Jhep12(2020)046

JHEP12(2020)046 Springer March 11, 2020 October 26, 2020 : December 9, 2020 : : September 27, 2020 : Received Accepted Revised Published Published for SISSA by https://doi.org/10.1007/JHEP12(2020)046 [email protected] , . 3 2002.05170 The Authors. c Beyond Standard Model, Cosmology of Theories beyond the SM

We propose a new mechanism where asymmetric dark matter (ADM) and the , [email protected] Department of Physics andRiverside, Astronomy, University CA of 92521, California, U.S.A. E-mail: Open Access Article funded by SCOAP long-lived WIMP may be within reach of future highKeywords: energy collider experiments. ArXiv ePrint: predicting relic abundances ofscenario matter. are Examples presented. ofscale renormalizable mass These that models models interacts realizing with genericallysignatures this Standard at predict Model quarks direct ADM or detectionphenomenological with leptons, experiments predictions thus sub-GeV rendering are sensitive to potential also to GeV- mediate discussed, low particles including: mass with LHC DM. color signatures of or Other new interesting electroweak inter- charge and DM induced nucleon decay; the baryon asymmetry are bothinteracting massive generated particle in (WIMP) after theare its same thermal connected freezeout. by decay a Dark chaintry matter generalized of and and baryon baryons a baryon number asymmetry that metastableDM-baryon compensate is weakly coincidence each conserved, other. while while the inheriting This DM unified the asymme- framework merit addresses of the the conventional WIMP miracle in Abstract: Yanou Cui and Michael Shamma WIMP cogenesis for asymmetricbaryon dark asymmetry matter and the JHEP12(2020)046 9 ], presents a coincidence 1 [ 10 5 7 ≈ B Ω 23 25 / ) ) 2 3 DM Ω 4 13 – 1 – about matter abundance in our Universe. 16 21 19 23 16 21 triple puzzle 8 15 11 13 4 1 22 The WIMP miracle, i.e. through thermal freezeout, DM with weak-scale interactions A.2 WIMP decay to leptons and ADM (section electroweak phase transition A.1 WIMP decay to baryons and ADM (section 4.1 Collider phenomenology 4.2 Dark matter4.3 direct detection Induced nucleon4.4 decay Other experimental constraints 3.1 Model3.2 setup Numerical results 2.1 Model2.2 setup WIMP freezeout2.3 and the generalized C WIMP and2.4 miracle CP violation Generalized baryon2.5 number conservation and WIMP generation decays2.6 of and asymmetries production of Numerical matter results asymmetries verse. These together form a and masses gives themodel-building. correct DM The WIMP abundance paradigm does today,while, not has address conventional been WIMPs the have DM-baryon a been coincidence. leading increasingly Mean- constrained paradigm by for indirect/direct detection DM The cosmic origins of baryonpuzzles and in dark particle matter physics and (DM)baryon cosmology. abundances abundances In have today been most are proposals, long-standing treatedtion the with that explanation separate their for mechanisms. abundances DM Meanwhile,problem, are and the strikingly and observa- similar, suggests a potential connection between DM and baryons in the early Uni- 1 Introduction 5 Conclusion A Relating baryon and lepton asymmetries for WIMP cogenesis before 4 Phenomenology and constraints 3 WIMP decay to leptons and ADM Contents 1 Introduction 2 WIMP decay to baryons and ADM JHEP12(2020)046 ] ]. kX 14 18 – )+ TeV). L ( 11 ] is one B 10 10 – ∼ 5 U(1) ] have sensitiv- 11 ]. However, the original model 21 – 19 – 2 – . There are two possible directions to pursue for B Ω ] is highly sensitive to various initial conditions, while 12 and DM ]. This has led to the proliferation of exploring alternative DM ] as well as the details of DM, and predicts a tighter, more Ω 4 – 14 2 ] where the post-freezeout decay of a grandparent WIMP generates both 14 and baryon asymmetries are generated in the same decay chain (instead ] (e.g. in the same multiplet or group representation), or consider a further X 14 ] and WIMP DM annihilation triggered “WIMPy baryogensis” [ 13 ADM of two different decay channelshave with the least potentially ambiguity arbitrary in branching predicting ratios) theirThe so “coincidence”; as model to possessesthat a is generalized conserved. baryon/lepton number symmetry UV complete, only involves renormalizable interactions; WIMP DM and ADM are both appealing proposals that address some aspect of the • • • DM and baryon asymmetries,explore thus the DM latter possibility, falls which we intoof naturally the our refer category to interest as of is “WIMPWe ADM. of cogenesis”. aim The conventional In at WIMP weak constructing this scale a mass work viable or we WIMP moderately cogenesis higher model (up with to the following guidelines: corporates the merits ofprecise connection [ between this purpose: consider aWIMP WIMP in DM [ thatdeviation closely from relates [ to the metastable baryon-parent and have become aof benchmark Baryogenesis from for Metastable related WIMPsthat studies does DM [ not is involve another specificsis species of addressed of DM, by WIMP only a that assuming building generalized is perspective WIMP stable, miracle it and would thus which the be is DM-baryon not more coincidence fully desirable quantitative. to further From develop model a framework which in- ity to washout details.was then The proposed mechanism as ofthe a “Baryogenesis baryon alternative from asymmetry where Metastable is theviolating WIMPs” prediction generated decays [ is by after robust a thestrong against long-lived thermal cosmological model motivation WIMP freezeout for details: that of long-lived the undergoes particle searches WIMP. CP- at and the Such collider B- models experiments also provide a aforementioned triple puzzle about matter.ity However, of it is a intriguing unified to mechanism explore thatpuzzle the combines simultaneously. possibil- their Recently merits and a addressesAmong few all these attempts three existing have aspects been proposals, of the both [ made in [ this direction [ component to dominate thelating DM DM and density baryons/leptons, today.generation through of The shared the core interactionsbaryogenesis-type idea in initial of the of DM mechanism. early ADM or Universe. ismerit baryon In of based The general asymmetry the on ADM WIMP for re- miracle models ADM in do predicting often not the requires absolute possess a amount the of separate attractive matter abundance. candidates beyond of the WIMPalternative paradigm. to WIMP Asymmetric DM, dark inspired by matterDM the (ADM) DM-baryon particle “coincidence”. [ is In distinct this framework, fromnumber the its densities antiparticle, is and generated annent asymmetry in in is the the early annihilated particle-antiparticle universe. away by Subsequently, the efficient symmetric CP-conserving compo- interactions, leaving the asymmetric and collider experiments [ JHEP12(2020)046 5 and (1.2) (1.1) B . Given introduces . Section 2.1 3 4 , which consists of 1 . 2 i , the SM B-number sym- v X in the GeV range. This pos- , we consider a model where )+ depends on whether the EW X L 2 (TeV) ( WIMP / , m B (1) ann 2 weak O σ , h U(1) α →∞ n τ WIMP ∼ ) m Ω X ( L ) B X in the benchmark models we will demon- − B B WIMP X Ω Ω n B ( m n m 1 k B WIMP s = 2 m c – 3 – = m CP k = s 1 . c CP ) generally predicts 0 X m ≈ ≈ 1.1 X Ω rational number that parametrizes the ratio of ADM num- ∼ B ]. (1) Ω 28 O – ], while concrete examples remain to be seen. The third guideline, ]. In particular, the second guideline leads to a neat prediction of the 25 26 , 24 24 – when the WIMP decays: 22 GeV is the neutron mass, 1 B from observation, eq. ( Ω 5 ≈ n ≈ and m B X Ω Ω , or between DM and anti-DM originates from this stage. X The rest of the paper is organized as follows. In section The schematic idea of this new mechanism is illustrated in figure ¯ ADM. While this stagemetry conserves is the violated. generalized This occurs well afterB the freezeout and before BBN. The asymmetry between as a consequence ofmiracle the relic abundance WIMP predicted freezeout. forΩ the This grandparent step WIMP establishes that will a be “would-be” inherited WIMP by is a model-dependent The decay of the intermediate exotic baryons/leptons into SM baryons/leptons and C- and CP-violating decay of the WIMP to intermediate states of exotic baryons/leptons. Metastable WIMP freezeout. The out-of-equilibrium condition is automatically satisfied the related general formulations anda leptogenesis numerical model results where will the bethe WIMP baryon given. directly asymmetry decays by Section to sphaleron leptons effecttranstion. provided and that ADM, Experimental the which decay signatures induces occursconcludes and before this EW constraints work. phase are discussed in section 3. the WIMP decay products are SM quarks and ADM leading to direct baryogenesis, where 2. 1. sibility of producing DM andunification baryons in scenario the [ same decay chaini.e., was the suggested in idea the of warped also DM seen and in e.g., baryon [ sharing a conserved globala baryon sequence number of symmetry three is stages that satisfy each of the three Sakharov conditions in order. where strate, the baryonsphaleron distribution is factor active whenthat the decays occur, and will be elaborated in section ber to baryon (lepton)distinguish number our model produced from in somedecay, such the other as decay existing [ ADM chain. proposalsADM based mass: These on first massive two particle guidelines k JHEP12(2020)046 2 1 χ , . 1 0 Y (2.1) to be . and φ α and their udd and ψ SM Baryon/ Lepton Asymmetry DM Asymmetric ψ h.c. ) i flavor symmetry + and φ µ k φ ∂ u ( R † and vector-like Dirac U(3) ) P i i j φ φ ¯ ψ µ i ∂ φ Exotic Baryon Decay ijk + ( β χ ) − χ c m χ ) would be too small to be observed. L − P i / ∂ ¯ d 4.2 i i (

Unstable φ χ Asymmetry Exotic Baryon ii + ¯ α i – 4 – − is the ADM, all Yukawa couplings are generic ψ ) i ψ ψ χ . This Lagrangian possesses a R m P 1 Violation Number Violation Baryon 2 − , Decay WIMP 1 / ∂ ¯ Metastable Y i i ( i φ ¯ 2 ψ , 1 is anti-symmetric in its indices. Two Majorana fermions , there is no effect on the prediction for matter abundances + η 1 2 . , ). Three generations of diquark scalars ijk − 0 1 β φ is essential for the interference process that enables C- and CP- † / ∂Y . 2.3 WIMP φ 2 2 plays the role of the WIMP grandparent for the ADM and baryon , Abundance 2 φ Metastable 1 Y α transform as fundamentals. The model is thus consistent with minimal ¯ 1 Y m i are the SM quark fields. With the chiral projectors, only right-handed decays produce asymmetries in intermediate states Y 1 2 . i i − flavor symmetry is optional for the purpose of suppressing FCNC: with , φ 1 i d 7 Y = ψ − are the exotic baryons that are the intermediate decay products of metastable out L i 10 and U(3) ψ . Schematic diagram outlining the key stages in WIMP cogenesis mechanism. Each i WIMP u Metastable Freeze as described in Stage-2 in section 1 Departure from Equilibrium C/CP the potential DM directCP-violating detection signal (section conjugates. These states subsequentlyand decay their to conjugates. produce For asymmetriesdegenerate simplicity, between in we mass. have taken This the will different be flavors the of case throughout the rest of the paper. The Feynman Y under which flavor violation and forbids newthat sources of the flavor-changing neutral currentscouplings (FCNC). Note in our model, while the FCNC constraint can be satisfied. Nevertheless with complex numbers, and are introduced: asymmetry, while violation (see section fermions where quarks are relevant. The SM singlet 2.1 Model setup To implement the picturelowing discussed Lagrangian: in the introduction, we extend the SM with the fol- In this section, wealong explore with ADM a via specific SM B-violating modelfollowed interactions. by which The discussions fields directly and on produces interactions are howrelated a introduced Sakharov cosmological baryon conditions evolution. asymmetry are This section metspace ends by for with their these numerical interactions analyses types and of of the the models. parameter Figure 1 dynamical stage of WIMP cogenesis, shown in the bubbles, satisfies one of the Sakharov conditions. 2 WIMP decay to baryons and ADM JHEP12(2020)046 1 χ Y (2.2) ¯ χ χ and charge 1 decays to Y 1 Y annihilations 1 ψ, φ, χ Y , 1 S freezeout. − 1 which permit decays Y . These would permit 1 2 S 2 | ¯ charge LHY is forbidden by imposing an φ 3 | 1 1 1 1 Y Y Y µS d χ and − ¯ LHY d ¯ ¯ χχ S S ψψ S δS φ − . The above symmetries allow additional 2 2 , u χ 1 Y 1 such as mediated the gauge boson of a spontaneously 2 Y φ , ψ – 5 – symmetric component depletion, we introduce 1 S ¯ Y χ symmetry also ensures the stability of asymmetric S 1 1 2 , 4 Y Y 1 )) are insensitive to the detailed realization of such Z ρ , respectively. Nevertheless, we are not committed to ψ, φ, χ − 1.2 4 = 1 Y S S . This f.o. and L +1 3 . freeze-out and χ 1 Y ]. annihilating to . Annihilation processes that potentially contribute to annihilate into SM singlet scalar S. Feynman diagrams for S 30 1 , Y , χ 29 [ 1 0 Y Figure 3 symmetry with the following charge assignments: . Feynman diagram of the WIMP decay chain producing baryon and DM asymmetries. . It is technically natural for this coupling to remain small such that 4 U(1) Z 1 1 Hl Y Y Specifically, for Just like with WIMP DM freezeout, there are various possibilities of are dominant. Alternatively, the Yukawa interaction → 1 , and all SM charges are Figure 2 additional interactions as follows: There may be additional interactions for case where annihilation are shown in this choice: asfreezeout, said e.g., there arebroken other potentially more complex possibilities to realize dark matter candidate that can leadmechanism to and a result metastable (e.g.annihilations/freezeout. WIMP eq. abundance To ( through give thermal a freezeout. concrete example, Our we core choose to consider the simple interactions between the Majorana singletY and the SM through φψ exact i diagram for the decay chain is shown in figure JHEP12(2020)046 2 | ) = H may GeV | ’s for S S SS χ are de- = 5 0 . → µ ¯ σ χ ¯ χ , χ 2 χ . ( 0 . σ for p-wave) and S S = 0 undergoes t- and 1 δ which is sufficiently χ i i i 1 4 charge assignments in = 1 /s +1 +1 +1 + + + − Z , its annihilation cross 3 G χ n cm X 22 χ +2 − B freeze-out and ADM symmetric 3 3 2 6 6 10 / / / / / 1 0 0 1 1 × Y ]. The cross sections, 3 +1 +1 − − +1 U(1) ¯ χ χ 31 ≈ [ ) Y 3 3 3 3 ), ADM candidate . Without a symmetry protection, / / / / 0 0 0 SS limit, the cross section is 2 2 χ 2.2 − +4 − +2 U(1) WIMP S , → . To give an example, for 0 S S m 2 χ ¯ σ χ – 6 – L χ × ( πm for s-wave annihilation, 0 χ σ 64 m / few . We will further explain the 1 1 1 1 1 1 1 SU(2) )] G = 0 2 χ & ). The shared interactions fix the relationship between the annihilation cross section. That said, the interactions in C m n ) ( 2 1 S / udd Y 2 n SS . In the s. Following eq. ( ) µ S / 3 3 1 1 3 3 ¯ 1 SU(3) 3 → T/m cm ) + ( 2 ¯ χ , ( χ 1 0 χ 26 ( d u S χ φ ψ Y σ m − 0 asymmetry remains the dominant contribution to the DM abundance. 3 . Annihilation process that depletes the symmetric component of σ 10 = χ ¯ χ χ µδ/ number density to near triviality. This leaves an abundance of two × GeV, the cross section is |i . Quantum numbers of the relevant particles in WIMP cogenesis with baryons. ~v 5 ¯ 5 χ | . (20 with conserved number . The generalized baryon and other charges are given in table σ h ≈ − Figure 4 X = 2 2 ) constitute a minimal, renormalizable model for 2.4 δ χ +2 Table 1 B 2.2 m After the decay processes have taken place, efficient matter-antimatter annihilations With these interactions we can also define a generalized global baryon symmetry In order to efficiently deplete the symmetric component of 24 WIMP 2 , 0 δ U(1) section deplete the every unit of baryon number ( and efficient to deplete the symmetric componentdecay of to the SMterm. states, Thus e.g. the through a mixing with the SM Higgs enabled by an section must be fined by σ s-channel annihilations to 3 further contributions to the eq. ( component depletion. JHEP12(2020)046 ) ): → 2.3 , we ] for 1 (2.4) (2.3) . The EWPT Y A.1 ). It is 33 1 T Y eq. ( ( 2.6 1.1 EWPT σ h T = 1 Y φ,ψ would lift this n relative to the H m S N . Combining these ) = ψ, φ and final states, as shown . If the asymmetry is    values: ¯ EWPT χ, SS s 0 = 3 c = 1 T χ σ EWPT χ, S are in chemical equilibrium f s EWPT 1 0 T c T N σ → χ m 1 , 1 Pl mass according to eq. ( characterizes the potential effect m ψ φ,ψ Y is preserved, while in this model annihilation rate falls below the , 1 M Pl L χ m 2 φ Y 1 − φ,ψ φ,ψ B L / M Y n 1 B 2 m m Γ( n − − ∗ / for 1 g B ≡ − ∗ , there is no s-wave contribution to the 79 H H ) g s / 152 H S c mediated annihilation to the hidden sec- H . N N 0 N N 152 S . 2 0 when the + = 28 / – 7 – + 13 + 4 + 13 3 f s f f f c ln N f.o. N N N T    8 4( or GeV if the asymmetry is produced after EWPT and 14 22 ]. Although pseudoscalar coupling to 5 has a dependence on the masses of ln . is conserved. Putting all these together we can solve for          s 34 numbers due to sphaleron interactions. If the asymmetry ' c for this model. = X . Given the large uncertainty in determining , = 2 annihilation cross section are to EWPT L 1 2 couple to scalar L T . This then fixes the ADM χ / 1 f.o. A +2 m provides the out-of-equilibrium condition for asymmetry gen- − B Y χ T χ m ], SM charged particles and B L n 1 and EWPT proceeds through = 1 n Y ≡ 32 − T B 1 and = φ,ψ B Y f.o DM s 1 x m GeV if produced before EWPT. c . The solutions for the two limits are (details given in appendix Y /n are the number of generations of fermions and number of Higgs, respec- L 89 for . − H 0 . The annihilation rate is given by B N 55 EWPT n / T ), we find that . Since GeV– S, χ . The freezeout occurs at and |i 1.1 3 ~v f = 16 72 | . ) s N φ,ψ 0 c m The freezeout of Next we demonstrate how WIMP cogenesis satisfies the Sakharov conditions [ ≈ χ . As explained in appendix ¯ χ, SS s in figure Hubble expansion rate, which can be estimated as follows: χ cross section because ofCP-invariance in helicity the suppression scalar in casesuppression, the [ velocity suppressed fermionic annihilation case isp-wave and sufficient, contributions as the to we the imposition will see of in section The thermal freezeout of eration upon the subsequent decays. tor states m generating a primordial asymmetry in both baryon and DM sectors. 2.2 WIMP freezeout and the generalized WIMP miracle where tively. For matter asymmetries producedgives before EWPT with and eq. ( well as sphaleron processes.the linear With combination the SMc alone, temperature at EWPT, consider two limits of interest which wouldand define the range of the apparent that of redistribution among is produced after theproduced electroweak before phase EWPT transition [ (EWPT), and their chemical potentials are related by the active gauge and Yukawa interactions as asymmetries of baryons and JHEP12(2020)046 , ) ]. 08 . 35 and does (2.6) (2.7) (2.5) GeV 1 ( 1 = 0 Y ). ψ 1 φ ρ > m ∼ O 2.6 , χ 2 2 . m following their m 0 1 2 . Y ≈ Y S GeV. Its comoving δ m 303 ψ φ ≈ ). 5 2 1 . Y ) ) m 16 f.o. 4 , ψ ψ 1 δ ∗ ∗ Y ] ≈ in the non-resonant region. For φ φ Y + , . 36 0 o 0 2 1 2 1 . 1 ≈ → → ρ σ f σ is the effective degrees of freedom [ m 2 Y 2 f.o. 1 T 1 1 2 µ ∗ x Y Y , we expect the observed abundances of gives rise to a non-vanishing numerator m 2 g 2 1 →∞ / + 1 and 5 1 τ Pl 1 Γ( ∗ Y decays is defined as µ g 1 Y 0 πm 3 1 M − 1 ρ m ψ S 58 φ Y ) ) + Γ( 3 . 64 ∗ 20 ¯ ¯ → 7 ψ ψ with g – 8 – φ φ 1 − S = − 4 1 decay may generate a CP asymmetry as well, its m → → x ρ 0 2 1 1 f.o. , 2 σ 24 Y Y Y 1 Y Y Γ( Γ( 1 3 Y . but in-equilibrium decay of ¯ ψ |i ' m 1 = = / ~v | ∗ ) can be approximated as twice the tree-level decay rate, 1 0 φ σ ann 2.7 1 ψ Y φ and σ TeV WIMP with freeze-out Yukawa couplings h GeV is the Planck mass and 5 , we take 19 φ/ψ freezes out as a cold relic with as ) ≈ at the time of freezeout is given by [ 1 10 S 1 Y 1 × m TeV Y s 2 m ( . n . For complex WIMP Yukawa couplings, interference between the tree-level ) ≡ 1 ¯ (leading to sizable = 1 GeV, decays to is the effective number of degrees of freedom in entropy. Note that if ψ ). Although in analogy ∼ O 1 | φ m 1 Y . Loop diagrams interfere with the tree-level diagram to produce a nonzero asymmetry 2 S Pl 1 1 Y Y ∗ 2.7 η Y = 5 g → M m 1 µ In many baryogenesis models based on massive particle decay, the decay products are Following the schematic illustration in figure Y | | ( 1 0 η in eq. ( contribution to the DM/baryon| asymmetry is generally washed out with much lighter than the decaying particle and thus can be approximately taken as massless. The denominator ofΓ eq. ( and loop-level Feynman diagrams shown in figure DM and baryons to be proportional to2.3 the freeze out abundance C found and inC- CP eq. and violation ( CP-violation are achievedfreeze by the out. decay The of CP the asymmetry Majorana fermions arising from where not decay, its would-be relic abundance today while example, with and density where Since efficient depletion of the symmetric component of ADM requires Figure 5 between where we parametrize the p-wavethe contributions limit to the thermally averaged cross-section in JHEP12(2020)046 . 2 2 2 m ). are − , we (2.9) (2.8) 2 1 2 1 ψ (2.10) (2.11) 2.8 decays m m − 2.6 1 2 φ Y ). and m 2 φ 4.1 ≡ 2 c #) ) ) , a a 2 . In section − 2 φ (section ψ m ) 2 1 m (1 (1 + − . Then requiring all the m a a 2 2 2 ψ b b 2 2 m TeV . Furthermore, due to the ( and + + 3 = 0 / taking the form of eq. ( 2 2 O , 1+ 1 c c φ 1 Y , − 1 " φ ψ Y G a = 1 is conserved (remains 0 assuming ln G G G , m q ≡ 2 1 X − − c GeV 2 B − Y . The net result of the decay chain is b χ φ ψ + , 1 + 2 = G G and baryonic matter sharing interactions # 2 G b q 2 φ B and their conjugates, which is inherited by χ (100) charge is + m G plane with 4 1 + 3 + 3 + O ) produce an asymmetry between intermedi- = 2 ψ ψ φ m ) / / X x m G & G 4 ,ρ is conserved. So the generalized baryonic charge – 9 – 1 +2 2.3 − 1 . The above expression shows how the asymmetry and = = 1 = 1 − B G 1 ) reproduces the familiar CP-asymmetry result for m 2 φ ( χd ψ,φ φu ( φψ 2 φ 2.8 → → → m U(1) m 2 φ 1 2 1 ψ ) are (nearly) degenerate in mass. Under this assumption, Y + 1 m G G ψ 2 , and ultimately becomes the source of all (asymmetric) TeV while the intermediate decay products η ψ G , we may obtain the solutions for the charge assignments: . , as listed in table in the 1 b ∆ ∗ 2 m ∆ 6 2 G ∆ η | m 10 / ( − 1 udd decays to a single generation. To simplify our analyses, we 1 φ, ψ DM and η 1 decay (section − | 1 − Ω φ 1 π Im Y " 8 Y and = 2 xa − , its natural GeV ψ χ 1 √ G Y 2 φ 3 m − 2 1 − − (100) m = 2 ψ = ] in the limit of m φ 1 37 G ∼ O 1+ , . The factor of 3 represents the color multiplicity. Note this is the contribution 1 2 2 2 2 1 / , violating the SM baryon number and DM number by 1 and 2 units respectively, m m m ≡ 1 a χχ − = x The CP-violation in With this in mind and using the Optical Theorem, we find the CP-asymmetry: + = χ G udd while the net generalized baryon number carried by the ADM densityhas cancels trivial that net of generalized a baryon baryon number. asymmetry density and the universe where we have usedMajorana the nature fact of thatabove for interactions quarks to conserve their decay products, matter today. The changesgiven in by: the generalized baryon number for each decay process are Nevertheless a generalized baryon number no pre-existing asymmetry) thanks to thethrough ADM intermediate states ate states (i.e., baryon/ADM parents), show contours of constant 2.4 Generalized baryonIn number order conservation for and a generation mattermust asymmetry of be to asymmetries be violated produced, by the theand corresponding interactions DM baryon in number or the are DM model. violated number in In the this last model stage both of SM the baryon decay number chain as illustrated in figure assume the three flavors of there is an additional multiplicativeto factor the all of flavors. 3 Also toleptogenesis note account [ that for eq. the ( contributions is intimately tied to the mass and couplings of the where and to the CP-asymmetry of requires experimentally constrained to have masses For WIMP cogenesis we include full mass-dependence since WIMP freezeout generically JHEP12(2020)046 |i |i which (2.14) (2.12) (2.13) where ~v ~v | | . number ) ) o G -number . ¯ ¯ f ψ ψ n , χ ∗ ∗ 1 decays and Y φ φ Y φ, ψ 1 Y → → of this stage of ≈ 1 Y φψ φψ (0) ( Y ( . The requirement 1 σ - and DM σ 1 Y h h Y Y B γ γ ), the freezeout occurs n n , G G 2.4 i i i n n ) ) ) ) 2 ∗ 2 decay. This assumption also 1 ¯ ¯ eq φ eq ψ eq eq ψ Y , i.e., in equilibrium, so that 1 − − n n n Y Y H − − ¯ − 1 ψ − 1 evolves according to ∗ Y eq ¯ asymmetry is eq Y ¯ ψ n ψ 1 φ n n Y φ n n n 2 ψ 1 ( − 1 ( Y is the photon radiation density. The ∆ G ( G ’s are thermally averaged decay rates, ( i Y n ψ 2 Y 2 − i − γ − Γ ) n ) ) n h can be set as equilibrium distribution. ) ≡ after its freezeout: − − eq ψ eq ψ + ∗ 1 φ 1 eq φ φψ ), 1 . Following eq. ( ) n φ n Y eq , decays well after its freezeout but before eq Y Y n ∗ 1 1 1 n , n n n φ → . The initial condition for 2.8 − m − Y ψ m − ) π , and n 2 ( | − 1 − 8 − 1 GeV for TeV-scale mass ψ n ψ – 10 – φ )] 1 2 Y 1 − φ 1 n η ¯ n H n ψ | m Y ( Y ( ( n 2 φ n h Γ( h n h n 300 h n = i i ≈ – i ) x ) − ) i i u T u = d − ) ) ψ ( are prompt relative to 200 , so that we can treat the freezeout and decay-triggered dec n + , G . + + scattering to their conjugates (and vice versa), and CP- H 1 = o φψ φψ n . φ Y φ f χ ∼ 1 Γ T Y → → ) + ( → ) = → → dx φ/ψ ∗ 1 1 is udd, χ 1 asymmetry, f.o. . dY φ ψ Y φ ψ Y T ). m 1 n φ ( to Γ( Γ( dec Γ( Γ( Γ( , h h − h 2.6 1 H 1 1 Y φ − h − h + . For simplicity we assume the subsequent SM T n φ, ψ 9 asymmetries: = = [( T < m and − . mediated s ψ φ 1 (as well as their conjugates) decays. 2 1 10 ∆ ∆ /T Y φ/ψ freezeout occurring well before its decay, the late-time evolution of comoving 1 = . satisfies the following Boltzmann equation for a decaying species: Hn Hn | 1 φ/ψ m 1MeV 1 1 Y /s η Y is the CP asymmetry given in eq. ( | = G + 3 + 3 Y 1 n is given in eq. ( x φ ψ . ∆ ∆ Once simplified, the For convenient notations, we define the generalized baryon number density We now write down the Boltzmann equations governing the evolution of With ˙ ˙ f.o. ≡ 15 n n decay rate at , 1 − 1 G Y equation governing the cosmological evolution of the where Y their inverse, conserving is the sum of where evolution is set by the would-beY abundance of densities. This evolution is determined by three processes: CP-violating density that it decay10 between freezeout andviolating BBN decay gives of thethe range matter asymmetries of are allowed immediatelysimplifies distributed decay the upon Boltzmann couplings: equations, since We consider the asymmetryBBN, i.e., grandparent, cogenesis as nearly decoupledY processes and retain thearound conventional success the of temperature BBN. The 2.5 WIMP decays and production of matter asymmetries JHEP12(2020)046 B × f.o. , are 5 ) in and 1 . 5Ω GeV Y leads ¯ 3 χ ) (2.17) (2.18) (2.19) (2.15) (2.16) Y ¯ ≈ 1.1 χ S 89 G ¯ . , ≈ d Y 1 0 ¯ u ,m – DM ¯ u χ or πG , the above and the CP 72 8 . χ → G = Ω ,m / 1 2 can potentially n ψ 0 Y χ and eq. ( , = 0 Ω H s G ,m ψ c χ Y . Taking our sim- φ -number increasing m = 3 ψ uddχχ ,m c dT and = 0 2 ). This yields a robust ρ ! with the robust relation: φ 0 and 0 ,m χ ! 1 2.16 1 T f.o. n , dT initial GeV or Y 2 B Boltzmann evolution is that 1 m T ) dT / ( Y 5 0 Y ) . 0 χ ) Y ψ → T ) 1 , T n ( T ( T ( and the 2-2 scattering). Assuming ( = 2 W f.o. = , H 1 f.o. ≈ W , and Γ 1 χ H Y 1 B ) Γ Y Y T m n φ Y uddχχ 0 Y ∞ 1 GeV is the SM baryon mass. Z 1 ( 1 0 G initial − 0 2 = s T Y s fixes / n 0 ≈

c c ) , such that the contribution from these decays χ Z ρ ρ n m B ψ eq ψ m s − 2 = ∆ 2 c n exp m – 11 – / n

) 1 5 Ω = Y + ∞ ) = ) = ≈ ψ dT ( φ exp dY χ ∆ ∞ ∞ , n Y ( ( n DM dec and DM asymmetry density χ eq φ B T Ω initial n Ω 0 B Ω B = ( ) = Z Y give rise to the baryon and DM abundances today: n = 1 G ∞ decays well after its freeze out, we automatically work in the χ + φ ( n 1 n B , n Y Y B n is the radiation entropy density today and decays changes sign and there is no term for (0) = and our earlier discussion, upon decays of 3 G ψ − 2 Y cm today: : G 1 decays, we set is the critical energy density, Y is the rate of processes washing out the asymmetry. Assuming that there is 4 = 2970 , the observed relation W φ, ψ 0 1 Γ s decay after or before EWPT, respectively. GeV 1 The general solution of the Boltzmann equations gives the comoving generalized matter Based on figure 47 Y − decays. Note that in these evolution eqs., the terms proportional to for 2.6 Numerical results We now scan parameter space toas demonstrate viable observed. regions that The predicts relevant parameters includes the masses where 10 have been calculated in earliersection sections. Based on the discussion about Provided efficient annihilation thatasymptotic solution depletes of the symmetric component of plifying assumption that weak washout regime andsolution drop depending the exponential solely factor onasymmetry in the eq. would-be ( WIMP miracle abundance of where no primordial asymmetry before WIMP cogenesis occurs, asymmetry negligible owing not only toeffective Boltzmann operators suppression, responsible but for also these to processes. the high dimensionto of baryon the asymmetry density the term governing φ wash out the produced asymmetries (inverseprompt decay of vanish. Additional potential washout processes of We can see that the main difference between the JHEP12(2020)046 , , ) 1 2 Y . 2.8 GeV 001 GeV, . 0 0 = 0 72 . . In our ± δ ) → 2 = 0 for different θ S 1 120 χ . m such that the TeV, m m . Because the S 7 sin(2 . 2 6 = 0 1 | 2 GeV, mass 2 η > m ≈ | h 1 2 χ | Y ψ 1 = 5 m DM η m µ Ω and , → | 1 2 ] . ρ 2 ) TeV, 2 remains kinematically open for 2 η . = 0 ∗ 1 1 η δ φψ [( ≈ ) are required to produce the observed | φ → 2 η , which requires : Im m 1 | 2 Y η decays, it may be produced before or after plane, as shown in figure SS 1 ) Y 1 TeV, → – 12 – , ρ ¯ TeV. χ ] we plot contours of 10 1 5 χ . , their masses are effectively constrained by collider 38 m & [ ψ to be real such that the CP-asymmetry in eq. ( ( decay before vs. after EWPT, we see that a smaller (for a given 2 1 1 1 = 10 Y η m 2 and m TeV such that m φ 3 as a function of Yukawa coupling ). This immediately constrains the mass of the lighter of ] in the & 1 B [ Ω 1 to bound the CP-asymmetry from above. 4.1 , Mathematica χ m 4 . We take TeV, and ) and larger Ω 7 0001 π/ . . S 0 = = 1 2 ± θ ,ρ,δ,µ ψ 2 TeV. The symmetric component of ADM is efficiently depleted through m ,η 1 GeV, with ∼ 0224 in WIMP cogenesis for baryons. The solid (dashed) lines correspond to the case where η . GeV). The benchmark parameters used are: 5 ( 2 φ 5 . Contours of . TeV, η ≈ m 2 . = 0 = 2 µ 2 & Taking benchmark values of Due to the color charges of = 1 h χ ψ φ B m Ω baryon asymmetry is directlythe produced EWPT. by Comparing the case of Yukawa coupling to DM abundance when the asymmetry is produced before EWPT due to the sphaleron’s m annihilations to the hiddenannihilation sector, process e.g. is kinematically open. and can be written inanalyses, terms we of fix a complex phase of experiments (see section the Majorana fermion asymmetries in DM( and baryons arem produced before (after) the EWPT with couplings Figure 6 values of JHEP12(2020)046 . . 4 1 ) /ρ 2 1 U(3) TeV, (3.1) , and TeV EWPT m 2 ( / T is flavor ∼ = 5 the U(3) & 3 0 are the SM 1 2 = 1 , ∼ O 2 /σ 1 m 0 φ dec , 1 decay through with conserved m G , such that the 1 , Z, ` , ∼ Y > T Y X = 1 ± TeV, -number. After all i +2 f.o f.o. = 0 , 5 ) and L . T X 1 U(1) 1 Y h, W 0 Y Y × 2.1 , is a SM gauge singlet, . G U(1) 1 = 10 L , Y 2 1% i 2 / χ i m ¯ ψ | ≈ , SU(2) = 1 1 5 H . | 0 χ . The CP asymmetry is generated ii β G 7 . A key difference from the model in = 0 , while the DM direct detection signal − L 1 2 . c k η 0 χ is the Higgs doublet, i are possible, where and ¯ . L i H . χ χ` -number and 2 units of α φ ), must be sufficient to produce the observed (as discussed in section 5 L – 13 – . ijk → 2.8 1 . α 7 φ 0 − ) up to modification of the Yukawa interactions: ∼ 10 → − and ρ 2.2 , the second stage of the decay chain violates SM lepton , undergoes freezeout via Yukawa and cubic interactions ± 1 7 Y Yukawa coupling TeV the CP-asymmetry is χW . Again, the Majorana fermion, 1 Yukawa ) and ( 2 Y ψ L . abundance to compensate for this washout. The CP-asymmetry → 1 2.1 ± Y = 1 and ψ φ followed by out-of-equilibrium and CP-violating decays to (unstable) , φ m S is antisymmetric in flavor indices. Note that this model possesses a decays, as given in eq. ( 1 symmetry is imposed to ensure DM stability and prevent ijk Y χh, χZ 4 α . As shown in figure Z permit a generalized global lepton number symmetry → 2 TeV, and . The corresponding charge assignment is: is the left-handed lepton doublet, / 0 0 is that the asymmetry must be produced before EWPT such that sphalerons con- 7 1 . G ψ 2 L .A portal. The decay chain is illustrated in figure − φ, ψ 2 In analogy to WIMP cogenesis with baryons, the shared interactions through interme- = 1 = LH ψ ψ 0 1 and DM number, givingthe rise decays to have 1 takenADM place, unit and efficient of leptons, annihilations leaving depletesection an the abundance symmetric of components of vert the lepton asymmetry into the observed baryon asymmetry, i.e., Y by the same process as illustrated in figure diate charge G indices, and flavor symmetry which prevents newsymmetry sources is of optional FCNC. provided As that may discussed be in section absenttable with such small couplings. The charge assignments are summarized in Higgs, electroweak gauge bosons, andidentical left-handed to leptons, that respectively. in The eqs. Lagrangian ( is where above: the Majorana fermion, with singlet scalar intermediate states but now the intermediatedecays states are charged under SM asymmetry. Here, weWIMP introduce cogenesis the with fields, baryons interactions, presented in and the discuss last3.1 the section. differences from Model setup The first two stages of WIMP cogenesis with leptons are identical to the model discussed 3 WIMP decay toIn leptons the following and section, we ADM present aasymmetry. WIMP As cogenesis with model that other directly models producesEWPT of a such leptogenesis, lepton that the sphalerons asymmetry must may be transfer produced the before lepton asymmetry into the observed baryon giving a larger decaying produced by abundances of DM and baryons for To give an example,m with moderate washout of the SM baryon asymmetry. This is because JHEP12(2020)046 may also + − " " ψ ]. Feynman 39 . This depletion S 1 i i i 4 Z − + + + +1 +1 +1 φ X +2 by analogy, with some mod- L depletion. 2 2 2 ¯ χ χ / / / ¯ χ 2.5 1 1 0 0 0 h χ χ – U(1) − +1 − +1 2.2 Y . 8 1 1 " 0 0 0 χ U(1) +1 − − +1 φ ψ . L – 14 – ± W -mediated annihilation to leptons, due to the weaker φ SU(2) 1 ¯ 2 2 1 1 2 ¯ 2 and 1 Z C Y . Diagrams contributing to S S depletion occurs through annihilation to ¯ χ SU(3) 1 1 1 1 1 1 1 χ 2 , Figure 8 1 Y ψ φ χ S L H χ . Quantum numbers of the relevant particles in WIMP cogenesis with leptons. . Feynmann diagram of the decay chain for WIMP cogenesis with leptons. ¯ χ χ Table 2 We can then apply most results from sections may also receive contributions from constraints on ADM-lepton couplingsdiagrams (relative for to these ADM-quark processes are couplings) shown [ in figure ifications. The most straightforward change is the dropping of the color factor in the As in the quark model, Figure 7 decay to electroweak gauge bosons JHEP12(2020)046 . χ ± n or and m ) on | (3.4) (3.2) (3.3) χW 1 ) s in this S − mass c s 4.1 5 → c TeV, the EWPT | ψ ) 2 T 1 , m ± χ ψ = ∼ in this model GeV and 1 GeV. χ ( L , m φ m O m − 37 B φ,ψ ψ . n B 1 m n – -S Yukawa coupling and/or . Following the same 1 , m = 93 φ Y B . for decays to happen after s Y 0 | c 1 1 . With a , m s Y − EWPT EWPT decays to 2 103 c s f.o T T / c ). χh, χZ, | T φ , m . . 2.4 → 1 2 = = 28 0 masses is f.o. m , / φ,ψ φ,ψ dec ( ψ . 1 s χ χ Y c Y, f.o. m m , Y Y T 1 the EWPT, thus its lepton asymmetry 1 2.6 Y = . There is a caveat to this: if the mass of . Y c H 1 1 L 0 ρ H H | Y H N s Y 0 1 N N after n N s GeV ): c χ − m ρ s + 4 + 13 + 4 s + 4 m c . Similarly, since – 15 – c f f f | 2 100 f ) with gives 2.17 W N N N ), the range of N ) 8 m 8 3.2 , as in section 30 22 fixes the mass of the ADM candidate ) = ) = 2 3.2 5 η          ∞ ∞ A.2 ( ( is required. That said, collider constraints (see ≈ = χ B . All together, the relation between lepton, baryon, and ) Ω and B Ω L in eq. ( Ω 1 − B / η 1 B n GeV . We also take the same parametrization for the CP-asymmetry ( EWPT n ). More subtle is the change to the DM mass prediction. Due to ) T DM → O , in the weak washout regime we obtain ADM abundance with the = shows the DM abundance as a function of Ω given in eq. ( 2.8 ): H s & 9 s c 2.5 c N φ , and even the grandparent, are again the number of generations of fermions and Higgs, respectively. 2.18 ψ φ,ψ m , ρ, δ, µ , H m 2 greater than at least and φ N ψ 3 , η contributes to the matter asymmetry via for 1 m η and ψ → ( 79 F f / N N Since The constraints arising from colliders on exotic electroweak states ( The observed ratio = 28 s it requires and SM leptons, new electroweak states requirerequirements. these Figure states be much heavier than the above kinematic TeV masses for the decaying WIMP is tooproducing light, decays it would freezes occur out whenthe sphaleron observed processes, baryon necessary asymmetry, forfreezeout, the are but conversion no before into EWPT, longer wefreezeout effective. require occurs at For or just after EWPT, according to eq. ( dances. The relevant parameterscouplings includes the masses relevant Yukawa couplings, model) are less stringent than those on exotic colored states, allowing us to explore sub- With the values for 3.2 Numerical results We now scan model parameters to find viable region giving the observed matter abun- With c ADM comoving densities is akinprocedure to as eq. section ( same form as eq. ( where the different Yukawa interactions, thediffers from prediction that of in the thenesis relation WIMP with cogenesis leptons with needs baryons. tolimits In occur of addition, before as interest noted, EWPT are WIMP whenthese the coge- sphaleron two same limits processes as are are those (see active. detailed appendix The in the previous section. The solutions in CP-asymmetry of eq. ( JHEP12(2020)046 . . ), χ χ m com- ρ EWPT GeV and T 93 for different . respectively, 1 i m = 0 φ,ψ ψ χ m m and mass i 1 φ Y TeV. 5 . and decays through intermediate 1 ρ decays to an SM quark and ψ = 10 φ , GeV. Other benchmark parameters 2 2 In the model where the WIMP de- m = 0 , and S ). χ is required in the case with smaller m 1 2 ρ Yukawa and gauge interactions contribute GeV, and mass S TeV. In these numerical analyses, we take the ψ, φ – 16 – . = 740 1 10 ) for the CP-asymmetry and freezeout abundance − ψ σ < m 2.6 1 ∝ ∞ GeV, Y < m as a function of Yukawa coupling , a smaller coupling 9 B TeV ) and eq. ( = 700 Ω 1 , φ ), SM charged colored scalars and fermions, GeV, both cases with χ 2.8 m 2 Ω 37 . = 1 GeV, χ m = 5 µ for WIMP cogenesis with leptons. The solid lines correspond to , 2 2 . . Contours of η to 2 SM quarks and singlet ADM candidate , in the range of 1 φ = 0 , respectively. m δ As can be seen in figure 1 Y WIMP decay to baryons andcays ADM to (section quarks (section are introduced. Owing tobounds the on color their charges masses carried arescalar strong. by these As outlined intermediate in states, section the LHC pensates for this washout since 4 Phenomenology and constraints 4.1 Collider phenomenology of This is related toto whether chemical interactions equilibration of along withthere sphalerons. is further When washout they of contribute ( the produced asymmetry. A smaller Yukawa coupling dashed lines to are: and functional form of eq. ( Figure 9 values of JHEP12(2020)046 ˜ g T / are E has TeV 0 1 + χ and ˜ χ j 13 4 ψ . TeV which → ¯ d 11 χ d 3 ¯ ¯ χ . ψ 1 ψ ¯ χ ¯ χ d and & → ∗ ]. ψ d φ 10 φ pp , since both squarks m 40 φ u ¯ u ∗ φ TeV [ φ ¯ ψ ψ 5 . Specifically, both . mass is ψ 1 φ ψ ψ & and ψ g m φ g g g ≈ ˜ g in our model. In particular the bound in m , in the presence of neutralino LSP ˜ g ψ – 17 – and ¯ ¯ ¯ χ ¯ d χ χ d d χ φ , rendering typical signatures: T d / E ∗ searches at hadron colliders (WIMP cogenesis with baryons). + searches at hadron colliders (WIMP cogenesis with baryons). φ φ , and gluinos, ψ ]. The lower bound on the φ jj ˜ q ¯ u u 40 ∗ φ [ → φ 0 1 of data place bounds on the gluino mass in the presence of a ψ ¯ ˜ . The relevant diagrams are shown in figures ψ χ ψ , T 1 T − / . The recent searches at CMS place bounds on three generations of E / E T fb + / + E j , significantly smaller than those of via intermediate colored scalars with production cross sections differing jj ) + 137 T j → g g → / E φ ∗ GeV ( + g g φφ O . Diagrams relevant for . Diagrams relevant for jj → decay to pp φ LHC searches for mass degenerate squarks bound the mass of LHC searches for squarks, is from the gluino boundaccount. with In the the different group casethe theory where bound factor the on in the gluino cross gluino decays section mass to taken is top into a quarks bitand via stronger: intermediate top squark, a mass of decay to only by a groupfrom theory factor, CMS for with whichmassless we LSP, correct. neutralino Simplified model searches at quent decays and relevant for constraining the massesthe massless of LSP limit applies since the corresponding particle in WIMP cogenesis, Figure 11 These states are pair-produced at the LHC dominantly through gluon fusion, with subse- Figure 10 JHEP12(2020)046 . 1 ¯ ¯ T χ χ χ χ − / and E fb 0 2 ˜ χ → + 139 m 0 are both h ν + W l φ = 0 ψ φ + + 0 0 ± the same sig- , ˜ ψ φ χ ψ φ 0 1 T and m ˜ χ / E + + φ ± bosons, and subse- l + W W in WIMP cogenesis, ]. Since we make the ` i → 2 φ 40 bound the neutral com- ± W, Z l ˜ → ]. We apply these bounds 0 2 ! ! ¯ ¯ ˜ q q q q χ − 41 [ . φ . Consequently, these lead to 0 1 + ˜ , and χ bound the charged components φ 13 νχ 0 , ± In this model, ψ ¯ ¯ χ χ χ χ l ˜ T → / and E 0 ). φ + − + TeV. TeV. produces the same collider signature as 12 , 3 − 3 W W − χ l + 0 1 l 13 ˜ ± χ . & W ` 1 ± + + − + − ψ ψ φ & → ψ φ W m W φ ± – 18 – + → φ m → φ , ± γ Z/ γ Z/ − TeV assuming massless LSP [ χ ˜ χ m ± ψ 13 ≥ and charged sleptons + . searches at hadron colliders (WIMP cogenesis with leptons). W 1 1 ψ production at hadron colliders (WIMP cogenesis with leptons). ± φ ¯ ¯ q q q q , ˜ χ m ψ & → GeV assuming massless LSP T ˜ q / ± E m ψ , the relevant LHC searches are in the cases of 740 , ψ ¯ ¯ ) + χ χ χ χ the same signature as decaying & j hχ 0 2 0 1 . Since we assume mass degeneracy among the different generations ˜ χ (4 ˜ and χ b ± → h m 4 φ φ 0 h h ν = ¯ ν ψ → → TeV, requiring ± 0 2 . † 0 2 ˜ 0 χ 0 ˜ ˜ τ 0 χ † – ψ 0 φ φ ψ 1 0 , m m . Specifically, searches for , respectively, while searches for heavier neutralinos ψ ± ψ . Diagrams relevant for ∼ φ ψ TeV, ATLAS places bounds on the masses charginos and neutralinos with . Diagrams relevant for = ψ φ ˜ µ 13 Z Z m m and At LHC searches for charginos Thus, for successful models where a matter asymmetry is produced from WIMP decays & = ψ, ˜ e ψ ¯ ¯ q q q q Figure 13 nature as decaying and components of m of data with signals: of The figures for these processes are shown in figures of ponent of decaying WIMP decay to leptonselectroweak and doublets. ADM (section Thusnew states at are the produced through LHCquently EW decay the processes as with neutral intermediate and charged components of these assumption of three flavors ofwe mass apply degenerate this exotic bound scalar quarks directly, leading to directly to baryons andm ADM, the intermediate state masses are bound from below as mass degenerate squarks of Figure 12 JHEP12(2020)046 ], is H 1 − 19 (4.1) Y , S 14 , leading to ]) and leave ) 43 GeV. With the χd )( 2 in the low energy ). However, 740 ) ¯ 1 dχ 2 d φ ( Y & α 1 2 φ 2 i scattering. Y α -nucleon cross section is 0 m ψ χ 967 . → m χN 0 ) = − → ∗ ( 0 2 s The only available channel for ± χ α Z ψ χN SI DM-nucleon interactions come d is depleted to triviality in the early ]. The SI 26 m ). ) . . The Feynman diagram for ADM- → ¯ χ : 48 φ (0 2 ψ ) qq GeV n ( m O n . By integrating out + m χ χ φ 14 m m – 19 – ( 2 φ mediated by ]. We apply these bounds directly to the charged m 42 χd 1 π → ≈ . In the case that the asymmetry is produced before the 2 ) d χ GeV [ ]. This can lead to rare or invisible Higgs decay through χd GeV. cm 44 χN [ 700 42 , in WIMP cogenesis (for both the quark and lepton models we 2 − → 700 | 1 & . Dominant process contributing to Y 10 H l ˜ & | 2 χN φ ]: for DM masses within 2–3 GeV, the upper limit on the DM-nucleon m × ( S 2 m 7 SI – : σ or 5 φ ]. The specifics of the signal channel depends on model details about -nucleon effective interaction following [ 2 Figure 14 . | 47 χ χ – H | 45 S [ SS A complementary signal at colliders is possible via the S mixing with the SM Higgs Finally, note that just like in the earlier studied WIMP baryogenesis models [ to interact with quarks is → As we have seen, the DMto mass GeV in range. WIMP cogenesis The modelfrom strongest is DarkSide-50 current predicted [ to limits be on cross in the section sub-GeV is effective theory, the effectivespin-independent DM-quark (SI) interactions interaction between the operator DMbutions is and to nucleon. a These translate to contri- universe, indirect detection rates areprospect negligible. of Therefore we focus on the directWIMP detection decay toχ baryons and ADMdown (section quark scattering is shown in figure h interactions which is beyond the scope of this4.2 work. Dark matterAs direct expected detection in most of asymmetric DM models, since Nevertheless it may bespectacular within signatures reach involving both ofenergy displaced future (ADM). vertices high (baryon energy asymmetry) colliders and missing (e.g. [ through the long-lived WIMP, presented) is alsoproduced expected at to a leavea distinctive collider SM displaced experiment singlet vertex (e.g. with signatures through typically if O(TeV) mass it which can makes be it hard to access with the LHC. directly to the chargedsame and set neutral components of of datadegenerate ATLAS limit places of boundscomponents on of the masses of charged sleptons in the mass JHEP12(2020)046 2 ]. . 49 cm ± (4.2) l GeV, 40 → − 89 . ν 10 × = 0 and 4 . χ 2 ± and scalar mass ), that allow for – m φ 1 GeV, the SI DM- . GeV. However, we 15 1 → 5 . = 1 0 ≈ s φ 700 α ) exchange. The diagram = 2 ∼ − ]. χ = φ χ ψ χe d 51 m [ α 2 → , m 2 φ ! − cm χ . This is not only currently safe m 2 ]. 2 φ χe TeV, we obtain a benchmark value In this model, the dominant process m 37 ( 2 m 51 ]. In the case that − σ cm α TeV and which is well below the bound set by . Taking the benchmark parameters of 52 10 = 2 ). 42

ν – scattering via − φ 3 42 × π 1 = 2 50 gives − Z 4 with the replacements − 2 m 10 0 e – φ α > g 10 φ 1 ≈ × χq m − = 1 ) 2 × . – 20 – χ − → α ≈ SI 02 . χe σ χq ) ν 1 GeV, the upper limit on DM-nucleon scattering is → 1 ≈ – χN − 5 ) . 0 GeV and . χe → ( 2 χN σ and scalar masses cm χN → ( ] and we can have = 700 36 σ GeV. For this mass range, Xenon100 constrains the cross-section qq χ − 39 φ = 1 χN d 10 m 37 ( . – α 1 SI – 38 σ = ]. − : 93 s GeV, . φ 52 10 α . Furthermore, the ADM annihilation to leptons is less constrained than 0 ) of 37 . ∼ ≈ φ,ψ 1 4.1 – SI . Loop diagram contributing to direct detection rate in WIMP cogenesis with leptons. χ m σ m 93 . There are 1-loop processes in WIMP cogenesis with leptons (figure Owing to less stringent collider constraints, the masses of the intermediate states can Now we give numerical examples from our model. With = 0 χ annihilation to quarks [ m which is just below the current bound by Xenon100our [ sub-GeV ADM to scatter with nucleons at direct detection experiments. However, the mass is of DM-scattering with electrons to be be lighter in the modelneed of WIMP WIMP cogenesis cogenesis with to leptons: occuror before below the EWPT, when the temperature would be around Similar to WIMP cogenesisbaryonic with matter today. quarks, In the our ADM example mass model of is WIMP fixed cogenesis by with the leptons, ratio the ADM of DM to WIMP decay to leptons andfor ADM (section direct detection comeis from identical tree-level to thatplaced for with ADM-nucleon electrons. scattering Weintegrating in can out the estimate quark the model, cross with section the for ADM-electron quarks scattering re- by other upcoming direct detectionwe again experiments take [ from eq. ( CRESST but can beLUX-ZEPLIN [ within reach of future searches for sub-GeV DM such as with the between at the lower boundnucleon provided cross by section colliders, is from the most stringent bound, but also within reach future iterations of DarkSide and Figure 15 There is another diagram contributing to EWPT, the DM massSpecifically is below for 1 GeV DM and the masses strongest of bounds come from CRESST [ JHEP12(2020)046 . ∼ v ) 2 + GeV. m π charge . + 4 2 2 Z S S GeV, m 5 . → carry χ = 2 2 , with S + χ 2 years. p S m ( 2 36 σ ! meson momentum from + χ 10 K DM K m × n p 2 2 S ¯ u s m 3 2 = 2 ∼ m 1 p − τ p βγη τ 2 α ), new sources of FCNC are absent due

effectively proceeds with a dimension-7 which then requires χ 3 3 2 , the outgoing ] while this model is fully renormalizable. π χ 2 1 S S R . This interaction, together with the set of 24 16 φ and P + 2 2 2 Y / is much more suppressed due to the very small ¯ ∼ + Y – 21 – depend on model specifics beyond our minimal > m 2 1 ) 2.1 K 2 Y χ + = 1 ψ ]. A benchmark example is: γS S ] while within reach of future experiments such as m 2 K can be a stable subdominant DM, or may decay, e.g. → 55 , a potential signal of B-violating (induced) nucleon S φ 53 2 , and can be estimated as: + χ G 2 ) S 2 L ⊃ d . + S R 1 p Y comes a plethora of potential interactions. Of particular in- → leads to proton lifetime of uP 2 χ )(¯ 1 χ u u d S d + ∼ R p p ) allows for the possibility of induced nucleon decay, as shown in ] and DUNE [ ( χP σ (¯ 54 2.1 2 S 3 2 2 m 2 βγη π 2 flavor symmetry of the model and thus the model is consistent with related α 16 . Potential induced nucleon decay signature arising in a model of WIMP cogenesis with ∼ . The analogous diagram with U(3) 16 . The final decay channels from The scattering process of S to ensure a long lifetime of and generalized baryon number TeV, and all couplings 1 3 4.4 Other experimentalAs constraints discussed in the Modelto Setup the (section This leads to aThis prediction model for can theset lead proton by to lifetime SuperKamiokande a as searchesHyperKamiokande proton [ [ lifetime that is consistent with current lower bound topology here resembles that in Hylogenesis [ operator η to model, which we will deferfor for down-scattering future consideration. processes, Nevertheless where IND a common will feature be is that larger than those resulting from standard nucleon decays. The IND event extension, for instance, byWith introducing this an introduction additional of singletterest scalar, is the Yukawai interaction interactions in eq. ( figure 4.3 Induced nucleonIn decay the model presenteddecay is in highly suppressed section and undetectableservable with induced foreseeable nucleon experiments. decay However, (IND) an signature ob- may arise with a minimal, well-motivated Figure 16 baryons. loop suppression combined with minimalmakes bounds the on rate sub-GeV DM well scattering below with the nucleons sensitivity reach of foreseeable experiments. JHEP12(2020)046 ¯ d ¯ d ¯ u GeV. tripple 5 → . 2 – 7 udd . 0 ∼ DM m ]. The reason is that, the interference 57 , 56 flavor symmetry together forbid couplings. (1) – 22 – U(3) O ]. The authors are supported in part by the US Department , even with 58 φ , and ψ , 2 ) leading to CP violation do not involve SM quarks or leptons, and the , 1 5 Y about cosmic matter abundance in a unified framework: asymmetric dark matter WIMP cogenesis with baryons evades bounds from neutron-antineutron oscillation: the Brian Shuve and Raman Sundrumwere for drawn commenting using on JaxoDraw [ the manuscript.of Feynman Energy diagrams grant DE-SC0008541.(supported by YC the thanks Nationalthe the Science support Foundation Kavli and under Institute hospitality Grant while for No. the Theoretical NSF work PHY-1748958) Physics was for being completed. Acknowledgments We thank Matthew Dolan, Aniket Joglekar and Brian Shuve for discussions. We thank These models can leadmass) to DM direct testable detection, signatures nucleonat decay at and the a the LHC. variety production of offuture Furthermore new experiments, the high SM including charged long-lived energy particles (low WIMP colliders,matter in in leaving these the spectacular early models signals Universe. may by be reproducing accessible the with cogenesis of WIMP miracle. The threeorder. Sakharov ADM conditions and are baryons satisfied (leptons)that in is share three conserved. a subsequent generalized We stages present baryonthe two in (lepton) renormalizable idea, number models symmetry and as benchmarkstates, find examples the that realizing observed DM with and baryon perturbativewith relic relevant densities couplings constraints. can The and be models explained weak-scale neatly while predict being masses ADM compatible for with mass the new and a baryon or lepton asymmetryof are a simultaneously freezeout generated from population the offor same metastable decay the WIMPs. chain matter The abundance WIMPbaryon in plays abundances the the Universe, is role meanwhile of automatically theWIMP grandparent addressed “coincidence” decay via between chain their DM readily co-production. and permits DM Additionally, and the baryon asymmetries to inherit a generalized 5 Conclusion In this paper we proposedpuzzle WIMP cogenesis, a novel mechanism which addresses the intrinsic interactions in the model andconversion the at tree-level and 1-loop (alternativelyflavor with symmetry). small Higher couplings order without process invokingscale is the masses strongly suppressed of by loop factors and the TeV- for the asymmetry generation, themoments model (EDMs) for is the exempt neutron from anddiagrams the electron (figure constraints [ on electricnew dipole fields couple exclusively to right-handed quarks or left-handed leptons. constraints on FCNC. In addition, despite the presence of CP violation source necessary JHEP12(2020)046 . and (A.4) (A.2) (A.3) (A.1) which deter- EWPT are the ) 5 T c i i d ≈ EWPT Q c i T u B i and the wide Ω = 0 Q / i χ ! φ Q is the number of i ( Ω ψ m f EWPT i µ = 0 Y T N ∼ + ! ∼ i ψ H φ m µ µ gives rise to inst H ) f + i O N N L H ) 2 i µ 2 Q + i , we have: H f ) = 0 i i Q e N N i d , we have: µ also contribute, while the magnitude 2 ) = 0 µ Q i ( − ψ EWPT L + − i i T i µ i Y e L u EWPT µ + µ µ and T ∼ i − − φ Q φ − i i µ i sph m d L – 23 – φ Q interact via gauge, Yukawa, and sphaleron pro- µ µ (3 O ∼ µ m i χ − − ψ (2 X i i ∼ u d m i ψ µ µ X ). In the high temperature plasma of the early universe m − , and + 2 1.1 i ψ bear a Boltzmann suppression in their equilibrium density u i . This relationship and the observed ratio , µ Q χ ψ φ µ

+ 2 . With i are the LH leptons. and i Q determines the relationship between number densities of baryons, i , we consider possibilities at two limits: X . These interactions are described by ], while adding in the eﬀects from new particles in WIMP cogenesis φ i µ φ L χ d EWPT

m 60 T , i ∼ is the number of Higgs bosons (1 in the SM) and QCD instanton processes lead to interactions between LH quarks and RH X and 59 ψ , , and i H φ is an index counting the number of generations of fermions and u m ψ N i 32 m , SU(3) φ ∼ ψ where generations of fermions. With to relativistic species. Given theranges unknowns around determining m the hypercharge carried by SMof states, the contribution depends onNon-relativistic their masses relative todistribution which EWPT makes temperature their contribution to hypercharge density negligible relative quarks leads to where LH quarks and electroweak phase transition The total hypercharge of the plasma must vanish at all temperatures. In addition to The The effective sphaleron interaction 3. 2. 1. leptons, and ADM candidate mines the ADM mass asthe in quarks, eq. ( leptons, Higgs, cesses. The interactions that constrain the chemical potentials in thermal equilibrium are: A.1 WIMP decayBefore to the baryons electroweak and phase ADM transitionand (EWPT), (section right-handed chemical quarks equilibrium and ofcogenesis leptons, SM Higgs left-handed bosons, and new fields introduced by WIMP In this appendix we derivecogenesis the before relation electroweak between phase baryon transition. andfor We lepton will the asymmetries follow SM for the WIMP general [ proceduremodels. laid out A Relating baryon and lepton asymmetries for WIMP cogenesis before JHEP12(2020)046 . . , 2 2 H T µ i (A.8) (A.5) (A.6) (A.7) (A.9) XT + (A.10) 1 6 gµ 1 6 Q = µ = − X i n φ ¯ n µ − i and the Yukawa Q Q n , while in equilib- µ µ j ) = , and k allows us to write 2 u H j He H H ψ µ i ¯ ψ LT µ i N N ¯ L H H + . Substituting this and 1 6 φ , Q N N Q ≡ j = µ µ ijk Q Q + + 13 + + 11 3 i which allows us to write all = 0 L µ µ ˜ ψ f f f f Hu − n , β (13 i χ µ Q H H c , N N N N 1 2 ¯ µ µ Q 2 = , χ N N ) i is preserved, while in our model − φ f 14 14 i H , ¯ d L d j . Using the Yukawa interactions of µ i + + + 2 N N BT L µ µ = 0 = 0 = 0 = 0 = 0 φ f f 2 1 2 1 1 6 ) = ) j j j k χ ≡ Hd − + e e d u N N u i − − ∼ L ) µ = i µ µ µ i µ i µ ): ¯ EWPT u Q B e − φ = = = = + B T µ − + − µ − − µ ) give i d ∼ φ n χ B H A.5 i φ L in terms of ( H + µ , H µ + H µ φ WIMP µ µ µ q 1 2 i µ i µ µ A.1 . Thus the preserved combination, per gener- µ SM φ H µ O Q L ) (2 − − e − − µ + O µ µ – 24 – − Q m i i µ i i − d ≡ = j µ (2 (2 L Q Q ψ ∼ µ 2.1 d + χ i µ χ µ i i µ µ µ q ψ µ µ X X L H µ Q µ + m using eqs. ( H N = = = , µ u e (2 Q N Q H µ L f µ B µ X µ + 9 H + N N + H f N f H ≡ N Q N = N N + 3 + i µ number densities are e + 10 L 2 f f + µ Q χ , N N µ f ) , 4 1 2 3 d Nf ) allows us to solve L N µ 2 − − − µ ) can be recast as + A.3 = = = = ≡ u e u L ψ µ A.9 i µ µ µ µ we take the massless limit where their number densities are L + would be preserved. Assuming equilibrium amongst the various generations µ χ Q , X µ Q ) in eq. ( ), eq. ( (2 µ + 2 f interactions introduced in section rium give rise to A.5 A.5 N ≡ L The Yukawa interactions of the SM Let us first analyze the case of 4. i = − Q chemical potentials in terms of eqs. ( The effective sphaleron interactionseqs. of ( eq. ( With SM alone, theB combination of asymmetry µ B ation, is leptons, and The baryon, lepton, and respectively, where Since the temperature before the EWPT is much greater than the masses of the quarks, JHEP12(2020)046 ). is : L n Q χ µ m − | (A.16) (A.17) (A.18) (A.19) (A.11) (A.12) (A.13) (A.14) (A.15) 1 s − c B/B s 5 c | ≡ 2 s c Q Q in terms of = µ µ χ χ H H m H H N N and Q N N µ Q ⇒ + + + 13 + 11 µ H B B yields = f f 1 1 f f H H N φ, ψ, H H ) − s − s L f N N allows us to write the relations N N ) ). In this case, we need only use c c H N N 2 2 + H N N N − N L 3 22 10 4 f + + ≡ ≡ N ,f.o. A.4 B Q Q f f N 1 − Q Q + Y 2 1 2 2 1 µ µ + 4 + 13 + 13 N N µ µ f f f Y B f f f 6 2 f f − − − 1 and N N N N N N N N 0 = = = = 8 H H 4( n ρ H H and 22 14 d H φ | χ H H N N m H 1 N N µ µ µ H N ]. L 0 µ N N s , − N B, L, ) = ) = s + 9 + + 9 32 , we use eq. ( + c s B + – 25 – L L Q f f f + 13 + 13 + c 5 f Q Q | f µ f f f N N N − − µ µ N 2 N f f which changes the last two Yukawa interactions in N N N 14 10 2 = B B EWPT H N N ( ( Q H T 22 14 − − N Q ¯ µ WIMP cogenesis, the biggest change is to the Yukawa B ψχ N µ B/ B/ = 4 = = = = = 4 H 3 H + 9 + H H φ ≡ ≡ L L L L N B B N ,H f f N N s s c m − − = 5Ω c c N N + − + + 3 2 ∼ ¯ f B B Lχ 14 f f f Q φ ) to find the chemical potentials of ψ N N N N ,f.o. µ 2 1 2 2 2 1 2 m 3 ∼ Y A.9 − − − − Y 1 = = = = 0 e u L ψ s WIMP µ 0 µ χ µ µ ρ O m 2 ) in a straightforward fashion. We note also the mass of the ADM candidate = A.5 In the other limit, Plugging these into the equations for DM Ω interactions: eqs. ( fixed by the observed ratio of DM to baryon energy densities fixed by: which is the same as the result inA.2 the SM [ WIMP decayIn to the leptons model and outlined ADM in (section section where Plugging these into the same equations for the SM Yukawa interactions toWe find can the still SM use chemical eq. potentials ( (and thus where between them: JHEP12(2020)046 , JCAP (A.20) (A.21) (A.22) (A.23) (A.24) , 651 ) is found, to be Q A.19 µ Q Q Astron. Astrophys. µ µ , H H H H N N N N ]. Q Q + + J. Phys. Conf. Ser. + 19 + 13 µ µ , B f f f f 1 H H H N N − s SPIRE N N N N N 2 2 c f . IN H 42 22 + + + N H ≡ ][ N 4 f f f Q N H H H Q 1 2 1 2 µ N N N H H H µ N N N f 2 6 2 − − f + 13 + 4 N N N N N = = = = f f + + + H + 19 + 13 + 13 H u φ N N ψ H H f f f N 8 f f f µ µ ]. µ H N µ ]. N 30 N N N ]. N N N N 2 2 2 + 9 + = are 34 30 22 Q + – 26 – f f + 13 µ Q SPIRE f L χ SPIRE f N N µ 1 2 1 2 1 2 IN SPIRE 2 N arXiv:1802.06994 f IN − N B H 22 2 [ − − − IN ][ N Q ][ and H B 30 N − ][ µ = = = Q N ψ H ≡ = = 4 = φ χ ψ µ ), which permits any use, distribution and reproduction in , H + µ µ s µ N + 13 H H L L φ B c N f f N N are heavy, the same result as that given in eq. ( Low-Mass Dark Matter Search with the DarkSide-50 Experiment − N + 3 + N 2 ψ − + Planck 2018 results. VI. Cosmological parameters f f B 30 f f (2018) 081307 N N Q N N 2 µ and 2 2 10 1 2 3 Identifying WIMP dark matter from particle and astroparticle data CC-BY 4.0 φ 121 − − − − arXiv:1807.06209 arXiv:1402.3673 arXiv:1712.04793 [ This article is distributed under the terms of the Creative Commons = = = = [ [ Overview of searches for dark matter at the LHC e d χ L collaboration, µ µ µ µ collaboration, (2020) A6 (2018) 026 Phys. Rev. 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