Baryogenesis and dark matter from B mesons

We present a new mechanism of baryogenesis and dark matter production in which both the dark matter relic abundance and the baryon asymmetry arise from neutral B meson oscillations and subsequent decays. This setup is testable at hadron colliders and B factories. In the early universe, decays of a long lived particle produce B mesons and antimesons out of thermal equilibrium. These mesons/antimesons then undergo CP violating oscillations before quickly decaying into visible and dark sector particles. Dark matter will be charged under the baryon number so that the visible sector baryon asymmetry is produced without violating the total baryon number of the Universe. The produced baryon asymmetry will be directly related to the leptonic charge asymmetry in neutral B decays: an experimental observable. Dark matter is stabilized by an unbroken discrete symmetry, and proton decay is simply evaded by kinematics. We will illustrate this mechanism with a model that is unconstrained by dinucleon decay, does not require a high reheat temperature, and would have unique experimental signals — a positive leptonic asymmetry in B meson decays, a new decay of B mesons into a baryon and missing energy, and a new decay of b -flavored baryons into mesons and missing energy. These three observables are testable at current and upcoming collider experiments, allowing for a distinct probe of this mechanism. DOI


I. INTRODUCTION
The Standard Model of Particle Physics (SM), while now tested to great precision, leaves many questions unanswered.At the forefront of the remaining mysteries is the quest for dark matter (DM); the gravitationally inferred but thus far undetected component of matter which makes up roughly 26% of the energy budget of the Universe [2,3].Many models have been proposed to explain the nature of DM, and various possible production mechanisms to generate the the DM relic abundancemeasured to be Ω DM h 2 = 0.1200 ± 0.0012 [3] -have been proposed.However, experiments searching for DM have yet to shed light on its nature.
Another outstanding question may be stated as follows: why is the Universe filled with complex matter structures when the standard model of cosmology predicts a Universe born with equal parts matter and anti-matter?A dynamical mechanism, Baryogenesis, is required to generate the primordial matter-antimatter asymmetry; Y B ≡ (n B −n B )/s = (8.718± 0.004)×10 −11 , inferred from measurements of the Cosmic Microwave Background (CMB) [2,3] and Big Bang Nucleosynthesis (BBN) [4,5].A mechanism of Baryogenesis must satisfy the three Sakharov conditions [6]; C and CP Violation (CPV), baryon number violation, and departure from thermal equilibrium.
It is interesting to consider models and mechanisms that simultaneously generate a baryon asymmetry and produce the DM abundance in the early Universe.For instance, in models of Asymmetric Dark Matter [7][8][9][10][11][12], DM carries a conserved charge just as baryons do.Most models of Baryogenesis and/or DM production involve very massive particles and high temperatures in the early Universe, making them impossible to test directly and in conflict with cosmologies requiring a low inflation or reheating scale.
In this work we present a new mechanism for Baryogenesis and DM production that is unconstrained by nucleon or dinucleon decay, accommodates a low reheating scale T RH ∼ O(10 MeV), and has distinctive experimental signals.
We will consider a scenario where b-quarks and antiquarks are produced by late, out of thermal equilibrium, decays of some heavy scalar field Φ (which can be, for instance, the inflaton or a string modulus).The produced quarks hadronize to form neutral B-mesons and anti-mesons which quickly undergo CP violating oscillations 1 , and decay into a dark sector via a ∆B = 0 four Fermi operator i.e. a component of DM is assumed to be charged under baryon number.In this way the baryon number violation Sakharov condition is "relaxed" to an apparent violation of baryon number in the visible sector due to a sharing with the dark sector (in similar spirit to [1,14]).The decay of B mesons into baryons, mesons and missing energy would be a distinct signature of our mechanism that can be searched for at experiments such as Belle-II.Additionally, the ∆B = 0 operator allows us to circumvent constraints arising in models with baryon number violation.We will show that the CPV required for Baryogenesis is directly related to an experimental observable in neutral B meson decays -the leptonic charge asymmetry A q .Schematically, where we sum over contributions from both B 0 s = | b s and B 0 d = | b d , and Br(B 0 q → φξ + Baryon + X) is the branching fraction of a B meson into a baryon and DM (plus additional mesons X).Note that a positive value of A q will be required to generate the asymmetry.Given a model, the charge asymmetry can be directly computed from the parameters of the B 0 q oscillation system (for instance see [5,15] for reviews), and as such it is directly related to the CPV in the system.Meanwhile, A q is experimentally extracted from a combination of various analysis of LHCb and B-factories by examining the asymmetry in various B 0 q decays [5].The SM predictions for A d and A s [15,16] are respectively a factor of 5 and 100 smaller than the current constraints on the leptonic asymmetry.Therefore, there is room for new physics to modify A d, s .We will see that since generating the baryon asymmetry in our set-up requires a positive charge asymmetry, there is a region of parameter space where we can get enough CPV from the SM prediction (which is positive) of A s alone to get Y B ∼ 10 −10 (provided A d = 0).However, generically the rest of our parameter space will assume new physics.Note that there are many BSM models that allow for a substantial enlargement of the leptonic asymmetries of both B 0 d and B 0 s systems over the SM values (see e.g.[15,17] and references therein).Note that the flavorful models invoked to explain the recent B-anomalies also induce sizable mixing in the B s system (see e.g.[18][19][20][21]).
We summarize the key components of our set-up which will be further elaborated upon in the following sections: • A heavy scalar particle Φ late decays out of thermal equilibrium to b quarks and anti-quarks.
• Since temperatures are low, a large fraction of these b quarks will then hadronize into B mesons and antimesons.
• The neutral mesons undergo CP violating oscillations.
• B mesons decay into into the dark sector via an effective ∆B = 0 operator.This is achieved by assuming DM carries baryon number.In this way total baryon number is conserved.
• Dark matter is assumed to be stabilized under a discrete Z 2 symmetry, and proton and dinucleon decay are simply forbidden by kinematics.
Our set up is illustrated in Figure 1, and the details of a model that can generate such a process will be discussed below.This paper is organized as follows: in Section II we introduce a model that illustrates our mechanism for Baryogenesis and DM generation, this is accompanied by a discussion of the unique way in which this set-up realizes the Sakharov conditions.Next, in Section III we analyze the visible baryon asymmetry and DM production in the early Universe, by solving a set of Boltzmann equations, while remaining as agnostic as possible about the details of the dark sector.Our main results will be presented here.Next, in Section IV we discuss the various possible searches that could probe our model, and elaborate upon the collider, direct detection, and cosmological considerations that constrain our model.In Section V we outline the various possible dark sector dynamics.We conclude in Section VI.

II. BARYOGENESIS AND DARK MATTER: SCENARIO AND INGREDIENTS
We now elaborate upon the details of our mechanism, and in particular highlight the unique way in which this proposal satisfies the Sakharov conditions for generating a baryon asymmetry.Afterwards we will present the details of an explicit model that will contain all the elements needed to minimally realize our mechanism of Baryogenesis and DM production.

A. Cosmology and Sakharov Conditions
Key to our mechanism is the late production of bquarks and anti-quarks in the early Universe.To achieve this we assume that a massive, weakly coupled, long lived scalar particle Φ dominates the energy density of the early Universe after inflation but prior to Big Bang nucleosynthesis.Φ could be an Inflaton field, a string modulus, or some other particle resulting from preheating.Φ is assumed to decay, out of thermal equilibrium to b-quarks and anti-quarks.While our mechanism will work in scenarios in which Φ is produced after inflation, for simplicity we will call Φ the Inflaton.We only require that Φ decays late enough so that the Universe is cool enough ∼ O(10 MeV) for the b quarks to hadronize before they decay i.e.
The lower bound ensures that Baryogenesis completes prior to nucleosynthesis.Note that given a long lived scalar particle late b quark production is rather genericthere is no obstruction to scenarios in which Φ decays to a variety of heavy particles: Φ particles mainly decay to massive particles, namely t, b quarks, and Higgs bosons.Therefore, particles produced by the late decays of Φ will typically be either b-quarks, or will have prompt decay modes with substantial branching fractions into b-quarks.For definiteness we will simply assume that Φ decays out of thermal equilibrium directly into b and b quarks.
The b quarks, injected into the Universe at low temperatures, will mostly hadronize as B mesons -B 0 d , B 0 s , and B ± .Upon hadronization the neutral B 0 q mesons will quickly undergo CP violating B 0 q − B0 q oscillations [5].Such CPV occurs in the SM (and is sizable in the B systems), but could also be augmented by new physics.In this way a long lived scalar particle realizes, rather naturally, two of the Sakharov conditions -departure from thermal equilibrium and CPV.Interestingly, we will find a region in parameter space where our mechanism can work with just the CPV of the SM, contrary to the usual lore in which the CPV condition must come from beyond the SM physics.
Let us now address the remaining Sakharov condition: baryon number violation.While baryon number violation appears in the SM non-perturbatively [22], and is utilized in Leptogenesis models [23][24][25][26][27], the SM baryon number violation will be suppressed at the low temperatures we consider here (as it must to ensure the stability of ordinary matter).It is possible to engineer models that utilize low scale baryon number violation, but this usually requires an arguably less than elegant construction.For instance, in the setup of [28,29] baryon number violation occurred primarily in heavy flavor changing interactions so as to sufficiently suppress the di-nucleon decay rate, which required a very particular flavor structure.In the present work, we assume that DM is charged under baryon number, thereby allowing for the introduction of new baryon number conserving dark-SM interactions.
If the B mesons, after oscillations, can quickly decay to DM (plus visible sector baryons), the CPV from B 0 q − B0 q oscillations will be transferred to the dark sector leading to a matter-antimatter asymmetry in both sectors.Critically, the total baryon number of the Universe, which is now shared by both visible and dark sectors, remains zero.In this way we have "relaxed" the baryon number violation Sakharov condition to an apparent Baryon number violation in the visible sector.

B. An Explicit Model
We now present an explicit model which realizes our mechanism.Minimally, we introduce four new particles; a long lived weakly coupled massive scalar particle Φ (discussed above), an unstable Dirac fermion ψ carrying baryon number, and two stable DM particles -a Majorana fermion ξ and a scalar baryon φ.All are assumed to be singlets under the SM gauge group.To generate effective interactions between the dark and visible sectors, we introduce a TeV mass, colored, electrically charged scalar particle Y .We assume a discrete Z 2 symmetry to stabilize the DM.Table I summarizes the new fields (and their charge assignments) introduced in this model.Possible extensions to this minimal scenario will be considered in later sections.

Operators and Charges
To generate renormalizable interactions between the visible and dark sectors, we a assume a UV model similar to that of [28,29].We introduce a −1/3 electrically charged, baryon number −2/3, color triplet scalar Y which can couple to SM quarks.Such a new particle is theoretically motivated, for instance Y could be a squark of a theory in which a linear combination of the SM baryon number U (1) B and a U (1) R symmetry is conserved [30].The details of the exact nature and origin of Y are not important for the present set-up.Additionally, we introduce a new neutral Dirac fermion ψ carrying baryon number −1.The renormalizable couplings between ψ and Y allowed by the symmetries include 2 : We take the mass of the colored scalar to be m Y ∼ O(TeV) and integrate out the field Y for energies less than its mass, resulting in the following four fermion operator in the effective theory: Other flavor structures may also be present but for simplicity we consider only the effects of the above couplings (see Appendix 4 for other possible operators).Assuming ψ is sufficiently light, the operator of Equation ( 3) allows the b-quark within B q = | b q to decay; b → ψ u s, or equivalently B q → ψ+Baryon+X, where X parametrizes mesons or other additional SM particles.Critically, note that O = u s b in Equation ( 3) is a ∆B = 1 operator, so that the operator in Equation ( 3) is baryon number conserving since ψ carries a baryon number −1.
In this way our model allows for the symmetric out of thermal equilibrium production of B mesons and antimesons in the early Universe, which subsequently undergo CP violating oscillations i.e. the rate for B 0 → B0 will differ from that of B0 → B 0 .After oscillating the mesons and anti-mesons decay via Equation (3) generating an asymmetry in visible baryon/anti-baryon and dark ψ/ ψ particles (the decays themselves do not introduce additional sources of CPV), so that the total baryon asymmetry of the Universe is zero. 2 We have suppressed fermion indices for simplicity as there is a unique Lorentz and gauge invariant way to contract fields.In particular, the s c and b c are SU(2) singlet right handed Weyl fields.Under SU (3)c, the first term of Equation ( 2) is the fully anti-symmetric combination of three 3 fields, which is gauge invariant.While the second term is a 3 × 3 = 1 singlet.Since, no net baryon number is produced, this asymmetry could be erased if the ψ particles decay back into visible anti-baryons.Such decays may proceed via a combination of the coupling in Equation ( 3) and weak loop interactions, and are kinematically allowed since m ψ > 1.2 GeV to ensure the stability of neutron stars [31].To preserve the produced visible/dark baryon asymmetry, the ψ particles should mainly decay into stable DM particles.This is easily achieved by minimally introducing a dark scalar baryon φ with baryon number −1, and a dark Majorana fermion ξ.We further assume a discrete Z 2 symmetry under which the dark particles transform as ψ → ψ, φ → −φ and ξ → −ξ.Then the ψ decay can be mediated by a renormalizable Yukawa operator: which is allowed by the symmetries of our model.And in particular, the Z 2 (in combination with kinematic constraints), will make the two dark particles, ξ and φ, stable DM candidates.In this way an equal and opposite baryon asymmetry to the visible sector is transferred to the dark sector, while simultaneously generating an abundance of stable DM particles.The fact that our mechanism proceeds through an operator that conserves baryon number alleviates the majority of current bounds that would otherwise be very constraining (and would require less than elegant model building tricks to evade).Furthermore, the decay of a Bmeson (both neutral and charged) into baryons, mesons and missing energy would yield a distinctive signal of our mechanism at B-factories and hadron colliders.An example of a B meson decay process allowed by our model is illustrated in Figure 2.
Note that, as in neutrino systems, neutral B meson oscillations will only occur in a coherent system.Additional interactions with the mesons can act to "measure" the system and decohere the oscillations [32,33], thereby suppressing the CPV and consequently diminishing the generated asymmetry.Spin-less B mesons do not have a magnetic moment.However, due to their charge distribution, scattering of e ± directly off B mesons can still decohere the oscillations (see Appendix 1 for details).To avoid decoherece effects, the B mesons must oscillate at a rate similar to or faster then the e ± B 0 → e ± B 0 scattering in the early Universe.

Parameter Space and Constraints
To begin to explore the parameter space of our model we note that the particle masses must be subject to several constraints.For the decay ψ → φ ξ to be kinematically allowed we have the following: Note that there is also a kinematic upper bound on the mass of the ψ such that it is light enough for the decay B/ B → ψ/ ψ + Baryon/anti-Baryon + Mesons to be allowed.This bound depends on the specific process under consideration and final state visible sector hadrons produced, for instance in the example of Figure 2 it must be the case that m ψ < m B 0 d − m Λ 4.16 GeV.A comprehensive list of the possible decay processes and the corresponding constraint on the ψ mass are itemized in Appendix 4.
As mentioned above, DM stability is ensured by the Z 2 symmetry, and the following kinematic condition: The mass of a dark particle charged under baryon number must be greater then the chemical potential of a baryon in a stable two solar mass neutron star [31].This leads to the following bound3 : Additionally, the constraint (7) automatically ensures proton stability.The corresponding restrictions on the range of particle masses, along with the rest of our model parameter space, is summarized in Table II.

Dark Sector Considerations
Throughout this work we remain as model independent as possible regarding additional dark sector dynamics.Our only assumption is the existence of the dark sector particles ψ, ξ and φ.In general the dark sector could be much richer; containing a plethora of new particles and forces.Indeed, scenarios in which the DM is secluded in a rich dark sector are well motivated by top-down considerations (see for instance [35] for a review).Additionally, there are practical reasons to expect (should our mechanism describe reality) a richer dark sector.
The ratio of DM to baryon energy density has been measured to be 5.36 [3].Therefore, for the case where φ is the lightest dark sector particle, it must be the case that m φ n φ ∼ 5m p n B .Since ξ does not carry baryon number and ψ decays completely, once all of the symmetric ψ component annihilates away we will be left with: n B = n φ , implying that m φ ∼ 5m p -inconsistent with the kinematics of B mesons decays (m φ < m B −m Baryon ).Introducing additional dark sector baryons can circumvent this problem.
For instance, imagine adding a stable dark sector state A. We assume A carries baryon number Q A , and in general be given a charge assignment which allows for A − φ interactions (e.g.Q A = 1/3).Then the condition that ρ DM ∼ 5ρ B becomes: Interactions such as φ + φ * ↔ A + A * can then reduce the φ number density, such that in thermodynamic equilibrium we need only require that m A ∼ 5Q A m p , while φ can be somewhat heavier.In principle A may have fractional baryon number so that both B decay kinematics and proton stability are not threatened.
Additionally, the visible baryon and anti-baryon products of the B decay are strongly interacting, and as such generically annihilate in the early Universe leaving only a tiny excess of baryons which are asymmetric.Meanwhile, the ξ and φ particles are weakly interacting and have masses in the few GeV range.Since, as given the CP violation is at most at the level of 10 −3 the DM will generically be overproduced in the early Universe unless the symmetric component of the DM undergoes additional number density reducing annihilations.One possible resolution is if the dark sector contained additional states, which interacted with the ξ and φ allowing for annihilations to deplete the DM abundance so that the sum of the symmetric (m ξ n ξ + m φ [n φ + n φ ]) and the antisymmetric (m φ [n φ − n φ ]) components match the observed DM density value.
We defer a discussion of specific models leading to the depletion of the symmetric DM component to Section V.In what follows, we simply assume a minimal dark particle content and consider the interplay between ψ, φ, and ξ via Equation (4), and account for additional possible dark sector interactions with a free parameter.

III. BARYON ASYMMETRY AND DARK MATTER PRODUCTION IN THE EARLY UNIVERSE
Using the explicit model of Sec.II B, we now perform a quantitative computation of the relic baryon number and DM densities.We will show that it is indeed possible to produce enough CPV from B meson oscillations to explain the measured baryon asymmetry in the early Universe.Interestingly, there will be a region of parameter space where the positive SM asymmetry in B 0 s oscillations is alone, without requiring new physics contributions, sufficient to generate the matter-antimatter asymmetry.Additionally, we will see that a large parameter space exists that can accommodate the measured DM abundance.To study the interplay between production, decay, annihilation and radiation in the era of interest we study the corresponding Boltzmann equations.

A. Boltzmann Equations
The expected baryon asymmetry and DM abundance are calculated by solving Boltzmann equations that describe the number and energy density evolution of the relevant particles in the early Universe: the late decaying scalar Φ, the dark particles ξ, φ, φ and radiation (γ, e ± , ν, ...).The processes of hadronization, oscillations and decay happen very rapidly compared with the Φ lifetime; therefore allowing for approximations that significantly simplify the Boltzmann equations.We justify these assumptions below and in Appendix 2.

Radiation and the Inflaton
First we describe the evolution of Φ and its interplay with radiation.Φ need not be the Inflaton, but for simplicity we assume that at times much earlier than 1/Γ Φ , the energy density of the Universe was dominated by nonrelativistic Φ particles, and that all of the radiation and matter of the current Universe resulted from Φ decays.Furthermore, the inflaton decay products are very rapidly converted into radiation, and as such the Hubble parameter during the era of interest is: The Boltzmann equations describing the evolution of the inflaton number density and the radiation energy density read: where the source terms on the right-hand side of (9) describe the Φ decays which cause the number density of Φ to decrease as energy is being dumped into radiation.Note that if we pick an initial time t 1/Γ Φ , then ρ rad is small enough that there is no sensitivity to initial conditions and may set ρ rad = 0.In practice, we assume that at some high T > m Φ , Φ was in thermal equilibrium with the plasma and that at some temperature T dec it decouples; fixing the Φ number density to n Φ (T dec ) = ζ(3) π 2 T 3 dec .This number density serves as our the initial condition and is subsequently evolved using Equation (9).For numeric purposes, we assume that the scalar decouples at T dec = 100 GeV.We note that, as expected, our results will not be sensitive to the exact decoupling temperature provided T dec > 15 GeV i.e. when all the SM particles except the top, Higgs and Electroweak bosons are still relativistic.

Dark Sector
The Boltzmann equation for the dark Majorana fermion ξ, the main DM component in our model when m ξ < m φ , reads: where we have assumed that the processes of b/ b production, hadronization and decay to the dark sector (see Appendix 2), all happen very rapidly on times scales of interest i.e. the ψ particle production and subsequent decay happens rapidly and completely and we need not track the ψ abundance.Therefore, the second term on the right hand side of Equation ( 11) entirely accounts for the dark particle production via the decays Φ → B B → dark sector + visible, and so we have defined: Here Γ Φ is the Φ decay width, and Br(B → φξ+Baryon+ X) is the inclusive branching ratio of B mesons into a baryon plus DM.The b quarks and anti-quark within all flavors of B mesons and anti-mesons (both neutral and charged B 0 d,s and B ± ), will contribute to the ξ abundance via decays through the operators in Equations ( 3) and ( 4).Therefore, in Equation ( 11), we have implicitly set the branching fraction of Φ into charged and neutral B mesons: Br(Φ → BB) = 1.Note that only the neutral B 0 d,s mesons can undergo CP violating oscillations thereby contributing to the matter-antimatter asymmetry.Therefore, we should account for the branching fraction into B 0 s,d mesons and anti-mesons when considering the asymmetry.
The first term on the right hand side of Equation ( 11) allows for additional interactions, whose presence we require to deplete the symmetric DM component as discussed above.
For the region in parameter space where m ξ > m φ , DM is composed of the scalar baryons and anti-baryons, and the DM relic abundance is found by solving for the symmetric component, namely: Analogously to the Boltzmann equation describing the ξ evolution, the second term on the right hand side of Equation ( 13) accounts for possible dark sector interactions and self-annihilations, while the first term describes dark particle production via decays.Again we assume the ψ fermion decays instantaneously, and DM can be produced from the decay of both neutral and charged B mesons and anti-mesons.
As previously discussed, DM generically tends to be overproduced in this set-up.Additional interactions are required to deplete the DM abundance in order to reproduce the observed value.Whether the DM is comprised primarily of ξ or φ + φ * , the scattering term in the Boltzmann equations allows for the dark particle abundance to be depleted by annihilations into lighter species.In our model, the thermally averaged annihilation cross sections for the fermion and scalar will receive contributions from φ − ξ generated by the Yukawa coupling of Equation ( 4) (see Appendix 3 for rates).This interaction will transform the heavier dark particle population into the lighter DM state.The annihilation term can, in general, receive contributions from additional interactions.Therefore, when solving the Boltzmann equations, we simply parametrize additional contributions to σv ξ and σv φ+φ * by a free parameter.In Sec.V, we will outline a couple of concrete models that accommodate a depletion of the symmetric DM component.
We have derived Equation ( 13) by tracking the particle and anti-particle evolution of the complex φ scalar using the following Boltzmann equations: where we sum over contributions from B 0 q=s,d oscillations.Likewise, Since the the φ and φ * particles are produced via several combinations of meson/anti-meson oscillations and decays, we encapsulate the corresponding decay width difference in a quantity A q (defined explicitly below in Equation ( 17)), which is a measure of the CPV in the B 0 d and B 0 s systems.A q is weighted by a function f q deco describing decoherence effects -these will play a critical role in the evolution of the matter-antimatter asymmetry as we discuss below.For the symmetric DM component, the solution of Equation ( 13), the dependance on A q cancels off as expected.
Finally, note that Equations ( 13) and ( 11) hold in the regime where the two masses m φ and m ξ are significantly different.For the case where m φ ∼ m ξ coannihilations become important i.e. there will be rapid φ + φ * ↔ ξ + ξ processes mediated by ψ which will enforce a relation between n ξ and n φ+φ * .Specifically, in the non-relativistic limit n ξ /n φ = exp (m φ − m ξ )/T D , so that the equilibrium abundance depends on the dark sector temperature.It is reasonable to consider a construction where T D < |m φ − m ξ |, so that it is justified to set the equilibrium abundance of the heavier particle to zero.However, since coannihilations represents a very small branch in our parameter space, for simplicity and generality, we simply assume we are far from the regime where coannihilations effects are important so that we can solve Equations ( 11), ( 14) and ( 15) for the dark sector particle abundances.

Baryon Asymmetry
The Boltzmann equation governing the production of the baryon asymmetry is simply the difference of the particle and anti-particle scalar baryon abundances Equation (14) and Equation (15): where we must consider contributions from decays of the b anti-quarks/quarks within both B 0 d and B 0 s mesons/anti-mesons: we take the branching fraction for the production of each meson to be Br( b → B 0 d ) = 0.4 and Br( b → B 0 s ) = 0.1 according to the latest estimates [5].
Interestingly, we see from integrating Equation ( 16) that the baryon asymmetry is fixed by the product A q × Br(B 0 q → ξφ + Baryon + X) -a measurable quantity at experiments.In particular, A q is defined as: which is directly related to the CPV in oscillating neutral B meson systems.Here f and f are taken to be final states that are accessible by the decay of b/ b only.Note that as defined, Equation ( 17) corresponds to the semi-leptonic asymmetry (denoted by A q SL in the literature) in which the final state may be tagged.However, at low temperatures and in the limit when decoherence Annihilation Xsec for ξ (6 − 20) × 10 −25 cm 3 /s 10 −24 cm 3 /s Depends upon the channel [3] TABLE II.Parameters in the model, their explored range, benchmark values and a summary of constraints.Note that the benchmark value for A q × Br(Bq → φξ + Baryon + X), for σv φ and σv ξ are fixed by the requirement of obtaining the observed Baryon asymmetry (YB = 8.7 × 10 −11 ) and the correct DM abundance (ΩDMh 2 = 0.12) respectively.
effects are small, this is effectively equivalent to the leptonic charge asymmetry for which one integrates over all times.Therefore, in the present work we will use the two interchangeably.
Maintaining the coherence of B 0 oscillation is crucial for generating the asymmetry; additional interactions with the B mesons can act to "measure" the state of the B meson and decohere the B 0 q − B0 q oscillation [32,33], thereby diminishing the CPV and so too the generated baryon asymmetry.B mesons, despite being spin-less and charge-less particles, may have sizable interactions with electrons and positrons due to the B's charge distribution.Electron/positron scattering e ± B q → e ± B q , if faster than the B 0 q oscillation, can spoil the coherence of the system.We have explicitly found that this interaction rate is two orders of magnitude lower than for a generic baryon [29], but for temperatures above T 20 MeV the process Γ(e ± B → e ± B) occurs at a much higher rate than the B meson oscillation and therefore precludes the CP violating oscillation.We refer the reader to Appendix 1 for the explicit calculation of the e ± B → e ± B scattering process in the early Universe.
Generically, decoherence will be insignificant if oscillations occur at a rate similar or faster then the B 0 meson interaction.By comparing the e ± B q → e ± B q rate with the oscillation length ∆m Bq , we construct a steplike function (we have explicitly checked that a Heaviside function yields similar results) to model the loss of coherence of the oscillation system in the thermal plasma: We take ∆m B d = 3.337 × 10 −13 GeV and ∆m Bs = 1.169 × 10 −11 GeV [5], and Γ e ± B 0 q → e ± B 0 q = 10 −11 GeV (T /20 MeV) 5 (see Appendix 1 for details).
Even without numerically solving the Boltzmann equations, we can understand the need for additional interactions in the dark sector σv ξ,φ .From Equations ( 11) and ( 13), we see that the DM abundance is sourced by Br(B → φξ + Baryon + X)); the greater the value of this branching fraction, the more DM is generated.From Equation ( 16), we see that the asymmetry also depends on this parameter but weighted by a small number; A q < 4×10 −3 .Therefore, generically a region of parameter space that produces the observed baryon asymmetry will overproduce DM, and we require additional interactions with the DM to deplete this symmetric component and reproduce Ω DM h 2 = 0.120.

B. Numerics and Parameters
We use Mathematica [36] to numerically integrate the set of Boltzmann Equations ( 9), (10), (11), (13), and ( 16) subject to the constraint Equation (8).To simplify the numerics it is useful to use the temperature T as the evolution variable instead of time.Conservation of energy yields the following relation [37,38]: which above the neutrino decoupling temperatures T 3 MeV simplifies to [39]: We can therefore use Equation (20) in place of Equation (10).For the number of relativistic species contributing to entropy and energy g * ,s (T ) and g * (T ), we use the values obtained in [40].Finally, since the DM particles generically have masses greater then a GeV we can safely neglect the inverse scatterings in the DM Boltzmann equations i.e. the n 2 eq term.To make the integration numerically straightforward we change variables and solve the equations for log n and log T , such that nient yield variables Yx = nx/s.
The parameter space of our model includes the particle masses, the inflation decay width, the dark Yukawa coupling, the branching ratio of B mesons to DM and a hadrons, the leptonic asymmetry, and the dark sector annihilation cross sections.Table .II summarizes the parameters and the range of over which they are allowed to vary taking into account all constraints.DM masses are constrained by kinematics, proton and neutron star stability -Equations ( 5), ( 6) and (7).We take the Yukawa coupling in the dark sector to be 0.3 since this value enables an e cient depletion of the heavier DM state to the lower one, thus simplifying the phenomenology.For su ciently lower values of this coupling we may require interactions of both the ⇠ and states with additional particles.
The current bounds [4] on the leptonic asymmetry read A d ``= 0.0021 ± 0.0017 and A s ``= 0.0006 ± 0.0028 for the B 0 d and B 0 s systems respectively.Note that these values allow for additional new physics contributions beyond those expected from the SM alone: A s ``|SM = (2.22 ± 0.27) ⇥ 10 5 and A d SL |SM = ( 4.7 ± 0.6) ⇥ 10 4 .While there is no direct search for the branching ratio Br(B 0 q !⇠ + Baryon + X), we can constrain the range of experimentally viable values.For instance, in the example of Figure 2 where the produced baryon is a ⇤ = |u s si, we can, based on the B + decay to cX, set the bound Br(B !⇠ + Baryon) < 0.1 at 95% CL.
⌦DMh 2 = 0.12 ( 24) Br (B !⇠ + Baryon + X) = 5.6 ⇥ 10 3 (26) A s ``= 10 4 (28) A s ``= 10 3 (32) that we also convert to the conve- ce of our model includes the partiion decay width, the dark Yukawa ing ratio of B mesons to DM and ic asymmetry, and the dark sector tions.Table .II summarizes the pae of over which they are allowed to unt all constraints.
strained by kinematics, proton and -Equations ( 5), ( 6) and (7).We pling in the dark sector to be 0.3 s an e cient depletion of the heavower one, thus simplifying the pheciently lower values of this coupling actions of both the ⇠ and states les.
[4] on the leptonic asymmetry read 17 and A s ``= 0.0006 ± 0.0028 for ms respectively.Note that these itional new physics contributions ed from the SM alone: . ect search for the branching ratio n + X), we can constrain the range ble values.For instance, in the where the produced baryon is a based on the B + decay to cX, set + Baryon) < 0.1 at 95% CL.
⌦ DM h 2 = 0.12 ( 24) Br (B !⇠ + Baryon + X) = 5.6 ⇥ 10 3 (26) A s ``= 10 4 (28) A s ``= 10 3 (32) The parameter space of our model includes the particle masses, the inflation decay width, the dark Yukawa coupling, the branching ratio of B mesons to DM and a hadrons, the leptonic asymmetry, and the dark sector annihilation cross sections.Table.II summarizes the parameters and the range of over which they are allowed to vary taking into account all constraints.
DM masses are constrained by kinematics, proton and neutron star stability -Equations ( 5), ( 6) and (7).We take the Yukawa coupling in the dark sector to be 0.3 since this value enables an e cient depletion of the heavier DM state to the lower one, thus simplifying the phenomenology.For su ciently lower values of this coupling we may require interactions of both the ⇠ and states with additional particles.
The current bounds [4] on the leptonic asymmetry read A d ``= 0.0021 ± 0.0017 and A s ``= 0.0006 ± 0.0028 for the B 0 d and B 0 s systems respectively.Note that these values allow for additional new physics contributions beyond those expected from the SM alone: A s ``|SM = (2.22 ± 0.27) ⇥ 10 5 and A d SL |SM = ( 4.7 ± 0.6) ⇥ 10 4 .While there is no direct search for the branching ratio Br(B 0 q !⇠ + Baryon + X), we can constrain the range of experimentally viable values.For instance, in the example of Figure 2 where the produced baryon is a ⇤ = |u s si, we can, based on the B + decay to cX, set the bound Br(B !⇠ + Baryon) < 0.1 at 95% CL.
⌦DMh 2 = 0.12 ( 24) Br (B !⇠ + Baryon + X) = 5.6 ⇥ 10 3 (26) A s ``= 10 4 (28) A s ``= 10 3 (32) f Majorana ⇠ particles, as we take m⇠ = 1 GeV and m = 1.5 GeV.We take both the B 0 s and B 0 that we also convert to the convex = nx/s.e of our model includes the partion decay width, the dark Yukawa ng ratio of B mesons to DM and ic asymmetry, and the dark sector ions.Table.II summarizes the pae of over which they are allowed to nt all constraints.trained by kinematics, proton and -Equations ( 5), ( 6) and (7).We ling in the dark sector to be 0.3 s an e cient depletion of the heavwer one, thus simplifying the pheiently lower values of this coupling ctions of both the ⇠ and states les.
[4] on the leptonic asymmetry read 7 and A s ``= 0.0006 ± 0.0028 for ms respectively.Note that these itional new physics contributions d from the SM alone: A s ``|SM = nd A d SL |SM = ( 4.7 ± 0.6) ⇥ 10 4 .ect search for the branching ratio + X), we can constrain the range ble values.For instance, in the where the produced baryon is a ased on the B + decay to cX, set + Baryon) < 0.1 at 95% CL.
Lets match to the usual SCET notation.Under RPI-I: ) (1.5) Under RPI-II: ) [GE: I'm not sure why we originally chose a sign discrepancy -either sign is valid.Should we stick to what we have or change to all positive?] Lets check the transformations of the d s: ) FIG. 3: Evolution of comoving number density of various components for the benchmark points we consider {m , , Br(B !⇠ + Baryon), m , yd} = {25.5 GeV, 10 22 GeV, 5.6 ⇥ 10 3 , 3.3 GeV, 0.3}.The left panel corr DM mainly composed of Majorana ⇠ particles, as we take m⇠ = 1 GeV and m = 1.5 GeV.We take both the contributions to the leptonic asymmetry to be positive, A s ``= 10 4 = A d ``.The change in behavior of the asym at T ⇠ 15 MeV corresponds to decoherence e↵ects spoiling the B 0 d oscillations while B 0 s oscillations are still activ panel corresponds to the DM being composed mainly of dark baryons + ⇤ , with m = 1.3 GeV and m⇠ = 1.8 G take A s ``= 10 3 , and A d ``= A d ``SM = 4.2 ⇥ 10 4 -the dip in the asymmetry can be understood from the nega A d ``chosen in this case to correspond to the SM prediction.Both benchmark points reproduce the observed DM ⌦DMh 2 = 0.12, and baryon asymmetry YB = 8.7 ⇥ 10 11 .[GE: Gilly will beautify] The parameter space of our model includes the particle masses, the inflation decay width, the dark Yukawa coupling, the branching ratio of B mesons to DM and a hadrons, the leptonic asymmetry, and the dark sector annihilation cross sections.Table .II summarizes the parameters and the range of over which they are allowed to vary taking into account all constraints.DM masses are constrained by kinematics, proton and neutron star stability -Equations ( 5), ( 6) and (7).We take the Yukawa coupling in the dark sector to be 0.3 since this value enables an e cient depletion of the heavier DM state to the lower one, thus simplifying the phenomenology.For su ciently lower values of this coupling we may require interactions of both the ⇠ and states with additional particles.
The current bounds [4] on the leptonic asymmetry read A d ``= 0.0021 ± 0.0017 and A s ``= 0.0006 ± 0.0028 for the B 0 d and B 0 s systems respectively.Note that these values allow for additional new physics contributions beyond those expected from the SM alone: A s ``|SM = (2.22 ± 0.27) ⇥ 10 5 and A d SL |SM = ( 4.7 ± 0.6) ⇥ 10 4 .While there is no direct search for the branching ratio Br(B 0 q !⇠ + Baryon + X), we can constrain the range of experimentally viable values.For instance, in the example of Figure 2 where the produced baryon is a ⇤ = |u s si, we can, based on the B + decay to cX, set the bound Br(B !⇠ + Baryon) < 0.1 at 95% CL.  .II summarizes the parameters and the range of over which they are allowed to vary taking into account all constraints.DM masses are constrained by kinematics, proton and neutron star stability -Equations ( 5), ( 6) and (7).We take the Yukawa coupling in the dark sector to be 0.3 since this value enables an e cient depletion of the heavier DM state to the lower one, thus simplifying the phenomenology.For su ciently lower values of this coupling we may require interactions of both the ⇠ and states with additional particles.
The current bounds [4] on the leptonic asymmetry read A d ``= 0.0021 ± 0.0017 and A s ``= 0.0006 ± 0.0028 for the B 0 d and B 0 s systems respectively.Note that these values allow for additional new physics contributions beyond those expected from the SM alone: A s ``|SM = (2.22 ± 0.27) ⇥ 10 5 and A d SL |SM = ( 4.7 ± 0.6) ⇥ 10 4 .While there is no direct search for the branching ratio Br(B 0 q !⇠ + Baryon + X), we can constrain the range of experimentally viable values.For instance, in the example of Figure 2 where the produced baryon is a ⇤ = |u s si, we can, based on the B + decay to cX, set the bound Br(B !⇠ + Baryon) < 0.1 at 95% CL. ⌦DMh 2 = 0.12 ( 24) Br (B !⇠ + Baryon + X) = 5.6 ⇥ 10 3 (26) A s ``= 10 4 (28) A s ``= 10 3 (32) The parameter space of our model includes the particle masses, the inflation decay width, the dark Yukawa coupling, the branching ratio of B mesons to DM and a hadrons, the leptonic asymmetry, and the dark sector annihilation cross sections.Table .II summarizes the parameters and the range of over which they are allowed to vary taking into account all constraints.DM masses are constrained by kinematics, proton and neutron star stability -Equations ( 5), ( 6) and (7).We take the Yukawa coupling in the dark sector to be 0.3 since this value enables an e cient depletion of the heavier DM state to the lower one, thus simplifying the phenomenology.For su ciently lower values of this coupling we may require interactions of both the ⇠ and states with additional particles.
The current bounds [4] on the leptonic asymmetry read A d ``= 0.0021 ± 0.0017 and A s ``= 0.0006 ± 0.0028 for the B 0 d and B 0 s systems respectively.Note that these values allow for additional new physics contributions beyond those expected from the SM alone: A s ``| SM = (2.22 ± 0.27) ⇥ 10 5 and A d SL | SM = ( 4.7 ± 0.6) ⇥ 10 4 .While there is no direct search for the branching ratio Br(B 0 q !⇠ + Baryon + X), we can constrain the range of experimentally viable values.For instance, in the example of Figure 2 where the produced baryon is a ⇤ = |u s si, we can, based on the B + decay to cX, set the bound Br(B !⇠ + Baryon) < 0.1 at 95% CL.
⌦ DM h 2 = 0.12 (24) Br (B !⇠ + Baryon + X) = 5.6 ⇥ 10 3 (26) A s ``= 10 4 (28) A s ``= 10 3 (32) The parameter space of our model includes the particle masses, the inflation decay width, the dark Yukawa coupling, the branching ratio of B mesons to DM and a hadrons, the leptonic asymmetry, and the dark sector annihilation cross sections.Table .II summarizes the parameters and the range of over which they are allowed to vary taking into account all constraints.DM masses are constrained by kinematics, proton and neutron star stability -Equations ( 5), ( 6) and (7).We take the Yukawa coupling in the dark sector to be 0.3 since this value enables an e cient depletion of the heavier DM state to the lower one, thus simplifying the phenomenology.For su ciently lower values of this coupling we may require interactions of both the ⇠ and states with additional particles.
The current bounds [4] on the leptonic asymmetry read A d ``= 0.0021 ± 0.0017 and A s ``= 0.0006 ± 0.0028 for the B 0 d and B 0 s systems respectively.Note that these values allow for additional new physics contributions beyond those expected from the SM alone: A s ``| SM = (2.22 ± 0.27) ⇥ 10 5 and A d SL | SM = ( 4.7 ± 0.6) ⇥ 10 4 .While there is no direct search for the branching ratio Br(B 0 q !⇠ + Baryon + X), we can constrain the range of experimentally viable values.For instance, in the example of Figure 2 where the produced baryon is a ⇤ = |u s si, we can, based on the B + decay to cX, set the bound Br(B !⇠ + Baryon) < 0.1 at 95% CL.
⌦ DM h 2 = 0.12 ( 24) Br (B !⇠ + Baryon + X) = 5.6 ⇥ 10 3 (26) A s ``= 10 4 (28) A s ``= 10 3 (32) where either sign choice preserves o Lets match to the usual SCET [GE: I'm not sure why we ori valid.Should we stick to what Lets check the transformations  The parameter space of our model includes the particle masses, the Inflation decay width, the dark Yukawa coupling, the branching ratio of B mesons to DM and a hadrons, the leptonic asymmetry, and the dark sector annihilation cross sections.Table II summarizes the parameters and the range of over which they are allowed to vary taking into account all constraints.
The upper limit on the Φ mass is imposed because above ∼ 100 GeV, the scalar could potentially have a small branching fraction to b quarks (see e.g.[41]).
DM masses are constrained by kinematics, and neutron star stability -Equations ( 6) and (7).We take the Yukawa coupling in the dark sector to be 0.3 since this value enables an efficient depletion of the heavier DM state to the lower one, thus simplifying the phenomenology.For sufficiently lower values of this coupling we may require interactions of both the ξ and φ states with additional particles.The current bounds [5] on the leptonic asymmetry read A d = −0.0021± 0.0017 and A s = −0.0006± 0.0028 for the B 0 d and B 0 s systems respectively.Note that these values allow for additional new physics contributions beyond those expected from the SM alone [15,16]: While there is no direct search for the branching ratio Br(B → ξφ + Baryon + X), we can constrain the range of experimentally viable values.For instance, in the example of Figure 2 where the produced baryon is a Λ = |u d s , we can, based on the B + decay to cX, set the bound Br(B → ξφ + Baryon) < 0.1 at 95% CL [5].

C. Results and Discussion
The recent Planck CMB observations imply a comoving baryon asymmetry of Y B = (n B − n B )/s = (8.718± 0.004) × 10 −11 [3].In our scenario, even without fully solving the system of Boltzmann equations, we can see from integrating Equation ( 16) that the baryon asymmetry directly depends upon the product of leptonic asymmetry times branching fraction: Meanwhile, the DM relic abundance is measured to be Ω DM h 2 = 0.1200 ± 0.0012 [3] and reads Consider the plot on the right panel of Figure 3, which corresponds to the case where DM is comprised of φ and φ * particles.We can understand the behavior of the particle yields as follows: Φ particles starts to decay at T ∼ 50 MeV, thereby increasing the abundance of the dark particles ξ and φ + φ * until T ∼ 10 MeV at which point Φ decay completes (as it must, so that the predictions of BBN are preserved).The dip in the dark particle yields at lower temperatures is the necessary effect of the additional annihilations -which reduce the yield to reproduce to the observed DM abundance.Meanwhile, the The blue region is excluded by a combination of constraints on the leptonic asymmetry and the branching ratio [5].The lower bound (red region) comes from requiring the Inflaton not to spoil the measured effective number of neutrino species from CMB and the measured primordial nuclei abundances [42].
MeV, as it is only then that the B 0 s CPV oscillations are active in the early Universe.The decrease in the asymmetric component at T ∼ 10 MeV is due to the negative contribution of the B 0 d decays, since in this case the leptonic asymmetry is chosen to be negative.Note that for the case in which the DM is mostly comprised of φ and φ * particles the observed baryon asymmetry and DM abundance imply an asymmetry of The plot on the left panel of Figure 3 corresponds to the case where DM is mostly comprised of ξ particles.In this case the evolution of the dark particles is rather similar.Here we have chosen A d = A s > 0, so that the asymmetric component gets two positive contributions at T 30 MeV from both B 0 d and B 0 s CPV oscillations.While at T ∼ 15 MeV the change in behavior of the yield curve corresponds to the contribution from the B 0 d oscillations -given that the B s oscillation time scale is 20 times smaller than the B d one, the B s contribution it is active at higher temperatures.

The Baryon Asymmetry
In order to make quantitative statements, beyond the benchmark examples discussed above, we have explored the parameter space outlined in Table II and mapped out the regions that reproduce the observed baryon asymmetry of the Universe.From Equation ( 16), we see the baryon asymmetry depends on the product of the leptonic asymmetry times branching fraction (with contributions from both B 0 d and B 0 s mesons), as well as the Inflaton mass and width.The result of this interplay is displayed in Figure 3, where the contours correspond to the value the product of A q ×Br(B 0 s → φξ +Baryon+X) needed to reproduce the asymmetry Y B = 8.7 × 10 −11 for a given point in (m Φ , Γ Φ ) space.For simplicity, the left and right panels show the effect of considering either the B 0 d or the B 0 s contributions but generically both will contribute.
While the entire parameter space in Figure 4 is allowed by the range of uncertainty in the experimentally measured values of A q , our range of prediction is further constrained.In particular, the blue region in Figure 4 is excluded by a combination of constraints on the leptonic asymmetry and the branching ratio [5] (see Section IV), while the lower bound comes from requiring that the Inflaton not spoil the measured effective number of neutrino species from CMB and the measured primordial nuclei abundances [42].Therefore, to reproduce the expected asymmetry coming from, for instance, only B 0 s , we find A s × Br(B → φξ + Baryon + X) ∼ 10 −6 − 5 × 10 −4 (depending upon the Inflaton width and mass).
Interestingly, the baryon asymmetry can be generated with only the SM leptonic asymmetry A s = 2 × 10 −5 , provided that Br(B → φξ + Baryon + X) = 0.05 − 0.1 and that A d = 0 (which is compatible with current data) -see the green region in the right panel of Figure 4. Additionally, if new physics enhances A s up to the current limit ∼ 4 × 10 −3 , Baryogenesis could take place with a branching fraction as low as 2 × 10 −4 .Figure 5 shows that even with a negative A d , as expected in the SM, the baryonic asymmetry can be generated with Br(B → φξ + Baryon + X) > 2 × 10 −3 provided that the A s ∼ O(10 −3 ).We reiterate that both the leptonic asymmetry and the decay of a B meson to a baryon and missing energy are measurable quantities at B-factories and hadron colliders (see Section IV).

The Dark Matter Abundance
As previously argued, in the absence of additional interactions, our set-up generically tends to overproduce the DM since the leptonic asymmetry is < 5 × 10 −3 .By examining the DM yield curve in Figure 3 we see that annihilations (the dip in the curve) deplete the DM abundance that would otherwise be overproduced from the Inflaton decay.
Recall that for a stable particle species annihilating into 2 particles in the early Universe when neglecting inverse-annihilations: Ωh 2 ∝ x FO / σv .For WIMPs produced through thermal freeze-out x FO = m DM /T FO ∼ 20, while, in our scenario m DM /T ∼ 400.Therefore, an annihilation cross section roughly one order of magnitude higher than that of the usual WIMP is required to obtain the right DM abundance.We have analyzed the extrema of the parameter space and found that we require the dark cross section to be Finally, note that since we are considering rather low reheat temperatures, there could be a significant change to the primordial antimatter abundance.In the case of a high reheat temperature scenario, the primordial antinucleon abundance is tiny: Y N = 10 18 ×e −9×10 5 [43].In our scenario, we can track the antinucleon abundance from the following Boltzmann equation: where f N 1 is the produced number of antinucleons per Φ decay [44].By solving this Boltzmann equation we find that for Γ Φ > 3 × 10 −23 GeV the primordial antinucleon abundance is Y N < 10 −26 (and usually way smaller) and too small to have any phenomenological impact at the CMB or during BBN.

IV. SEARCHES AND CONSTRAINTS
Developing a testable mechanism of Baryogenesis has always been challenging.Likewise, should a DM detection occur, nailing down the specific model in set-ups where a rich hidden dark sector is invoked, is generally daunting.The scenario described in the present work is therefore unique in that it is potentially testable by future searches at current and upcoming experiments, while being relatively unconstrained at the moment.

A. Searches at LHCb and Belle-II
As discussed above, a positive leptonic asymmetry in B meson oscillations, and the existence of the new decay mode of B mesons into visible hadrons and missing energy, would both indicate that our mechanism may describe reality.Both these observables are testable at current and upcoming experiments.

Semileptonic Asymmetry in B decays
As shown in Section III C, the model we present requires a positive and relatively large leptonic asymmetry: A ∼ 10 −5 − 10 −3 .The current measurements of the semileptonic asymmetry [5] (recall that in our setup the semileptonic and leptonic asymmetries may be used interchangeably) are: These are extracted from a combination of various analysis of LHCb and B-factories.Future and current experiments will improve upon this measurement.In particular, the future reach of LHCb with 50 fb −1 for the measurement of the leptonic asymmetry is estimated to be σ(A s SL ) ∼ 5 × 10 −4 [15], and a similar sensitivity should be expected for A d SL .To our knowledge, the reach of Belle-II on the semileptonic asymmetries has not been addressed [45].However, a naive rescaling of the Belle 2005 result [46] could optimistically lead to sensitivities at the level of ∼ 2 × 10 −4 for A d SL .In addition, Belle-II is planning on collecting 1ab −1 of data at the Υ(5S) resonance [45] which could potentially result on a sensitivity comparable to that of LHCb for A s SL .

B meson decays into a Baryon and missing energy
For our mechanism to produce the observed Baryon asymmetry in the Universe, from Figure 5, we notice that moderately large Br(B → ξφ + Baryon+X) = 10 −4 −0.1 are required.To our knowledge there are no searches available to measure this branching fraction, and no published data on the inclusive branching fraction for B mesons Br(B → Baryon + X) either.We expect that existing data from Babar, Belle and LHC can already be used to place a meaningful limit.The search for this channel should in principle be similar to other B meson missing energy final states like B → Kνν or B → γνν with current bounds at the level of O(10 −5 ) [5].Given this, the reach of Belle-II [45] could be of O(10 −6 ).Thus, potentially our mechanism is fully testable.

Exotic b-flavored Baryon decays
Our Baryogenesis and DM production mechanism requires the presence of the new exotic B meson decays.However, once these decays are kinematically allowed, the b-flavored baryons will also decay in an apparently baryon violating way to mesons and DM in the final state.For instance, given the interaction (3) the Λ 0 b baryon could decay into ψ + K + + π − provided m ψ < 4.9 GeV which will always be the case since m ψ < m B − m Λ in this case.In addition, the rate of this process should be very similar to that of B mesons.To our knowledge there is no current search for this decay channel, but in principle LHCb could search for it.In particular, Ref. [47] pointed out that it is possible to identify the initial energy of a Λ b if it comes from the decay of Σ ± b , Σ ± b → Λ b + π ± by measuring the kinematic distribution of the process.The LHCb collaboration has very recently observed ∼ 20000 [48] Λ b candidates produced via this process, thus making the measurement of Λ b → ψ + mesons potentially viable at hadron colliders.We refer to Appendix 4 where the lightest states of the possible decay processes are outlined for the four different flavor operators.

Considerations from Flavor Observables
Recall that, the semileptonic asymmetry may be computed theoretically from the off-diagonal elements of the Hamiltonian describing the B 0 − B0 system: In particular, In the SM, oscillations arise from quark-W box diagrams, whose vertices contain CPV phases from the CKM matrix.In particular, the SM predictions for A q SL read A s | SM = (2.22 ± 0.27) × 10 −5 and A d SL | SM = (−4.7 ± 0.6) × 10 −4 [15,16].Since these are substantially smaller then the current measurements (24) there is room to accommodate new physics.
The large positive leptonic asymmetry required in our set-up could differ considerably from the SM values, depending on the value of Br(B → ξφ + Baryon + X).There are many BSM models that allow for a substantial enlargement of the semileptonic asymmetries of both the B 0 d and B 0 s systems (see e.g.[15,17] and references therein).In addition, it is worth mentioning, that the flavorful models invoked to explain the recent B-anomalies also induce sizable mixing in the B 0 s system (see e.g.[18][19][20][21]).
Note, that while the elements of the evolution Hamiltonian (25) are not directly probed in experiment, they can be related to additional experimental observables as: where, for instance ∆m B , the B meosn oscillation length, is related to the mass eigenstates.Therefore, any new physics that modifies A q SL away from the SM value will also modify ∆m B and ∆Γ B , and must not be in conflict with current bounds on these observables.For an overview of the allowed BSM modifications to ∆m B and ∆Γ B see [15].

B. Constraints
Here we comment on collider, cosmological, and DM direct detection constraints.

Collider Constraints
Within our set-up, the heavy colored scalar Y is responsible for inducing the B meson decays into the dark sector via Equation (2).The colored scalar may be produced at colliders and its decay products searched for, thus resulting on an indirect constraint on the model.This branching ratio was calculated in [29] and we quote the result here; From Equation ( 2), note that Y is dominantly pairproduced at colliders through the strong interaction.The produced Y 's could then decay as either Y → ū b or Y → s ψ.So that the expected collider signatures are 4-jets (two tagged b quarks) or 2-jets plus missing energy.If the former decay dominates then 4-jet searches [49] apply, implying a bound on the colored scalar mass of m Y > 500 GeV.While, if Y → s ψ dominates, then s-quark searches apply for a single light quark resulting in the bound m Y > 960 GeV [49].Such constraints allow for sizable Br(B → ξφ + Baryon) ∼ 10 −3 with moderately large couplings √ y ub y ψs > 0.25, and are thus not in tension with our model's prediction of Br(B → ξφ + Baryon + X) = 2 × 10 −4 − 0.1.Finally, note that the Inflaton field Φ is too weakly coupled to be produced at a collider.

Cosmological Constraints
Our mechanism requires a low reheat temperature T RH ∼ O(10 MeV).The lower bound on the reheat temperature comes from the agreement of CMB and BBN observations on the number of relativistic species in the early Universe.The current bound reads T RH > 4.7 MeV [42] at 95% CL which in turn implies that Γ Φ < 3 × 10 −23 GeV ≡ 45 s −1 at 95% CL, where we take Γ Φ = 3H(T RH ).Note that this bound is not expected to be substantially modified by the Planck 2018 final data release since N 2015 eff > 2.74 [2] and N 2018 eff > 2.70 [3] both at the 95% CL.

Dark Matter Direct Detection
The DM in our scenario could scatter through protons and neutrons, as in the Hylogenesis model [14,50], with signatures similar to those in nucleon decay searches (although with somewhat different kinematics).Such searches would test for the presence of interactions that are not needed in a minimal model for Baryogenesis.However, the existing bounds do not constrain either the Hylogenesis model or the mechanism presented here.Within our model, given the interaction with the b quark, the kinematics preclude a direct scattering to B mesons.The scattering to lighter mesons must therefore be accompanied by a penalty due to a weak loop insertion, which makes the expected rate at nucleon decay experiments negligible unless a larger coupling to light quarks exists.

V. POSSIBLE DEPLETION MECHANISMS
As discussed in Sec III, DM is initially over produced.The DM abundance must be depleted sufficiently in order to obtain the measured relic abundance Ω DM h 2 = 0.12.This requires annihilations of the dark particles with a thermally averaged cross section of order 10 −25 cm 3 /s.We will now outline some possibilities for dynamics which can reduce the symmetric DM component.

A. Annihilations to Sterile Neutrinos
Right handed neutrinos N R , are massive singlets under the SM symmetries, and as such provide a simple possible depletion mechanism [51,52] for the DM particles.For instance, for the case where m φ < m ξ , we can introduce another dark, heavy, Z 2 odd, Dirac sterile particle Ψ carrying both baryon and lepton number.The interaction allows for the DM, φ, to annihilate via φ φ * → N N , thereby depleting the abundance of the symmetric φ−φ * component.For the case where m φ > m ξ , we could deplete the excess of ξ particles by introducing a Z 2 odd scalar Φ , charged under lepton number such that the interaction: is allowed.The process ξ ξ → N N can annihilate away the overproduced ξ abundance.The annihilation cross section to sterile neutrinos is swave and as such is subject to strong constraints from the CMB observations as measured by the Planck satellite [3,53]: σv v=0 (1 − 3) (m DM /GeV)×10 −27 cm 3 /s, where the range depends upon the annihilation channel (provided the annihilation is not to neutrinos).We note that both φ φ * → N N and ξ ξ → N N processes are s-wave but quirality suppressed [52] i.e. the s-wave contribution is suppressed like (m N /m DM ) 2 as compared with the p-wave.In particular, in the limit in which m ξ , m φ m N and in which the mediators are substantially heavier than the DM, the annihilation cross sections go as; So that in this limit the p-wave contribution is significantly enhanced, and CMB constraints are substantially ameliorated.Additionally, the decay of sterile neutrinos can be to invisible particles.For instance, if the N fermion is solely mixed with the τ neutrino (the least constrained scenario [54]), provided that m N < m π , the decay will entirely be to 3 ν, and CMB constraints are fully evaded.

B. Annihilations to Standard Model Neutrinos
Consider the same set-up as in the previous subsection, but assume the sterile leptons are heavier than the DM.In this case, mixings could generate couplings which would allow the DM particles to potentially annihilate into active neutrinos [55,56].This annihilation will evade CMB constraints and remain elusive to other experiments due to the weak interactions of neutrinos.
Generically, the coefficients of the mixing operators that generate the annihilation cross section to active neutrinos will be constrained.However, for very heavy neutrinos the only constraint on the mixing comes from the invisible width of the Z and various low-energy lepton universal process in the SM.Such measurements bound the mixing to be |U | 2 < 10 −2 [57] regardless of the heavy lepton mass and specific flavor structure.The annihilation cross section to neutrinos will scale as ∼ y 4 N |U | 4 /(16πm 2 med ) which for a mixing that saturates the bound requires Yukawa couplings of y N 0.6 m med /3 GeV.
Unfortunately, while SM neutrinos may be produced in this set-up, we do not expect a detectable signal at neutrino detectors given the required annihilation rate (22) [58].

C. Annihilations within the Dark Sector
As discussed in Sec.II, if the depletion of the symmetric part of DM is too efficient, then there will not be enough DM since the stable dark particle masses have to be m φ < m B −m p for the B decay process to occur, while the observed baryon asymmetry and DM abundances would require m φ = 5.36 × m p .This situation, however, could be different if additional baryons are present in the dark sector.For instance we can add another dark scalar particle A which carries baryon number 1/3, and mass m A ∼ 5 3 m p ∼ 1.6 GeV, (which is allowed by neutron star constraints) and is Z 2 odd with interactions: If A is lighter than φ, the reactions φ + φ * ↔ A + A * etc. will eventually turn an excess of φ particles into an excesses of A particles.If we now deplete the symmetric component of the A abundance we can arrive at the right DM relic abundance.In general the same set-up will hold in a situation where the dark sector contains many baryon number charged states.Rich dark sectors offer a variety of possible production mechanisms in the early Universe [59,60], that the initial abundance of A or other dark sector particles need not be fixed in this setup.The details of models with rich dark sectors containing baryon number charged particles is beyond the scope of this paper, and we leave this to to future work.

VI. CONCLUSIONS
In this work we have presented a new mechanism for low temperature Baryogenesis in which both the baryon asymmetry and DM relic abundance arise from the oscillation and subsequent decay of B mesons to visible baryons and dark sector states.We have illustrated our set-up with a model that is unconstrained by di-nucleon decay, does not require a high reheat temperature, and would have unique experimental signals -a positive leptonic asymmetry in B meson decays, the existence of the new decay of B mesons into a baryon and missing energy, and the b-flavored baryons decay into mesons and missing energy.These observables are testable at current and upcoming collider experiments.In summary, the novel features of our mechanism include: • Low reheat temperature.
• At least one component of DM charged under baryon number.
• Total baryon number of the Universe remains zero.
• Baryon asymmetry directly related to experimental observables.• Distinctive experimental signals: 1. Positive semileptonic asymmetry in B meson decays.2. Charged and neutral B meson decays to a baryon and missing energy.3. Charged and neutral b-flavored baryons decays to mesons and missing energy.
• Testable at both current and upcoming experiments.
The Baryon asymmetry scales fixed by the following product: where A q , the leptonic charge asymmetry (which in our set-up is effectively equivalent to the semileptonic asymmetry), is an experimental observable which parametrizes the CPV in the B 0 s and B 0 q oscillation systems.
We have solved the set of coupled Boltzmann equations and mapped out our model parameter space (allowed by kinematics and current constraints) that accommodates a DM relic abundance and baryon asymmetry that agrees with observation.From Figure 4 and Figure 5 (respectively), we find that our model predicts the following values for the branching ratio and leptonic asymmetry: These two observables are currently unconstrained but can be measured in future searches at LHCb and Belle-II.
We have seen that there is a region in our parameter space where it is possible to solely generate the baryon asymmetry with A s | SM = (2.22 ± 0.27) × 10 −5 > 0 (although new physics effects are required in this case to simultaneously suppress the negative SM value of A d SL | SM = (−4.7 ± 0.6) × 10 −4 ).However, generically our parameter space predicts values of A q larger then the SM expectation.Note that flavorful models invoked to explain the recent B-anomalies also induce sizable mixing in the B 0 s system, and therefore a potential link between our mechanism and the B-anomalies would be a very interesting avenue to explore.
We have seen that the baryon-symmetric component of DM will be generically overproduced, and as such we require additional interactions which allow for DM annihilations to deplete the abundance such that we reproduce the observed value.In particular we find that we require the dark sector cross section to be: ⇒ Ω DM h 2 ∼ 0.12 .
While, we have preliminarily outlined some classes of models that could that could explain the depletion of DM, formulating a detailed and complete model is one avenue for future investigation.
Another future direction on the model building front, would be to embed our mechanism in a more detailed UV model to explain the origin and nature of the colored scalar Y .Additionally, as discussed above, there is theoretical motivation for multiple dark sector states charged under Baryon number.An interesting investigation to pursue would be to consider various scenarios for dark sector states charged under baryon number.

APPENDICES
Here we give some details behind the calculations in the main text.Appendix 1 and 2 justify the assumptions we made in writing down the Boltzmann equation of Section III A. In Appendix 3 we itemize the dark sector annhilation cross sections.Finally, flavorful variations of the B meson decay operator (3) are outlined in Appendix 4.

Decoherence due to Elastic Scattering
In our mechanism, the coherence in the B 0 -B0 oscillation system in the early Universe is key to generating the baryon asymmetry.The elastic scattering of e ± B 0 → e ± B 0 represents the only possible source of decoherence in the early Universe, and in this subsection we calculate the thermal rate of this process in the expanding Universe.
As the B 0 is neutral pseudoscalar particle the only possible interaction that an electron can have with it is through the effective charge distributed within it.This charge distribution is parametrized in terms of a an elastic electromagnetic form factor F B0 (q 2 ).The actual form of F B0 (q 2 ) requires either data (which is not possible to obtain in the laboratory for this reaction) or some modelling of the quarks distributed within the B 0 meson.The form factors are usually parametrized in terms of the charge radius which is defined as: which for a neutral particle leads to form factors: Since r 2 B0 is not measured, we use an estimate provided by [61]; r 2 B0 ∼ −0.187 fm 2 .For comparison, the measured value for K 0 : r 2 K 0 = −0.077± 0.010 fm 2 [5].We can safely use the quadratic expansion for the form factor, (36), since it will be valid for |q| < 1/ r 2 B0 ∼ 100 MeV and we are interested in T ∼ 10 MeV.Since the quadratic form factor approximation holds, we can calculate the differential scattering cross section for the process e ± B 0 → e ± B 0 , which in the lab frame (and ignoring the B 0 recoil) reads 4 : where α is the fine structure constant.The momentum exchanged is: where E is the energy of the incoming electron.We can therefore rewrite the differential cross section as: Upon integration we obtain the total scattering cross section By substituting the energy E by its average in the early Universe; E ∼ 3T , we obtain the thermally averaged rate for this process: Notice that the e ± B 0 → e ± B 0 scattering rate will be higher than the B s oscillation rate ∆m Bs = 1.17 × 10 −11 GeV for temperatures above ∼ 20 MeV and therefore through the Zeno effect electron/positrons scatterings will damp the B 0 -B0 oscillations.An identical analysis applies for the B d oscillations, but since ∆m B d = 3.34 × 10 −13 GeV oscillations will only be efficient for T < 10 MeV.We note that the rate calculated in (41) has a very strong temperature dependence and therefore is fairly independent on possible unaccounted details in the B 0 form factor.In Figure 6 we show the resulting decoherence function (18) for the B s and B d systems given the interaction rate in (41) and the B-meson mass diferences.In the Boltzmann equations of Section III A, we have omitted the possibility that B mesons annihilate prior to their decay into the dark sector.In this subsection, we explicitly show that, at the temperatures of interest T ∼ 20 MeV, this is indeed a valid approximation.Additionally, we now determine in which range of temperatures will the decays dominate over annihilations.
Since the Φ particle decays at the same rate to B and B, we can assume that n B = n B upon hadronization.In reality, due to CP-violating oscillations, n B (1 + 10 −3 )n B , but this will not impact the calculation at hand.The Boltzmann equation that governs the the B number density is: Equation ( 42) involves very different time scales, and its numerical solution will require time steps of t < 1/Γ Bwhich are 10 −10 smaller than those of the Φ lifetime.
We determine if a produced B meson will decay or annihilate as follows: integrate Equation ( 42) with only the first term on the right hand side (so that we ignore both B decay and oscillation), this will give us the maximum number density of B's prior to decay ∆n B .We can then compare the B decay and the annihilation rates, in order to determine which one dominates.Integration of the first term in Equation (42)  So that now, we can clearly compare the decay and annihilation rates: When solving numerically for the Φ number density we found that even with an annihilation cross section of σv = 10 mb, the decay rate overcomes the annihilation rate for T 60 MeV even for Γ φ = 10 −21 GeV (and T 120 MeV for Γ φ = 10 −22 GeV).Thus, for practical purposes it is safe to ignore the effect of annihilations in the Boltzmann equations.

Dark Cross Sections
Here we list the dark sector cross sections to lowest order in velocity v that result from the interaction (4):

B Meson Decay Operators
Here we categorize the lightest final states for all the quark combinations that allow for B mesons to decay into a visible baryon plus DM, and for Λ b baryons decaying to mesons and DM.Note that the mass difference between final and initial state for the B-mesons will give an upper bound on the dark Dirac fermion ψ mass.In Table III

12 Y B = 8 . 7 ⇥ 10 11 ⇠ 4 ⇠ m 2 FIG. 1 .
FIG. 1. Summary of our mechanism for generating the baryon asymmetry and DM relic abundance.b-quarks and anti-quarks are produced during a late era in the history of the early Universe, namely TRH ∼ O(10 MeV), and hadronize into charged and neutral B-mesons.The neutral B 0 and B0 mesons quickly undergo CPV oscillations before decaying out of thermal equilibrium into visible baryons, dark sector scalar baryons φ and dark Majorana fermions ξ.Total Baryon number is conserved and the dark sector therefore carries anti-baryon number.The mechanism requires of a positive leptonic asymmetry in B-meson decays (A q ), and the existence of a new decay of B-mesons into a baryon and missing energy.Both these observables are testable at current and upcoming collider experiments.

FIG. 2 .
FIG. 2. An example diagram of the B meson decay process as mediated by the heavy colored scalar Y that results in DM and a visible baryon, through the interactions of Equation (2) and Equation (4).

FIG. 3 :
FIG.3: Evolution of comoving number density of various components for the benchmark points we consider in TableII: {m , , Br(B !⇠ + Baryon), m , yd} = {25.5 GeV, 10 22 GeV, 5.6 ⇥ 10 3 , 3.3 GeV, 0.3}.The left panel corresponds the DM mainly composed of Majorana ⇠ particles, as we take m⇠ = 1 GeV and m = 1.5 GeV.We take both the B 0 s and B 0 d contributions to the leptonic asymmetry to be positive, A s ``= 10 4 = A d ``.The change in behavior of the asymmetric yield at T ⇠ 15 MeV corresponds to decoherence e↵ects spoiling the B 0 d oscillations while B 0 s oscillations are still active.The right panel corresponds to the DM being composed mainly of dark baryons + ⇤ , with m = 1.3 GeV and m⇠ = 1.8 GeV.We now take A s ``= 10 3 , and A d ``= A d ``SM = 4.2 ⇥ 10 4 -the dip in the asymmetry can be understood from the negative value of A d ``chosen in this case to correspond to the SM prediction.Both benchmark points reproduce the observed DM abundance ⌦DMh 2 = 0.12, and baryon asymmetry YB = 8.7 ⇥ 10 11 .[GE: Gilly will beautify] d log n d log T = T n

d
tonic asymmetry to be positive, A s ``= 10 4 = A d ``.The change in behavior of the asymmetric yield nds to decoherence e↵ects spoiling the B 0 d oscillations while B 0 s oscillations are still active.The right e DM being composed mainly of dark baryons + ⇤ , with m = 1.3 GeV and m⇠ = 1.8 GeV.We now d ``= A d ``SM = 4.2 ⇥ 10 4 -the dip in the asymmetry can be understood from the negative value of to correspond to the SM prediction.Both benchmark points reproduce the observed DM abundance yon asymmetry YB = 8.7 ⇥ 10 11 .[GE: Gilly will beautify] , that we also convert to the convenient yield variables Yx = nx/s.

3 .
FIG. 3. Evolution of comoving number density of various components for the benchmark points we consider in Table II: {mΦ, ΓΦ, Br(B → ξφ + Baryon), mΨ, y d } = {25 GeV, 10 −22 GeV, 5.6 × 10 −3 , 3.3 GeV, 0.3}.The left panel corresponds the DM mainly composed of Majorana ξ particles, as we take m ξ = 1 GeV and m φ = 1.5 GeV.We take both the B 0 s and B 0 d contributions to the leptonic asymmetry to be positive, A s = 10 −4 = A d .The change in behavior of the asymmetric yield at T ∼ 15 MeV corresponds to decoherence effects spoiling the B 0 d oscillations while B 0 s oscillations are still active.The right panel corresponds to the DM being composed mainly of dark baryons φ + φ * , with m φ = 1.3 GeV and m ξ = 1.8 GeV.We now take A s = 10 −3 , and A d = A d | SM = −4.2× 10 −4 -the dip in the asymmetry can be understood from the negative value of A d chosen in this case to correspond to the SM prediction.Both benchmark points reproduce the observed DM abundance ΩDMh 2 = 0.12, and baryon asymmetry YB = 8.7 × 10 −11 .
where s 0 is the current entropy density and ρ c is the critical density).In Figure3we display the results (the comoving number density of the various components) of numerically solving the Boltzmann equations for two sample benchmark points that reproduce the observed DM abundance and baryon asymmetry.

FIG. 4 .
FIG. 4. Left panel: required value of A d × Br(B → ξφ + Baryon) assuming A s = 0 to obtain YB = 8.7 × 10 −11 .Right panel: Required value of A s × Br(B → ξφ + Baryon) assuming A d = 0 to obtain YB = 8.7 × 10 −11 .The blue region is excluded by a combination of constraints on the leptonic asymmetry and the branching ratio[5].The lower bound (red region) comes from requiring the Inflaton not to spoil the measured effective number of neutrino species from CMB and the measured primordial nuclei abundances[42].

= ( 6 −
20) × 10 −25 cm 3 /s , where σv WIMP = 3 × 10 −26 cm 3 /s, and the spread of values correspond to varying the DM mass over the range specified in Table II (with only a very slight sensitivity to other parameters).In particular σv dark 25 σv WIMP min[m φ , m ξ ]/GeV.Primordial Antimatter with a low Reheat Temperature

ACKNOWLEDGMENTS
This project has received support from the European Union's Horizon 2020 research and innovation programme under the Marie Sk lodowska-Curie grant agreement No 690575 (InvisiblesPlus RISE) and No 674896 (Elusives ITN).ME is supported by the European Research Council under the European Union's Horizon 2020 program (ERC Grant Agreement No 648680 DARK-HORIZONS).ME acknowledges the hospitality of the Particle, Field, and String Theory group at the University of Washington.GE and AEN are supported in part by the U.S. Department of Energy, under grant number de-sc0011637.AEN is also supported in part by the Kenneth K. Young Memorial Endowed Chair.AEN acknowledges the hospitality of the Aspen Center for Physics, which is supported by National Science Foundation grant PHY-1607611.We would like to acknowledge David Mc-Keen, Sheldon Stone and Ville Vaskonen for their very useful comments on the first version of this draft.

FIG. 6 .
FIG.6.The decoherence function(18)  as a function of temperature for the B 0 s and B 0 d systems.

2 .
Do B Mesons Decay or Annihilate?

TABLE I .
Summary of the additional fields (both in the UV and effective theory), their charges and properties required in our model.
in the time interval t → t + 1/Γ B leads to: Φ (t) .

TABLE III .
we list the minimum hadronic mass states for each operator.Here we itemize the lightest possible initial and final states for the B decay process to visible and dark sector states resulting from the four possible operators.The diagram in Figure 2 corresponds to the first line.The mass difference between initial and final visible sector states corresponds to the kinematic upper bound on the mass of the dark sector ψ baryon.