WIMP Cogenesis for Asymmetric Dark Matter and the Baryon Asymmetry

We propose a new mechanism where asymmetric dark matter (ADM) and the baryon asymmetry are both generated in the same decay chain of a metastable weakly interacting massive particle (WIMP) after its thermal freeze-out. Dark matter and baryons are connected by a generalized baryon number that is conserved, while the DM asymmetry and baryon asymmetry compensate each other. This unified framework addresses the DM-baryon coincidence while inheriting the merit of the conventional WIMP miracle in predicting relic abundances of matter. Examples of renormalizable models realizing this scenario are presented. These models generically predict ADM with sub-GeV to GeV-scale mass that interacts with Standard Model quarks or leptons, thus rendering potential signatures at direct detection experiments sensitive to low mass DM. Other interesting phenomenological predictions are also discussed, including: LHC signatures of new intermediate particles with color or electroweak charge and DM induced nucleon decay; the long-lived WIMP may be within reach of future high energy collider experiments.


Introduction
The cosmic origins of baryon and dark matter (DM) abundances have been long-standing puzzles in particle physics and cosmology. In most proposals, the explanation for DM and baryon abundances today are treated with separate mechanisms. Meanwhile, the observation that their abundances are strikingly similar, Ω DM /Ω B ≈ 5 [1], presents a coincidence problem, and suggests a potential connection between DM and baryons in the early Universe. These together form a triple puzzle about matter abundance in our Universe.
The WIMP miracle, i.e. through thermal freeze-out, DM with weak-scale interactions and masses gives the correct DM abundance today, has been a leading paradigm for DM model-building. The WIMP paradigm does not address the DM-baryon coincidence. Meanwhile, conventional WIMPs have been increasingly constrained by indirect/direct detection and collider experiments [2][3][4]. This has led to the proliferation of exploring alternative DM candidates beyond of the WIMP paradigm. Asymmetric dark matter (ADM) [5][6][7][8][9][10] is one alternative to WIMP DM, inspired by the DM-baryon "coincidence". In this framework, the DM particle is distinct from its antiparticle, and an asymmetry in the particle-antiparticle number densities is generated in the early universe. Subsequently, the symmetric component is annihilated away by efficient CP-conserving interactions, leaving the asymmetric component to dominate the DM density today. The core idea of ADM is based on relating DM and baryons/leptons, through shared interactions in the early Universe. The generation of the initial DM or baryon asymmetry for ADM often requires a separate baryogenesis-type of mechanism. In general ADM models do not possess the attractive merit of the WIMP miracle in predicting the absolute amount of matter abundance.
WIMP DM and ADM are both appealing proposals that address some aspect of the aforementioned triple puzzle about matter. However, it is intriguing to explore the possibility of a unified mechanism that combines their merits and addresses all three aspects of the puzzle simultaneously. Recently a few attempts have been made in this direction [11][12][13][14][15][16][17][18]. Among these existing proposals, [12] is highly sensitive to various initial conditions, while both [13] and WIMP DM annihilation triggered "WIMPy baryogensis" [11] have sensitivity to washout details. The mechanism of "Baryogenesis from Metastable WIMPs" [14] was then proposed as a alternative where the prediction is robust against model details: the baryon asymmetry is generated by a long-lived WIMP that undergoes CP-and B-violating decays after the thermal freeze-out of the WIMP. Such models also provide a strong cosmological motivation for long-lived particle searches at the collider experiments and have become a benchmark for related studies [19][20][21]. However, the original model of Baryogenesis from Metastable WIMPs does not involve specifics of DM, only assuming that DM is another species of WIMP that is stable, and thus the DM-baryon coincidence is addressed by a generalized WIMP miracle which is not fully quantitative. From model building perspective it would be more desirable to further develop a framework which incorporates the merits of [14] as well as the details of DM, and predicts a tighter, more precise connection between Ω DM and Ω B . There are two possible directions to pursue for  this purpose: consider a WIMP DM that closely relates to the metastable baryon-parent WIMP in [14] (e.g. in the same multiplet or group representation), or consider a further deviation from [14] where the post-freeze-out decay of a grandparent WIMP generates both DM and baryon asymmetries, thus DM falls into the category of ADM. In this work we explore the latter possibility, which we naturally refer to as "WIMP cogenesis". The WIMP of our interest is of conventional weak scale mass or moderately higher (up to ∼ 10 TeV). We aim at constructing a viable WIMP cogenesis model with the following guidelines: • UV complete, only involves renormalizable interactions; • ADM X and baryon asymmetries are generated in the same decay chain (instead of two different decay channels with potentially arbitrary branching ratios) so as to have the least ambiguity in predicting their "coincidence"; • The model possesses a generalized baryon/lepton number symmetry U (1) B(L)+kX that is conserved. k is a model-dependent O(1) rational number that parametrizes the ratio of ADM number to baryon (lepton) number produced in the decay chain. These first two guidelines distinguish our model from some other existing ADM proposals based on massive particle decay, such as [22][23][24]. In particular, the second guideline leads to a neat prediction of the ADM mass: where m n ≈ 1 GeV is the neutron mass, k = 2 in the benchmark models we will demonstrate, the baryon distribution factor c s = n B n B−L ∼ O(1) depends on whether the EW sphaleron is active when the decays occur, and will be elaborated in Sec. 2.1. Given that Ω X Ω B ≈ 5 from observation, Eq. 1.1 generally predicts m X in the GeV range. The third guideline, i.e., the idea of DM and baryon sharing a conserved global baryon number symmetry is also seen in e.g., [24][25][26].
The schematic idea of this new mechanism is illustrated in Fig. 1, which consists of a sequence of three stages that satisfy each of the three Sakharov conditions in order.
WIMP miracle relic abundance predicted for the grandparent WIMP that will be inherited by Ω X and Ω B when the WIMP decays: 2. C-and CP-violating decay of the WIMP to intermediate states of exotic baryons/leptons. This occurs well after the freeze-out and before BBN. The asymmetry between B and B, or between DM and anti-DM originates from this stage. The rest of the paper is organized as follows. In Section 2, we consider a model where the WIMP decay products are SM quarks and ADM leading to direct baryogenesis, where the related general formulations and numerical results will be given. Section 3 introduces a leptogenesis model where the WIMP directly decays to leptons and ADM, which induces the baryon asymmetry by sphaleron effect provided that the decay occurs before EW phase transtion. Experimental signatures and constraints are discussed in Section 4. Section 5 concludes this work.

WIMP Decay to Baryons and ADM
In this section, we explore a specific model which directly produces a baryon asymmetry along with ADM via SM B-violating interactions. The fields and interactions are introduced followed by discussions on how Sakharov conditions are met by their interactions and the related cosmological evolution. This section ends with numerical analyses of the parameter space for these types of models. Figure 2: Feynman diagram of the WIMP decay chain producing baryon and DM asymmetries.

Model Setup
We extend the SM with the following Lagrangian: These states subsequently decay to produce asymmetries between udd and χ and their conjugates. The Feynman diagram for the decay chain is shown in Fig. 2. The above symmetries allow additional interactions between the Majorana singlet and the SM throughLHY 1 which permit decays Y 1 → Hl. It is technically natural for this coupling to remain small such that Y 1 decays to φψ are dominant. Alternatively, the Yukawa interactionLHY 1 is forbidden by imposing an exact Z 4 symmetry with the following charge assignments: Y 1 charge −1, ψ, φ, χ charge i, and all SM charges are +1. This Z 4 symmetry also ensures the stability of asymmetric dark matter candidate χ.
In order to give a concrete example of the annihilation processes of Y 1 that leads to its freeze-out, a U (1) gauge symmetry and the associated Z gauge boson is also introduced. Meanwhile this U (1) provides processes that deplete the symmetric component of χχ Figure 3: Annihilation processes that potentially contribute to Y 1 freezes out. leaving an asymmetry dominated DM abundance when m χ > m Z . The annihilation processes for Y 1 , χ are shown in Figs. 3, 4. Although χ annihilation to dd through φ exchange is available, it is generally insufficient given the constraints on couplings from DM direct detection [27]. With these interactions we can also define a generalized global baryon symmetry U (1) B+2X with conserved number G. We will further explain the G charge assignments in Sec. 2.4. The generalized baryon and other charges are given in Table 1. Table 1: Quantum numbers of the relevant particles in WIMP cogenesis with baryons.
After the decay processes have taken place, efficient matter-antimatter annihilations deplete theχ number density to near triviality. This leaves an abundance of two χ's for every unit of baryon number (udd). The shared interactions fix the relationship between the asymmetries of baryons and χ. This then fixes the ADM χ mass according to Eq. 1.1. It is apparent that n B−L /n DM = 1/2 for this model. c s ≡ n B n B−L characterizes the potential effect of redistribution among B and L numbers due to sphaleron interactions. If the asymmetry is produced after the electroweak phase transition (EWPT), c s = 1. If the asymmetry is produced before EWPT [28], SM charged particles and φ, ψ, χ are in chemical equilibrium and their chemical potentials are related by the active gauge and Yukawa interactions as well as sphaleron processes. With the SM alone, B −L is preserved, while in this model the linear combination B − L + 2X is conserved. Putting all these together we can solve for c s . As explained in Appendix A, c s has a dependence on the masses of ψ, φ relative to the temperature at EWPT, T EWPT . Given the large uncertainty in determining T EWPT , we consider two limits of interest which would define the range of the c s values: m φ,ψ T EWPT and m φ,ψ T EWPT . The solutions for the two limits are (details given in Appendix A.1): where N f and N H are the number of generations of fermions and number of Higgs, respectively. For matter asymmetries produced before EWPT with N f = 3 and N H = 1 Eq. 2.2 gives c s = 16/55 for m φ,ψ T EWPT or c s = 28/79 for m φ,ψ T EWPT . Combining these and Eq. 1.1, we find that m χ = 2.5 GeV if the asymmetry is produced after EWPT and m χ ≈ 0.72 GeV − 0.89 GeV if produced before EWPT.
Next we demonstrate how WIMP cogenesis satisfies the Sakharov conditions [29] for generating a primordial asymmetry in both baryon and DM sectors.

WIMP Freezeout and the Generalized WIMP Miracle
The thermal freeze-out of Y 1 provides the out-of-equilibrium condition for asymmetry generation upon the subsequent decays.
The freeze-out of Y 1 proceeds through Z mediated annihilation to the hidden sector states φ, ψ, χ. There is an additional annihilation to Z Z when m 1 > m Z . The annihilation rate is given by Γ In the case that m 1 < m Z , annihilation to Z is not kinematically allowed and the swave cross section is suppressed in both fermionic and scalar channels. In the case that m 1 > m Z , there are the (dominantly) p-wave contributions from Y 1 annihilating to ψ, χ, φ and the s-wave contribution from Y 1 annihilating to Z Z . The freeze-out occurs at T f.o. when the Y 1 annihilation rate falls below the Hubble expansion rate, which can be estimated as follows: where we parametrize the s-and p-wave contributions to the thermally averaged cross- GeV is the Planck mass, and g * is the effective degrees of freedom [30]. The step function Θ(m 1 − m Z ) approximation represents the Figure 5: Loop diagrams interfere with the tree-level diagram to produce a nonzero asymmetry between Y 1 decays to φ/ψ and φ * /ψ threshold when the Z Z annihilation channel opens up and s-wave contribution becomes significant. The Z width Γ Z in Eq. 2.4 depends on model specifics and has the most impact around the resonance region where m Z ≈ 2m Y 1 and Γ Z = (Z decay to φ, ψ, χ included). For TeV-scale WIMP mass and coupling strength g ∼ 0.05, Y 1 freezes out as a cold relic with T f.o. ∼ m 1 15 , and its comoving density where g * S is the effective number of degrees of freedom in entropy. Note that if Y 1 does not decay, its would-be relic abundance today Y τ →∞ Following the schematic illustration in Fig. 1, we expect the observed abundances of DM and baryons to be proportional to the freeze out abundance found in Eq. 2.5.

C and CP Violation
C-and CP-violation are achieved by the decay of the Majorana fermions Y 1 following their freeze out. The CP asymmetry arising from Y 1 decays is defined as The denominator of Eq. 2.6 can be approximated as twice the tree-level decay rate, Γ 0 (Y 1 → φψ). For complex WIMP Yukawa couplings, interference between the tree-level and looplevel Feynman diagrams shown in Fig. 5 gives rise to a non-vanishing numerator in Eq. 2.6. Although in analogy Y 2 decay may generate a CP asymmetry as well, its contribution to the DM/baryon asymmetry is generally washed out with m 2 > m 1 and |η 1 | |η 2 | (leading to sizable 1 but in-equilibrium decay of Y 2 ).
In many baryogenesis models based on massive particle decay, the decay products are much lighter than the decaying particle and thus can be approximately taken as massless. For WIMP cogenesis we include full mass-dependence since WIMP freeze-out generically requires With this in mind and using the Optical Theorem, we find the CP-asymmetry: . The factor of 3 represents the color multiplicity. Note this is the contribution to the CP-asymmetry of Y 1 decays to a single generation. To simplify our analyses, we assume the three flavors of φ and ψ are (nearly) degenerate in mass. Under this assumption, there is an additional multiplicative factor of 3 to account for the contributions Y 1 decays to the all flavors. Also note that Eq. 2.7 reproduces the familiar CP-asymmetry result for leptogenesis [32] in the limit of m 1 m ψ,φ . The above expression shows how the asymmetry is intimately tied to the mass and couplings of the Y 1 , m φ , and m ψ . In Section 2.6, we show contours of constant Ω DM in the (m 1 , g) plane with 1 taking the form of Eq. 2.7.

Generalized Baryon Number Conservation and Generation of Asymmetries
In order for a matter asymmetry to be produced, the corresponding baryon or DM number must be violated by the interactions in the model. In this model both SM baryon number and DM number are violated in the last stage of the decay chain as illustrated in Fig. 2. Nevertheless a generalized baryon number G = B + 2X is conserved (remains 0 assuming no pre-existing asymmetry) thanks to the ADM χ and baryonic matter sharing interactions through intermediate states φ, ψ.
The CP-violation in Y 1 decay (Section 2.3) produce an asymmetry between intermediate states (i.e., baryon/ADM parents), φ and ψ and their conjugates, which is inherited by their decay products, χ and udd, and ultimately becomes the source of all (asymmetric) matter today. The changes in the generalized baryon number for each decay process are given by: where we have used the fact that for quarks G q = B q = 1/3. Furthermore, due to the Majorana nature of Y 1 , G Y 1 = 0. Then requiring all the above interactions to conserve G, we may obtain the solutions for the charge assignments: Table. 1. The net result of the decay chain is udd+χχ, violating the SM baryon number and DM number by 1 and 2 units respectively, while the net generalized baryon number G is conserved. So the generalized baryonic charge carried by the ADM density cancels that of a baryon asymmetry density and the universe has trivial net generalized baryon number.

WIMP Decays and Production of Matter Asymmetries
We consider the asymmetry grandparent, Y 1 , decays well after its freeze-out but before BBN, i.e., 1MeV T Y 1 ,dec T f.o. , so that we can treat the freeze-out and decay-triggered cogenesis as nearly decoupled processes and retain the conventional success of BBN. The , the freeze-out occurs around the temperature T f.o. ∼ 200 − 300 GeV for TeV-scale mass Y 1 . The requirement that it decay between freeze-out and BBN gives the range of allowed decay couplings: 10 −15 |η 1 | 10 −9 . For simplicity we assume the subsequent SM B-and DM χ-number violating decay of φ, ψ to udd, χ are prompt relative to H, i.e., in equilibrium, so that the matter asymmetries are immediately distributed upon Y 1 decay. This assumption also simplifies the Boltzmann equations, since n ψ , n φ can be set as equilibrium distribution.
With Y 1 freeze-out occurring well before its decay, the late-time evolution of comoving density Y Y 1 satisfies the following Boltzmann equation for a decaying species: We now write down the Boltzmann equations governing the evolution of φ, ψ number densities. This evolution is determined by three processes: CP-violating Y 1 decays and their inverse, Y 1 mediated φ/ψ scattering to their conjugates (and vice versa), and CPconserving φ/ψ (as well as their conjugates) decays.
For convenient notations, we define the generalized baryon number density n G which is the sum of φ/ψ asymmetries: Once simplified, the φ asymmetry, n φ − n φ * ≡ n ∆φ evolves according tȯ where 1 is the CP asymmetry given in Eq. 2.7, Γ 's are thermally averaged decay rates, , and n γ is the photon radiation density. The equation governing the cosmological evolution of the ψ asymmetry iṡ We can see that the main difference between the φ and ψ Boltzmann evolution is that the term governing ψ decays changes sign and there is no term for ψ-number increasing φ decays. Note that in these evolution eqs., the terms proportional to Y G can potentially wash out the produced asymmetries (inverse decay of Y 1 and the 2-2 scattering). Assuming prompt φ, ψ decays, we set n φ = n eq φ , n ψ = n eq ψ , such that the contribution from these decays vanish. Additional potential washout processes of uddχχ → Y 1 and uddχχ →ūūdχχ are negligible owing not only to Boltzmann suppression, but also to the high dimension of the effective operators responsible for these processes.
Based on Fig. 2 and our earlier discussion, upon decays of φ and ψ, n G or Y G leads to baryon asymmetry density n B and DM asymmetry density n χ with the robust relation: n G = (n ∆φ + n ∆ψ )/2 = n B = n χ /2 (2.14) The general solution of the Boltzmann equations gives the comoving generalized matter asymmetry Y G today: where Γ W is the rate of processes washing out the asymmetry. Assuming that there is no primordial asymmetry before WIMP cogenesis occurs, Y initial B = 0. Taking our simplifying assumption that Y 1 decays well after its freeze out, we automatically work in the weak washout regime and drop the exponential factor in Eq. 2.15. This yields a robust solution depending solely on the would-be WIMP miracle abundance of Y 1 and the CP asymmetry Provided efficient annihilation that depletes the symmetric component of χ, the above asymptotic solution of n B , n χ give rise to the baryon and DM abundances today: where s 0 = 2970 cm −3 is the radiation entropy density today and ρ c = 3H 2 0 /8πG ≈ 3.5 × 10 −47 GeV 4 is the critical energy density, m n ≈ 1 GeV is the SM baryon mass.
Due to the color charges of φ and ψ, their masses are effectively constrained by collider experiments (see Section 4.1). This immediately constrains the mass of the lighter of the Majorana fermion m 1 3 TeV such that Y 1 → φψ remains kinematically open for m ψ m φ ∼ TeV. The symmetric component of ADM is efficiently depleted through annihilations to the hidden sector, e.g. χχ → Z Z , which requires m χ > m Z such that the annihilation process is kinematically open. Taking benchmark values of m 2 ≈ 10 TeV, m φ ≈ 1.2 TeV, m ψ ≈ 1.7 TeV, and m Z ≈ 0.5 GeV, with Mathematica [33] we plot contours of Ω DM h 2 = 0.120 ± 0.001, Ω B h 2 = 0.0224 ± 0.0001 [1] in the (m 1 , g) plane, as shown in Fig. 6. Because the baryon asymmetry is directly produced by Y 1 decays, it may be produced before or after the EWPT. Comparing the case of Y 1 decay before vs. after EWPT, we see that a smaller U (1) gauge coupling g is required to produce the observed DM abundance when the asymmetry is produced before EWPT due to the sphaleron's moderate washout of the SM baryon asymmetry. The CP-asymmetry produced by Y 1 decays, as given in Eq. 2.7, must be sufficient to produce the observed abundances of DM and baryons for g ∼ g weak and m 1 ∼ O (TeV). To give an example, with Y 1 Yukawa coupling η 2 = 1, m 2 = 10 TeV, m 1 = 4 TeV, m ψ = 1.7 TeV, and m φ = 1.2 TeV the CP-asymmetry is 1 ≈ 6%.

WIMP Decay to Leptons and ADM
In the following section, we present a WIMP cogenesis model that directly produces a lepton asymmetry. As with other models of leptogenesis, the asymmetry must be produced before EWPT such that sphalerons may transfer the lepton asymmetry into the observed baryon asymmetry. Here, we introduce the fields, interactions, and discuss the differences from WIMP cogenesis with baryons presented in the last section.

Model Setup
The first two stages of WIMP cogenesis with leptons are identical to the model discussed above: the Majorana fermion, Y 1 , undergoes freeze-out via U (1) mediated annihilations followed by out-of-equilibrium and CP-violating decays to (unstable) intermediate states φ and ψ. Again, the Majorana fermion, Y 1 , is a SM gauge singlet, but now the intermediate states are charged under SM SU (2) L ×U (1) Y , such that the decays ψ → χh and φ → χ are possible, where h, are the SM Higgs and left-handed leptons, respectively. The Lagrangian is identical to that in Eq. 2.1 up to modification of the Yukawa interactions: where L is the left-handed lepton doublet, H is the Higgs doublet, i = 1, 2, 3 is flavor indices, and α ijk is antisymmetric in flavor indices. Note that this model possesses a U (3) flavor symmetry which prevents new sources of FCNC. As discussed in Sec. 2 the U(3) symmetry is optional provided that 10 −7 α 0.1, while the DM direct detection signal may be absent with such small couplings. The charge assignments are summarized in Table  2. A Z 4 symmetry is imposed to ensure DM stability and prevent Y 1 decay through Y 1 LH portal. The decay chain is illustrated in Fig.7. The CP asymmetry is generated by the same process as illustrated in Fig. 5. In analogy to WIMP cogenesis with baryons, the shared interactions through intermediate φ, ψ permit a generalized global lepton number symmetry U (1) L+2X with conserved charge G . The corresponding charge assignment is: G χ = 1/2, G Y 1 = 0, G φ = 1/2, and G ψ = −1/2. As shown in Fig. 7, the second stage of of the decay chain violates SM lepton A key difference from the model in Sec. 2 is that the asymmetry must be produced before EWPT such that sphalerons convert the lepton asymmetry into the observed baryon asymmetry, i.e., T f.o > T dec T EWPT . In this case, χχ depletion may occur through φ-mediated annihilation to leptons and/or through the annihilation to Z Z (if kinematically allowed) in analogy to our model where WIMPs decay to baryons. Due to the weaker constraints on ADM-lepton couplings (relative to ADM-quark couplings) [27] χ annihilation into leptons alone can be sufficient for depleting the symmetric component. We can then apply most results from Sections 2.2-2.5 by analogy, with some modifications. The most straightforward change is the dropping of the color factor in the CP-asymmetry of Eq. 2.7. More subtle is the change to the DM mass prediction. Due to the different Yukawa interactions, the prediction of the relation c s = n B n B−L in this model differs from that in the WIMP cogenesis with baryons. In addition, as noted, WIMP cogenesis with leptons needs to occur before EWPT when sphaleron processes are active. The limits of interest are the same as those detailed in the previous section. The solutions in these two limits are (see Appendix A.2) where N F and N H are again the number of generations of fermions and Higgs, respectively. With N f → 3 and N H → 1 in Eq. 3.2 with gives c s = 28/103 for m φ,ψ T EWPT or c s = 28/79 for m φ,ψ T EWPT . All together, the relation between lepton, baryon, and ADM comoving densities is akin to Eq. 2.16: cs Y B . Following the same procedure as Sec. 2.5, in the weak washout regime we obtain ADM abundance with the same form as Eq. 2.17: The observed ratio Ω DM /Ω B ≈ 5 fixes the mass of the ADM candidate m χ = 5cs 2|cs−1| m n . With the values for c s given in Eq. 3.2, the range of χ masses is 0.93 − 1.37 GeV.

Numerical Results
We now scan model parameters to find viable region giving the observed matter abundnances. The constraints arising from colliders on exotic electroweak states (φ and ψ in this model) are less stringent than those on exotic colored states, allowing us to explore sub-TeV masses for φ, ψ, and even the grandparent, Y 1 . There is a caveat to this: if the mass of the decaying WIMP is too light, it freezes out after the EWPT, thus its lepton asymmetry producing decays would occur when sphaleron processes, necessary for the conversion into the observed baryon asymmetry, are no longer effective. For Y 1 decays to happen after freeze-out, but before EWPT, we require 100 GeV T Y,dec T f.o . With a m 1 ∼ 1 TeV, the freeze-out occurs at or just after EWPT, according to Eq. 2.3.
Since ψ contributes to the matter asymmetry via ψ → χH, it requires m ψ > 125 GeV. Similarly, for φ decays to O(GeV) mass χ and SM leptons, m φ O(GeV) is required. Fig.  9 shows the DM abundance as a function of U (1) gauge coupling and m 1 , in the range of 1 TeV < m 1 < 10 TeV. In these numerical analyses, we take the functional form of Eq. 2.7 and Eq. 2.5 for the CP-asymmetry and freeze-out abundance of Y 1 , respectively. Fig. 9 illustrates the viable model parameter regions rendering the observed matter abundances. Since a light Z with m Z < m χ is not essential for depleting symmetric χ in this leptogenesis model, we consider both cases of heavy and light Z , with dashed and solid lines respectively. The dip and peak in the dashed lines (heavy Z case) result from the resonance region (when m Z ≈ 2m 1 ) and the kinematic threshold of opening Z Z annihilation channel (when m Z ≈ m 1 ), respectively. The shaded regions are not viable, as these correspond to Y 1 freeze-out after EWPT. Although for benchmark values shown in Fig. 9 this region is avoided, for smaller m φ and m ψ this region becomes relevant. LHC searches for squarks,q, and gluinos,g, in the presence of neutralino LSPχ 0 1 are relevant for constraining the masses of φ and ψ in our model. In particular the bound in  the massless LSP limit applies since the corresponding particle in WIMP cogenesis, χ has a mass of O(GeV), significantly smaller than those of φ and ψ. Specifically, both ψ andg decay to jj + / E T via intermediate colored scalars with production cross sections differing only by a group theory factor, for which we correct. Simplified model searches at 13 TeV from CMS with 137 fb −1 of data place bounds on the gluino mass in the presence of a massless LSP, neutralinoχ 0 1 [34]. The lower bound on the ψ mass is m ψ 1.3 TeV which is from the gluino bound with the different group theory factor in cross section taken into account. In the case where the gluino decays to top quarks via intermediate top squark, the bound on the gluino mass is a bit stronger: mg ≈ m ψ 1.5 TeV [34]. LHC searches for mass degenerate squarks bound the mass of φ, since both squarks and φ decay to j + / E T . The recent searches at CMS place bounds on three generations of mass degenerate squarks of mq 1.13 TeV assuming massless LSP [34]. Since we make the assumption of three flavors of mass degenerate exotic scalar quarks φ i in WIMP cogenesis, we apply this bound directly, leading to m φ 1.13 TeV.
Thus, for successful models where a matter asymmetry is produced from WIMP decays directly to baryons and ADM, the intermediate state masses are bound from below as m ψ m φ ∼ 1 − 2 TeV, requiring m 1 ≥ m φ + m ψ 3 TeV.
In this model, φ and ψ are both electroweak doublets. Thus at the LHC the neutral and charged components of these new states are produced through EW processes with intermediate W, Z bosons, and subsequently decay as ψ 0 → hχ, ψ ± → W ± χ, φ ± → ± χ, φ 0 → νχ. Consequently, these lead to signals:  Figure 13: Diagrams relevant for φ searches at hadron colliders (WIMP cogenesis with leptons).
LHC searches for charginosχ ± and charged sleptonsl ± bound the charged components of ψ, and φ, respectively, while searches for heavier neutralinosχ 0 2 bound the neutral component of ψ. Specifically, searches forχ ± → W ±χ0 1 produces the same collider signature as decaying ψ ± ,χ 0 2 → hχ 0 1 the same signature as decaying ψ 0 , andl ± → l ±χ0 1 the same signature as decaying φ ± . Since we assume mass degeneracy among the different generations and components of φ and ψ, the relevant LHC searches are in the cases of mχ± = mχ0 2 and mẽ = mμ = mτ . At 13 TeV, ATLAS places bounds on the masses charginos and neutralinos with 139 fb −1 of data with mχ± = mχ0 2 740 GeV assuming massless LSPχ 0 1 [35]. We apply these bounds directly to the charged and neutral components of ψ: m ψ ± = m ψ 0 740 GeV. With the same set of data ATLAS places bounds on the masses of charged sleptons in the mass degenerate limit of ml 700 GeV [36]. We apply these bounds directly to the charged components of φ: m φ 700 GeV.
Finally, note that just like in the earlier studied WIMP baryogenesis models [14,19], the long-lived WIMP, Y 1 , in WIMP cogenesis (for both the quark and lepton models we presented) is also expected to leave distinctive displaced vertex signatures if it can be produced at a collider experiment (e.g. through qq → Z ( * ) → Y 1 Y 1 ). However, Y 1 is a SM singlet with typically O(TeV) mass which makes it hard to access with the LHC. Nevertheless it may be within reach of future high energy colliders (e.g. [37]) and leave spectacular signatures involving both displaced vertices (baryon asymmetry) and missing energy (ADM).

Dark Matter Direct Detection
As expected in most of asymmetric DM models, sinceχ is depleted to triviality in the early universe, indirect detection rates are negligible. Therefore we focus on the direct detection prospect of χ.
Since the SM quarks are uncharged under the U (1) gauge symmetry, the only available channel for χ to interact with quarks is χd → χd mediated by φ. By integrating out φ in the low energy effective theory, the effective DM-quark interaction operator is leading to spin-independent (SI) interactions between the DM and nucleon. These translate to contributions to a χ-nucleon effective interaction following [38]. The SI χ-nucleon cross section is As we have seen, the DM mass in WIMP cogenesis model is predicted to be in the sub-GeV to GeV range. The strongest current limits on O(GeV) SI DM-nucleon interactions come from DarkSide-50 [2]: for DM masses within 2-3 GeV, the upper limit on the DM-nucleon cross section is 5 − 7 × 10 −42 cm 2 . In the case that the asymmetry is produced before the EWPT, the DM mass is below 1 GeV and the strongest bounds come from CRESST [39]. There is another diagram contributing to χq → χq with the replacements φ 0 → φ ± and ν → l ± .
Specifically for DM masses of 0.5 − 1 GeV, the upper limit on DM-nucleon scattering is between σ SI ∼ 10 −38 − 10 −36 cm 2 . Now we give numerical examples from our model. With α d = α s = 1 and scalar mass at the lower bound provided by colliders, m φ = 2 TeV and m χ = 2.5 GeV, the SI DMnucleon cross section is σ(χN → χN ) ≈ 2×10 −42 cm 2 . This is not only currently safe from the most stringent bound, but also within reach future iterations of DarkSide and other upcoming direct detection experiments [40][41][42]. In the case that m χ = 0.89 GeV, we again take α s = α d = 1 and scalar masses m φ = 2 TeV, we obtain a benchmark value from Eq. 4.1 of σ SI (χN → χN ) ≈ 1.02 × 10 −42 which is well below the bound set by CRESST but can be within reach of future searches for sub-GeV DM such as with the LUX-ZEPLIN [42].
WIMP Decay to Leptons and ADM (Sec. 3) In this model, the dominant process for direct detection come from tree-level χ − e − scattering via φ exchange. The diagram is identical to that for ADM-nucleon scattering in the quark model, with the quarks replaced with electrons. We can estimate the cross section for ADM-electron scattering by integrating out φ: Similar to WIMP cogenesis with quarks, the ADM mass is fixed by the ratio of DM to baryonic matter today. In our example model of WIMP cogenesis with leptons, the ADM mass is m χ ≈ 0.93 − 1.37 GeV. For this mass range, Xenon100 constrains the cross-section of DM-scattering with electrons to be σ SI 1 − 2 × 10 −37 cm 2 [41].
Owing to less stringent collider constraints, the masses of the intermediate states can be lighter in the model of WIMP cogenesis with leptons: m φ , m ψ ∼ 700 GeV. However, we need WIMP cogenesis to occur before the EWPT, when the temperature would be around or below m φ,ψ . Furthermore, the ADM annihilation to leptons is less constrained than annihilation to quarks [27] and we can have α > g. Taking the benchmark parameters of m χ = 0.93 − 1.37 GeV, m φ = 700 GeV and α = 1 gives σ(χe − → χe − ) ≈ 1.1 − 2.4 × 10 −40 cm 2 which is just below the current bound by Xenon100 [41].
There are 1-loop processes in WIMP cogenesis with leptons (Fig. 15), that allow for our sub-GeV ADM to scatter with nucleons at direct detection experiments. However, the loop suppression combined with minimal bounds on sub-GeV DM scattering with nucleons makes the rate well below the sensitivity reach of foreseeable experiments. In the minimal model presented in Sec. 2, a potential signal of B-violating (induced) nucleon decay is highly suppressed and undetectable with foreseeable experiments. However, an observable induced nucleon decay (IND) signature may arise with a minimal, well-motivated extension. We consider the scenario of a light Z with ∼ GeV mass. An additional Higgs, ξ with m ξ ∼ GeV, is generally expected to give Z its mass through spontaneous symmetry breaking of the U (1) . With this introduction of ξ comes a plethora of potential interactions. Of particular interest is the Yukawa interaction ξY 2 χ which then requires ξ carry Z 4 charge i and G ξ = 1/2. This interaction, together with the set of interactions in Eq. 2.1 allows for the possibility of induced nucleon decay, as shown in Fig. 16. The analogous diagram with Y 1 is much more suppressed due to the very small η 1 to ensure a long lifetime of Y 1 . ξ can be a stable subdominant DM, or may decay, e.g. to Z Z if kinematically allowed and subsequently to light SM charged leptons provided a kinetic mixing between Z and photon. The final decay channels from ξ therefore depend on model specifics beyond our minimal model, which we will defer for future consideration. Nevertheless a common feature is that for down-scattering processes, where m χ > m ξ , the outgoing K meson momentum from IND will be larger than those resulting from standard nucleon decays. The IND event topology here resembles that in Hylogenesis [24] while this model is fully renormalizable.

Induced Nucleon Decay
The scattering process of p + χ → K + + ξ effectively proceeds with a dimension-7 operator ∼ α 2 βγη 2 16π 2 m 3 2 ξ(χP R d)(ūP R d), and can be estimated as: This leads to a prediction for the proton lifetime as τ −1 p = n DM σ(p + χ → ξ + π + )v. This model can lead to a proton lifetime that is consistent with current lower bound set by SuperKamiokande searches [43] while within reach of future experiments such as HyperKamiokande [44] and DUNE [45]. A benchmark example is: m χ = 2.5 GeV, m 2 ∼ 1.5 TeV, and all couplings ∼ 1, which lead to τ p ∼ 2 × 10 34 years.

Other Experimental Constraints
As discussed in the Model Setup (Sec. 2.1 and 3), new sources of FCNC are absent due to the U (3) flavor symmetry of the model and thus the model is consistent with related constraints on FCNC. In addition, despite the presence of CP violation source necessary for the asymmetry generation, the model is exempt from the constraints on electric dipole moments (EDMs) for the neutron and electron [46,47] . The reason is that, the interference diagrams (Fig. 5) leading to CP violation do not involve SM quarks or leptons, and the new fields couple exclusively to right-handed quarks or left-handed leptons.
WIMP cogenesis with baryons evades bounds from neutron-antineutron oscillation: the intrinsic interactions in the model and the U (3) flavor symmetry together forbid udd →ūdd conversion at tree-level and 1-loop (alternatively with small couplings without invoking the flavor symmetry). Higher order process is strongly suppressed by loop factors and the TeVscale masses of Y 1,2 , ψ, and φ, even with O(1) couplings.

Conclusion
In this paper we proposed WIMP cogenesis, a novel mechanism which addresses the tripple puzzle about cosmic matter abundance in a unified framework: asymmetric dark matter and a baryon or lepton asymmetry are simultaneously generated from the same decay chain of a freeze-out population of metastable WIMPs. The WIMP plays the role of grandparent for the matter abundance in the Universe, meanwhile the "coincidence" between DM and baryon abundances is automatically addressed via their co-production. Additionally, the WIMP decay chain readily permits DM and baryon asymmetries to inherit a generalized WIMP miracle. The three Sakharov conditions are satisfied in three subsequent stages in order. ADM and baryons (leptons) share a generalized baryon (lepton) number symmetry that is conserved. We present two renormalizable models as benchmark examples realizing the idea, and find that with perturbative couplings and weak-scale masses for the new states, the observed DM and baryon relic densities can be explained while being compatible with relevant constraints. The models neatly predict ADM with mass m DM ∼ 0.7 − 2.5 GeV. These models can lead to testable signatures at a variety of experiments, including (low mass) DM direct detection, nucleon decay and the production of new SM charged particles at the LHC. Furthermore the long-lived WIMP in these models may be accessible with future high energy colliders, leaving spectacular signals by reproducing the cogenesis of matter in the early Universe.
were drawn using JaxoDraw [48]. The authors are supported in part by the US Department of Energy grant DE-SC0008541. YC thanks the Kavli Institute for Theoretical Physics (supported by the National Science Foundation under Grant No. NSF PHY-1748958) for the support and hospitality while the work was being completed.
A Relating Baryon and Lepton Asymmetries for WIMP Cogenesis before Electroweak Phase Transition In this Appendix we derive the relation between baryon and lepton asymmetries for WIMP cogenesis before electroweak phase transition. We will follow the general procedure laid out for the SM [28,49,50], while adding in the effects from new particles in WIMP cogenesis models.

A.1 WIMP Decay to Baryons and ADM (Sec. 2)
Before the electroweak phase transition (EWPT), chemical equilibrium of SM left-handed and right-handed quarks and leptons, Higgs bosons, and new fields introduced by WIMP cogenesis φ, ψ, and χ determines the relationship between number densities of baryons, leptons, and ADM candidate χ. This relationship and the observed ratio Ω χ /Ω B ≈ 5 determines the ADM mass as in Eq. 1.1. In the high temperature plasma of the early universe the quarks, leptons, Higgs, φ, ψ, and χ interact via gauge, Yukawa, and sphaleron processes. The interactions that constrain the chemical potentials in thermal equilibrium are: where i is an index counting the number of generations of fermions and Q i are the LH quarks and L i are the LH leptons.
2. The SU (3) QCD instanton processes lead to interactions between LH quarks and RH quarks u i and d i . These interactions are described by 3. The total hypercharge of the plasma must vanish at all temperatures. In addition to the hypercharge carried by SM states, φ and ψ also contribute, while the magnitude of the contribution depends on their masses relative to EWPT temperature T EWPT . Non-relativistic φ and ψ bear a Boltzmann suppression in their equilibrium density distribution which makes their contribution to hypercharge density negligible relative to relativistic species. Given the unknowns around determining T EWPT and the wide ranges m ψ ∼ m φ , we consider possibilities at two limits: m ψ ∼ m φ T EWPT and m ψ ∼ m φ T EWPT . With m ψ ∼ m φ T EWPT , we have: where N H is the number of Higgs bosons (1 in the SM) and N f is the number of generations of fermions. With m ψ ∼ m φ T EWPT , we have: 4. The Yukawa interactions of the SM O SM ∼Q i Hd j ,Q iH u j ,L i He j and the Yukawa interactions introduced in Sec 2.1 O WIMP ∼ φ idi χ c , β ijk φ iψj u k , while in equilibrium give rise to Since the temperature before the EWPT is much greater than the masses of the quarks, leptons, and χ we take the massless limit where their number densities are n i −n i = 1 6 gµ i T 2 . The baryon, lepton, and χ number densities are n B = 1 6 BT 2 , n L = 1 6 LT 2 , and n X = 1 6 XT 2 , respectively, where With SM alone, the combination of asymmetry B − L is preserved, while in our model B − L + 2X would be preserved. Assuming equilibrium amongst the various generations µ Q i ≡ µ Q , µ L i ≡ µ L , µ e i ≡ µ e , µ q i ≡ µ q , µ φ i ≡ µ φ , µ ψ i ≡ µ ψ allows us to write B = N f (2µ Q +µ u +µ d ), L = N f (2µ L +µ e ). Thus the preserved combination, per generation, is 2µ Q + µ u + µ d − (2µ L + µ e ) + 2µ χ = 0 (A.9) Let us first analyze the case of m ψ ∼ m φ T EWPT . Using the Yukawa interactions of Eqs. A.5 , Eq. A.9 can be recast as µ χ = − 1 2 (B − L) = − 1 2 (13µ Q + µ H ) = µ φ − µ Q + µ H . The effective sphaleron interactions of Eq. A.1 give µ L = −3µ Q . Substituting this and Eqs. A.5 in Eq. A.3 allows us to solve µ H in terms of µ Q which allows us to write all chemical potentials in terms of µ Q using Eqs. A.5: Plugging these into the equations for B, L and B − L allows us to write the relations between them: In the other limit, m ψ ∼ m φ T EWPT , we use Eq. A.4. In this case, we need only use the SM Yukawa interactions to find the SM chemical potentials (and thus c s ≡ B/B − L). We can still use Eq. A.9 to find the chemical potentials of φ, ψ, and χ in terms of µ Q : Plugging these into the same equations for B, L, and B − L yields which is the same as the result in the SM [28].