perform a detailed analysis of the LHC Run-II reach on the monotop signature for the top-charm avour-changing DM model. For the detailed illustration, we take two benchmark points which are characterized by the light or heavy mediator case: A) mZ0 = 400 GeV ; B) mZ0 = 800 GeV ; (3.1) with m = 30 GeV and (g ; g23) = (3; 0:6), and present the kinematical distributions to discuss the selection cuts. We then summarise the signal signi cance on the (m ; mZ0 ) plane for a given value of the couplings. HJEP03(216) At the end of this subsection we propose two strategies to distinguish the top-charm model from the top-up one on the LHC based analyses. The rst one exploits the charge asymmetry of the lepton in the nal state. The second one makes use of a charm-tagging technique to distinguish charm-quark jets from light-quark (u; d; s) or gluon jets. In this section we study in detail the prospects for discovery of the top-charm changing DM model in proton-proton collisions at a centre-of-mass energy of 13 TeV. Signal. We consider the monotop process (2.10) and also take into account extra jets in nal state. In this paper we focus on the leptonic top decay, t ! b + W (! ` + `), where ` is an electron or a muon. Therefore, the signal is characterised by an isolated lepton, a b-tagged jet and extra jets in association with large missing energy. SM background. The following SM backgrounds may mimic the new physics signature: Top pair: The semileptonic decays give rise to the similar nal state to the signal, and this is the main background after the selection cuts as shown below. The larger jet multiplicity is expected due to the hadronic decay of one of the top quark. Single top: Single top production is the only irreducible background. Unless it is produced in association with a W boson we expect the missing energy to be aligned with the lepton since it originates from the same decaying W boson, and hence suitable kinematic cuts can reduce this background e ciently. W +jets: The production of a W boson (with a leptonic decay) in association with jets should also be considered since the total cross section is many orders of magnitude larger than the signal. The presence of only one lepton in the nal state for the signal removes all processes with Z bosons from the list of relevant backgrounds. Furthermore the presence of large missing transverse energy, the jet multiplicity, and speci c angular distributions of the nal-state particles can be exploited to distinguish the signal from the background. These speci c features are the motivation behind the cuts that will now be discussed. We generate the inclusive signal and SM background samples by employing the ME+PS merging scheme with Pythia6 [70], implemented in MadGraph5 aMC@NLO [71]. The fast detector simulation is performed by the Delphes3 package [72] with the CMS-based detector setup. We employ MadAnalysis5 [73, 74] for the analyses. The tt and single-t cross sections are normalised to 831 pb and 299 pb, respectively [75], while the W +jets sample is normalised to NLO(W j) of about 3 The nal state contains leptons (muons or electrons) and jets as visible objects. Leptons are required to be isolated.2 Jets are reconstructed by employing the antikT algorithm [76] with a radius parameter of 0.5. Leptons and jets are required to have pT > 30 GeV and j j < 2:4. 2All the energy surrounding the lepton in the cone ( R = 0:4) divided by the lepton pT is below 0.2. after having required N` = 1. signal: We pre-select the events by demanding exactly one isolated lepton, N` = 1. In gure 6 we show distributions for the number of jets and some kinematical variables,3 which the ATLAS analysis uses, both for the SM background and the signal (benchmarks A and B) The following set of cuts are employed in order to maximise the signi cance of the N` = 1 ; mT (`; E/ T ) > mTmin ; 1 Nj 2 ; E/ T > E/ Tmin ; Nb = 1 ; j (`; b)j < max : 1 Nj 2: The \pure" monotop signal contains exactly one jet which should be b-tagged, coming from the top decay, and the most of the previous works including the ATLAS analysis select only the one-jet sample. Here, as discussed, we propose to include an extra jet to enhance the signal and to utilise it to distinguish the topcharm model from the top-up one. The selection is still e cient to reduce the tt background in which the average jet multiplicity is higher; see gure 6(top-left). For convenience, we de ne two signal regions (SRs): (3.2) HJEP03(216) SR1) Nj = 1 and Nb = 1 ; SR2) Nj = 2 and Nb = 1 : (3.3) Nb = 1: The signal contains one b-tagged jet. Requiring exactly one b-tagged jet reduces the W +jets background since processes with a W boson in association with bottom quarks are rare, and reduces also the tt background where there is a second jet expected to originate from a bottom quark; see gure 6(top-right). For b-tagging we use a parametrisation of the e ciency of the combined secondary vertex (CSV) algorithm of the CMS collaboration [77], as a function of the pT , and avour of the jet. We employ the so-called medium operating point, which overall results in b-tagging e ciencies of about 70 % for b- avour jets, about 1 % for u,d,s- avour and gluon jets, and about 20 % for c- avour jets. mT (`; E/ T ) > mTmin: The mT (`; E/ T ) distributions in gure 6 display a remarkable shape di erence between the DM signal and the SM background. For the SM background the E/ T and the lepton originates from the same W boson and as a consequence the mT (`; E/ T ) distribution drops around the W boson mass. This is not the case for the DM signal, where the E/ T originates from the invisible Z0 decay. The heavier Z0 case (benchmark B) presents slightly larger mT distribution. E/ T > E/ Tmin: The presence of DM in the signal introduces a lot of missing energy in the detector. The missing transverse energy will therefore be much larger on average for the signal in comparison to the SM background processes in which the E/ T originates from neutrinos only. j (`; b)j < max: In the DM signal, the lepton and the b-jet always originate from the decay of one top quark and hence they display a small azimuthal angle separation. 3The transverse mass is de ned as mT (`; E/ T ) = q2p`T E/ T (1 cos (`; E/ T )). point A and B) and the SM backgrounds after the pre-selection, i.e. we require only N` = 1. For the (`; b) distribution Nb = 1 is also required. Instead, the SM backgrounds can also present events where the b-jet and the lepton arise from di erent decay chains. In particular, in the W +jets background, the lepton and the b-jet are most likely back to back. N` = 1 Nj Nj 1 2 1.56 1.53 signal for benchmark point A and B, consecutively applying the cuts outlined in the text. Results and discovery reach. We now present the results of our analysis and the discovery reach of the LHC-13TeV with integrated luminosity L = 100 fb 1. benchmark point A and B for each consecutive cut up to the Nb = 1 selection. Although the tt and single t backgrounds reduce by a factor of ten and the W +jets drops by a factor of a hundred, the background is still larger than the signal. We now use the information of the kinematical distributions shown in gure 6, and maximise the statistical signal signi cance HJEP03(216) S0 = S pS + B + (0:1B)2 : S + B to nd each optimal cut in the rest of the selection steps. We nd that mTmin = 150 GeV ; E/ Tmin = 200 GeV ; max = 1:6 : ing the integrated luminosity L = 100 fb 1 Table 3 presents the continuation of table 2 together with the signal signi cance S assum. The sensitivities of each of the two signal regions (3.3) are also shown at the bottom of the table. The main SM background after all the cuts is tt. We can easily obtain the signi cance larger than 5 for the light mediator case (benchmark A) with 100 fb 1 . The heavier case (benchmark B) is instead at reach to be excluded. It is important to note that the signal signi cance is larger than the pure monotop sample (SR1) when we include an extra jet in the analysis, i.e. SR2. We also note that the shape of the distributions slightly depends on the value of the Z0 mass. In particular the mT and E/ T distributions for heavier Z0 are centred around larger values. Hence the e ciency of these cuts for the benchmark point B is slightly higher. The statistical signi cance S is not the only representative for an analysis which has to cope with systematic uncertainties, such as the ones on the cross sections of the SM background processes. For instance, given that the tt is the most relevant SM background, a large systematic uncertainty will originate from the uncertainty on the tt cross section, which was estimated of about 7 % at p s = 8 TeV [78]. Considering also other sources of systematic uncertainties, we conservatively assume a 10 % uncertainty in the SM background estimation and de ne the signi cance as (3.4) (3.5) (3.6) 1:45 signal signi cance (3.4) for L = 100 fb 1. signal for benchmark point A and B, after the Nb = 1 selection. The columns S show the statistical signi cance including a 10 % systematic uncertainty (3.6) for L = 100 fb 1 . Same as table 3, but with the tighter cuts. The columns labelled S0 show the signal We repeat the same procedure, but maximise the signi cance (3.6) to nd a new set of optimal cuts. We nd a tighter set of cuts mTmin = 300 GeV ; E/ Tmin = 350 GeV ; max = 1:0 : (3.7) Table 4 gives the results of these selection cuts, and clearly shows that even after including systematic uncertainties the potential remains to discover the top-charm avour-changing DM events during the run of the LHC with 13 TeV proton-proton collisions and an expected 100 fb 1 of collected data. In order to establish the reach of the LHC in the parameter space of the model, we perform a parameter scan in the m mZ0 plane. Figure 7 shows the three sigma and ve sigma contours of the signal signi cance without (S) and with (S0) a systematic uncertainty in this mass plane. There is essentially no dependence on the DM mass since the mediator is always produced on-shell in this mass range, and subsequently decaying into a pair of the DM particles. On the other hand, the LHC reach is largely dependent on the mediator mass that determines the production cross section for a given coupling. We nd that a large part of the mass space is accessible in the 13 TeV run of the LHC for the reasonable choice of the coupling parameter such as (g ; g23) = (3; 0:6). Following the same analysis strategy, one can easily explore the corresponding top-up avour-changing DM model, setting g = 3:0 and g13 = 0:6 and varying the DM and the Z0 masses. The enhancement of the production cross section due to the up-quark PDF (see gure 4) determines a much higher reach for the top-up model with respect to the contours of the signal signi cance in the m mZ0 parameter space without (solid) and with (dotted) including a systematic uncertainty in the calculation of the signi cance. top-charm model for analogous values of the couplings. Indeed we nd that the top-up DM model can be discovered at the LHC-13TeV for a Z0 mass up to about 1.5 TeV. 3.1.2 Top-charm vs. top-up in monotop As discussed, the top-charm and top-up avour-changing DM models essentially give the same monotop signature at the LHC. The main di erence is the overall cross sections, and hence the mass reach is di erent if we assume the same couplings between the two models. However, there is no other direct observable which is related to the Z0 mass, since we have seen in gure 6 that the kinematical distributions are similar between the di erent Z0 mass. Hence, even if the monotop signal is discovered at the LHC Run-II, it may be very di cult to discriminate between the top-charm and the top-up DM models. In this subsection we propose possible techniques to distinguish between the two models in the monotop signature, not based on the overall signal cross sections. For this purpose we de ne two benchmarks for the top-up DM model: A) B) fg ; g13; m ; mZ0 g = f3:0; 0:19; 30 GeV; 400 GeVg ; fg ; g13; m ; mZ0 g = f3:0; 0:19; 30 GeV; 800 GeVg ; (3.8) where we choose the same parameters as in the benchmarks of the top-charm model (3.1) except the g13 coupling. The value of the coupling g13 is chosen so that the top-up monotop cross sections become comparable to the top-charm ones. Lepton charge asymmetry. The rst strategy that we adopt to distinguish the topcharm avour-changing DM model from the top-up one is to exploit the lepton charge asymmetry in the leptonic monotop nal state. Since the up-quark PDF is much larger than the up-antiquark one in protons, the monotop process for the top-up DM model in proton-proton collisions produces much more top quarks than top anti-quarks, leading to a large majority of events with a positively charged lepton [28]. For the top-charm model, on the other hand, we expect an equivalent number of events with a positively and negatively charged lepton as the charm PDF is equal to the charm-antiquark one. S (A: mZ0 = 400 GeV) S (B: mZ0 = 800 GeV) S0 (A: mZ0 = 400 GeV) S0 (B: mZ0 = 800 GeV) Top-charm model Top-up model ` ` + + ` ` + + ` charged lepton in the nal state. In order to quantify this observation, we look at the signal signi cance again, but for positively and negatively charged leptons separately. Note that the main SM background, i.e. tt, is charge symmetric. In table 5 we report the result of these investigations for both the top-charm (3.1) and the top-up (3.8) benchmarks. We display the signi cance (both without and with a systematic uncertainty) for the combined signal region SR1+SR2 of each benchmark depending on the lepton charge selection. The `+ + ` columns correspond to the analysis discussed in the previous section, which does not distinguish the lepton charge. The charge selection can e ciently distinguish between the top-charm and top-up DM models. For the top-up model, the signi cance increases (decreases) remarkably by requiring only positively (negatively) charged leptons. The predominance of positively charged con gurations in the top-up model implies that the signi cance of the analysis targeted to a positively charge lepton is even larger than the one without the charge identi cation. For the top-charm DM model, on the other hand, the signi cance for the positively charged case and the negatively charged case are essentially equivalent, and they are both smaller than the combined one. In short, S`++` > S`+ ' S` S`+ > S`++` S` for the top-charm DM model ; for the top-up DM model ; (3.9) (3.10) and we conclude that the lepton charge identi cation provides an e cient technique to distinguish between the top-charm and top-up DM models in the monotop signature. Charm-jet tagging. The second strategy that we investigate to distinguish between the top-charm and the top-up models makes use of a charm tagging for an extra jet in SR2. Such a charm-tagging algorithm has been recently released by ATLAS [79] and it exploits the properties of displaced tracks, reconstructed secondary vertices and soft leptons inside jets. In our analysis, we assume a constant tagging e ciency for simplicity, without any dependence on pT and of the jets. This is accurate enough for a rst estimation of the e ect of charm tagging as the pT and dependence is quite mild [79]. Based on the needs of a speci c analysis, di erent working points can be chosen to select the desired charm-jet tagging e ciency and to either improve the rejection of light- avour jets or bottom-quark jets. To select the charm- avour jet with a low mistag rate for light (u; d; s; g) jets, we employ a tight c-tagging working point. Taking inspiration from the e ciency performance S (top-up; A) S (top-charm; A) S0 (top-up; A) S0 (top-charm; A) Before c-tagging After c-tagging SR1 Signal signi cance for the benchmark point A in both top-up and top-charm models before and after the charm-tagging requirement. reported by the ATLAS Collaboration [79], we assume an overall c-tagging e ciency of 20 % for c- avour jets, 1 % for u; d; s- avour and gluon jets, and 15 % for b- avour jets. We note that the mistag rate is extremely low, but we are compromised by the rather low c-tagging e ciency. Ideally, if the charm tagger would have a 100 % e ciency, the signal cross section would be suppressed by roughly a factor of a hundred for the top-up model, while by about a factor of three for the top-charm model, as seen in gure 4. Considering the same cuts of the previous section, we require the second jet of the SR2 to be a charm-tagged jet, and compute the signi cance for the benchmark point A (mZ0 = 400 GeV) for both top-up and top-charm models. Table 6 shows that after c-tagging the signi cance of the SR2 for the top-charm model becomes twice larger than that for the top-up model although the signal signi cance itself su ers a sharp drop for both models. Even though this technique is probably much less e cient than the lepton charge asymmetry, it represents nevertheless an alternative strategy to distinguish between the top-up and top-charm DM models in the monotop signature. More detailed investigations of charm-tagging techniques could result in better performances in the search for DM described in this paper. 3.2 Canonical dark matter searches A stable new particle that interacts predominantly with a top-charm or a top-up quark pair has interesting implications for DM phenomenology, in particular for relic density and canonical DM searches such as direct and indirect detection experiments. In the following we discuss in detail these considerations, devoting special attention to a tentative explanation of the galactic centre excess in terms of avour-changing DM. Relic density. As mentioned in section 2, we focus on the parameter space where mZ0 is parametrically the highest scale of the theory. In this case, the typical energy scale of the thermal freeze-out process is smaller than the mass of the mediator mZ0 . We then expect that the description of the dynamics in terms of a simpli ed model or an EFT makes no practical di erence.4 Indeed, for the parameter points of interest, we checked that the results in the simpli ed model (2.2) and in the EFT description (2.11) agree very well, by using MicroOMEGAs [66, 67] and MadDM [68, 69]. 4Apart from parametrically separating mZ0 from the other scales of the theory, one has to ensure that the width of Z0 is not too large, i.e. Z0 < mZ0 . (a) We assume the observed DM relic density in all (b) We do not make such assumption as in gof the parameter plane. The area within the dashed ure 8(a), and hence the FERMI limit is rescaled acboundary shows the parameter region that can t cording to the relic density of the model. The dark the galactic centre excess. The grey area is excluded grey area is excluded by the DM overabundance. by FERMI. (1 ) and yellow (2 ) expected uncertainty bands), and the parameter region that ts the galactic centre excess (light grey region) for the top-charm avour-changing DM model. In the simpli ed model, the annihilation of the DM candidate to the quark pair during the thermal freeze-out occurs exclusively via s-channel mediation of a Z0 boson, as shown in eq. (2.4). The relic density of can be equal to the observed relic density of DM, h2 = 0:12 [80] for reasonable values of the e ective coe cient gi3g =m2Z0 . This is illustrated for the top-charm model in gure 8, while the corresponding plot for the top-up model looks practically the same, as the mass di erence between the charm and up quarks has little e ect on both the calculation of the relic density and the photon uxes of the annihilation products. In gure 8(a), the proper relic density is depicted by the blue contour, however it is assumed that the relic density of is equal to the observed DM relic density in all of the parameter space. For m < mt=2 the annihilation to t{c or t{u quark pair is kinematically forbidden and the correct relic density is achieved if we invoke extra dynamics, e.g. an entropy dilution mechanism. For values of the parameter space to the right of the h2 = 0:12 line, would annihilate too much and the proper relic density is achieved if we assume non-thermal production. In gure 8(b), on the other hand, we do not make such assumptions, so that the region of the parameter space with overabundant DM is excluded while in the region where DM is underabundant we provide indicative relic density contours. Indirect searches. The latest FERMI data on photon uxes from dwarf spheroidal galaxies of the Milky Way [81] provide strong constraints on the parameter space of the model, as illustrated in gure 8. Although the published results do not include annihilation to avour-violating pairs such as t-c=u, the photon ux is very similar to that of bb for the DM mass range under focus [82]. Therefore, the limit on DM annihilating to t-c=u is similar to that of a bottom-quark pair. The dashed green line shows the observed limit while the green and yellow bands depict the 1 and 2 uncertainties of the expected sensitivity. We notice that the observed limit is nearly probing the thermal relic density line of the model. In gure 8(b) we show the FERMI limits rescaled by ( h2=0:12)2 to account for the varying relic density. We note that, while in gure 8(a) FERMI excludes all the large m region (because of the increased annihilation), in gure 8(b) the decreased relic density dominates over the increased cross section so that FERMI turns out to be sensitive only up to the h 2 ' 0:05 line. The latest results from the searches for antiprotons by the AMS-02 experiment [83] can also be used to set limits on DM annihilation in the centre of our galaxy. The reach of these limits depends on the uncertainties of the astrophysical background and the propagation of the antiprotons in the galaxy [84{86], and under reasonable assumptions the limit on DM annihilating to bb is equivalent or even stronger than the one obtained from FERMI. Due to the relatively larger uncertainties, we have not used these limits in this work, however, it would be interesting to see how much further they can constrain the models discussed here. We also report on the excess of gamma rays from the galactic centre that has been observed [34] and updated [35] by the FERMI telescope. Initial proposals that t the photon pro le of the excess included DM annihilating to bb pairs (see eg [87, 88] for phenomenological analyses). The top-charm model leads to a simlar photon ux, and hence can t the excess [33]. In gure 8(a) we show, based on the results of [33], the region of the parameter space of the model that can t the galactic centre excess. The t to the excess corresponds to DM that is slightly over-annihilating, so that a non-thermal production mechanism is required to ensure the observed relic density. The abrupt stop at m = 120 GeV is an artifact of extracting photon uxes from PPPC [82]; in principle one expects the t region to expand to lower DM masses.5 We also note that, since the photon ux from an up quark is practically the same to that from a charm quark [82], the top-up model ts the galactic centre excess, too. Direct searches. The DM candidate in the top avour-changing model has radiatively induced avour-conserving interactions with quarks so that, in principle, direct search experiments can be relevant.6 The reactor response depends on the strength of the interaction between the DM candidate and the reactor nucleus, typically described in terms of non-relativistic e ective operators that in general depend on the momentum exchange between the two particles, their relative velocity and their spins. These, in turn, are described in terms of e ective -N operators, themselves described in terms of a set of e ective interactions between and the quarks or gluons. 5The photon ux for annihilation to a top-quark pair given in PPPC starts from m = 180 GeV. When recasting the top-pair and charm-pair uxes to get the ux of the top-charm pair, this translates into a minimum value of m = 120 GeV. 6There are also e ective interactions with gluons which are however higher dimensional and two-loops suppressed, therefore they are negligible in our simpli ed model. In describing the scattering of the DM candidate against nuclei for low-energy experiments, we can take the limit of small relative velocity and momentum transfer. In this limit and neglecting higher derivative operators, the scalar ( qq) and vector ( q q) DMquark interactions contribute to the scattering cross section that does not depend on the spin of the colliding particles, the axial-vector ( interactions contribute to spin-dependent scattering, while all the other e ective operators can be neglected. For the top-up model the interaction of DM with a nucleus is achieved via box diagrams with two Z0 bosons, one top quark and one DM eld running in the loop, while for the top-charm model the connection with the valence quarks of the nucleon requires a second loop. We have calculated them in the zero momentum transfer limit for the top-up model and matched the Wilson coe cients to the simpli ed model computation. Regarding the spin-independent cross sections, in the limit of a massless up-quark, the contribution to the scalar operator vanishes, while the nite contribution to the vector operator cV q q is given by the following Wilson coe cient: cV = 6 g2 g123 dx dy x Z 1 Z 1 x h 3m2 0 0 2m2Z0 z Iln12=4 Iln22=4 where z = 1 x y when it is not the variable of integration and m2 z I0n1=4 In=4 + 2 dz z m2 (Iln2=5 02 1 Z 1 x y 0 In2=5)i; l 2 I 0ni = Iln2 = i Z d4li Z d4li (2 )4 (l2 i (2 )4 (l2 i 1 l 2 i i)n = 2i i)n = i where p, k and q are the DM, the quark and the loop momentum respectively. For reasonable values of the model parameters, the size of the Wilson coe cient turns out to be . 10 50 cm2, orders of magnitude smaller than current observational sensitivities, due to the cancellation among the box diagrams. This is true also for the spin-dependent cross section, where the experimental constraints are less strong. Therefore, the top-up DM model is not constrained by direct search experiments and consequently, neither is the top-charm model. 3.3 Complementarity between the LHC and non-collider experiments In the previous subsections we have studied the LHC and non-collider phenomenology separately for the top avour-changing simpli ed DM model. Here we combine the two analyses to provide a complete picture of the experimental reach on the parameter space of the model and the complementarity among di erent DM search experiments. Aggregated gures of the relic density, FERMI limits and LHC reach for the DM candidate of the top-charm (left) and top-up (right) avour-changing models in the DM-mediator mass plane, where we assume the observed DM relic density in all of the parameter plane. The grey area with dashed boundary shows the parameter region that can t the galactic centre excess. The dashed green line is the observed FERMI limit, while the green and yellow bands correspond to 1 and 2 uncertainties on the expected limit. The dark and light blue bands depict the 3 and 5 reach of monotop searches at LHC-13TeV with 100 fb 1. The results are summarised in gure 9, where we show the prospects from LHC-13TeV and the FERMI constraints together with the region of the parameter space that ts the tentative galactic centre excess for both the top-charm and the top-up models. In these plots the FERMI limits are obtained assuming that the relic density of the DM is equal to the observed one in all the parameter plane, allowing for other mechanisms than thermal production, same as in gure 8(a). If we would instead assume only thermal production for the DM candidate, the observed relic abundance is obtained only along the blue lines and on the rest of the parameter space the bounds from FERMI are much weaker (see gure 8(b) and discussion there). The LHC-13TeV reach, on the other hand, does not depend on these assumptions. This is already a basic di erence between the limits derived from colliders and from indirect detection. The LHC reach depends almost exclusively on the mediator mass, which sets the size of the cross section (for xed couplings). On the other hand, the reach of indirect detection experiments depends also on the DM mass, which a ects the e ciency of the DM annihilation. This implies that the LHC and indirect DM experiments can probe di erent regions of the parameter space of the model. Another interesting point we observe is that, by analysing the two plots in gure 9, a combined interpretation of the top avour-changing DM models at LHC-13TeV and in indirect DM searches reveals di erent features between the top-charm and the top-up DM model. In the top-charm DM model ( gure 9(left)), the FERMI exclusion covers most of the parameter space that can be probed by LHC-13TeV. However, the blue line where the dark matter abundance is obtained via usual thermal production is not constrained by FERMI, and instead it will be probed by LHC-13TeV for a DM mass around 90 GeV. The region capable of explaining the galactic center excess, characterized by the mediator heavier than a TeV, lies beyond the reach of LHC-13TeV. The top-up DM model ( gure 9(right)) presents the same limit from indirect detection as in the top-charm DM model but has a much larger reach at LHC-13TeV. The LHC13TeV will be able to probe the thermal relic DM line up to a mass of around 130 GeV, and to cover almost completely the region capable of accommodating the galactic center excess. Even though in the gures we have xed the coupling as (g ; gi3) = (3; 0:6), the previous discussion is robust under modi cations of the gi3 coupling as long as the invisible decay of the Z0 remains dominant. This is due to the fact that the monotop signature scales as gi23=m4Z0 B(Z0 ! ) and the DM annihilation scale as gi23g2 =m4Z0. Hence, reducing the coupling gi3 (keeping the Z0 invisible decay as the dominant one) will shift down by the same amount both the region capable of tting the galactic centre excess as well as the 3 and 5 discovery lines of LHC-13TeV, and thus it will not a ect qualitatively our conclusions. In this perspective, one can argue that the monotop signature at the LHC and the canonical DM searches in this simpli ed model allow for a straightforward comparison, because of their similar scaling with the couplings. 4 Conclusions and discussions In this work we have studied the phenomenology of a simpli ed model of DM with avourchanging interactions. Given the strong constraints on avour-changing interactions of the down-quark sector from low-energy experiments, we focused on DM interacting with a right-handed top-up or top-charm pair via a neutral vector mediator Z0. The simpli ed model is parametrised by the mass of the DM candidate, the mass of the mediator and the couplings of the Z0 to the DM and the quark pair. Depending on these parameters, the model provides rich signatures at colliders as well as at non-collider experiments, as summarised in table 1 and described in section 2.1. We focused on the top-charm avour-changing DM model whose most relevant signature at the LHC is a single top quark plus missing energy, i.e. a monotop nal state. For our benchmark point g = 3 and g23 = 0:6, the limit from LHC-8TeV is approximately mZ0 & 400 GeV. For the prospects of LHC-13TeV with 100 fb 1, we nd that, for the same couplings, the 3 (5 ) reach can go up to mZ0 760 (640) GeV, roughly independent of the DM mass. We then discussed how to distinguish the top-charm DM model from the top-up one in the monotop signatures by making use of lepton charge determination and by employing a charm-tagging technique. For non-collider DM signatures, we showed that the DM candidates with top avourchanging interactions can be thermal relics for reasonable values of couplings and for a mass of the order of the electroweak scale. We found that direct searches do not pose bounds on the simpli ed models under study, due to the cancellation of the box diagrams involved in the scattering of DM against nuclei. On the other hand, indirect searches pose strong bounds. We used the results from FERMI on photon galaxies to constrain the parameter space of the models and identi ed the part of the parameter space that ts the galactic centre excess. Since the photon uxes of the top-up and top-charm models are practically same, both models t the excess equally well. Finally, combining the LHC and non-collider analyses, we showed the complementarity among the di erent DM search experiments in probing the parameter space of the model and how the combination of these analyses will be able to distinguish between the topcharm and top-up avour-changing DM models. Before closing, we would like to comment on the UV completion of the model for what concerns the origin of the avour-changing couplings and the extra degrees of freedom needed in order to make the model anomaly free. Considerations regarding the UV completion of simpli ed models with Z0 bosons have been recently discussed in [89]. One way to build the avour-changing terms is to impose di erent charges under the U(1)0 gauge symmetry for each generation of quarks. After switching to the mass eigenstate basis, the coupling of the quarks to Z0 can be written as g0QijuiR Qij = Q0kViRkyVkRj and V R;L are the unitary matrices that diagonalise the quark mass matrix and Q0i is the gauge charge of the quark of the ith generation under the U(1)0. In our model, ujRZ0 , where we assumed that gi3 = g0Qi3, where i = 1; 2, are the dominant couplings. Since we do not want to charge the left-handed quarks under U(1)0, there are two ways to render the SM Yukawa couplings gauge invariant. One way is to charge the Higgs boson. Since every generation has di erent charge Q0i, we would need to introduce a di erent Higgs boson (with charge Q0i) for every generation. This leads to theories with extra Higgs doublets, discussed in the past in the context of the forward-backward asymmetry [90]. The second way is to use the Froggatt-Nielsen (FN) mechanism, i.e. to interpret the Yukawa coupling as the expectation value of a dynamical scalar eld that is charged under U(1)0. Either way, the construction of the avour-changing Z0 coupling requires extra scalars that are charged under U(1)0, either extra Higgs doublets or an extra FN type scalar. In our work we focused on model-independent aspects of the top avourchanging DM model by assuming that these extra states are heavy enough so as not to play a role in LHC or DM detection experiments. As for the second point, the model per se is anomalous. Charging only the right-handed quarks under the U(1)0 introduces gauge anomalies from triangle diagrams that involve the Z0 and SM gauge bosons. Phenomenological and theoretical aspects of anomalous U(1)0 extensions of the SM have been extensively discussed, see [91{93] and references therein. In order to cancel the anomalies, new chiral fermions L;R need to be added that are also charged under U(1)0 and the SM gauge groups. These chiral fermions get their mass by the spontaneous breaking of the U(1)0 gauge symmetry, via Yukawa interactions of type L R, so that m y v' while mZ0 = g0v'=2. Therefore, for moderate gi3 and for typical U(1)0 charge assignments we expect that the mass of these fermions is not much heavier than mZ0, however leaving enough room to consider these extra states beyond the reach of LHC for large Yukawa couplings. Indeed, in our phenomenological analysis we take gi3 = 0:6 which suggests that the extra fermion masses can be easily larger than the TeV scale, which is e.g. beyond the current bound on heavy quarks of 950 (782) GeV from the ATLAS [94] (CMS [95]) experiments. Furthermore, in our analysis we assumed that the Z=Z0 kinetic mixing is negligible. This term could be typically induced via radiative e ects and its size depends on the speci c UV completion of the model. We expect that with loop suppression and for mZ0 & 400 GeV there are no bounds from current direct search experiments [92], leaving a detailed investigation to future work. Summarizing, in our work we have focused on model-independent aspects of the top avour-changing DM model and neglected extra states related to possible UV completions by assuming that they are heavy enough to not a ect the phenomenology signi cantly. It would be interesting to study the signatures of these states and obtain combined constraints by associating it with the analyses we performed. Acknowledgments The authors would like to thank fruitful discussions with P. Anastasopoulos, L. Calibbi, E. Dudas, F. Maltoni and B. Zaldivar. This work is supported in part by Vrije Universiteit Brussel through the Strategic Research Program `High-Energy Physics', and in part by the Belgian Federal Science Policy O ce through the Inter-university Attraction Pole P7/37. 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Jorgen D’Hondt, Alberto Mariotti, Kentarou Mawatari. Signatures of top flavour-changing dark matter, Journal of High Energy Physics, 2016, 60, DOI: 10.1007/JHEP03(2016)060