Flavor and Collider Signatures of Asymmetric Dark Matter

We consider flavor constraints on, and collider signatures of, Asymmetric Dark Matter (ADM) via higher dimension operators. In the supersymmetric models we consider, R-parity violating (RPV) operators carrying B-L interact with n dark matter (DM) particles X through an interaction of the form W = X^n O_{B-L}, where O_{B-L} = q l d^c, u^c d^c d^c, l l e^c. This interaction ensures that the lightest ordinary supersymmetric particle (LOSP) is unstable to decay into the X sector, leading to a higher multiplicity of final state particles and reduced missing energy at a collider. Flavor-violating processes place constraints on the scale of the higher dimension operator, impacting whether the LOSP decays promptly. While the strongest limitations on RPV from n-\bar{n} oscillations and proton decay do not apply to ADM, we analyze the constraints from meson mixing, mu-e conversion, mu ->3 e and b ->s l^+ l^-. We show that these flavor constraints, even in the absence of flavor symmetries, allow parameter space for prompt decay to the X sector, with additional jets and leptons in exotic flavor combinations. We study the constraints from existing 8 TeV LHC SUSY searches with (i) 2-6 jets plus missing energy, and (ii) 1-2 leptons, 3-6 jets plus missing energy, comparing the constraints on ADM-extended supersymmetry with the usual supersymmetric simplified models.


I. INTRODUCTION
The notion that Dark Matter (DM) may be related to the baryon asymmetry originates from a time almost as early as the weakly interacting massive particle (WIMP) paradigm itself [1,2]. In these models, a mechanism sets the DM and baryon asymmetries such that n X − nX ∼ n b − nb, where n X , nX are the DM and anti-DM number densities, and n b , nb are the baryon and anti-baryon asymmetries. Since the ratio of DM to baryon densities is observed to be ρ DM /ρ B ∼ 5, this suggests m X ∼ 5m p 5 GeV, where m X is the DM mass and m p is the proton mass. Thus in these models, the natural mass scale for the DM is around 1-10 times the proton mass, significantly below the weak scale.
The idea that the DM and baryon densities have a common mechanism setting their densities is a simple and compelling framework. The challenge for a model of DM that relates the DM and baryon asymmetries is, however, that it must satisfy the many requirements from our observations of the weak scale and below. Many of the earliest models, especially those making use of electroweak sphalerons [3][4][5], had become highly constrained by these observations, particularly those from LEP, making models of DM relating the DM and baryon asymmetries observationally less than compelling.
Employing ideas from hidden sector model building [6], the Asymmetric Dark Matter (ADM) paradigm [7] showed how to evade these constraints by making use of higher dimen- where O B−L has dimension m and O X has dimension n. The operators in Eq. I.1 share a primordial matter-anti-matter asymmetry between the visible and DM sectors, realizing the relationship n X − nX ∼ n b − nb. For a review and list of references of DM models employing the higher dimension operators, see [8].
ADM can be embedded within supersymmetry (SUSY), which stabilizes the ADM particle There are, however, several important differences between ADM operators and RPV operators. First of all, with the presence of O X , R-parity is no longer violated, if the operator O X itself carries R-parity of -1. This new R-parity stabilizes the lightest R-parity odd scalar,x, of supermultiplet X. Second, DM now effectively carries baryon or lepton number, so that globally B and L are not violated. That forbids n −n oscillations as well as proton decay (when the X fermion is heavier than the proton). For certain types of X sectors, the DM can induce proton decay, but it must be catalyzed by the DM, and for this to happen frequently enough to be observable, the scale M must be quite low, around a TeV [15,16]. Thus the worst of the usual constraints on RPV is lifted for ADM. Depending on the constraints on M and mq, χ 0 may be collider stable though cosmologically unstable. Therefore, it is important to consider constraints from a displaced secondary vertex search for generic ADM models. Previously, some lifetime estimates have been made using naive dimensional analysis [7,17], but it is desirable to refine the displaced vertex analysis.
The goal of this paper is to study the flavor structure and constraints on ADM and its implications for collider searches for SUSY. We compute the flavor constraints on the scale M of the operator, relate these constraints to the lifetime of the LOSP, and derive constraints on the ADM-extended MSSM from standard SUSY searches. Unlike many recent efforts to lift constraints on RPV operator coefficients through flavor structures [18,19], we will assume no flavor symmetry, but rather examine the range of possible signatures that could arise in a general flavor structure. Note that the flavor constraints we place on DM in ADM models will have applications to many models with flavorful DM [20][21][22][23][24], because the UV completion of the ADM models we consider contain some of the same interactions.
The outline of our paper is as follows. In Sec. II, we carry out a thorough analysis We emphasize that we take a conservative approach without assuming a flavor structure, since there are many ways to relax flavor constraints by imposing a flavor structure on the model. For example, since both meson oscillations and lepton flavor constrain products of couplings to different generations, if the couplings to one of the generations is much larger than to the other generations the constraints will be considerably relaxed. In the case of meson oscillations the usefulness of this change is somewhat limited, however, since rotating from a flavor basis to the mass basis will induce couplings to the other generations which are generically not small unless the flavor and mass bases are closely aligned (which would constitute a tuning in the absence of a flavor symmetry). In such cases, a flavor symmetry can alleviate these constraints. Therefore, our results on flavor constraints and the corresponding discussion of displaced vertices from LOSP decay must be taken as conservative. Even without the assumption of a flavor symmetry, we will find that prompt flavor violating decays of the LOSP are still possible at the LHC. In addition, deriving constraints in the absence of a flavor symmetry leaves open the interesting possibility for exotic flavor signatures at the LHC.

A. Xq d c
We begin by analyzing the Xq d c operator, assuming only one flavor of DM: There are three UV completions at the renormalizable level: where i, j, k are generation indices. Note that the effective scale of W is determined by for a mediator M = D, L, Q with mass m M . This relation also holds for the UV completion, given an appropriate mediator M , of the Xu c d c d c and X e c operators, as will be shown in the next subsections. In these expressions, as throughout this paper, a lowercase letter indicates a SM field and an uppercase letter represents exotic heavy states, which are integrated out to generate the higher dimension operator. Note that we define fields in the mass eigenstate basis here. For simplicity, we consider only one flavor of DM, as well as a single pair of heavy mediator fields (D, D c ), (L, L c ) or (Q, Q c ). If we extend this simple model with multiple DM flavors or multiple mediator states, we have more freedom in assigning a flavor structure that could lift some of the flavor constraints that we study, but we do not pursue this direction. We also assume only one of the UV completions is dominant, and we will label the UV completion by the state which is being integrated out. Our results do not qualitatively change if we consider mixed UV completions.
We consider the constraints on Xq d c derived from K −K, D −D, B −B mixing, µ − e conversion, µ → 3e and b → s + − in turn.

Meson Mixing
Both tree and loop level processes give rise to meson mixing through the UV completions for the operator in Eq. (II.5). Sample processes are shown in Fig. 2. While the tree level For (s L,R γ µ d L,R ) 2 , we only show a representative diagram for each UV completion.
Here, we use 2-component spinor notation to reduce confusion.
processes in principle give rise to a stronger constraint on the mediator mass, they do not constrain the DM coupling λ XM to the UV particle M , nor do they constrain all UV completions (the D and Q UV completions are untouched by the tree level constraint). An exhaustive compilation of the couplings constrained by K −K, D −D and B −B mixing is given in Table V in Appendix A; we highlight the conclusions here.
Meson mixing is most strongly constraining for the operator (s R d L )(s L d R )/Λ 2 , where K −K mixing gives Λ 2 × 10 4 TeV [25]. For the L UV completion, Fig. 2a will generate K −K mixing at tree level,  Loop diagrams, on the other hand, probe a wider array of flavor-changing couplings, since any of the superpartner flavors may appear in the loop. In some cases, they also probe precisely the combination of couplings that enters into M ijk which ultimately determines whether decays are prompt or displaced at the LHC.
occur, and the loop functions which characterize the constraints are detailed in Appendix A. In the limit that the fermions and the scalars in the loop have a common mass m F and m φ respectively, the amplitude simplifies considerably: where λ 2 represents the appropriate combination of couplings shown in Table V where we rearrange spinors using the Fierz identities, The branching ratio of µ − e conversion is obtained for the various nuclei, and can be translated into the value for Al, Br µN →eN (Z = 13) ≤ 10 −12 (see Appendix A 2). We then derive the constraint The number of coefficients constrained by the tree level process is, however, limited. On the other hand, loop level contributions, as also shown in Fig. 3, constrain all three UV completions for various combinations of couplings. These are detailed exhaustively in Table VI in Appendix A 2. At loop level, the constraints on M from µ − e conversion are at the level of 10-100 TeV, and therefore not important from the point of view of displaced vertices at the LHC. µ → eγ and µ → 3e appear only at loop level and also are not strong constraints.
We detail the constraints from µ → 3e in Appendix A, Table VIII. While not significant for the q d c model, µ → 3e will become important for the e c model.
At tree level, we also have contributions to b − s conversion with a pair of leptons, as for example in B s → µ + µ − . Processes are shown in Fig. 4 (a) and (b), where we again rearrange spinors using the Fierz identities, similarly as in Eq. (II.11).
Currently, the experimental bound for We can also constrain the scale of four-fermion effective operators through the process

Summary of Constraints for Xq d c
There are many combinations of couplings constrained in Tables V-VIII, but it is important to see the over-arching patterns.
where i, j are flavor indices.
Similar to the case of Xq d c , the combinations of the couplings which are constrained are shown in Table V. Because all fields involved are right-handed, the strongest constraint from (s L d R )(d L s R ) is eliminated, and more modest constraints on m M /λ 2 between 10 and 100 TeV result. In addition, when the operator is completed via D, M ijk = m D /λ i XD λ jk D , which enters into the LOSP lifetime, is directly constrained, though only in particular generational combinations. Note in addition that λ 3 XU is the only coupling which remains unconstrained. A variety of other processes from q i → q j qq meson decays will constrain λ 2 /m 2 M , similar to µ − e conversion or B s → µ + µ − constraints on the q d c model. These constraints are, however, rather weak. Since no constraints on M ijk from exceed 100 TeV, prompt decays of the LOSP are unconstrained by flavor.
C. X e c Lastly, we consider the UV completions for X e c , 16) where i and j are again flavor indices.
The L UV completion of the e c model has tree level contribution to the µ → eee process as shown in Fig. 5, which leads to effective operators: The branching ratio Br(µ → 3e) is smaller than 10 −12 , and thus the mass mL and λ's involved are constrained to be mL λ2 ≥ 87 TeV , Loop processes are also constrained and we detail their contributions in Table VIII. The conclusion of the detailed results in the Appendix A is that no process constrains M > 100 TeV, and therefore, the LOSP decays at the LHC will be prompt.

III. PROMPT VERSUS DISPLACED VERTEX LOSP DECAYS AT COLLIDERS
In this section, we connect the flavor constraints on the scale M ijk summarized in the previous section to the lifetime of the LOSP decaying through the ADM operator Eq. (I. 3) in the processes of Fig. 1 2 . LOSPs that participate in W ADM , such as squarks or sleptons, can decay directly into two SM particles and the ADM through the W ADM operator, as in the left panel of Fig. 1. If the LOSP does not appear in W ADM directly (e.g. neutralinos or charginos), they will decay through an off-shell squark or slepton, as in the right panel of Fig. 1. Three-body decay and four-body decay of the LOSP lead to completely different lifetime scales and thus result in very different constraints from displaced vertex measurement at the LHC. In Appendix B, we derive the LOSP decay width for general three-and four-body decay as shown in Fig. 24 with various group representations for participating particles. We summarize the results of Appendix B here.
For three-body LOSP decay of a squark or a slepton, the secondary vertex displacement cτ is of the form where m LOSP is the LOSP mass and F (3−body) is the coefficient that can be calculated from Eq. (B.7). Here, we ignore the SM particle masses, which, in particular, excludes top quark final state cases. Note that we also ignore the ADM mass in Eq. (III.20) since the squark mass and the slepton mass must be much larger than a typical ADM mass around 10 GeV due to other direct collider constraints. We use the millimeter unit for the displacement since the detectors at the LHC can roughly resolve the displaced vertex up to a millimeter.
Assuming that the LOSP decays through only one dominant coupling 1/M ijk that does not involve the third generation 3 , we list the 3-body LOSP decays for each superpotential operator and obtain F (3−body) for each case in Table I Table I.
For four-body LOSP decay, the displacement is given by the following expression if we assume that a contribution from a single intermediate particle φ dominates: 3 The third generation complicates the general discussion because the top quark mass cannot be ignored and the third generation squarks generally have a large mixing. We leave the third generation specific scenarios for the future work.
• For Xq d c : • For Xu c d c d c : • For e c :    Instead, we only consider special cases to show typical constraints.
In Fig. 6, we consider the case with pure Bino (neutralino) LOSP with one light righthanded d-squarkd c . We assume that only the first generation coupling 1/M 111 for the Xq i j d c k operator is dominant. In this scenario, we obtain (F (4−body) ) −1 = 2.04 × 10 2 mm. In the case of displaced decays, by searching for the displaced vertex, we can clearly identify DM creation inside the detector and probe the nature of the DM directly at the LHC.
Thus, displaced vertex searches are very important for ADM searches at the LHC. In the case of prompt decays, however, one basic question is how ADM models fare when subjected to the usual supersymmetric searches. In the next section we compare the constraints from two standard searches for SUSY against those obtained in ADM when the LOSP is unstable to decay.

IV. LHC CONSTRAINTS
In order to compare the standard searches for SUSY against those obtained in ADM, we consider two ATLAS analyses with 20.3 fb −1 of data at 8 TeV. We have chosen the ATLAS, instead of CMS, analyses in this study since the collaboration quotes the 95% confidence limit, S 95 exp , on the number of events from new physics, once the cuts of the analysis have been applied. This allows us to simulate the SM plus new physics and easily extract the constraint by simply taking the difference with a simulation having the SM only. We utilize 1. an analysis with a lepton veto, 2-6 hard jets and high missing transverse energy (MET) E miss T [32]. We will refer to this analysis as"0 lepton+2-6 jet+MET analysis" (or "0 lepton analysis" for short); 2. an analysis with 1 or 2 leptons, 3-6 hard jets and high E miss T [33]. We will refer to this analysis as the "1-2 lepton+3-6 jet+MET analysis" (or "1-2 lepton analysis" for short).
Both of these analyses are the most standard SUSY searches for typical gluino or 1st/2nd generation squark pair production modes in R-parity conserving SUSY scenarios. We aim to compare the ADM models with the ordinary SUSY models, represented by Simplified Models [34,35] analyses may also be relevant for constraining certain ADM models (such as the ATLAS and CMS high jet multiplicity analyses [36,37] for the u c d c d c model). We have not explored these constraints here, instead choosing a representative sample which utilizes the most standard types of SUSY analyses. In addition, we do not consider gluino and slepton/sneutrino LOSPs, or the constraints on e c operators. A more exhaustive analysis including these other cases is very interesting for future work. neutrino. The 4-body decay of neutralino decay is through off-shell squark as shown in Fig. 1 The u c d c d c model has the same diagrams with a lepton/neutrino replaced by a jet in the neutralino decay.

A. Analyses
We briefly review the 8 TeV ATLAS 0 lepton+2-6 jet+MET analysis and 1-2 lepton+3-6 jet+MET analyses and how these analyses may constrain ADM q d c and u c d c d c models, in comparison to the Simplified Models that are utilized in the original ATLAS analysis. We also summarize the definition of the observables and the notation used in the analyses in Appendix C.

0 lepton+2-6 jet+MET analysis
The ATLAS 0 lepton+2-6 jet+MET analysis with 20.3 fb −1 at √ s = 8 TeV is summarized in Table II For comparision, we consider the Simplified Model process shown in Fig. 7. The Simplified Model has the gluinog, the lightest neutralino χ 0 1 and all the left-handed squarks q i L and right-handed squarksq i R of the first and second generation with degenerate mass.
through the SUSY QCD processes. The gluino decays throughg → qq ( * ) → qqχ 0 1 with 100% branching ratio (BR), where the intermediate squarkq ( * ) can be either on-shell or off-shell depending on mass parameters, and a squark directly decays into the neutralino and a quark.
To distinguish this from other simplified models we consider for the 1-2 lepton analysis, we denote this model "Sim0." The most important features that will be relevant for distinguishing the constraints on the ADM model versus the Simplified Model are: (i) E miss T > 160 GeV, which we will see rather dramatically reduces the acceptance of the ADM models; (ii) N jet with p T > 60 GeV, which improves the acceptance for the ADM models with a large number of jets; (iii) m eff and E miss T /m eff , both of which improve the acceptance of the ADM model over the Simplified Model. Overall, we will find that the E miss T cut is severe enough that in most cases the constraint on the ADM models will be much weaker than for the Simplified Model.
Our discussion will also show, however, that better searches could easily be implemented replacing the hard missing energy cut with a higher multiplicity of hard jets or leptons.
Thus, it is desirable to compare the ADM model with the conventional SUSY models by performing similar LHC analyses with higher multiplicity (such as [36,37]). We postpone this study for the future work.

1-2 lepton+3-6 jet+MET analysis
The ATLAS 1-2 lepton+3-6 jet+MET analysis with 20.3 fb −1 at √ s = 8 TeV is summarized in Table III and in Table IV Tables III, IV. For the 1-2 lepton analysis, we compare the q d c model with the Simplified Models by varying the relative ratio between colored SUSY particle masses and the LOSP mass. To this end, we use two Simplified Models as shown in Fig. 8, which are referred to as "one-step" Simplified Models in the ATLAS analysis [38]. The first model, shown in Fig. 8a, which we call "Sim1g," has the gluinog, the lightest chargino χ ± 1 and the lightest neutralino χ 0 1 . Production is gluino pairs, with the gluino decaying viag → qq χ ± 1 → qq W ( * ) χ 0 1 with 100% branching, where q and q are quarks with different isospin and W ( * ) is the on-shell (off-shell) W boson, depending on the mass gap between χ ± 1 and χ 0 1 . The second model shown in Fig.  8b, which we call "Sim1q," has the left-handed squarkq L , the lightest chargino χ ± 1 and the lightest neutralino χ 0 1 . Note that only left-handed squarks are involved since χ ± 1 and χ 0 1 are assumed to be mostly Wino-like. Now the production is only through squark pairs with the squark decaying throughq L → q χ ± 1 → q W ( * ) χ 0 1 . For simplicity 4 , we fix the ratio among the colored superparticle (g/q L ), χ ± 1 and χ 0 Similarly to the 0 lepton analysis, we will find E miss T to be a key variable in distinguishing the ADM model from the Simplified Models, though both the p T cut on the hardest lepton   and jet will play an important role. Note, however, that the E miss T cut here is stronger than in the 0 lepton analysis in order to filter the SM W and top-quark events. For some soft channels, b-tagging is employed, and thus the b-tagging efficiency affects the event acceptance. In the ATLAS analysis, different b-tagging efficiency has been applied by adjusting a b-tagging parameter for different channels. However, in our analysis, we simply rely on the detector simulator we use; since the efficiency difference is at the ∼ 10% level and cross section differences between two adjacent scan points are much higher, our results will not be significantly changed because of the b-tagging method.

B. Event Generation
We use MadGraph5 v1.5.8 for the Matrix-Element (ME) event generation [39]. The generated events are reweighted to match the Next-to-Leading-Order (NLO) cross section.
We employ Prospino 2.1 to obtain the cross section of gluino and squark pair production at NLO [40,41].
Since the processes under consideration consist of cascades of multiple decay chains through on-shell states with very narrow decay width, it is desirable to divide a single process into one 2-to-2 process and multiple decay subprocesses for each on-shell particle in the process, to generate events for them separately, and to merge all of the sub-parts into a single process by doing the appropriate Lorentz transformation and color flow matching 5 . We 5 In this paper, we do not consider spin correlation. For the 0 lepton analysis, we scan mass parameters in the gluino-common squark mass plane by fixing the neutralino mass m χ 0 1 . For the ADM model, we fix the mass of the ADM to be 10 GeV (a well-motivated value), and we consider four different cases: squark LOSP (with the neutralino decoupled), and neutralino LOSP with m χ 0 1 =100, 300 and 500 GeV. The Simplified Model Sim0 is scanned in the same (mg, mq) mass plane with the neutralino mass m χ 0 1 = 10, 100, 300 and 500 GeV, where 10 GeV is chosen for comparison with the ADM model with squark LOSP. The gluino and squark mass parameters are scanned by generating 10,000 events for each parameter, from 100 GeV to 3000 GeV with 100 GeV spacing. For a squark LOSP, we additionally impose the condition mg > mq. For high cross section regions where mg or mq is below 1000 GeV, we scale the number of events as needed to reduce statistical errors.
For the 1-2 lepton analysis, in which only the q d c model is relevant, we additionally scan the mass parameters in the plane of (mg, m χ 0 1 ) and (mq, m χ 0 1 ) with decoupled squarks and gluino, respectively. The (mg, m χ 0 1 ) scan is compared with the Simplified Model Sim1g and the (mq, m χ 0 1 ) scan is compared with the Simplified Model Sim1q, so that we generate events for those Simplified Models in the same scanning. Due to reduced experimental sensitivity, the scan region is confined to 1500 GeV for mg, to 1300 GeV for mq, and to 1000 GeV for m χ 0 1 . We reduce the grid spacing to 50 GeV for this scan. We also show the 1-2 lepton 6 PYTHIA 6 does not support the color-triplet vertex ( ijk ) as an acceptable color flow structure.

C. Results
We discuss our results for the q d c model, followed by the u c d c d c . For the former model, we apply both the 0 lepton and 1-2 lepton analyses, while for the latter we apply the 0 lepton analysis only. In each case, we consider a squark LOSP decay into the ADM sector first (which is topologically most similar to the Simplified Model for comparison), before constraining a neutralino LOSP decay into the ADM sector.

Squark LOSP
We first present the squark LOSP case of the q d c model via the diagrams of Fig. 9.
We assume the first two generation squarks are nearly degenerate in mass, but have a large enough mass splitting that the heavier squarks decay promptly to very soft (undetectable) jets and leptons and a lighter squark until the lightest squark is reached at the bottom of the cascade. We implement this by putting a 5 GeV mass splitting between the lightest squark and the others. The LOSP squark finally decays to the ADM with a quark and a lepton/neutrino. Hence, additional jets and leptons appear in the event, but the missing energy is reduced.  Table II (for Fig. 11a) and Table III  To see this, we show the MET distribution and the p T distribution of the hardest lepton in Fig. 12 at a mass parameter point (mg, mq) = (1500 GeV, 1000 GeV). The MET distribution in Fig. 12a is obtained after applying signal object identification/isolation, the lepton veto, and the two hardest jet p T cuts: p T (j 1 ) > 130 GeV, p T (j 2 ) > 60 GeV, from the 0 lepton analysis. The p T distribution of the hardest lepton in Fig. 12b is obtained after applying the same cuts except the lepton veto cut, instead applying the MET cut: E miss T > 160 GeV.
One can easily see the MET distribution in Fig. 12a is not very different for the Simplified Model Sim0 than for the q d c model, though the rate is different due to the lepton veto as 7 A correct interpretation of the confidence level by combining such multiple non-exclusive channels must be taken with care, and it is beyond the scope of this paper. one can see in the lepton p T distribution in Fig. 12b: the Simplified Model Sim0 has 100% no-lepton events, while the qld c model has 45% no-lepton events.

Neutralino LOSP
Next, we present the constraints for the neutralino LOSP case of the q d c model via the diagrams of Fig. 10. In this case, we do not have to assume a splitting between squarks since squarks decay promptly into the neutralino. The (mg, mq) scan results of the ATLAS 0 lepton and 1-2 lepton analyses are shown in Fig. 13  The constraints for the neutralino LOSP q d c model are generically weaker than the Simplified Model Sim0 for small m χ 0 1 (100 GeV and 300 GeV), but reveal more complicated behavior in the m χ 0 1 = 500 GeV case. Several factors contribute to these results. One obvious factor that tends to give weaker constraints on the ADM model in the 0 lepton GeV and m χ 0 1 = 100, 300 and 500 GeV. In the right panel, the first bin shows the number of events that passes lepton veto cut of the 0 lepton analysis. We indicate the first bin using arrows in the right panel. The color scheme for the neutralino mass is the same for both graphs.
analysis is the branching fraction to charged leptons, which we have already seen in the squark LOSP case. More importantly, the missing energy of the neutralino is reduced as it decays to two additional jets plus a lepton. This feature is transparently comparable with the Simplified Model Sim0 since both models share the same event topology before the neutralino decay. On the other hand, as the neutralino mass is set heavier, the energy of the jets from gluino/squark decay into the neutralino becomes smaller as the mass difference shrinks. Therefore, the experimental sensitivity to the Simplified Model Sim0 (and ordinary R-partiy conserving MSSM scenarios generically) is reduced for a heavier neutralino mass, while the ADM models are subject to more severe constraints since a massive neutralino is able to "store" and transfer energy to the ADM particle. Therefore, for large neutralino mass, the ADM model can actually become substantially more constrained than the Simplified Model.
In Fig. 14, we compare the MET distribution and the hardest lepton p T distribution of the neutralino LOSP q d c model and the Simplified Model Sim0 for mg = mq = 1000 GeV and m χ 0 1 = 100, 300 and 500 GeV. Here, we use the same cuts as in Fig. 12. Note that E miss T is distinctively smaller for the q d c case. For the lepton p T distribution, the first bin  Fig. 16, we applied the p T cut of the "Soft 1-" class (in Table III) to the hardest three jets for soft lepton events, and applied the p T cut of the "Hard 1-3 jet" class (in Table III) to the hardest three jets for hard lepton events. One can easily see that the MET  processes at the LHC are given in Fig. 9 with a lepton/neutrino replaced by a jet in the lightest squark decay. The ADM mass is 10 GeV here, and for Sim0, we set m χ 0 1 = 10 GeV for a fair comparison. show three different neutralino masses: m χ 0 1 = 100, 300 and 500 GeV. For each histogram, we apply cuts in the 0 lepton analysis similarly to the case of Fig. 12: after signal object identification/isolation, we apply the lepton veto, and the two hardest jet p T cuts: p T (j 1 ) > 130 GeV, p T (j 2 ) > 60 GeV for the MET distribution, and additionally the MET cut E miss T > 160 GeV for the other distributions.
One sees that the actual kinematic distributions are much different between the Simplified and u c d c d c models. Nonetheless, the reason why the u c d c d c model and Sim0 have similar constraints is due to saturation of cut acceptance. Near the 95% C.L. experimental sensitivity, the cuts in Table II are not very effective in distinguishing one model from other since the p T of relevant objects and the MET are already very high. The channels with harder cuts (for example, BT and CT) do not dominate the constraints, and hence do not distinguish between models. For example, the acceptance of the AL channel cut is saturated above mq = 1000 GeV for a fixed gluino mass mg = 2500 GeV, to ∼ 0.5 for u c d c d c and ∼ 0.75 for Sim0. Then, the constraints are simply determined by the production cross section, which is identical for both models.
It is clear, however, that additional shape information from the kinematic distributions in Fig. 18 is available for discrimination between the Simplified Model and ADM, so that the analysis could be better targeted to ADM models.

Neutralino LOSP
Next we consider the u c d c d c model with a neutralino LOSP via the diagrams of Fig. 10 with the lepton/neutrino replaced with a jet. The results are shown in Fig. 19. In this case, as for the q d c model with neutralino LOSP, we do not have to assume a splitting between squarks since squarks decay promptly into the neutralino. The (mg, mq) scan results of the ATLAS 0 lepton analysis is shown in Fig. 19 for three different neutralino mass choices: The constraints for the neutralino LOSP u c d c d c model are generically weaker than the Simplified Model Sim0 for small m χ 0 1 (100 GeV and 300 GeV), but reveal more complicated behavior in the m χ 0 1 = 500 GeV case. Several factors contribute to these results. One obvious factor that tends to give weaker constraints on the ADM model in the 0 lepton analysis is that the missing energy of the neutralino is reduced as it decays to three additional jets, as shown in Fig. 20. This feature is transparently comparable with the Simplified Model Sim0 since both models share the same event topology before the neutralino decay. On the other hand, as the neutralino mass is set heavier, the energy of the jets from gluino/squark decay into the neutralino becomes smaller as the mass difference shrinks. Therefore, the experimental sensitivity to the Simplified Model Sim0 (and ordinary R-parity conserving MSSM scenarios generically) is reduced for a heavier neutralino mass, while the ADM models are subject to more severe constraints since a massive neutralino is able to "store" and transfer energy to the ADM particle. Therefore, for large neutralino mass, the ADM model can actually become substantially more constrained than the Simplified Model.
In Fig. 20, we compare the the E miss On the other hand, these states may have flavor violating decays to pairs of quarks, which may include only the light quarks, but also may result in flavor violating decays U → tj or D → bj. A study of these signatures could give rise to additional constraints on ADM sectors.

V. CONCLUSION AND OUTLOOK
We have carried out the first detailed study of flavor constraints and collider signatures of Asymmetric Dark Matter. We found that while flavor constraints from meson oscillations and lepton flavor conservation place significant requirements on the scale M of the ADM operators, this scale M is not so high that a variety of collider prompt decays of the lightest ordinary supersymmetric particle (LOSP) into the X-sector, including exotic flavor combinations, could not arise. We applied two standard 8 TeV LHC searches for SUSY to LOSP decays to ADM plus additional jets and leptons. These analyses involved 2-6 jets plus missing energy, or 1-2 leptons plus 3-6 jets and missing energy. We found that the constraints from these analyses, whether the LOSP is a squark, slepton, or neutralino, are somewhat weakened, depending on the spectrum, in comparison to the standard searches. However, the detailed kinematic distributions show significant difference between the conventional SUSY models and the ADM models. This suggests that other SUSY searches at the LHC might be sensitive to the ADM-extended MSSM, in particular searches which involve an extremely high multiplicity of jets [36,37]. It also suggests that dedicated searches tuned to ADM could significantly extend the reach at the LHC.
One of the interesting conclusions of this work is that the source of large flavor violation may not be much beyond our current reach. The suppression scale of the ADM operator could be as low as 10 TeV, and the leptoquark-type states being integrated out could be as low as 1 TeV. These states, when they decay to the ADM sector or to the visible sector, could give rise to exotic flavor-violating signatures. Performing ADM model analyses for other SUSY searches, e.g. high jet multiplicity searches, third-generation focused searches, and exotica searches (e.g. leptoquark searches) will provide a better understanding of the current status of ADM models. We aim to carry out this study in the future. It will also be interesting to design searches for ADM to learn how much the LHC reach can be extended. The well-motivated, simple extension of an ADM sector shows interesting interplay between flavor physics and collider physics, and opens new unexplored directions for LHC phenomenology.

We thank Yuval Grossman, Michele Papucci and Lian-Tao Wang for discussions and
Anson Hook for pointing out a problem in one of the Monte Carlo tools that we employ.
We also thank the theory group at Lawrence Berkeley National Laboratory for hospitality while part of this work was being completed. This work is supported by by NSF CAREER award PHY 1049896 and by the DoE under contract de-sc0007859.
where m A is the mass of the particle A in the loop, λ i 's are four couplings involved in the diagram and (Sym) is an appropriate symmetry factor if there are identical particles in final states. We denote the chirality of each particle by P, P = L, R and P , P for the opposite chirality, as shown in Fig. 21. Note that the contribution B m can be reinterpreted denote chirality L or R, and P and P are opposite chirality to P and P , respectively. Here, we use 4-component notation to easily match with Feynman amplitude expressions.
as vector-vector current interaction due to Fierz identities: The loop functions in Eq. (A.1) are defined by .
For the loop contributions under consideration, we have m F 1 = m F 2 or m φ 1 = m φ 2 in most cases. If m F 1 and m F 2 are the same, H and K are given by and similarly for m In the following subsections, we present the corresponding expressions in the UV completemodels for various flavor constraints.

Meson mixing constraints
Experimental constraints from K-, D-, B-meson mixing put stringent constraints on the UV models for the Xq d c and Xu c d c d c operators. The effective operators generated from the models are summarized by the following effective Lagrangian: where K P P , D P P , B dP P and B sP P are the coefficients of the corresponding operators. For B dP P and B sP P , the results can be easily read from K P P by changing the generation index to b-quark, so we will omit them in the following.
Operator  Under the assumption that m X ∼ mx m soft m D , m L , m Q , m U , we summarize the tree-level and one-loop-level constraints on the mass and the coupling from meson mixing in Table V. In the table, R Φ denotes log(m 2 Φ /m 2 soft ) − 1. The coupling combinations for RR operators for K-and B-meson mixing in the D UV completion for Xu c d c d c are given by For the model (D) defined by Eq. (II.6), we obtain the operators for Kaon physics, For the model (L) from Eq. (II.7), we have Now, we show the result for the model (Q): 2H(m X , m X , mQ, mQ) + 2H(m Q , m Q , mx, mx) , As in the Xq d c case, we specify each model by the superscripts (U ) and (D). For the model (U ), and for the model (D), Among the models under consideration, only the Xq d c -type model is subject to the constraint from µ-e conversion [46,47]. Box diagrams can contribute only to the following vector-vector current interactions: where C q P P is the coefficient of the corresponding diagram. From the effective operators, we obtain the µ − e conversion branching ratio for 13 Al [48]: where G F is the Fermi constant.
For the model (D), where i, j are flavor indices and the tilde over a particle name implies its supersymmetric scalar partner with odd R-parity. Note that we can safely ignore the masses of quarks and leptons except the top quark mass although we show generic results for the purpose of completeness.
Similarly, for models (L) and (Q) from Eq. (II.7) and (II.8), Operator i, j are flavor indices that runs over 1,2 and 3 and the summation is implied, but denotes an electron or muon external state, and thus is not summed over.
As with µ−e conversion described in the previous section, the Xq d c model is also subject to constraints from b → s transition measurements. At one-loop level, the contributing Feynman diagrams are listed in Fig. 4 and Fig. 23. The one-loop contributions lead to where denotes electron and muon. Note that there are no contributions to (scalar current)-(scalar current) interactions, such ass R b L R L , since the UV completions of the Xq d c model involve only left-handed leptons. These induced effective couplings are constrained from various rare B-meson decays, for which the constraints on the scales of the effective operators are computed in [31].
We present the full one-loop Z P P from each UV completion (D), (L) and (Q). For the model (D), where denotes the generation index of the external leptons, such that = 1 for electron and 2 for muon. For the (L) UV completion, We summarize the b−s transition constraints in Table VII assuming m X ∼ mx m soft m D , m L , m Q , m E , using the result from [31]. Since the constraints depend on whether the couplings are real or complex, we show both the strongest and weakest lower bounds in the table.
4. µ ± → e ± e ∓ e ± For the Xq d c and X e c models, we have constraints from rare muon decays, with box diagrams contributing to µ → 3e decay. The relevant effective operators are where A P P 's are the coefficient generated from the one-loop contribution. Note that we have symmetry factors for the RR and LL couplings.

Model
Tree λ 2 One loop λ 4 The partial decay width of a muon to three electrons is where m µ is the muon mass. The branching fraction is currently constrained to be 10 −12 , with the total muon width being Γ µ = G 2 F m 5 µ /(192π 3 ). For the Xq d c operator, we have only a contribution to A LL since only left-handed leptons take part in the new physics couplings. We obtain the following effective operators for the UV completion models (D), (L) and (Q), respectively: Note that we generally a factor of two larger contribution since two electrons are identical.
We now summarize the results for X e c here. We have two UV completion models (L) and (E), as defined in Eq. (II.16) and (II.17), respectively. For the model (L), we have +2H(m L , m L , mνi, mνj ) + 2H(m ν i , m ν j , mL, mL) , For the model (E), (2H(m X , m X , mẼ, mẼ) + 2H(m E , m E , mx, mx)) , where the index j runs over only the second and the third generation since the indices in λ E couplings are antisymmetric.
We summarize the µ − → e − e + e − constraints in Table VIII Fig. 1. Here, we denote scalar fields by φ and fermion fields by ψ.
for the model (L) and for the model (E).
are the coefficient of the superpotential term, which is factorized by a flavor-dependent coefficient λ ijkl and a purely gauge-group dependent Clebsh-Gordon coefficient c abcd .
The three-and four-body decays of an R-parity odd scalar φ 1 or an R-parity odd fermion ψ 0 are shown in Fig. 24 (identical to the diagram Fig. 1, though with the particles labeled now with numerical subscripts for notational clarity in what follows). We parameterize the ordinary MSSM interaction among ψ 0 , φ 1 and ψ 5 by where ψ 3 , ψ 4 and ψ 5 are SM fermions, and g 1 and g 2 are the coefficients. Here, we again use the collective notation for gauge and flavor indices using I = (i, a), J = (j, b) and K = (k, c). g 1 and g 2 are factorized into a flavor-dependent coupling y 1 and y 2 , and a Clebsch-Gordon coefficientc for the gauge group. We will take ψ 3 , ψ 4 and ψ 5 to be massless since they are SM fermions, ignoring top quarks in the final state. φ 2 will be the scalar particle of an ADM chiral multiplet X. In natural ADM scenarios, the mass of φ 2 will be around 10 GeV. We can additionally simplify resultant expressions if we treat φ 2 as being massless.

Three-Body Decay Through a Contact Interaction
The spin-averaged amplitude square for the process of Fig. 24a is given by where d IJKL is the coefficient of the effective superpotential operator in Eq. (B.1), and I, J, K and L denote the gauge and flavor indices collectively for φ 1 , φ 2 , ψ 3 and ψ 4 , respectively.
Here, the notation p X implies the momentum of particle X. We average the amplitude squared over the initial states of the decayed particle, so we have the number of internal degrees of freedom N 1 of φ 1 in the denominator. For example, if φ 1 is a color-triplet SU (2)doublet scalar particle, N 1 is 3×2 = 6. Then, the differential decay width for the three-body decay process can be expressed in terms of invariant masses: where m 23 = (p 2 + p 3 ) 2 and m 34 = (p 3 + p 4 ) 2 . The limits of integration for obtaining the total decay width is determined by the kinematic constraints on the system. In general cases   By integrating over the domain, we obtain the total decay width Note that we factorize the coupling factor i,j,k,l |d ijkl | 2 into the flavor-dependent coupling squared i,j,k,l |λ ijkl | 2 and the group theoretical factor C SU (2) C SU (3) assuming only SU (2) and SU (3) groups are relevant. In Table IX, we summarize C SU (2) and C SU (3) for various possible combinations of the representations of participating particles.

Four-Body Decay Through An Intermediate Off-Shell Particle
Next we consider the case of Fig. 24b. The spin-averaged amplitude square is For nonzero m 2 , the analytic result from the integration in Eq. (B.10) is rather complicated. For the most non-degenerate cases where SUSY particle mass difference is larger than the typical ADM mass (∼ 10 GeV), we can safely assume that m 2 = 0. In such cases, the total decay width has a simplified form: where we factorize the coupling factor (g * 1 g 1 + g * 2 g 2 )(dd * ) into the flavor-dependent coupling squared in terms of y 1 and y 2 defined in Eq. We summarize the experimental observables used for the ATLAS 0 lepton+2-6 jet+MET and 1-2 lepton + 3-6 jet + MET analyses in the following. • p T (j i ) : the transverse momentum p T of the i-th hardest jet in p T size ordering.
Without →, it implies the magnitude.
• ∆φ(obj, E miss T ) : Azimuthal angle between p T of a given object (jet or lepton) and p miss T .
• m eff (nj) : Effective Mass with the hardest n jets in p T size ordering. m eff (nj) = p T ( )+ i=1,...,n p T (j i ) +E miss T including all signal leptons. In the 0 lepton analysis, m eff (N j) means N = 2, 3, 4, 5, 6 for channel A,B,C,D and E, respectively. In the 1-2 lepton analysis, m excl. eff is defined similarly.
• m eff (incl.) : Inclusive Effective Mass. Effective mass defined with all jets with p T > 40 GeV for the 0 lepton analysis, or with all signal jets for the 1 lepton analysis.
• N b−tag : Number of b-tagged jets. • ∆R min (jet, ) : The minimum of ∆R = ∆η 2 + ∆φ 2 between the lepton (for a single lepton event) and each signal jet.
• m CT : Contransverse Mass of the two b-jets (for 2 b-jet events) defined by m 2 Appendix D: evchain: Subprocess Chaining for Event Generation The event generation that is required for the analyses we have carried out in this paper has a few technical challenges. As we see in Figs. 9 and 10, the cascade decay from the gluino and/or the squarks gives rise to a large number of outgoing particles at parton level, so that the phase space becomes very high-dimensional. In addition, the LOSP decays through a non-renormalizable interaction, and especially the neutralino LOSP leads to a 4-body decay through an intermediate off-shell squark or slepton. We also have exotic color vertices that involve color index contraction with the invariant tensor ijk (i, j, k's are color indices) in the case of the u c d c d c models.
Such technical challenges strongly restrict the choice of available tools. As of now, nonrenormalizable interactions and exotic color vertices can be treated successfully by using MadGraph5 [39]. However, MadGraph5 generates events by a Monte Carlo integration of   the matrix element over the full phase space, and with a higher multiplicity of final state particles, the integration often leads to unbearably slow performance and a big accumulation of error. This problem becomes worse if we have several on-shell particles in the process with narrow decay widths since more careful sampling near on-shell poles is needed for a given required accuracy, which will take more sampling iterations and will thus be more prone to numerical errors.
Therefore, it is much more desirable to generate events by splitting a process into a few subprocesses: production channels and decay modes, and to connect the subprocesses into a single big event by doing appropriate transformation. Many Monte Carlo event generators indeed do the job in this way. For MadGraph5, an external tool called BRIDGE is designed to address this issue [49]. However, as far as we know, the BRIDGE tool is restricted to 2-body or 3-body decays for each decay subprocess, and it is not clear whether the tool has been actively maintained with the recent rapid changes of MadGraph5.
We address this difficulty by creating our own in-house tool called evchain [42]: an event chaining tool that automatically orders MadGraph5 event generation for each subprocess and combines resultant Les Houches Event (LHE) format files [50] into a single LHE format file by doing appropriate Lorentz transformations and color flow number adjustments.
Although the current version is tightly incorporated with MadGraph5, the general idea of evchain is not restricted to MadGraph5 since we treat each subprocess as a module with an interface of incoming and outgoing particles. Insofar as incoming and outgoing particle  types are matched, any event generator with any specific process can be used for generating each subprocess. We also note that we do not aim to provide an automatic decay width calculation, differently from BRIDGE. The total decay width must be provided by MadGraph5 or equivalent, while a relative branching ratio in one specific subprocess is automatically given by actual event generation. By this design choice, we simplified program requirements and we were able to generalize easily to any N-body decay processes. In the following, we describe the tool in more detail.
evchain works as a "meta-event-generator" that supervises MadGraph5 event generation for subprocesses. In Fig. 25, we show the overall pipeline of evchain event generation. The tool is written in haskell [51], which is buildable by using ghc 7.4 or higher [52]. evchain currently exists in a library form, so a user makes a program executable linked with evchain.
In the source code of the user's program, the total event process is specified as a haskell tree data structure. The specification language as an Embedded Domain Specific Language (EDSL) for evchain inside the haskell program is self-explanatory. We provide one example of such a specification description in Fig. 26, which is gluino pair-production of the q d c model with neutralino LOSP as shown in Fig. 26. A total process is a production process module with two incoming particles and arbitrary number of outgoing particles. Each outgoing particle can be either a terminal particle or a decay process, which is a module with one incoming particle and an arbitrary number of outgoing particles, where again an outgoing particle of a decay process is either a terminal particle or a decay process, re- cursively. An incoming/terminal particle is specified by a list of PDG codes, so that we can define a collection of particles as incoming or outgoing particles for convenience. Each subprocess is mapped into MadGraph5 processes. In the example, the total process is defined in total process, which has decay gluino, and decay gluino is again defined by decay neutralino. madgraph process map defines actual MadGraph5 commands for each subprocess.
When running, the program will first prepare MadGraph5 directories for each subprocess.
As shown in Fig. 25, the on-shell particles (denoted as i, j, k, l in the figure) that connect mother and daughter subprocesses can be multiple particles. evchain automatically prepares for all of the cases as different working directories and avoids a name clash by making different hash numbers for distinct subprocesses and particles. Since the same hash number is produced for the same process specification, the preparation step can be efficiently done only once for repeating event generations with different parameter sets. evchain provides a configuration method for customizing the directory paths of relevant tools and working directories, which is adjustable for various cluster computing setups.
After the preparation step, the event generation is done in two stages: (i) generating LHE event files for each subprocess in the order of subprocess dependency, (ii) combining LHE event files into a single LHE file to pass to the rest of the event generator (event file sanitization, parton shower and hadronization using PYTHIA, and detector simulation using PGS). evchain facilitates an event counter and classifier. In every step after finishing each subprocess event generation, evchain counts the number of outgoing particles, and orders the next dependent subprocess event generation for only the required number as determined by the previous step. Once all of the subprocess event generation is done, the combining routine runs through all events of the root subprocess, and recursively finds