TUM-HEP 1299/20

Collider Signals of Baryogenesis and Dark Matter from B Mesons: A Roadmap to Discovery

1, 2, 3, 4, Gonzalo Alonso-Alvarez,´ ∗ Gilly Elor, † and Miguel Escudero ‡ 1McGill University Department of Physics & McGill Space Institute, 3600 Rue University, Montr´eal,QC, H3A 2T8, Canada 2Institut f¨urTheoretische Physik, Universit¨atHeidelberg, Philosophenweg 16, 69120 Heidelberg, Germany 3Department of Physics, University of Washington, Seattle, WA 98195, USA 4Physik-Department, Technische Universit¨at,M¨unchen,James-Franck-Straße, 85748 Garching, Germany Low-scale baryogenesis could be discovered at B-factories and the LHC. In the B-Mesogenesis paradigm [G. Elor, M. Escudero, and A. E. Nelson, PRD 99, 035031 (2019), arXiv:1810.00880], the CP violating oscillations and subsequent decays of B mesons in the early Universe simultaneously explain the origin of the baryonic and the dark matter of the Universe. This mechanism for baryo- and dark matter genesis from B mesons gives rise to distinctive signals at collider experiments, 0 ¯0 which we scrutinize in this paper. We study CP violating observables in the Bq − Bq system, discuss current and expected sensitivities for the exotic decays of B mesons into a visible baryon and missing energy, and explore the implications of direct searches for a TeV-scale colored scalar at the LHC and in meson-mixing observables. Remarkably, we conclude that a combination of measurements at BaBar, Belle, Belle II, LHCb, ATLAS and CMS can fully test B-Mesogenesis.

CONTENTS B. Outlook: Future Directions 27

I. Introduction1 VIII. Appendices 29 A. B Meson Oscillations in the Early Universe 29 II. B-Mesogenesis4 B. Missing energy spectrum from b-decays at A. The Mechanism in a Nutshell4 ALEPH 31 0 B. The Dark Sector5 C. Exclusive vs. Inclusive decays: Bs and Λb 32 C. Exotic B Meson Decays7 D. LHC Bounds on Color-Triplet Scalars 33 E. New physics in neutral meson mixing 33 III. CP Violation in the B Meson System7 A. Current Measurements and Implications8 References 34 B. Future Prospects at the LHC and Belle II9 C. Baryogenesis with the SM CP Violation? 10 I. INTRODUCTION IV. Searches for B ψ + Baryon 10 → A. Current Limits 10 The Standard Model of particle physics (SM) is a 1. Inclusive Considerations 11 highly successful framework describing the known par- 2. Missing Energy from b decays at LEP 12 ticles and their interactions, and it has been tested to B. Possibilities at B Factories 14 great precision at collider experiments. Meanwhile, as- C. Possibilities at the LHC 14 trophysical and cosmological data are consistent with the D. Relating Exclusive to Inclusive Decays 16 standard cosmological model in which a very hot early Universe is preceded by a stage of inflationary expan- V. Color-Triplet Scalar 18 sion, describing the birth and evolution of our Universe. arXiv:2101.02706v3 [hep-ph] 6 Sep 2021 A. Requirements for B-Mesogenesis 18 Strikingly, these two highly successful models are in con- B. LHC Searches for Color-Triplet Scalars 19 flict with one another, leaving many unanswered ques- C. Flavor Mixing Constraints 21 tions and manifesting the need for physics beyond the D. New Tree-Level b Decays 22 Standard Model (BSM). E. Implications for Searches and Models 23 Precision measurements of the Cosmic Microwave Background (CMB) by the Planck satellite [2] show that VI. Discussion: Collider Complementarity 24 only about 16% of the matter content of the Universe cor- VII. Conclusions 26 responds to known baryonic matter, while the remaining A. Summary 26 84% is due to yet undiscovered dark matter. The SM does not contain a candidate dark matter particle [3,4]. Fur- thermore, a hot Big Bang governed only by SM physics leads to a Universe with equal parts of matter and anti- ∗ [email protected]; ORCID: 0000-0002-5206-1177 matter [5,6], thereby necessitating a dynamical mech- † [email protected]; ORCID: 0000-0003-2716-0269 anism, dubbed baryogenesis, to generate a primordial ‡ [email protected]; ORCID: 0000-0002-4487-8742 asymmetry of baryonic matter over antimatter. 2

The mysteries of dark matter and baryogenesis have As briefly discussed in [1] and as extensively explored been at the forefront of both the experimental and the- in this work, there are three robust predictions that make oretical particle physics programs for many years. The the key elements of B-Mesogenesis testable at current existence and properties of dark matter have been gravi- experimental facilities: tationally inferred (for instance, the CMB anisotropies point towards a particle description of dark matter), 1. Both neutral and charged B mesons should have a but its actual nature is yet to be unveiled. Since the large branching ratio firm observational establishment of dark matter in the 4 Br(B ψ ) > 10− (2) 1970’s [7,8], several well-motivated candidates have → BM been proposed: weakly interacting massive particles into a final state containing a SM baryon , missing (WIMPs) [9, 10], axions [11–13], sterile neutrinos [14–16], energy in the form of a dark sector antibaryonB ψ, and and primordial black holes [17], among others. On the ex- any number of light mesons denoted here by . perimental front, a multidisciplinary enterprise has been M 2. b-flavored baryons ( ) should decay into a dark set forth to test these scenarios. Unfortunately, thus far Bb no direct signal of dark matter has been found at labora- baryon and mesons at a rate tory experiments, particle colliders, or satellite missions. 4 Br( ψ¯ ) > 10− , (3) The baryon ( ) asymmetry of the Universe has been Bb → M measured withB sub-percent accuracy to be [2] (see where again, accounts for any number of light also [18]) mesons and ψ¯ Mwould appear as missing energy in the 11 Y = (n n ¯)/s = (8.718 0.004) 10− , (1) detector. B B − B ± × where s is the entropy density of the Universe. The phys- 3. The CP violation in the neutral B meson system ical requirements to generate an asymmetry of matter should be such that: over antimatter were outlined by Sakharov in the late q 4 1960’s [19], and since then many mechanisms of baryo- ASL > 10− , (4) genesis have been proposed [20–27]. However, they typi- where Aq is the semileptonic charge asymmetry in cally operate at very high energies in the early Universe, SL B0 B¯0 decays. see e.g. [28–31], and are therefore notoriously difficult to q − q test experimentally. Accompanying these unique signatures, there are two The standard lore, that baryogenesis is troublesome other key set of observables that are useful to indirectly to confirm experimentally, has been challenged in re- constrain B-Mesogenesis: cent years as potentially testable baryogenesis mecha- nisms have been put forward, see e.g. [32–39]. In this 1. The parameters describing B0 B¯0 oscillations q − q work, we concentrate on the mechanism proposed in [1], d,s which achieves not only MeV-scale baryogenesis but also φ12 , ∆Γd,s , and ∆Md,s . (5) dark matter production. This scenario relies on the CP- d,s violating oscillations and subsequent decays of B mesons Here and as usual, φ12 denotes the CP violating phase 1 0 into a dark sector in the early Universe , and as such in Bd,s oscillations, and ∆Md,s and ∆Γd,s are the we hereafter refer to this mechanism as B-Mesogenesis2. 0 mass and width differences of the physical Bq states. The primary novelties of B-Mesogenesis, as envisioned d,s A combination of these quantities determines A and in [1], are: SL therefore their measurements indirectly constrain the • Contrary to typical baryogenesis scenarios, mechanism. B-Mesogenesis operates at very low temperatures, 2. Resonant jets and jets plus missing energy transfer 5 MeV T 30 MeV. . . (MET) at TeV energies. A color-triplet scalar, Y , is • Baryon number of the Universe is actually conserved. needed in order to trigger the exotic B meson de- This is achieved by linking baryogenesis to dark mat- cay into a baryon and missing energy in Eq. (2). ter, which is charged under baryon number. Such a scalar would also have implications for heavy- • The baryon asymmetry is directly related to B- resonance searches at the LHC. meson observables, and as such there are unique sig- In Fig.1, we summarize each of these direct and indirect natures at current hadron colliders and B factories. signals, as well as highlight the key collider experiments that can target each of them. We emphasize that these

1 signals are general features of B-Mesogenesis, indepen- We refer to [37], [38], and [39] for studies dealing with baryogen- dent of the details of a UV model. Given a model that esis using heavy baryons, B mesons oscillations, and charged D meson decays, respectively. We also refer the reader to [40] for a realizes this mechanism, there will likely be many other Supersymmetric UV completion of the mechanism of [1]. complementary probes (see e.g. [40]). 2 The B perfecter emphasizes that Baryogenesis is achieved by Surprisingly, there have been no experimental searches leveraging the properties of B mesons. for decay modes of the type B ψ for which baryon → B 3

FIG. 1. Summary of the collider implications of baryogenesis and dark matter from B mesons [1], i.e. B-Mesogenesis. The 0 distinctive signals of the mechanism are: i) the requirement that at least one of the semileptonic (CP) asymmetries in Bq q −4 decays is ASL > 10 , ii) that both neutral and charged B mesons decay into a dark sector antibaryon (appearing as missing energy in the detector), a visible baryon, and any number of light mesons with Br(B → ψ BM) > 10−4, iii) that b-flavored −4 baryons should decay into light mesons and missing energy at a rate Br(Bb → ψ¯ M) > 10 . In addition, we include as indirect 0 ¯0 q signals the various oscillation observables in the Bq − Bq system as they are linked to ASL, and the presence of a new TeV-scale color-triplet scalar Y that is needed to trigger the B → ψ BM decay. We also highlight the existing experiments that can probe each corresponding signal. Notation: B : B meson, B : SM baryon, M : any number of light mesons, ψ : dark sector antibaryon (ME in the detector). number is apparently violated3. At present, a bound current and upcoming measurements of CP violation in on such process at the Br(B ψ ) . 10 % level the neutral B meson system not only a powerful probe arises from inclusive decay measurements→ BM of B mesons of BSM physics but also a potential test of the physics of (see Sec.IV). In addition, searches for large missing en- baryogenesis. ergy events from b-quark decays at LEP can be used to Additionally and as discussed above, B-Mesogenesis 4 3 set constraints Br(B ψ ) 10− 10− across requires the existence of a new bosonic colored mediator → BM . − some regions of parameter space. Otherwise, the cur- in order for B mesons to decay into a baryon and miss- rent lack of dedicated searches for this B meson decay ing energy. Thus, searches for heavy colored scalars at mode renders B-Mesogenesis relatively unconstrained at ATLAS and CMS lead to relevant implications for the present. Given that B factories have reached sensitiv- mechanism. In particular, multi-jet and jet plus missing 5 ities of order 10− for exclusive decay modes involving energy searches at the LHC have a direct connection to missing-energy final states, such as B Kνν¯ , we ex- Br(B ψ ). → → BM pect a substantial improvement on the measurement of Given the exciting possibility of generating baryogen- Br(B ψ ) once this decay mode is targeted. Our → BM esis and dark matter from B mesons and the potential estimates indicate that BaBar and Belle should be able to for B-Mesogenesis to be tested at hadron colliders and B test large regions of the relevant parameter space, while factories, in this work we set up an enterprise to shape we expect that Belle II and LHCb could be able to fully the experimental signatures of the mechanism proposed test the mechanism by searching for these processes. in [1]. In particular, we study the reach of current and B-Mesogenesis directly relates the matter-antimatter upcoming collider experiments to the new decay mode asymmetry of the Universe to the CP violation in the 0 0 B ψ , the implications from CP violation mea- neutral Bd and Bs meson mixing systems. Although surements→ BM in the B meson system, and the phenomenol- many BSM scenarios can lead to non-standard CP vi- ogy of TeV-scale color-triplet scalars. The conclusion of olation in the B meson system, see e.g. [44], prior to this paper is that B-Mesogenesis could be fully confirmed the work of [1], there existed no mechanisms that could at current hadron colliders and B factories. It is our in- directly connect such CP violation to the baryon asym- tention for this work to provide a roadmap for experi- metry of the Universe. Therefore, B-Mesogenesis makes mental efforts directed to uncovering the mechanism re- sponsible for baryogenesis and dark matter production. This paper is organized as follows: in Sec.II we be- 3 There are however already several searches in development us- gin by reviewing the key ingredients and features of the ing BaBar [41] and Belle/Belle II data [42], and also feasibility B-Mesogenesis mechanism, including an updated calcu- studies at LHCb [43]. lation of the early-Universe dynamics that allow us to 4

FIG. 2. Summary of the mechanism of baryogenesis and dark matter from B mesons [1], i.e. B-Mesogenesis. Adapted from Figure 1 in [1]. refine the predictions for B-meson observables. Sec.III order for it to evolve into what we observe today: a Uni- is devoted to the study of the implications of current verse in which matter dominates over antimatter. These and upcoming measurements of CP violation in mixing Sakharov conditions [19] are: (i) C and CP violation. 0 0 in Bd and Bs mesons. In particular, we use these mea- Matter and antimatter need to interact differently if an surements to set a theoretical lower bound on Br(B excess of one over the other is to be generated. (ii) Depar- ψ ). In Sec.IV, we review the current experimen-→ ture from thermal equilibrium. In thermal equilibrium, talBM limits on B ψ decays and comment on the even if C and CP are violated, the rates of particle and prospects for B →factoriesBM and LHC experiments. Next, antiparticle production and destruction are equal. Thus, in Sec.V we consider the various collider implications of the system must be out of thermal equilibrium so that the new bosonic mediator needed to trigger the new de- the rate of producing particles is larger than that of an- cay mode B ψ , including dijet and jet plus MET tiparticles. (iii) Baryon number violation. One requires signatures of→ color-tripletBM scalars, as well as flavor mixing interactions which violate baryon number if an excess of constraints. After discussing the interplay of the different baryons over antibaryons is to be generated in the early searches in Sec.VI, we conclude in Sec.VII by summa- Universe. rizing our main results and outlining various avenues for The mechanism of B-Mesogenesis addresses each of the future work. Sakharov conditions as follows: (i) C and CP violation. The most novel feature of [1] II. B-MESOGENESIS is to leverage the C and CP violation within the oscillations in the SM neutral B meson systems. In this section, we explore how allowing B mesons to (ii) Departure from thermal equilibrium. It is assumed decay into a baryon and dark matter can lead to the gen- that the early Universe is dominated by a combina- eration of the baryon asymmetry and the dark matter of tion of radiation and a very weakly coupled scalar the Universe. We begin by briefly reviewing the mecha- particle, Φ, with mass MΦ & 11 GeV and a lifetime nism presented in [1], while referring to AppendixVIIIA 3 4 of τΦ 10− s . The Φ particle predominantly de- for a detailed discussion of the cosmological dynamics. cays into∼ b quarks, and in doing so reheats the Uni- We then continue by describing the new particles and verse at temperatures TR 20 MeV. Given that interactions necessary for the mechanism, with the goal ∼ T < TQCD 200 MeV during this era, the pro- of finding theory-motivated benchmark points for experi- duced b quarks∼ quickly hadronize to yield a substan- mental searches. This includes the minimal particle con- tial population of B mesons in the early Universe: tent required to trigger the new decay mode of B mesons nB/nγ 10 TR/MΦ 0.02. This population of B in all its possible flavorful variations. We refer to [1] for mesons∼ is in× this way out∼ of thermal equilibrium. more detailed and alternative discussions.

4 A. The Mechanism in a Nutshell These values are roughly those expected for a pseudo-Goldstone boson with Planck suppressed interactions with matter, see e.g. [45]. Note that these values imply that it is hopeless to In the late 1960’s, Sakharov outlined the three con- produce the Φ particle at colliders since the coupling to matter −10 ditions that must be satisfied in the early Universe in would be . 10 . 5

10 (iii) Baryon number violation? In this set up, B mesons see [47, 48]. Given that the Φ ¯b b coupling is < 10− , any posses a nonstandard decay channel into a dark sec- contribution to the baryon asymmetry arising from such tor antibaryon (ψ) and a SM baryon: B ψ . a 3-loop process is extremely suppressed and can safely This results in the generation of a baryon→ asymme-BM be neglected. try in the visible sector that is exactly compensated Eq. (6) clearly shows the direct connection that exists 0 by a dark antibaryon asymmetry. As a consequence, between baryogenesis, the CP violation in the Bq system 5 q total baryon number is actually conserved . parametrized by ASL, and the branching fraction for the new decay Br(B ψ ). In light of this relation, In summary, the late time out of equilibrium B0 and B¯0 q q current measurements→ ofBM CP violation in the B0 meson production, oscillation and subsequent decay into ψ and q systems can constrain B-Mesogenesis, as we illustrate in , results in the generation of an excess of baryons in the Sec.III. Furthermore, the aforementioned exotic decay visibleB sector and an excess of antibaryons in the dark mode of B mesons has important implications for B fac- sector. In this way, the origin of baryogenesis and that tories and the LHC, which we discuss in Sec.IV. of dark matter are linked. Before proceeding to analyze this in detail, it is neces- Importantly, following the chain of events described sary to address two important points regarding the new above and as depicted in Fig.2, it is possible to show particle content of the model, namely: i) what are the that the observed baryon abundance today (see Ap- minimal requirements of the dark sector, and ii) what pendixVIIIA) can be directly related to two observables additional particles are needed to trigger the new decay at collider experiments: mode B ψ . → BM q 11 Br(B ψ ) ASL Y 8.7 10− → BM αq , (6) B. The Dark Sector B ' × 10 3 10 3 − q − X A key element in B-Mesogenesis is that B mesons can where we have normalized to the observed baryon asym- decay into a SM (visible) baryon and a dark sector an- metry given in Eq. (1). tibaryon (ψ). However, this antibaryon ψ cannot rep- In Eq. (6), Br(B ψ ) is the inclusive branch- resent the dark matter of the Universe. The reason for ing ratio of B mesons→ intoBM a dark antibaryon, a visible this is that the decay B ψ can only proceed if ψ q → B baryon, and any number of light mesons; and ASL are the interacts with 3 quarks. The same operator that medi- 0 semileptonic asymmetries in neutral Bq meson decays, ates such an interaction can also allow the GeV-scale ψ which measure the amount of CP violation in mixing in to decay into light antibaryons, thereby washing out the 0 the Bq systems. Finally, αq are functions that encode generated asymmetry. Thus, successful baryogenesis de- the dependence on the mass and lifetime of the Φ field. mands that the ψ state must rapidly decay into other They are bounded to be 0 αq 1.4, see Fig. 14 in stable dark sector particles. This requirement is triv- AppendixVIIIA. ≤ ≤ ially met provided the existence of two additional states Although all relevant cosmological details are present coupled to the dark fermionic antibaryon: a SM singlet in [1] and detailed in AppendixVIIIA, some comments scalar antibaryon φ, and a SM singlet Majorana fermion on Eq. (6) are in order. First, the αq parameters are dif- ξ, coupling to ψ via the Yukawa interaction ferent for each B meson. The physical reason is that the q y ψφξ¯ + h.c.. (7) early Universe is a hot dense plasma in which electrons L ⊃ − d 0 can interact with Bq mesons and potentially decohere To write this Lagrangian, we have assumed the existence the B0 B¯0 oscillations. Given that B0 mesons oscillate of a symmetry that stabilizes both φ and ξ. q − q s Z2 35 times faster than B0 mesons, they are more resilient Given the interaction in Eq. (7), and provided that ∼ d against decoherence effects and αs αd for tempera- mψ > mφ + mξ, ψ rapidly decays into φ and ξ states tures in which decoherence is important. In addition and in the early Universe. In this way, a combination of although not explicitly stated in [1], it is clear that the number densities of φ and ξ particles can be such that baryon asymmetry generated by B-Mesogenesis is only their present-day abundance matches the dark matter 0 2 sourced by the CP violation in the Bq oscillation system density measured by the Planck satellite, ΩDMh = and is totally independent of any potential CP violation 0.1200 0.0012 [2]. in the Φ ¯b b coupling illustrated in Fig.2. The reason is With± the knowledge that the dark sector is made up as follows: at temperatures T < TQCD, a CP asymme- of at least 3 states (the dark Dirac antibaryon ψ, the 0 try in the Bq system appears at 1 loop since B mesons dark scalar baryon φ, and the dark Majorana fermion are hadronized, while the CP violation arising from a CP ξ), relevant limits on the mass of these particles can be violating Φ ¯b b coupling appears only at the 3-loop level, set given the requirements of baryogenesis in conjunction with several other kinematic constraints. First, the B ψ decay can only occur if → B 5 In a similar fashion to [46]. m < m m 4.34 GeV . (8) ψ B − p ' 6

Second, proton stability requires the dark matter to be comprised of φ and ξ particles, then there could also be additional detection signals of mψ > mp me 937.8 MeV . (9) the dark matter. For instance, the dark matter could − ' annihilate into SM neutrinos, as can occur in supersym- Third, the φ and ξ states need to be both stable. Oth- metric versions of the mechanism [40]. Although this an- erwise, they could decay into each other by emitting an nihilation channel is at present unconstrained [56, 57], it antiproton and an electron which would erase the gen- could be tested in upcoming neutrino experiments such erated baryon asymmetry from the B meson oscillations as Hyper-Kamiokande [58, 59]. Alternatively, the dark and decays. In addition to the Z2 symmetry, this require- matter could annihilate into sterile neutrinos. If the dark ment implies sector states are much heavier than the sterile neutri- nos, annihilation would be p-wave [60, 61] and would not m m < m + m 938.8 MeV . (10) | ξ − φ| p e ' yield any relevant signals for CMB or neutrino experi- ments. Finally, as was discussed in [1] (see also [62]), the Finally, allowing for the ψ ξφ decay requires → dark matter particles considered here do not yield typi- m > m + m . (11) cal WIMP-like scattering signals at underground labora- ψ φ ξ tories, as the dark matter states ξ and φ do not interact In light of the above constraints, we can conclude that directly with SM fermions. the mass of the dark antibaryon ψ needs to lie within the Of course, ψ, φ, and ξ need not be the only dark sector range states. Indeed, one may expect many other particles to be present in a full realization of the dark sector. A theo- retically motivated example of an additional dark species 0.94 GeV < mψ < 4.34 GeV. (12) is a SM gauge singlet carrying the opposite baryon number of a quark, i.e.A 1/3 [1]. The state can be stabilized via a symmetry− and representA the entirety We note that since both ψ and φ carry baryon number, Z2 of the dark matter and could provide an explanation for they can potentially be produced in high-density envi- why the dark matter and baryon energy densities are ronments, even if they interact very weakly with regular observed to be so similar, ΩDM/Ω 5. Since baryon matter. One of the most favourable environments for B number is conserved in our setup, n '= 3n if is the this is the interior of a neutron star, where light baryons A B only stable dark sector antibaryon. With this, assumingA can be produced provided that they are lighter than the that the asymmetric population makes up the entirety chemical potential of a neutron µ 1.2 GeV within the A n ∼ of the dark matter, we can solve for m to find star [49] (see also [50–55]). In [1], this motivated the A additional restriction to only consider masses above this 2 m ΩDMh threshold, i.e. mψ > mφ > 1.2 GeV at face value. How- m = B = 1680 20 MeV, (13) A 3 Ω h2 ± ever, there is in fact no dedicated study of these neutron B stars constraints on light baryons like the ones consid- where m is the average mass per baryon [63], and where B 2 ered here, which may not have interactions involving only we have used the current errors from Planck [2] on ΩDMh light quarks. Furthermore, these bounds are subject to and Ω h2. several uncertainties, such as the unknown equation of scalarsB can be produced in the early Universe via state of neutron stars. In this situation, we opt to take interactionsA of the type φ + φ? + ?, while the the conservative approach of not applying this further asymmetry in the dark sector can→ be transferredA A via pro- restriction to the masses of ψ and φ in this work. That cesses of the type φ+ ? + . For these processes to A → A A said, we note that the regime of light mass mψ . 1.5 GeV be active in the early Universe requires mφ > m . Since A may be subject to these astrophysical bounds once a ded- mψ > mφ > m , then for masses of mψ > 1.7 GeV B- icated study addressing the aforementioned uncertainties Mesogenesis withA this extended dark sector could provide is performed. an explanation for the observed dark matter-to-baryon An important observation at this stage is that the density ratio. energy density in asymmetric dark matter that is pro- Motivated by the above discussion, we suggest adopt- duced through B-Mesogenesis cannot be larger than ing the following benchmark value for the mass of ψ: mψ/mp Ω . In light of Eq. (10), this means that the × B full observed dark matter abundance cannot be generated mψ = 2 GeV (Benchmark) . (14) solely via this process. That said, other processes such as annihilation freeze-out can yield the correct amount of For this benchmark, the dark matter could be fully dark matter. In fact, and as discussed in [1], dark sector composed of antibaryons with baryon number 1/3, interactions are crucial in order to allow the annihilation thereby providing an explanationA for the observed− ratio of any symmetric abundance of dark sector particles that ΩDM/Ω 5. Needless to say, while this benchmark is would result in an overproduction of dark matter. The particularlyB ' theoretically appealing, the entire range (12) details of these processes depend on the exact matter is very well motivated as it can lead to an understanding content and dynamics of the dark sector. If we restrict of baryogenesis and dark matter generation. 7

C. Exotic B Meson Decays Operator Initial Final ∆M and Decay State State (MeV) As discussed in the Introduction, one of the key pre- Bd ψ + n (udd) 4340.1 dictions of B-Mesogenesis is the presence of a new decay Oud = ψ b u d Bs ψ + Λ (uds) 4251.2 mode of B mesons into a dark antibaryon ψ, a visible ¯ + baryon and any number of light mesons with a branch- b → ψ u d B ψ + p (duu) 4341.0 0 B 4 Λb ψ¯ + π 5484.5 ing fraction Br(B ψ ) 10− . → BM & In order for the B ψ decay to exist, a new BSM Bd ψ + Λ (usd) 4164.0 → BM 0 TeV-scale bosonic mediator is needed. In particular, this Ous = ψ b u s Bs ψ + Ξ (uss) 4025.0 state should be a color-triplet scalar Y which couples to ¯b → ψ u s B+ ψ + Σ+ (uus) 4090.0 ψ and SM quarks. The LHC and flavor observables set 0 Λb ψ¯ + K 5121.9 relevant constraints on the mass and couplings of this − color-triplet scalar which we discuss in detail in Sec.V. Bd ψ + Λc + π (cdd) 2853.6 0 This heavy mediator can be integrated out to yield a Ocd = ψ b c d Bs ψ + Ξc (cds) 2895.0 y2 ¯ + + ij b → ψ c d B ψ + Λc (dcu) 2992.9 low energy Lagrangian of the form eff = i,j uidj M 2 , 0 L O Y ¯ 2 Λb ψ + D 3754.7 with yij being the product of the two relevant dimen- P 0 sionless couplings. The four possible flavor combination Bd ψ + Ξc (csd) 2807.8 operators i of interest for B meson decays are Ocs = ψ b c s Bs ψ + Ωc (css) 2671.7 O ¯ + + b → ψ c s B ψ + Ξc (csu) 2810.4 ud = ψ b u d , (15a) ¯ − + O Λb ψ + D + K 3256.2 = ψ b u s , (15b) Ous = ψ b c d , (15c) TABLE I. The lightest final state resulting from the new decay Ocd of b quarks as necessary to give rise to baryogenesis and dark cs = ψ b c s , (15d) O matter production. We list each of the possible flavorful op- where all fermions are assumed to be right-handed6 and erators that can equally lead to B-Mesogenesis, see Eq. (15). color indices are contracted in a totally antisymmetric For a given operator, the rate of each decay is fairly similar given that mB± ' mB0 ' mB0 ∼ mΛ . ∆M refers to the dif- way. These operators can induce the decay of the ¯b d s b quark within the B meson into two light quarks and a ference in mass between the initial and final SM hadron. Note dark antibaryon ψ. The resulting possible hadronic pro- that additional light mesons can be present in the final state, which act to decrease ∆M by their corresponding masses. cesses are summarized in TableI for the different opera- tors in Eq. (15). Matrix elements involving the operators in Eq. (15) depend on the precise pairing of the spinors. a size Br ψ¯ Br(B ψ ), again given Each of the operators can come in three different versions: Bb → M ∼ → BM 1 2 that the masses of all the b-flavored hadrons are fairly “type-1” ij = (ψb)(uidj), “type-2” ij = (ψdj)(uib)
O 3 O similar to the B mesons ones. and “type-3” ij = (ψui)(djb). This distinction becomes relevant for someO of the constraints discussed in the next sections. III. CP VIOLATION IN THE MESON As we will see in Sec.V, flavor constraints on the Y B SYSTEM triplet scalar imply that only one of these operators can be active in the early Universe. In practice, this means that we only expect one dominant flavor combination of As described in the previous sections, B- these possible operators at collider experiments and not Mesogenesis [1] directly relates the CP violation in a combination of the above. Therefore, only one of the the neutral B meson systems to the observed baryon sets of decay channels listed in TableI is expected to asymmetry of the Universe. In this section, we discuss have a sizeable branching ratio, while all others should how current measurements of CP violating observables in B0 B¯0 mixing constrain the mechanism. In partic- be suppressed. q − q In view of the form of the effective operators in ular, as clearly seen from Eq. (6), there is a correlation Eq. (15), it is important to note that all B mesons should between Br(B ψ ) and the CP asymmetries in the B0 systems.→ BM Thus, current measurements on decay at a very similar rate given that mB± mB0 q ' d ' the CP violation of B0 mesons set a lower bound to mB0 . Additionally, b-flavored baryons (generically de- q s 4 noted by b) should also posses a branching fraction with Br(B ψ ) which we find to be 10− . B To set→ theBM stage, we first review the∼ origin of CP vio- 0 lation in Bq mesons and the associated observables. The 0 0 6 0 oscillations of neutral Bs and Bd mesons are described In principle, operators of the form ψ d QL QL, mediated by a q q color-triplet vector in the fundamental of SU(2), are also possi- by the mass (M12) and decay (Γ12) mixing amplitudes 0 ¯0 ble. Although for simplicity we do not expand on this possibility between the flavor eigenstates Bq and Bq — see [64] for here, they constitute another viable option. reviews on CP violation in the quark sector and B0 B¯0 q − q 8

0 oscillations. CP violation can be present in these systems the SM prediction for the Bd meson, and about 30 times q 0 and manifests itself as a relative phase between M12 and larger for the Bs system. q 0 q Γ12. The observables that connect the dynamics of Bq Existing measurements of ASL are already useful for mesons in the early Universe and observations in lab- constraining the parameter space of the mechanism. As oratory experiments are the semileptonic asymmetries, highlighted in Eq. (6), the baryon asymmetry of the Uni- defined as verse is proportional to both Br(B ψ ) and Aq . → BM SL 0 0 0 0 Thus, given the observed baryon asymmetry, a constraint Γ(B¯ B f) Γ(B B¯ f¯) q Aq = q → q → − q → q → , (16) on A can indeed be used to indirectly set a lower SL ¯0 0 0 ¯0 ¯ SL Γ(Bq Bq f) + Γ(Bq Bq f) limit on Br(B ψ ). In particular, the fact that → → → → q 3 → BM A 10− implies that s,d 0 SL . where ASL is the semileptonic asymmetry in Bs,d decays, 0 4 f is a CP eigenstate that is only accessible to the Bq Br(B ψ ) & 10− . (20) ¯ q → BM meson and f is its CP conjugate. Note that ASL is called Given the direct correlation between Aq and Br(B semileptonic asymmetry simply because the decays used SL → to quantify it are semileptonic (e.g. ¯b cν¯ `−). In terms ψ ) in generating the baryon asymmetry of the Uni- → ` BM q of the mass and decay mixing amplitudes, Eq. (16) can verse, a lower limit on ASL can be established given an be written as upper limit on Br(B ψ ). This correlation is clearly seen in Fig.3. As→ isBM discussed in Sec.IVA, at q ∆Γq q present we know that Br(B ψ ) < 0.5%, which ASL = tan (φ12) . (17) −∆Mq implies that in order for B-Mesogenesis→ BM to explain the observed baryon asymmetry of the Universe, at least one Here, ∆Mq and ∆Γq represent the physical mass and 0 semileptonic asymmetry should satisfy width differences of the Bq eigenstates, which are re- lated to the amplitudes by ∆Mq = 2 M12 and ∆Γq = q 4 q q | | ASL & 10− . (21) 2 Γ12 cos φ12, where φ12 is the relative phase between | q | q M12 and Γ12. CP violation in interference and global fits: In addition From Eq. (16), we can see why the semileptonic asym- q to the direct observation of ASL, one can also attempt to metries play a fundamental role in the mechanism and q place indirect limits on ASL by taking into account con- appear in Eq. (6): they precisely control how often more straints on other relevant B meson observables. As seen matter than antimatter is generated from the decays of from Eq. (17), the sign of the semileptonic asymmetries 0 ¯0 Bq and Bq mesons. As pointed out in [1], since the Uni- q is characterized by the phase φ12. As such, the value of verse is made out of only matter, one of the key pre- q φ12 is critical to baryogenesis. Recall that this phase de- dictions of the mechanism is that at least one of the q pends only on the difference between φM (the phase of semileptonic asymmetries should be positive and larger q q q 4 M12) and φΓ (the phase of Γ12). Of these two individual than 10− . q ∼ phases, φM can be reconstructed by measuring the inter- 0 ¯0 ference between Bq Bq oscillations and their decay into CP eigenstates. In particular,− the most favourable decays A. Current Measurements and Implications are the so-called golden modes in b ccs¯ transitions, 0 0 0 → 8 which are Bd J/ψ KS and Bs J/ψ φ . The extrac- Semileptonic Asymmetries. The current world aver- M → → q tion of φq from these modes depends on the experimen- ages for ASL, as reported in the PDG 2020 [64] and as tal uncertainties in the measurements along with poten- prepared by the HFLAV[65] group, at 68% CL, read tial contamination from penguin diagrams. At present, d 3 the theoretical uncertainty on the SM prediction from ASL = ( 2.1 1.7) 10− , (18a) d − ± × penguin diagrams is dominant for φM while the one for s 3 s ASL = ( 0.6 2.8) 10− . (18b) φ is dominated by current experimental uncertainties − ± × M (for a recent discussion see [68]). Including all relevant Meanwhile, the SM prediction for these quantities, which measurements, the HFLAV collaboration [65] reports an we take from [66]7, are average of d 4 ASL SM = ( 4.7 0.4) 10− , (19a) ccs¯ | − ± × φ = 0.050 0.019 = ( 2.9 1.1)◦ . (22) s 5 s A = (2.1 0.2) 10− . (19b) − ± − ± SL|SM ± × This number is to be compared with the SM prediction Comparing Eqs. (18) and (19), it is clear that the current which, neglecting contamination from penguin diagrams, experimental error bars are about four times larger than is φccs¯ = 2β = 0.037 0.001 [44]. s |SM − s − ±

7 Note that Ref. [67] has recently pointed out that renormalization- scale dependent effects could change these predictions by up to 8 The J/ψ and φ mesons are not to be confused with the dark Dirac a factor of two. antibaryon ψ and the dark scalar antibaryon φ of B-Mesogenesis. 9

for the semileptonic asymmetry that can be as large as q 3 ASL = 1.5 10− , which are comparable to current di- rect| | constraints× on these quantities, see Eq. (18). Thus, while CP-violation in interference represents an impor- q tant test of φM , current measurements allow for large values of the semileptonic asymmetries via modifications of tree-level b decays.

Cosmological uncertainties. The predictions shown in Fig.3 incorporate a number of uncertainties arising in our calculation of the generation of the baryon asymmetry in the early Universe. These uncertainties are discussed in detail in AppendixVIIIA, and are primarily dominated by the uncertainty in the fragmentation ratios of Φ decays 0 0 to B±, Bs , and Bd mesons. Clearly, these fragmentation ratios are unknown and the band simply covers the range FIG. 3. Contour lines for the minimum Br(B → ψ BM) re- of fragmentation ratios as measured in other environ- quired for baryogenesis and dark matter generation as a func- ments, namely in Z-boson decays: fs/fd = 0.25 0.02, 0 ± tion of the semileptonic asymmetries in Bq meson decays, at pp¯ collisions at Tevatron: fs/fd = 0.33 0.04, at at pp q ± + A . In red, we show the relevant parameter space in which collisions at the LHC: fs/fd = 0.247 0.009, and at e e− SL ± +0.05 baryogenesis can successfully occur. The dashed lines delin- collisions at the Υ(5S) resonance: fs/fd = 0.26 0.04 eate the cosmological uncertainties of our predictions (see text (see HFLAV[65]). In order to generate the band in Fig.− 3, for more details). The black rectangle corresponds to the SM we take fs/fd [0.22 0.37]. prediction for the semileptonic asymmetries [66], while the ∈ − orange contour corresponds to the current world averages for experimental measurements of these quantities [64]. The grey Another source of uncertainty arises from the fact that 0 line highlights the region of parameter space corresponding to the charge distributions within the Bq mesons are not Br(B → ψ BM) > 0.5%, which is disfavoured by an ALEPH precisely known. Neutral B mesons interact with the search as discussed in Sec. IV A 2. All contours are shown plasma in the early Universe through this charge distribu- at 95% CL. This figure showcases that, given current mea- tion; these interactions act to decohere the CP violating surements of the semileptonic asymmetries, a branching ratio 0 ¯0 −4 Bq Bq oscillations, therefore hindering the production Br(B → ψ BM) & 10 is required for successful baryogene- − 0 q −4 of a baryon asymmetry. Since the Bq system is spinless sis. Similarly, in light of the ALEPH constraint, ASL > 10 is necessary in order to explain the observed baryon asymme- and chargeless, its electromagnetic interactions can be try of the Universe. described by an effective charge radius for which we only have theoretical estimates that range within a factor of two, see [70–72]. This uncertainty, corresponding to the In order to gauge the relevance of these measurements width of the bands in Fig. 14, effectively translates into a for B-Mesogenesis, let us write the two phases in the most . 20% uncertainty on our prediction of YB and therefore of Aq and Br(B ψ ). general case where new physics can modify M12,Γ12, as SL → BM well as the penguin contributions, as Finally, the baryon asymmetry depends on the early s s,SM s,NP s,NP φ12 = φ12 + φM + φΓ , (23) Universe cosmology via the mass of the Φ field that re- heats the Universe to a temperature TR. Since MΦ and ccs¯ s,NP SM NP φs = 2βs + φM + δpen + δpen . (24) TR are free parameters that can vary over a certain range, − in Fig.3 we have marginalized over them so as to maxi- The lack of control over SM penguin diagrams as well as mize the baryon asymmetry of the Universe for each given q the possible NP effects on them translate into an uncer- ASL. Thus, the red contours in Fig.3 should be read as SM NP tainty of 1◦ in δpen + δpen [44]. However, the most im- a theoretical lower limit on Br(B ψ ). portant uncertainty∼ comes from the potential new physics → BM in tree-level decays, which are largely unconstrained and s,NP s ccs¯ can modify φΓ and thus φ12 without affecting φs . In fact, it has been recently shown in [66, 69] via a global fit that allowing for modifications in tree level decays such as B. Future Prospects at the LHC and Belle II d s b ccs¯ can lead to large values for the φΓ and φΓ phases. We→ note that in our scenario such tree-level decays are naturally expected to be modified, see Sec.VD. Depend- The sensitivity of upcoming studies at the LHC and 0 ing upon the exact flavor structure of the b uiu¯iqj Belle II to CP violation in the Bq systems are promis- q → decay the large modifications to φΓ in turn allow values ing [73–75]. In particular, the projected 1σ sensitivities 10 for the semileptonic asymmetries are9 rather than by 10 or more. The reason for this ulti- mately stems from the fact that B-Mesogenesis proceeds s 4 1 δA = 10 10− [LHCb (33 fb− ) 2025] , (25a) at much lower temperatures than other baryogenesis sce- SL × − s 4 1 δA = 3 10− [LHCb (300 fb− ) 2040] , (25b) narios – temperatures at which the SM CP violation is SL × − d 4 1 not suppressed. δA = 8 10− [LHCb (33 fb− ) 2025] , (25c) SL × − d 4 1 δA = 2 10− [LHCb (300 fb− ) 2040] , (25d) SL × − d 4 1 IV. SEARCHES FOR B → ψ + Baryon δA = 5 10− [Belle II (50 ab− ) 2025] . (25e) SL × − Comparing these numbers with the parameters necessary In B-Mesogenesis, the baryon asymmetry of the Uni- for baryogenesis shown in Fig.3, one can appreciate the verse depends upon the inclusive rate of B mesons de- great potential that upcoming measurements from LHCb caying into a dark sector antibaryon (ψ) and a SM or Belle II have for helping to confirm (or refute) B- baryon ( ) plus any number of light mesons, ( ) i.e. B M Mesogenesis. For instance, if all measurements are com- Br(B ψ ), see Eq. (6). Recall that any of the four → BM patible with the SM predictions by the year 2025, we will flavors of operators in Eq. (15) can yield such an inclu- 4 know that Br(B ψ ) & 6 10− . On the other sive rate; the contributing lightest final flavor states in hand, positive semileptonic→ BM asymmetries× potentially re- each case are summarized in TableI. To illustrate these ported by future measurements would be a clear sig- flavorful variations, in Fig.4 we display possible decays nal in favour of the mechanism and could point towards of B+ mesons for each of the distinct operators. 4 somewhat smaller branching fractions 10− & Br(B Experimental searches for B meson decays into missing 3 → ψ ) & 10− . As such, B-Mesogenesis provides a energy and a SM baryon have arguably been overlooked complementaryBM source of motivation for the LHCb Up- in experimental programs to date. In this section, we first 1 grade II [74], as measurements with 300 fb− would be summarize in Sec.IVA the current state of constraints on extremely useful in constraining the relevant parameter the branching fractions for these processes as relevant for space. baryogenesis. In Sec.IVB and Sec.IVC, we then discuss the potential reach of B factories and the LHC respec- tively, to exclusive decays of B mesons involving missing C. Baryogenesis with the SM CP Violation? energy and a baryon in the final state (these are easier to target than inclusive modes including mesons). Finally, According to common lore, the CP violation within the in Sec.IVD we perform a primitive phase space analysis SM is too small to generate a matter-dominated Universe to relate the inclusive decay rate Br(B ψ ) to the exclusive one Br (B ψ ), the result of→ whichBM suggests as we observe it. For instance, in electroweak baryoge- → B nesis [21, 22], which can occur during a 1st-order elec- that BaBar, Belle and especially Belle II and LHCb have troweak phase transition, the relevant quark CP violat- the potential to test wide regions of parameter space of 20 the baryogenesis and dark matter mechanism of [1]. ing invariant is such that (n n ¯)/nγ < 10− [77, 78]. This indeed requires newB BSM− B sources of CP viola- tion to generate the observed baryon asymmetry of the 10 A. Current Limits Universe at the (n n ¯)/nγ 10− level. How- ever, it is importantB − to noteB that∼ in the SM, the CP 0 asymmetries in the Bq mesons are not small compared There exists no current dedicated search for B me- 10 d 4 son decays into a visible baryon and missing energy plus with 10− . In particular, ASL SM 4.7 10− and s 5 | ' − × any number of light mesons at any experimental facil- ASL SM 2.1 10− [66]. As can be seen from Fig.3, B- Mesogenesis| ' could× in principle account for the observed ity. In [1], a loose bound Br(B ψ ) < 10% was → BM baryon asymmetry of the Universe with only the SM CP set on such a decay by taking into account the inclusive violation provided that Br(B ψ ) > 2.5%. Al- measurements of B (c + anything). This is only ap- → though this possibility is disfavored→ givenBM the constraints plicable provided that the baryon in the B ψ → BM on the new b decay modes from ALEPH, which tell us does not contain a charm quark— which can certainly that Br(B ψ ) < 0.5%, it is important to note be the case as can be seen in the two right panels of that, contrary→ toBM scenarios such as electroweak baryo- Fig.4. Similarly, one can set a very loose bound on the genesis, the generated baryon asymmetry with only the branching fraction by comparing the predicted SM de- SM CP violation is off by just an order of magnitude cay rate of b-hadrons to the measured value. Doing so leads to Br(B ψ ) . 40 % as a result of the large ( (20%)) uncertainties→ BM in the theoretical prediction of theO decay rate of b-hadrons in the SM [79]. 9 d The sensitivity for ASL at Belle II is not in the Belle II physics In this work, we find substantially stronger bounds by book [76]. We have obtained it from [75]. We also note that i) examining inclusive decays of B mesons into baryons d, s ATLAS and CMS also have the potential to measure ASL , but (which yield constraints at the Br(B ψ ) . the projected sensitivities are not available in the literature. 1 10% level), and ii) by recasting an inclusive→ BM ALEPH − 11

FIG. 4. The decay of the B+ meson to the lightest possible baryon as triggered by the four different flavor operators given in Eq. (15). Note that any of the four can lead to successful baryogenesis and dark matter production. As usual, the light dark sector antibaryon ψ would appear as missing energy in the detector, and Y is a heavy color-triplet scalar mediator with MY > 1.2 TeV (see Sec.V).

0 search [80] for events with large missing energy arising recently measured absolute branching fraction Br(Ξc + → from b-flavored hadron decays at the Z peak (which Ξ− +π ) = 1.43 0.32 % [64] (see also the original study 4 2 ± yield constraints at the Br(B ψ ) . 10− 10− by Belle [85]). level for the relevant range of the→ darkBM sector antibaryon− Eq. (28) can be used to constrain the operators that mass). lead to new B meson decays provided that an assumption regarding the final-state hadronization is made. A prob- 1. Inclusive Considerations lem arises since these bounds apply to an admixture of B mesons, thus the final state baryons could be produced by any of the B mesons depending upon the emission of The reasoning presented in [1] regarding inclusive mea- other charged light mesons. To illustrate the issue, let surements of B meson decays can be refined to ob- us take for concreteness the case of Eq. (28c). From the tain firmer bounds. Given some reasonable assumptions, third diagram in Fig.4, we clearly see that the B+ me- these apply to the different flavor final states possible in son can contribute to this inclusive rate. However, this is the ¯b ψu d decay. Firstly, the PDG [64] reports a + → i j only the case if no charged pions are emitted: if a π is measured inclusive rate of produced, the Λ baryon must be neutral and the decay is Br(B p/p¯ + anything) = (8.0 0.4) % , (26) not included in the inclusive measurement. However, we → ± can assume that the probability for this charged pion to where here B refers to an admixture of B+,B ,B0 and be emitted is the same as for an oppositely-charged pion − d 0 B¯0 mesons. If we assume that the process B ψ to be emitted in the decay of a Bd. If this is the case, then d 0 + → BM the B ψ Λ π− process contributes to the inclusive produces the same number of protons as neutrons (which d → c is reasonable based on isospin symmetry), we can use channel with a similar rate as the one that was excluded. Eq. (26) to find a 95% CL upper bound It is reasonable to assume that the emission of these light mesons is independent of the B meson that is decay- + 0 0 Br(B ψ + Baryon + Mesons) < 8.7 % . (27) ing, given that B , Bd, and Bs all have approximately → the same mass, and that the masses of the relevant light Other measurements of the inclusive decay rate of B charged and neutral hadrons are similar. Under this as- mesons into baryons can be used to set appropriate upper sumption, we can indeed assume that the new decays of limits on each flavor variation of these new decays modes. the b and ¯b quarks contribute to Eq. (28). Therefore, The relevant averages as reported by the PDG [64] are10 assuming the errors in Eq. (28) to be Gaussian, we can obtain the following 95% CL upper limits for the flavor- Br(B p/p¯(dir) + anything) = (5.5 0.5) % , (28a) → ± ful decays of B mesons into baryons and missing energy Br(B Λ/Λ¯ + anything) = (4.0 0.5) % , (28b) as generated by the interactions in (15): → ± Br(B Λ+/Λ− + anything) = (3.6 0.4) % , (28c) Br ¯b ψud 6 % , from Eq. (28a) , (29a) → c c ± → . Br(B Ξ0 + anything) = (1.4 0.2) % , (28d) Br ¯b ψus 5 % , from Eq. (28b) , (29b) → c ± →
. Br ¯b ψcd 4 % , from Eq. (28c) , (29c) where (dir) means that the secondary protons from Λ →
. ¯ baryon decays have been subtracted. In order to obtain Brb ψcs
. 2 % , from Eq. (28d) . (29d) Eq. (28d), we have additionally made use of the measure- → 0 0 + These bounds should,
however, be taken with a word of ment Br(B Ξc + anything) Br(Ξc Ξ− + π ) = → 4 × → caution given the assumptions that have been made to (1.9 0.3) 10− [64] (see also [84]) as well as the very ± × obtain them. We note that the above bounds could be slightly improved by subtracting off from Eq. (28) the contribution from measured exclusive B meson decays 10 These are based on measurements by ARGUS [81] and CLEO [82] with a baryon in the final state. However, the total sum for Eqs. (26), (28a), and (28b), by BaBar [83] for Eq. (28c), and of the branching fraction for such processes is still far by BaBar [84] for Eq. (28d). from the upper limit and doing so would not lead to 12

a substantial improvement with respect to the bounds X`ν¯`. In the analysis for b sνν¯ events, which are clos- quoted in (29). est to our decays, the relevant→ kinematic signal region was chosen to correspond to events with Emiss > 30 GeV. In this window, the events were subdivided into three bins 2. Missing Energy from decays at LEP b with the following observed and expected background counts (see Table 5 of [80]): The ALEPH experiment at LEP collected and ana- lyzed events with large missing energy arising from b- obs background N30 35 = 31 ,N30 35 = 37.0 2.7 , (31a) hadron decays [80, 86, 87]. These studies were originally − − ± obs background designed to target inclusive b c τ −ν¯τ decays [86], which N35 40 = 1 ,N35 40 = 2.5 1.6 , (31b) → − − ± lead to events with large missing energy as a result of the N obs = 1 ,N background < 1 . (31c) neutrinos in the final state. Since these searches select >40 >40 events only based on their missing energy and do not dis- These can be compared with the predictions for the miss- criminate based on the hadronic or leptonic content of the ing energy distribution in our decays to set a limit on final state, they are completely inclusive. In fact, soon their branching fractions. To this end, we simulate the after [86, 87] appeared, the authors of Ref. [88] pointed ¯ missing energy spectrum of b ψ ui dj and B ψ uidj out that such searches could be used to set the first con- → ¯ → B 3 decays. For the inclusive decays (b ψ ui dj) we calcu- straint on inclusive b sνν¯ transitions at the Br 10− → → . late the missing energy spectrum from the parton-level level. Because of their inclusive nature, these searches 3-body differential decay width, while for the exclusive can be used to constrain our decays both at the inclusive 11 decays the missing energy is fixed by the 2-body decay and the exclusive levels . In what follows, we summa- kinematics. In addition, we simulate the initial energy rize the main ingredients and results from our recast of of the decaying b by taking into account the Peterson [80], and point the interested reader to AppendixVIIIB fragmentation function used in [80]. Finally, in order to where we describe the details of the simulation of the set limits, we compare the predictions from our missing missing-energy spectrum of B ψ decays at LEP. → BM energy spectrum to the observations in Eq. (31) given In Ref. [80], the ALEPH collaboration studied events Eq. (30). We set the limits by assuming a Poisson likeli- with large missing energy at LEP arising from the decays hood for the measurements and by following the Bayesian of b-flavored hadrons, Z ¯bb. The sample of Ref. [80] → 6 procedure outlined in the PDG review for statistics for consists of approximately 4 10 hadronically decaying likelihoods with backgrounds, see Eq. (40.63) of [64]. Z bosons collected at energies× near the Z peak. In or- The result of this procedure is showcased in Fig.5, der to target only b-flavored hadron decays, an algorithm where we show the resulting constraints from the ALEPH was used to mainly select events with a decaying parti- search at 95% CL for exclusive and inclusive decays. In cle with a lifetime similar to that of the b-quark [89]. the left panel of Fig.5, we can appreciate that the ex- This requirement has an efficiency of f = 0.567 and tag clusive constraints on B decays are at the 10 4 level reduces backgrounds significantly [80]. In addition, a cut − for the final state involving hyperons or nucleons for of cos θ < 0.7, where θ is the angle between the beam axis m 4.2 GeV. For final states containing charmed and the thrust axis, was applied. The goal of this cut is to ψ . baryons, the exclusive constraints are at the Br 10 3 reject events that are not well contained within the detec- − level for m 2 2.5 GeV. These results are∼ easy to tor, for which missing energy cannot be determined reli- ψ . understand with the− knowledge that in B ψ de- ably. Following the discussion in [86], we believe that this ud cays, for m < 4 GeV, roughly 20% of the→ signalB events likely implies an efficiency factor of f = 0.45. Given ψ thrust have E > 35 GeV. For the case of B ψ de- these known cuts, the number of candidate b¯b events in miss cd cays and due to the heaviness of charmed baryons,→ B only the sample of [80] can be estimated to be12: 10% of the events have missing energy Emiss > 30 GeV, BR(Z b¯b) which explains the comparably weaker limits (note that N sample = f f N had → , (30) b¯b tag thrust Z BR(Z hadrons) the number of background events is moderately large in → the 30-35 GeV bin). The left panel of Fig.5 only shows 2.2 105 . ' × the constraints for B+ decays, but very similar results 0 Within this sample, events with large missing energy hold for B decays. For the case of Bs and Λb decays were searched for and compared with the expected back- the constraints are relaxed by roughly a factor of 4 as a grounds arising from other SM processes, such as b consequence of the smaller fragmentation ratio of these → states at LEP. In the right panel of Fig.5, we show the resulting 11 We are grateful to our anonymous Referee for pointing out the constraints on inclusive ¯b ψ ui dj decays. We can existence of [80] and for highlighting its potential relevance for appreciate that the bounds→ are at the level of Br our scenario. 5 2 ∼ 12 3 10− 5 10− depending upon the exact final We note that in [80] several other cuts and corrections to the × − × missing energy spectrum were applied. However, their impact state flavor and the ψ mass. These results are rather on the efficiency is not stated in [80] and it falls beyond the important in that they constrain the inclusive branching scope of our paper to analyze them. fraction Br(B ψ ) that is directly related to the → BM 13

FIG. 5. Constraints on B mesons decays into a dark sector antibaryon ψ and a baryon B. The colored lines show the resulting constraints from our recast of a search at ALEPH for decays of b-flavored hadrons with large missing energy at LEP [80]. The global bound Br < 10% arises from inclusive considerations, see Eq. (27). Left panel: constraints on exclusive channels containing no additional mesons in the final state. We also highlight the expected reach of dedicated analyses using old BaBar/Belle data and of Belle-II with 50 ab−1 of data, as well as that of LHCb with 15fb−1 [43]. Right panel: Constraints on the inclusive decay including any number of mesons in the final state. Note that these constraints are derived assuming a parton-level missing-energy spectrum, which may suffer from relevant modifications when effects from the b quark momentum inside the B meson and QCD corrections are included. We expect that including these effects will relax the constraints by a factor of 2-4 (see main text), and we thus incorporate this theoretical uncertainty in order to obtain the conservative results depicted by the solid lines. The dashed lines correspond to the bounds taking the decay kinematics and our recast of the ALEPH analysis [80] at face value. baryon asymmetry of the Universe, see Eq. (6). How- In summary, we find that the most stringent constraint ever, a word of caution is in order. We have derived to date on b-hadron decays involving missing energy plus these bounds by modelling the missing energy spectrum a baryon in the final state arises from a search made more by using a tree-level parton decay of a free b quark, and than twenty years ago at ALEPH [80]. By recasting it to 4 2 we have not considered the effect of hadronization or any our setup, we find constraints at the Br . 10− 10− QCD corrections in our simulations. Modeling these ef- level for the decays of interest for B-Mesogenesis.− We fects falls beyond the scope of this study but we believe stress once more that these bounds, and in particular that including them will yield relevant modifications to those appertaining the inclusive decays, should be taken the missing energy spectrum and therefore to the con- with some caution given our lack of detailed knowledge of straints. Including such corrections typically leads to a the ALEPH analysis and of the missing energy spectrum softer missing-energy spectrum and therefore to weaker in b ψ ui dj transitions. In view of these uncertainties, constraints than those derived using the free quark decay it is→ plausible that the constraints derived here may be model. In fact, in the erratum of [88] it is highlighted weakened by a factor of a few should a more sophisticated that the inclusion of such effects does indeed lead to a study be performed. In any case, these results highlight relaxation of the bound on b sνν¯ by a factor of 3. the power of inclusive searches for b-hadron decays with For our decays, one should expect→ a similar (and per- large missing energy and tell us that at 95% CL haps larger) uncertainty. For this reason, we have added to our constraints a relaxation factor of 4 for the opera- Br(B ψ ) < 0.5% [ALEPH], (32) → BM tors containing a charm quark, and a factor of 2 for the operators containing a u quark. The solid lines corre- irrespective of the value of mψ. + spond to the conservative limits, while the limits derived It is clear that searches of this sort in a future e e− directly from the free b quark decay are shown as the collider at the Z peak such as FCC-ee [90] would be able 7 dashed line. In addition, the derived constraints depend to potentially test branching fractions as small as 10− , slightly on the exact type of operator that triggers the and therefore make a definitive test of B-Mesogenesis. b decay, see Sec.IIC. Here we choose to show the con- Similarly, an inclusive search of this kind at B factories 1 straints for the ij = (ψb)(uidj) operators and we note could led to an excellent sensitivity to these decays as that the boundsO for the other operators are roughly the long as backgrounds can be kept under control. same for mψ & 2.5 GeV and that they are stronger by a factor of up to 2 for mψ . 2 GeV. 14

B. Possibilities at B Factories mechanism, all possible flavorful variations should be in- dependently searched for. Furthermore, and as discussed We now discuss the potential reach of B factories when in Sec.IIC, all B mesons (including charged ones) should decay into a visible baryon ( ) and missing energy at a searching for decays of B mesons to baryons and missing B energy. Given the difficulties of making theoretical pre- similar rate. This means that all the searches discussed dictions that can be matched to the kinematic distribu- here can in principle be performed using any of the B tions of inclusive measurements, here we focus on exclu- mesons, exploiting the channels listed in TableI. In prac- sive decays, and mostly on the simplest 2-body ones that tice, experimentally it may be easier to target B± decays do not contain any number of additional light mesons. as they leave a charged track at each interaction point. As illustrated by Eq. (28), B factories have sensitivities We conclude this section by mentioning that searches of less than about 0.5% to inclusive B meson decays with are currently under development at B factories for the final state baryons. The kinematic data used to mea- decay modes described in our study. Concretely, the de- cay B0 ψ Λ is being investigated using BaBar [41], sure (28) could in principle be used to constrain 2-body d → exclusive channels down to comparable levels. This can Belle [42], and Belle II [42] data. be done by comparing the number of observed baryons as a function of momentum with the theoretically predicted distribution for an exclusive channel like B ψ , since C. Possibilities at the LHC µ→ Bµ µ the 4-momenta in this case are related by p = pB pψ. This approach has been leveraged to motivateB a new− in- Targeting the missing energy in the decay B ψ → B clusive measurement of B Λc + anything [91] using is highly non-trivial at hadron colliders due to the fact Belle (and eventually Belle→ II) data. that there is no handle on the initial energy of the decay- Regarding exclusive measurements, B factories are ex- ing B meson. That said, there are two reasons to con- tremely sensitive to B meson decay modes involving miss- sider searches for these decays at hadron colliders: first, ing energy in the final state, such as B Kνν¯ . Indeed, Bs mesons and b-flavored baryons are not produced at for B Kνν¯ , BaBar and Belle’s sensitivity→ is about B factories when they run at the Υ(4S) resonance, and → 5 Br 10− [92, 93], while Belle II is expected to reach second, the number of B mesons produced at LHC ex- ∼ 6 1 13 a sensitivity 10− [76] with 50 ab− of data . In ad- periments is substantially larger than that of B factories. ∼ 1 12 dition to this, the BaBar collaboration has very recently For example, at LHCb with = 5 fb− , NB (10 ) 5 L ∼ O reported an upper limit Br(B− Λ¯pνν¯ ) < 3 10− [95]. have been produced [96], while at ATLAS and CMS with → × 1 14 This 4-body decay mode contains baryons and missing = 100 fb− , the figure reaches NB (10 )[97, 98]. L ∼ O energy in the final state. Therefore, given the reach of This should be compared with the number of B mesons 9 BaBar and Belle to similar B meson decays, we expect a that were produced at BaBar or Belle (NB 3 10 ), ∼ × sensitivity of or to those that are expected to be produced at Belle II 1 11 − 5 with = 50 ab , which will be NB 10 . Owing to Br (B ψ + Baryon) 3 10− (BaBar-Belle) , (33) L ∼ → ∼ × large number of B mesons produced at hadron colliders, 6 −1 Br (B ψ + Baryon) 3 10− (Belle II [50ab ]) , it is possible that LHC experiments could provide rele- → ∼ × (34) vant measurements on a new decay of the B meson with 4 a branching fraction Br(B ψ ) > 10− , despite for exclusive B ψ + Baryon decays. the complications related to→ taggingBM the missing energy 6 → 5 This 10− 10− expected sensitivity in exclusive in the decay. B meson decays− should be compared with the predic- tion from B-Mesogenesis for the inclusive rate Br(B 4 → ψ ) > 10− . In Sec.IVD, the ratio between exclu- 1. Prospects and Challenges for Direct Searches siveBM and inclusive rates is estimated to be (1 10)%, which implies that B factories have the potential∼ − to fully As discussed above, performing a dedicated search for test the mechanism. We therefore expect large regions B mesons decaying into missing energy at hadron collid- of parameter space of B-Mesogenesis to be explored via ers is complicated. In this section, we do not present a exclusive decay searches at B factories. study of the feasibility of searches for these new decay It should be noted that, as discussed in Sec.IIC, baryo- modes LHC experiments, but simply discuss some as- genesis can proceed via any of the operators in Eq. (15). pects that need to be addressed by any proposed search. Importantly and as we show in Sec.V, flavor mixing con- We also summarize some recent ideas that could lead to a measurement of Br(B ψ ) at LHC experiments. straints imply that only one of these operators can be ac- → BM tive in the early Universe. However, there is no a priori Three ingredients are necessary in order to perform a di- rect search for B ψ decays at the LHC i) a proper way to know which operator may be the one responsi- → B ble for baryogenesis. Therefore, in order to fully test the trigger, ii) good vertex resolution, and iii) a handle on irreducible backgrounds. Addressing points i) and ii) is beyond the scope of this work and would require a care- ful assessment by experimentalists at LHCb, ATLAS and 13 −1 See [94] for a recent inclusive search with 63 fb of data. CMS. However, we can comment on point iii) with the 15 goal of gaining an understanding of the potential sensi- has considered the case of excited baryons in the final tivity of LHC experiments given that the mass of the ψ state, B ψ ?. Excited baryons decay promptly, particle cannot be reconstructed, before points i) and ii) making the→ decayB point B ψ ? coincide with are addressed. that of ? and thus allowing→ oneB to trigger on the Let us consider the observed exclusive B meson decays decay. ThisB study has shown that for modes such rates into baryons ( ) (see [99] for a nice summary): as B0 ψ Λ(1520) the sensitivity of LHCb with B 1 → 7 − 3 15 fb of data can be at the Br (6 60) 10− Br B ¯0 10− , (35a) ∼ − × → BcBc ∼ level for mψ . 3.5 GeV. In addition, for the channel ¯ 3 B+ ψ Λ (1520) the sensitivity could reach values Br B c c0 M
10− , (35b) c → B B ∼ → 6 5 Br (2 4) 10− for mψ . 2.5 GeV. Although Br B c ¯ 10− , (35c) ∼ − × → B B
∼ the exact reach of the LHCb experiment to these de- 5 Br B c ¯M 10− , (35d) cays will depend upon the control of several back- → B B
∼ ¯ 7 grounds [43], these results highlight the high sensi- Br B 0 . 10− , (35e) → BB
tivity of the LHCb experiment to search the decay 5 Br B ¯0M 10− . (35f) → BB
. modes required by B-Mesogenesis. Here, c denotes a baryon containing
a c quark, is a • ψ¯ Searches: Within the context of B- B B b baryon containing just u, d, s quarks, and M corresponds Mesogenesis,B → M b-flavored baryons also posses an ex- to one light meson; π, K or D. otic decay into missing energy and light mesons Since the missing energy of the ψ state cannot be re- with Br b ψ¯ Br(B ψ ). Since b- constructed, decays of the type B n¯ yield a similar flavored baryonsB → areM not' produced→ atBMB factories, the signature as the decay B ψ . Of→ course,B antineutrons LHC is the only current
experiment potentially ca- → B deposit a signal in the calorimeter, but it may prove chal- pable of searching for these processes. In this con- lenging to associate this signal with the B n¯ decay text, Ref. [101] proposed a method to search for b- → B given the absence of a signature in the tracker. Thus, de- flavored baryon decays involving missing energy by cays of the type B n¯ could contribute to a significant studying baryons arising from the decay of reso- → B b irreducible background at the LHC. nant baryons,B ? π. In this way, the initial en- Bb → Bb Given the above consideration and using Eq. (35), one ergy of b could be inferred from the decay kinematics 5 ? B finds an irreducible background at the Br (10− ) of π, thus offering a handle on decay chan- ∼ O b b level for B ψ . If the baryon in the final state does nelsB of→ the B state involving missing energy. It would → Bc b not contain a c quark, then the irreducible background be interestingB to study the reach of such proposals for 7 ¯ 0 + ¯ would be at the Br (10− ) level. This is interesting as the decay b ψ . For example, Λb K π− ψ ∼ O 4 B → + ¯M → successful baryogenesis requires Br(B ψ ) & 10− and Λb D− K ψ decays as generated by operators → BM → and so, at least in principle, the LHC could probe the us and cs in Eq. (15) could be interesting chan- relevant parameter space. Of course, one should bear in nelsO to pursue.O In fact, it has been recently shown mind that these considerations are not specific; depend- in Ref. [43] that LHCb can have a sensitivity at the 5 4 ing on the exact final state baryon that is targeted in the level of Br 3 10− 10− for decays of the type 0 + ∼ × − B ψ decay, one would find a different contribution Λ K π− ψ¯. → B b → to the irreducible background. Such contributions would ? therefore need to be studied in a case by case basis and • Bs B ψ Searches: Very recently, the LHCb→ experiment→ B has been able to set the con- may very well differ from the ones we estimated above. + + + 5 straint Br (B K µ−τ ) < 3.9 10− [102] at 90% CL by using→ B+ mesons arising× from the res- 0? + 2. Possible Searches onant B meson decay Bs2 B K−. In [102], the τ + four-momentum is reconstructed→ from the kine- matics of the rest of the particles and is thus effec- We now highlight some recent ideas for potential LHC tively treated as a missing particle. Therefore, it is searches for the exotic decays of b-hadrons required potentially feasible that LHCb could also search for for baryogenesis. The focus here is on the LHCb B? B ψ processes following a similar ap- experiment [100], but we believe that similar ideas could s proach→ and→ achieveB sensitivities comparable to that be pursued at ATLAS and CMS. As discussed above, + + + of B K µ−τ [102]. targeting missing energy at hadron colliders is non → 0 trivial, but there have been some recent attempts that • Bs ψ with Oscillations: Measuring the mass of we find are worth discussing: ψ in→ hadronB colliders seems challenging. However, Ref. [103] has pointed out that one could gain a handle • B ψ ? Searches: Motivated by the excellent ver- on the mass of ψ by studying the oscillation pattern → B 0 tex resolution and high particle reconstruction effi- of Bs ψ decays. Given that this approach needs → B 0 ciencies of the LHCb experiment, the feasibility of to trigger on the Bs ψ decay explicitly, it neces- the direct search of B mesons into a visible baryon sarily requires searches→ suchB as the ones described in has been recently studied [43]. In particular, Ref. [43] the two previous paragraphs to find the decay first. 16

To conclude, although missing energy searches at the these considerations were used to understand the softness LHC seem at first complicated, there are interesting av- of the B Λc + X spectrum, and in [106] it was pre- enues that are currently being explored and that may dicted that→ Br (B + X) 5 10% which agrees well shed light on the new decay modes required for the B- with the observed→ inclusive B measurements,' − see Eq. (26). Mesogenesis. Of course, all of the above considerations We choose to follow this avenue and study the kinemat- could also apply to potential future hadron collider ex- ics of the B ψ+ + decays of interest. Defining the periments, see e.g. [104]. phase-space→ constrainedB M width of the parton-level decay ¯b u d ψ as → i j Λ2 D. Relating Exclusive to Inclusive Decays ∂Γ 2 γ(Λ) 2 dMuidj , (36) ≡ (m +m )2 ∂M Z ui dj uidj While the observable directly linked to baryogenesis is the inclusive B ψ branching ratio, the ex- the desired ratio of phase-space integrals corresponds to perimental searches→ discussedBM above are best suited to Br(B ij + ψ) γ(m ij ) test exclusive final states without additional mesons, → B B , (37) B ψ . In fact, the presence of additional hadronic Br(B ij + ψ + ) ' γ(mb mψ) → B M − states→ accompanyingB the final-state baryon can signif- where m ij denotes the mass of the lightest baryon with icantly modify the expected sensitivities in Eqs. (33) B and (34). It is therefore crucial to estimate the relative matching flavor content as listed in TableI. The ratio size of the exclusive modes that contribute to a given above critically depends on the mass of the dark Dirac inclusive channel. antibaryon ψ, which is unknown but bound to lie in the The task of obtaining form factors for the exclusive 0.94 GeV < mψ < 4.34 GeV window (see Eq. (12)). The branching ratios induced by the operators listed in Ta- resulting estimation for the expected fraction of decays bleI requires sophisticated methods that can deal with containing only a baryon and ψ in the final state is shown the non-perturbative hadronization process. In the sim- in Figs.6 and7 as a function of mψ. For brevity, here we plest case of B ψ , there is only one form factor which only display the results for charged B meson and neutral is a function of→ theB recoil energy q2 = m2 . Form fac- Bd decays, as they were found to be the most promis- ψ ing experimental targets in Sec.IVB. The results for tors are often obtained using data-driven methods, which 0 are, however, not helpful in this case given that baryon Bs mesons as well as Λb baryons are presented in Ap- number-violating B decays have never been observed. As pendixVIIIC. For each operator = ψbu d , the phase-space in- an alternative, one could hope to obtain a purely theoret- Oij i j ical estimate using the vacuum insertion approximation tegration depends on the matrix element obtained from in the lines of [105]. However, the presence of a spectator the effective Lagrangian (45a). Different combinations quark makes this technique challenging to apply to our of the quarks in the dimension-6 operators in Eq. (15) decays. Furthermore, the vacuum insertion approxima- lead to different contractions of external momenta. Given tion requires that all the states involved share the same this dependence on the kinematic structure of the ma- quantum numbers as the vacuum and can therefore only trix element, we choose to separate the results of dif- be applied to neutral decays. More sophisticated possi- ferent quark combinations in Figs.6 and7. In these figures, the left panel corresponds to the “type-1” oper- bilities would be to perform a lattice QCD calculation, 1 or use a QCD sum rule, which are, however, beyond the ator ij = (ψb)(uidj), while the right one corresponds O 2 scope of this paper. to the “type-2” and “type-3” cases ij = (ψdj)(uib) and 3 O In this humbling situation, the only way forward is to = (ψui)(djb), for which the phase-space integration Oij resort to phase-space considerations in order to obtain is very similar. Note that the type-2 and type-3 com- an estimate. The kinematic arguments that we use were binations always yields a larger phase-space ratio than first employed by Bigi in [106] to predict a sizeable decay the type-1 one. This means that it is easier to probe the rate of B mesons to baryons within the SM. In this pre- inclusive branching ratio B ψ by measuring the → BM scription, the probability for the final state of the B de- exclusive channel B ψ if the effective operators are → B cay induced by a ¯b u d ψ transition to contain a single of the former types. → i j baryonic state is calculated as the fraction of phase space An important question is related to the value of mb that should be used when evaluating the phase-space in- in which the invariant mass Muidj of the diquark system does not exceed a certain energy scale Λ, which we take tegral in Eq. (36). Arguments can be made in favour of pole to be the mass of the corresponding baryon. In the re- using the pole mass mb = 4.78 GeV [64] or the MS maining region of phase space, Muidj Λ and we would mass at the corresponding energy scalem ¯ b(µ =m ¯ b) = expect that resonant baryons are produced, which nat- 4.18 GeV [64], or even the mass of the decaying B me- urally leads to additional hadrons (mostly pions) in the son against which the diquark system is recoiling. In final state. Although simple in nature, the predictions order to be conservative regarding this choice, we decide made using this approach [106–109] were in all cases sub- to use this indetermination as one measure of the un- sequently validated by experiment. For example, in [108] certainty in our calculation. We choose the intermediate 17

+ 1 B decays through ij = (ψb)(uidj) + 2 3 B decays through ij = (ψdj)(uib) or ij = (ψui)(djb) + O + + B p + ψ ( = ψbud) B Λc + ψ ( = ψbcd) + O + O+ → O → O B p + ψ ( = ψbud) B Λc + ψ ( = ψbcd) B+ Σ+ + ψ ( = ψbus) B+ Ξ+ + ψ ( = ψbcs) → O → O → O → c O B+ Σ+ + ψ ( = ψbus) B+ Ξ+ + ψ ( = ψbcs) 0 → O → c O ) 10 0 ) 10 M M ψ ψ ij ij → B → B + +

B 1

B 1 10− 10− Br( Br( / / ) ) ψ ψ ij ij → B → B + 2 + 2 10− B 10− B Br( Br( 1.0 1.5 2.0 2.5 3.0 3.5 4.0 1.0 1.5 2.0 2.5 3.0 3.5 4.0 mψ [GeV] mψ [GeV] FIG. 6. Fraction of B+ → ψ BM decays that are not expected to contain hadrons other than B in the final state, as a function of the mass of the dark fermion ψ. Different colors correspond to decays induced by the different operators listed in TableI. Each panel corresponds to a different kinematic structure of the effective four-fermion operator as listed in TableII. The width of the band represents an estimation of the uncertainty in our computations, and is obtained by varying the b-quark mass used pole in the calculation betweenm ¯ b(µ =m ¯ b), m (solid line), and m 0 . b Bd

0 1 Bd decays through ij = (ψb)(uidj) 0 2 3 O Bd decays through ij = (ψdj)(uib) or ij = (ψui)(djb) 0 0 + O O Bd n + ψ ( = ψbud) Bd Λc + π− + ψ ( = ψbcd) 0 0 + → O → O Bd n + ψ ( = ψbud) Bd Λc + π− + ψ ( = ψbcd) 0 0 0 0 → O → O Bd Λ + ψ ( = ψbus) Bd Ξc + ψ ( = ψbcs) 0 0 0 0 → O → O Bd Λ + ψ ( = ψbus) Bd Ξc + ψ ( = ψbcs) 0 0 → O → O ) 10

) 10 M M ψ ψ ij ij → B → B 0 d 0 d

B 1

B 1 10− 10− Br( Br( / / ) ) ψ ψ ij ij → B → B 0 d 0 2 d 2 B 10− B 10− Br( Br( 1.0 1.5 2.0 2.5 3.0 3.5 4.0 1.0 1.5 2.0 2.5 3.0 3.5 4.0 mψ [GeV] mψ [GeV] 0 FIG. 7. Same as Fig.6 but for Bd → ψ BM decays.

pole value mb as our benchmark, corresponding to the solid ier ψ-particles, which restrict the available phase-space. lines in Figs.6 and7, while ¯mb(µ =m ¯ b) and mB respec- Although this estimate is clearly rough and a dedicated tively delineate the upper and lower edges of the shaded calculation using lattice QCD or QCD sum rules is highly bands in those figures. As can be seen in the figures, this desirable, we expect it to be a good order-of-magnitude amounts to a factor of 2 uncertainty in our predictions indicator of the behaviour of the actual form factor. for the inclusive vs. exclusive∼ rates, which is reasonable As a consequence, the searches proposed in Sec.IVB given the purely kinematic nature of our arguments. should aim to test exclusive B ψ modes down to 6 → 5B a branching fraction of 10− 10− in order to com- From this analysis and as can be seen in Figs.6 and7, pletely probe the parameter∼ space− that allows for suc- we learn that the exclusive modes that do not contain cessful B-Mesogenesis, see Eq. (20). It is also worth any extra pions in the final state are expected to con- noting that a search for B ψ ? with a sensitivity 5 4 → B stitute a 1 100% fraction of the inclusive width of B of Br 10− 10− would yield complementary infor- mesons, where− the larger numbers correspond to heav- ∼ − 18 mation to B ψ searches. The reason is that given in R-parity violating supersymmetric scenarios, see [40] that Br (B →ψ )B + Br (B ψ ?) Br(B ψ ) for the details of such a realization. and that Br→ (B B ψ ) is small→ B for light' ψ masses,→ BM one In this section we turn our attention to the phe- expect Br (B →ψ ?B) to be large in this regime. We be- nomenology associated with this color-triplet scalar. lieve that this→ servesB as further motivation to perform First, in Sec.VA we discuss the requirements on Y searches for these exotic B-meson decays at LHCb in ad- such that the requisite Br(B ψ ) needed for dition to BaBar, Belle and Belle II, taking advantage of baryogenesis is achieved. As we→ shallBM see, this requires the channels containing excited baryons as described in the triplet scalar to have a TeV-scale mass. Next in Sec.IVC. LHCb also offers the possibility to search for Sec.VB, we study constraints arising from LHC searches exotic b-baryon decays such as Λb ψ¯ . Fig. 17 shows for colored scalars on the couplings that contribute to that a large fraction of these decays→ areM expected to be Br(B ψ ), which can therefore indirectly test B- into final states with multiple mesons, which is to be ex- Mesogenesis.→ BM In Sec.VC, we also present a study of fla- pected given the large phase available in these decays if vor mixing constraints due to observables in the neutral ψ is not too heavy. This information should help design B, D, and K systems that shape the flavor structure of appropriate search strategies when targeting these decays the y coupling matrices but that do not necessarily test in order to test B-Mesogenesis. the mechanism indirectly. In particular, in Sec.VD we show that sizeable new tree-level b decays can arise in this setup. Finally, in Sec.VE we present a combined discus- V. COLOR-TRIPLET SCALAR sion of the searches for this color-triplet scalar in light of its role as mediator in the generation of the baryon asymmetry and the dark matter of the Universe. The four-fermion operator in Eq. (15), which triggers the new decay mode of the B mesons necessary for baryo- genesis, can arise in a UV model with a color-triplet A. Requirements for B-Mesogenesis scalar mediator with baryon number 2/3. We denote this scalar mediator by Y . It must− be a SU(2) sin- L Before diving into the experimental phenomenology of glet and carry hypercharge 1/3 or +2/3, just like a the triplet scalar Y , we first delineate the parametric right-handed d- or u-type squark.− While the discus- requirements of the Lagrangian in Eq. (38) to successfully sion in [1] focused on the Y (3, 1, 1/3) option, here generate the new B meson decay. The rate for a new we also consider the choice∼ of possible− charge assign- decay mode of the b-quark into lighter quarks forming a ment Y (3, 1, 2/3). Although the results are quali- ∼ baryon and ψ can be estimated as [1]14 tatively similar for both scenarios, current experimental B 4 constraints are less stringent for some flavorful variations 4 2 3 ∆m 1.5 TeV y of the hypercharge 2/3 version. As we will see, this has Br(B ψ ) 10− , → BM ' 3 GeV M 0.53 important consequences for determining which of the op-   Y p ! erators in TableI are best suited for B-Mesogenesis. (39) The most general renormalizable Lagrangian that can where ∆m = mB mψ m m is the mass difference be written for a (hypercharge 1/3 or 2/3) color-triplet − − B − M 2 − between the initial and final states and y yuidj yψdk scalar interacting with quarks and the SM singlet baryon ≡ or y2 y y represents the product of two of the ψ is didj ψuk couplings≡ in the interaction Lagrangians in Eq. (38), pro- ? c c ¯ vided a b-quark is involved and depending on the hyper- 1/3 = yuidj Y u¯iRdjR yψdk Y dkRψ + h.c. , L− − − charge of Y . The benchmark value for MY is chosen i, j X Xk to be consistent with LHC bounds on colored scalars, (38a) as is discussed in the following Sec.VB. Given the re- ? ¯ c c ¯ sults shown in Fig.3, successful baryogenesis requires 2/3 = ydidj Y diRdjR yψuk Y ukRψ + h.c. , L − − 4 i, j Br(B ψ ) > 10− . This implies that the size of X Xk → BM (38b) the couplings is bound to be 1 4 where the y’s are coupling constants, the sum is per- 2 MY 3 GeV Br(B ψ ) y > 0.3 → 4 BM , (40) formed over all up and down type quarks, and we are 1.5 TeV ∆m 10− working in the quark mass basis (i.e. where the Higgs- p   quark Yukawa matrix is diagonal). The color indices in which in turn implies rather large coupling constants for M 1.5 TeV. Unitarity of the processes qq¯ qq¯ and the diquark operators are contracted in a totally antisym- Y & → metric way, so that ydidj must be an antisymmetric ma- trix with only 3 relevant entries. Note that all quarks here are right handed and Y carries baryon number 2/3 so 14 This estimate should be accurate up to a 20% QCD correction, that Eq. (15) is a baryon number conserving Lagrangian.− compare the first number of the first and last rows of Table 1 The interactions of Y are reminiscent of those of squarks of [79]. 19

FIG. 8. Summary of the most important production and decay modes of a color-triplet scalar at the LHC, together with their associated signatures. Some of the couplings involved in these processes can be directly identified with the ones that mediate baryogenesis and dark matter production. qψ qψ require y2 < √4π. This means that if Y is The production cross-section varies significantly depend- to trigger→ the new decay mode of the b quark as needed ing on the exact combination of flavors in each y or p uidj for baryogenesis and dark matter production in the early ydidj coupling due to the proton PDFs, with a difference Universe, then Y cannot be too heavy. More concretely, of about two orders of magnitude between the most fa- we can put upper bounds on its mass depending on the vorable combination ud and the least favorable one cb (we branching ratio assumed: do not consider contribution from top quarks, as they are 2 too heavy to participate in the b-quark decay). While M < 5 (2.5) TeV for Br(B ψ ) = 10− , (41a) Y → BM the bounds on pair-produced triplet scalars have been 3 M < 9 (4.5) TeV for Br(B ψ ) = 10− , (41b) thoroughly inspected, single production has been less ex- Y → BM 4 plored (see, however, [115, 116] for recent studies of other M < 16 (8) TeV for Br(B ψ ) = 10− . (41c) Y → BM heavy colored resonances) and we therefore analyze it in The numbers with and without parentheses correspond detail below. to setting ∆m = 1.5 GeV and ∆m = 3 GeV, respectively. Once produced, the triplet scalar can decay via any of These are approximately the maximum mass differences the two types of Yukawa couplings in Eq. (38), either into for decays with and without a c-quark in the final state two quarks or into a ψ-quark pair. For MY mq, mψ, baryon. Comparing this with Fig.3, we conclude that the corresponding partial decay rates are  the color-triplet scalar may be within the reach of direct 2 2 searches at the LHC. This has important implications for yq q y Γ(Y q¯ q¯ ) = 2 i j M , Γ(Y ψq ) = ψqi M . upcoming ATLAS and CMS searches as detailed below. → i j 16π Y → i 16π Y (42)

B. LHC Searches for Color-Triplet Scalars These two decay channels lead to very different signa- tures at the LHC detectors. The qq final state can A color-triplet scalar baryon with a TeV-scale mass be targeted using dijet searches. In order to obtain has the potential to be copiously produced at the LHC. a limit, we perform a recast of the CMS analysis pre- 1 Depending on the production and decay channels, one ex- sented in [110], which uses 36 fb− of data at 13 TeV. For pects various different signatures as highlighted in Fig.8. that, we first implement our particles and interactions in Firstly, an ATLAS [112] search for resonant 4-jets with FeynRules [117] and then use MadGraph5 aMC@NLO [118] 1 36.7 fb− of data shows that pair-produced triplet scalars in order to calculate the lowest order (LO) Y produc- that decay into quarks should have MY > 0.5 TeV. In tion cross section as a function of yqiqj and MY . Then, addition, ATLAS [113] and CMS [114] SUSY searches for we compare the LO prediction with the constraints on pair-produced squarks decaying into a neutralino and a production cross section limits times the dijet branch- quark rule out the existence of this kind of strongly inter- ing fraction in Fig. 12 of [110] by taking the acceptance acting bosons in the mass region below 1.2 TeV with the A = 0.57 as relevant for the isotropic decays that we 1 current 139 fb− of data. For larger masses, pair produc- consider [110]. tion becomes kinematically suppressed and the bounds Finally, using the narrow width approximation and fol- weaken drastically. However, resonant single Y produc- lowing the previously described procedure, we can trans- tion is still possible above this threshold via the process late the constraints from [110] into a bound on the prod- q q Y , enabled by the first couplings in Eq. (38). uct y2 Br(Y j j). The corresponding results are i j → qiqj → 20

100 100

1 10− ) )

jj 1 10− ψj 2 → → 10− Y Y HL-LHC Br( Br(

· HL-LHC 3 · 10 j − j

q 2 q i 10 i 2

q − 2 q y y yud ycd ysb yud ycd yds 4 yus ycs ydb 10− yus ycs ydb yub ycb yds yub ycb ysb 3 10− 2 4 6 8 2 4 6 8 MY (TeV) MY (TeV) 2 FIG. 9. Left panel: Constraints on yqiqj Br(Y → j j) from dijet searches. Bounds are based on a recast of the CMS search −1 of [110] that used 36 fb of data at 13 TeV. We have assumed ΓY /MY = 0.04 and, as discussed in [110], an acceptance of 2 A = 0.56. Right panel: Constraints on yqiqj Br(Y → j ψ) from jet plus missing energy signals. Bounds have been recasted −1 from the analysis of ATLAS [111] that used 36 fb of data at 13 TeV. We have assumed ΓY /MY = 0.06 and performed a fit without correlating errors to the exclusive signal regions of [111].

shown in the left panel of Fig.9 as a function of MY and will remain dominated by systematics. This allows and for a fixed value of ΓY /MY = 0.04. We note that one to simply scale the uncertainties on the SM back- the bounds in Fig.9 can only be applied to y < 1 in ground given in [111] with the inverse square root of the order to maintain the validity of the narrow width ap- luminosity. proximation. For larger couplings, the Y particle has a wider width which in turn would lead to more relaxed The findings of both analyses described above can be 2 bounds on yud Br(Y j j), see [110]. In addition, we combined using Eq. (42), which allows us to compute the also display in this figure→ a forecast for the reach of the branching ratio relevant for each search in terms of the high luminosity (HL) LHC running at √s = 14 TeV with y couplings. The resulting constraints are compiled in 1 3 ab− of data, which has been obtained using the results Figs. 19 and 20 in App.VIIID. The information show- of Sec. 6.4 of [119]. Note that one does not expect a large cased in those figures can be further used to obtain an up- 2 4 improvement for the masses shown in Fig.9 as a result per limit on the product [ y TeV/MY ] and therefore to of the large SM backgrounds, though HL measurements directly constrain Br(B ψ ) through Eq. (39). We →p BM could be sensitive to MY 10 TeV scalars. show the obtained constraints in TableII and Fig. 10 for ∼ We now turn to the ψq final state which produces a all the possible flavor combinations corresponding to dif- ferent products of y couplings, for both hypercharge 1/3 jet and missing energy in the detector. In this case, we − perform a recast of the ATLAS search [111], again based and 2/3 triplet scalars. For all the possible effective op- 1 erators k , the first column of TableII gives the maxi- on 36 fb− of data at 13 TeV. To do this, we make use Ouidj 2 4 of a procedure similar to the one described in the previ- mum possible value of the [ y TeV/MY ] product, while ous paragraph, but for this channel we employ a publicly for the latter columns we use Eq. (39) to obtain the maxi- available MADANALYSIS5 [120–122] implementation [123] mum dark fermion mass thatp allows for Br(B ψ ) 4 3 2 → BM of the relevant analysis [111]. We use PYTHIA8 [124] at the 10− , 10− , and 10− levels. In order to show- to model the partonic showering and hadronization of case the dependence of the constraints on the mass of the the jets and use the DELPHES3 [125] program to simulate triplet scalar Y , in Fig. 10 we display the maximum possi- the ATLAS detector response following [123]. As before, ble Br(B ψ ) as a function of M , for a fixed dark → BM Y we use the narrow width approximation to translate the fermion mass mψ = 1.5 GeV, and once more for all the limit on the number of observed events for each signal possible flavor combinations. The red bands displays the 2 region in [111] to find a limit on yqiqj Br(Y j ψ); this region that allows for B-Mesogenesis with new-physics is shown in the right panel of Fig.9. The resulting→ limit enhanced semileptonic asymmetries. Fig. 10 shows that displayed there is the combination of the individual limits triplet scalars with masses in the 3 5 TeV range pro- obtained for each of the 10 different exclusive signal re- duce the largest exotic B branching∼ ratios− allowed by the gions in the analysis. In addition to the current bounds, dijet and jet+MET constraints on the triplet scalar me- we show the maximal reach of the HL-LHC with a to- diator. It also shows the strong dependence of the limits 1 tal of 3 ab− of data for the exemplary case of the yud on the flavor structure of the Y couplings, with diquark coupling (all other limits scale analogously). This fore- couplings to heavy flavors being much less constrained cast is obtained by assuming that the uncertainties are than the ones to light quarks. 21

yud yψb ycd yψb ydb yψu Max: Upper limit on mψ y y y y y y us ψb cs ψb db ψc  √ 4 Operator y2 1.5 TeV Inclusive Br(B → ψ BM) yub yψd ycb yψd ysb yψu −4 −3 −2 0.53 MY 10 10 10 yub yψs ycb yψs ysb yψc 1 1 10− Oud = (ψ b)(u d) 0.3 2.0 - - 2 Oud = (ψ d)(u b) 6.7 3.2 2.3 - ) 3 Oud = (ψ u)(d b) 16.2 3.4 2.8 1.6 M 2 Excluded by ALEPH 1

ψ 10 − Ous = (ψ b)(u s) 2.4 2.7 1.6 - 2 Ous = (ψ s)(u b) 6.7 3.2 2.3 -

→ B 3 Ous = (ψ u)(s b) 75.8 3.5 3.0 2.2

B 3 10− 1 Ocd = (ψ b)(c d) 10.4 2.0 1.2 - Br( B&DM 2 Ocd = (ψ d)(c b) 96.6 2.4 1.9 1.2 3 4 Ocd = (ψ c)(d b) 16.2 2.1 1.4 - 10− 1 Ocs = (ψ b)(c s) 50.9 2.0 1.5 - Maximum 2 Ocs = (ψ s)(c b) 96.6 2.4 1.9 1.2 5 3 10− Ocs = (ψ c)(s b) 75.8 2.1 1.7 - 2 3 4 5 6 7 8 M (TeV) Y p 2 4 TABLE II. Maximum possible value of [ y TeV/MY ] as constrained by a combination of constraints on color-triplet FIG. 10. Maximum possible exotic branching ratio of B me- scalars from ATLAS and CMS on resonant high pT jets and son decays mediated by a hypercharge −1/3 or 2/3 color- jets plus missing energy. The columns on the right hand side triplet scalar, in view of the LHC constraints displayed in show the heaviest expected possible dark fermion mass in the Fig.9. The value of Br( B → ψ BM) is obtained using ¯b → uidj ψ decay as a function of the operator that triggers p 2 4 Eq. (39) with a fixed value of mψ = 1.5 GeV (larger branching it given the constraint on [ y TeV/MY ] , see Eq. (39). ratios are possible for a lighter ψ). The red band highlights the values of Br(B → ψ BM) where B-Mesogenesis can pro- ceed, while the gray line shows the lower limit of the ALEPH bound on Br(B → ψ BM) as found in Sec. IV A 2.

in the neutral B, D and K meson systems, see e.g. [126– In light of Fig. 10, we conclude that despite the strin- 129]. The SM prediction for the mass differences matches gent ATLAS and CMS bounds, it is still possible for observations except for the K and D meson systems, in a color-triplet scalar to mediate the exotic decay B which the SM prediction cannot be reliably calculated 4 → ψ with a branching fraction above the 10− level, from first principles. In this situation, any new physics B M no matter what the flavor combination of its couplings contribution to ∆MK and ∆MD can only be bounded to in Eq. (38) is responsible for it. This means that B- be smaller than the corresponding experimentally mea- Mesogenesis can proceed through any of the operators sured value. CP violation is particularly constraining in listed in TableI, provided that the semileptonic asym- the Kaon sector, given that K is experimentally known 0 0 metries in the Bs and/or Bd system are enhanced by down to the half percent level [64], while recent theoret- new physics to a sufficient extent. That said, if the en- ical evaluations [130] have achieved a 10% uncertainty d,s in the SM prediction. ∼ hancement of ASL is relatively modest and a branching 3 fraction (10− ) is required, then colored scalar searches at the LHCO could be instrumental in determining which Triplet-scalar contributions to neutral meson mixing of the operators in TableII may give rise to the exotic B arise from box diagrams, which are only non-vanishing if meson decay. Excitingly, our projections using the final at least two different yqiqj or yψqi couplings are nonzero. 1 luminosity of 3 ab− show that the HL-LHC has great It is important to stress that such coupling combinations potential to discover a color-triplet scalar with the cou- are not the same ones that enter Eq. (39) and therefore plings required for B-Mesogenesis via searches for jet plus flavor mixing constraints do not directly constrain B- missing energy, as can be appreciated in the right panel Mesogenesis. The relevant diagrams and corresponding of Fig.9. amplitudes are given in AppendixVIIIE. Comparing the calculated values of ∆M and K with the most recent experimental measurements [64] and SM predictions [66, C. Flavor Mixing Constraints 130] allows us to obtain constraints on the couplings of the triplet scalar. A color-triplet scalar with inter-generation couplings as in (38) can induce ∆F = 2 processes and therefore con- We show first the results for a hypercharge 1/3 triplet tribute to mass differences and CP violating parameters scalar. The limits for the Y interactions involving− two 22

SM quarks are words, if the coupling responsible for generating a large Br(B ψ ) is yq q (1) for some particular fla- ? 2 → BM i j ∼ O yuidyuis < 4 10− (MY /1.5TeV) , ∆MK (43a) vor combination, all the other couplings y should be | | × qkql ? 3 1 2 4 y y < 1 10− (M /1.5TeV) ,  (43b) suppressed at the 10− 10− level (or up to 10− | ud us| × Y K ∼ − ∼ ? 4 depending on the complex phase and the exact flavor y y < 8 10− (M /1.5TeV) ,  (43c) | cd cs| × Y K structure). ? 4 y y < 3 10− (M /1.5TeV) ,  (43d) We end this section by noting that the study presented | td ts| × Y K ? 2 here of the flavor-mixing effects of the color-triplet scalar y y < 2 10− (M /1.5TeV) , ∆M (43e) | cdj udj | × Y D Y can be improved in a number of ways. First, we have ? 2 MY neglected any renormalization group running from the y y < (2 4) 10− , ∆M (43f) | uib uid| − × 1.5TeV Bd scale µ M at which the box diagrams in Fig. 18 are   Y computed∼ down to the relevant hadronic scale µ GeV. ? 1 MY ∼ yuibyu s < (1 2) 10− , ∆MBs (43g) Furthermore, for simplicity we have disregarded CP vio- | i | − × 1.5TeV   lation in the B and D systems. Although these CPV ob- while the ones for the Y -ψ-SM quark couplings read servables are generally less constraining than ∆M, they are relevant when considering the full dependence of the ? 2 y y < 4 10− (M /1.5TeV) , ∆M (43h) constraints on the complex phases of the Y couplings. Of | ψd ψs| × Y K ? 3 particular interest is the fact that modifications of the y y < 1 10− (M /1.5TeV) ,  (43i) | ψd ψs| × Y K width mixing Γq are possible as is discussed in the next ? 2 12 yψby < (2 4) 10− (MY /1.5TeV) , ∆MBd (43j) section. These caveats call for a more exhaustive study | ψd| − × ? 1 of this topic, ideally by means of a global fit including all yψby < (1 2) 10− (MY /1.5TeV) , ∆MB . (43k) | ψs| − × s CP-conserving and -violating observables along the lines The limits for the hypercharge 2/3 triplet scalar are of [131]. obtained analogously. For the Y interactions involving two SM quarks, we have D. New Tree-Level b Decays ? 2 y y < 4 10− (M /1.5TeV) , ∆M (44a) | db sb| × Y K ? 3 y y < 1 10− (M /1.5TeV) ,  (44b) The operators in Lagrangian (38) can induce three | db sb| × Y K ? 2 qualitatively distinct tree-level decays of a b quark. All of y y < (2 4) 10− (M /1.5TeV) , ∆M (44c) | ds sb| − × Y Bd them are mediated by the triplet scalar Y , which can be ? 1 ydbysd < (1 2) 10− (MY /1.5TeV) , ∆MBs (44d) integrated out to obtain different effective 4-fermion op- | | − × erators depending on the hyperharge of Y and the flavor while for the Y -ψ-SM quark couplings, we find variation. For hypercharge 1/3, we have − ? 2 y y < 2 10− (M /1.5TeV) , ∆M . (44e) 1 α β γ ψu ψc Y D ¯ ¯ =  y∗ y∗ b u d ψ | | × b u¯idj ψ 2 αβγ uib ψdj R iR jR R L → MY h     To be conservative, all the above constraints are given α β γ + y∗ y∗ d u b ψ , (45a) at 95% CL and assume that there is no cancellation uidj ψb jR iR R R between the contributions from different combinations 1 1    i of couplings. Note that there is no bound on y or α µ β ¯β α ψdi b uiu¯j dk = 2 yu∗j byuidk u¯iRγ bR dkRγµujR y couplings from D0 mesons because these interac- L → 2 MY didj h    tions only involve down-type quarks. Conversely, bounds α µ α ¯β β u¯iRγ bR dkRγµujR , (45b) for y arise only from D0 mesons. Although we quote − ψui    i the bounds in terms of the absolute value of the cou- 1 µ α α ¯ = y∗ y ψ¯ γ b d¯ γ ψ , (45c) plings, the dependence on the phase is important, es- b ψψdj 2 ψb ψdj R R jR µ R L → −2MY pecially for CP-violating parameters. In particular, the    while for hypercharge 2/3, we get bound from ∆MK only applies to the real part of the corresponding coupling product, while the one from K 1 α β γ ¯ ¯ =  y∗ y∗ b d u ψ , (46a) constrains the imaginary one. For the B mesons, the in- b u¯idj ψ 2 αβγ dj b ψui R jR iR R L → MY tervals quoted cover all the possible phases, ranging from     1 1 ¯α µ β ¯β α aligned to anti-aligned with the SM contribution. The b did¯j dk = 2 yd∗j bydidk diRγ bR dkRγµdjR L → 2 MY only case where the flavor of the internal quark in the h    β β box diagrams is relevant is K , due to the fact that the ¯α µ α ¯ diRγ bR dkRγµdjR . (46b) dominant contribution in this case comes from the right −    i diagram in Fig. 18, which depends on CKM factors. Here, α, β, and γ are color indices while ui and dj rep- In light of these results and given the size of the cou- resent any up- or down-type quark such that the corre- plings in Eq. (40) required for baryogenesis, we con- sponding decay is kinematically allowed. We have per- clude that the color-triplet scalar should preferentially formed Fierz rearrangements [132] to bring the operators couple to one particular flavor combination. In other into the above form. 23

The decay channels (45a) and (46a) are the ones re- sponsible for baryogenesis and are studied in detail in Sec.IVB. The remaining three are not strictly required for the baryogenesis mechanism, but appear if we con- sider a generic flavor structure for the couplings of the color-triplet scalar Y . While the channels in (45b) and (46b) are the “right-handed versions” of flavor- changing charged current and flavor-changing neutral current SM decays, Eq. (45c) constitutes a radically novel decay channel for the b quark. 0 Decays of neutral Bd,s mesons that are triggered by (45b), (45c), or (46b) can produce final states that are common to both mesons and antimesons. As a consequence, these tree-level b decays contribute to the d,s width mixing Γ12 , and can thus enhance the semilep- tonic asymmetries above the small values predicted in the SM. As discussed in Sec.III, these tree-level decays do not contribute to CP violation in interference and are FIG. 11. Maximum inclusive Br(B → ψ BM) as a function of as directly constrained by an ALEPH search [80] for therefore largely unconstrained. mψ b decays with large missing energy (see Fig.5), and indirectly In order to highlight the relevance of this phenomenol- by ATLAS & CMS searches for TeV-scale color-triplet scalars. ogy, we consider the particular decay b ccs¯ , as a → In red we highlight the region of parameter space compatible complete model-independent analysis of potential new with baryogenesis and dark matter production. Each line physics contributions to this channel was performed represents the constraints on each of the four possible b decay in [69]. In the notation of [69], our operators (45b) operators in TableI. c c can be mapped to Q10 and Q20. The strongest con- straints on these operators are found to be due to their loop-level contributions to the semileptonic decays of B asymmetry of the Universe. This interesting possibil- mesons (more specifically, to the operator Q90 V as de- ity would make the framework presented here completely scribed in [133]). From the bounds on the Wilson coef- self-contained. ficients displayed in Fig. 3 of [69], we can obtain the 1σ limit 2 2 E. Implications for Searches and Models y y∗ 7 10− (M /1.5 TeV) , (47) | cb cs| . × Y which is somewhat stronger than the corresponding We now combine the requirements found for success- 0 bound from ∆MBs in Eq. (43g). This showcases the fact ful baryogenesis and dark matter production with the that a full study of the impact of Y in the neutral meson multiple experimental constraints on color-triplet scalars q mixing system including modifications in Γ12 is highly discussed above. This provides a global perspective on desirable. As interesting as this may be, the matching of the implications for (i) direct searches of B ψ 0 → BM the operators (45b)-(45c) to observables of the Bq sys- at B factories and colliders, and (ii) model-building ef- tem would involve hadronic calculations that are out of forts to reproduce the flavor structure of the triplet scalar the scope of this paper. interactions required by B-Mesogenesis. In addition, the decays of the form b ψψs¯ and In Fig. 11 we highlight the implications of current → b ψψd¯ , which involve invisible dark sector states, can searches for TeV-scale color-triplet scalars at ATLAS and → d,s in principle significantly modify Γ12 and thus φd,s. That CMS on the possible size of Br(B ψ ). The dotted said, these decays containing missing energy are con- lines in Fig. 11 represent the region→ ofBM parameter space strained by the LEP search [80] discussed in Sec. IV A 2. excluded by the lack of BSM signals of high pT dijets and Although a dedicated recast would be required to obtain jets plus missing energy. From the results, it is clear that precise numerical values, the bound on the similar pro- the impact of these indirect constraints is very relevant 4 cess Br(b sνν¯) < 6.4 10− at 90% CL found in [80] for B-Mesogenesis. In particular, for operators contain- constitutes→ a conservative× comparison. ing a charm quark, the indirect constraint from ATLAS Overall, we conclude that our present setup has the po- and CMS is substantially more stringent than the di- q tential to significantly enhance Γ12 and thus the semilep- rect one set by ALEPH for mψ > 1.7 GeV. In addition, tonic asymmetries beyond their SM values through the achieving successful baryogenesis in light of these con- introduction of new tree-level b-quark decay channels. straints requires mψ . 3.5 GeV. This can be understood Although precise numerical evaluations are needed in or- as due to the strong dependence of Br(B ψ ) on der to make a more quantitative statement, these mod- ∆m, see Eq. (39). Globally, Fig. 11 showcases→ BM the rel- ifications may be the source of the extra CP viola- evant size and kinematic properties of each decay mode tion required by B-Mesogenesis to explain the baryon that should be targeted with direct searches at BaBar, 24

VI. DISCUSSION: COLLIDER COMPLEMENTARITY

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AAAB73icbVDJSgNBEK1xjXGLevTSGAQvxhkX9Bjw4sFDBLNIMoSeTk/SpKdn7K4RwpCf8OJBEa/+jjf/xs5y0MQHBY/3qqiqFyRSGHTdb2dhcWl5ZTW3ll/f2NzaLuzs1kycasarLJaxbgTUcCkUr6JAyRuJ5jQKJK8H/euRX3/i2ohY3eMg4X5Eu0qEglG0UuOhnR17J2fDdqHoltwxyDzxpqQIU1Taha9WJ2ZpxBUySY1pem6CfkY1Cib5MN9KDU8o69Mub1qqaMSNn43vHZJDq3RIGGtbCslY/T2R0ciYQRTYzohiz8x6I/E/r5lieOVnQiUpcsUmi8JUEozJ6HnSEZozlANLKNPC3kpYj2rK0EaUtyF4sy/Pk9ppybsouXfnxfLtNI4c7MMBHIEHl1CGG6hAFRhIeIZXeHMenRfn3fmYtC4405k9+APn8wfx949I 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 2 2 2 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 plored the various collider implications of B-Mesogenesis. Y 1/3 10 10 few 10 u 2 2 ⇥ 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 In this one, we take a global view and discuss the cor- few 10 few 10 1 c

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AAACA3icdVDLSgNBEJz1bXxFvellMAheXGZN1OQmePEkEYwKSQyzk14dnH0w06uGJeDFX/HiQRGv/oQ3/8bJQ1DRgoaiqpvuLj9R0iBjH87I6Nj4xOTUdG5mdm5+Ib+4dGLiVAuoiVjF+sznBpSMoIYSFZwlGnjoKzj1r/Z7/uk1aCPj6Bg7CTRDfhHJQAqOVmrlVzYbCLeowyyAm24DZQjGY+fZ5la3lS8wt1xhlVKZMre041V2i5Z4xfIOK1LPZX0UyBDVVv690Y5FGkKEQnFj6h5LsJlxjVIo6OYaqYGEiyt+AXVLI253NbP+D126bpU2DWJtK0LaV79PZDw0phP6tjPkeGl+ez3xL6+eYlBuZjJKUoRIDBYFqaIY014gtC01CFQdS7jQ0t5KxSXXXKCNLWdD+PqU/k9Otlxv22VHpcLe4TCOKbJK1sgG8cgu2SMHpEpqRJA78kCeyLNz7zw6L87roHXEGc4skx9w3j4Bb3iYEw== AAAB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0lE0WPRi8cW7Ae0oWy2k3btZhN2N0IJ/QVePCji1Z/kzX/jts1BWx8MPN6bYWZekAiujet+O4W19Y3NreJ2aWd3b/+gfHjU0nGqGDZZLGLVCahGwSU2DTcCO4lCGgUC28H4bua3n1BpHssHM0nQj+hQ8pAzaqzUcPvlilt15yCrxMtJBXLU++Wv3iBmaYTSMEG17npuYvyMKsOZwGmpl2pMKBvTIXYtlTRC7WfzQ6fkzCoDEsbKljRkrv6eyGik9SQKbGdEzUgvezPxP6+bmvDGz7hMUoOSLRaFqSAmJrOvyYArZEZMLKFMcXsrYSOqKDM2m5INwVt+eZW0LqreVdVtXFZqt3kcRTiBUzgHD66hBvdQhyYwQHiGV3hzHp0X5935WLQWnHzmGP7A+fwBemuMuA== Fig. 13 summarizes the prospects for the aforemen- Y 2 2 2 3 2 2/3 100 few10 10 few 1010 d

AAAB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0lE0WPRi8cW7Ae0oWy2k3btZhN2N0IJ/QVePCji1Z/kzX/jts1BWx8MPN6bYWZekAiujet+O4W19Y3NreJ2aWd3b/+gfHjU0nGqGDZZLGLVCahGwSU2DTcCO4lCGgUC28H4bua3n1BpHssHM0nQj+hQ8pAzaqzUcPvlilt15yCrxMtJBXLU++Wv3iBmaYTSMEG17npuYvyMKsOZwGmpl2pMKBvTIXYtlTRC7WfzQ6fkzCoDEsbKljRkrv6eyGik9SQKbGdEzUgvezPxP6+bmvDGz7hMUoOSLRaFqSAmJrOvyYArZEZMLKFMcXsrYSOqKDM2m5INwVt+eZW0LqreVdVtXFZqt3kcRTiBUzgHD66hBvdQhyYwQHiGV3hzHp0X5935WLQWnHzmGP7A+fwBemuMuA==

AAAB6XicdVDJSgNBEK1xjXGLevTSGAQvDj1ZzOQW8KK3KGaBZAg9nZ6kSc9Cd48QQv7AiwdFvPpH3vwbO4ugog8KHu9VUVXPTwRXGuMPa2V1bX1jM7OV3d7Z3dvPHRw2VZxKyho0FrFs+0QxwSPW0FwL1k4kI6EvWMsfXc781j2TisfRnR4nzAvJIOIBp0Qb6fbc6eXy2MbVqlNxEbZLRYzdC0OKhXK56iLHxnPkYYl6L/fe7cc0DVmkqSBKdRycaG9CpOZUsGm2myqWEDoiA9YxNCIhU95kfukUnRqlj4JYmoo0mqvfJyYkVGoc+qYzJHqofnsz8S+vk+rA9SY8SlLNIrpYFKQC6RjN3kZ9LhnVYmwIoZKbWxEdEkmoNuFkTQhfn6L/SbNgO2Ub35TytetlHBk4hhM4AwcqUIMrqEMDKATwAE/wbI2sR+vFel20rljLmSP4AevtE2UpjU4=

AAAD03icnVJNbxMxEHV2gZbwlcKRi0UUxIVo3VLBsQIJuBEQaSrFIXi9s6mVXe/K9pZGliWEuPLH+Af8DP4BTjaCNClSYCRLTzOeeW+eHZeZ0CaKfjSC8MrVazu715s3bt66fae1d/dYF5Xi0OdFVqiTmGnIhIS+ESaDk1IBy+MMBvH0xbw+OAOlRSHfm1kJo5xNpEgFZ8anxnuN7x0aw0RIW+bMKHHumh1LF3PtcyX49B0kjkQf7ON95/BDvFWtUtK8UUxOwFE/9VTlNoVPjhqRg8a/Oyhd4dqy599Z/nT0vEevFIB0ZI38PxddHdjsUJDJiotb2nrwd4mX71pvRtwGox632lE3WgTeBGQJ2mgZvXHrJ00KXuUgDc+Y1kMSlWZkmTKCZ+CatNJQMj5lExh6KJk3dmQXkhzu+EyC00L5Iw1eZFc7LMu1nuWxvzl/Hb1emycvqw0rkz4bWSHLyoDkNVFaZdgUeP6DcSIUcJPNPGBcCa8V81OmGDf+n1+YlJyJUi9Vn9eyvUdk3ZFNcLzfJYfd6O2T9tHLz7Vbu+g+eoAeIYKeoiP0GvVQH/GABIPgY8DCfmjDL+HX+mrQWDp8D12I8Nsvk7FDfw== tioned experiments to test B-Mesogenesis. As usual, we 2 ⇥ 2 ⇥ few 10 few 10 1 s 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 0 1

AAAB6HicbVBNS8NAEJ3Ur1q/qh69LBbBU0lE0WPRi8cW7Ae0oWy2k3btZhN2N0IJ/QVePCji1Z/kzX/jts1BWx8MPN6bYWZekAiujet+O4W19Y3NreJ2aWd3b/+gfHjU0nGqGDZZLGLVCahGwSU2DTcCO4lCGgUC28H4bua3n1BpHssHM0nQj+hQ8pAzaqzUcPvlilt15yCrxMtJBXLU++Wv3iBmaYTSMEG17npuYvyMKsOZwGmpl2pMKBvTIXYtlTRC7WfzQ6fkzCoDEsbKljRkrv6eyGik9SQKbGdEzUgvezPxP6+bmvDGz7hMUoOSLRaFqSAmJrOvyYArZEZMLKFMcXsrYSOqKDM2m5INwVt+eZW0LqreVdVtXFZqt3kcRTiBUzgHD66hBvdQhyYwQHiGV3hzHp0X5935WLQWnHzmGP7A+fwBemuMuA== 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 highlight in red the entire viable parameter space for 0 ⇥ 23 3 ⇥1 2 1 1 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 10 101 10101 10 1?0 b which the observed baryon and dark matter abundances

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 @ d 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 b A of the Universe are reproduced. This roughly corresponds to FIG. 12. Two examples of flavor structure of the couplings of the color-triplet scalar Y that can produce the observed s d 5 Br(B ψ ) 25 ASL + ASL > 10− . (48) baryon asymmetry and the dark matter abundance while sat- → BM × isfying all current constraints. The heavy scalar mass here is Note that the product of these quantities
is critically pos- fixed to MY = 1.5 TeV, but masses up to 20 TeV are possible itive since we live in a Universe dominated by matter with the subsequent relaxation of experimental constraints. rather than antimatter. The couplings controlling the → BM decay as relevant B ψ Guided by Eq. (48), one can appreciate that there is for baryogenesis are shown in green. Note that ybt and yψt are largely unconstrained. a strong complementarity between the various current collider experiments that • Directly search for B ψ decays, or Belle, Belle-II, and LHCb. Finally, we note that, barring → BM 0 a detection, these bounds will be significantly improved • constrain the CP violation in the Bq system, or by the High-Luminosity upgrade of the LHC, as shown in Fig.9. • indirectly constrain Br(B ψ ) by searches for the heavy colored scalar→ neededBM to trigger the We now turn our attention to the implications for B ψ decay. model building and the LHC. As shown in Figs. 10 → BM and 11, any of the operators in Eq. (15) could be re- At present, we know that Br(B ψ ) < 0.5% sponsible for baryogenesis. Depending upon the exact at 95% CL as a result of an old ALEPH→ BM search, see Br(B ψ ) needed for baryogenesis, the color- → BM Sec.IVA. This constraint on Br( B ψ ) in turn triplet scalar mediator Y could be much heavier and tells us that at least one semileptonic→ asymmetryBM should 4 potentially out of reach of direct LHC searches. Even be positive and larger than 10− . At present, the semilep- in such a scenario, indirect effects on flavor observables d tonic asymmetries are measured to be ASL = ( 2.1 such as neutral meson mixing can still shed some light on 3 s 3 − ± 1.7) 10− and ASL = ( 0.6 2.8) 10− , meaning that the flavor structure of the Y couplings. The important current× measurements have− error± bars× which are a factor observation is that flavor observables constrain the prod- of 20 30 larger than the minimum value required by uct of two different couplings as can be seen in Eqs. (43) successful− baryogenesis. That said, and as discussed in and (44), while baryogenesis only requires a single cou- Sec.III, Belle II and LHCb expect to improve the preci- pling to be (1). Therefore, flavor bounds can be evaded O sion on these quantities by a factor of 3 4 on a 5 year if, for instance, the couplings of Y have a hierarchical timescale. The impact of this improvement− on the pa- structure. In Fig. 12 we show two examples of such struc- rameter space is highlighted in orange in Fig. 13. We tures, one for the case of Y carrying hypercharge 1/3 − can clearly appreciate that the improved measurements and another one for hypercharge 2/3. It would be inter- s of ASL by LHCb will narrow down the minimum required esting to explore how flavor structures like the ones in value of Br(B ψ ). A potential measurement of 15 Fig. 12 may arise in a UV complete model . We leave a nonzero positive→ valueBM for the semileptonic asymmetry this interesting model-building task to future work. would not only represent a clear signal of new physics, but also a strong indication in favour of B-Mesogenesis. The most distinctive signal of B-Mesogenesis is the presence of a new decay mode of B mesons into a 15 We refer to [40] for a scenario where Y is a supersymmetric dark sector antibaryon (missing energy in the detec- squark with hypercharge 1/3. − tor), a visible baryon and any number of light mesons, 25

The B-Mesogenesis Parameter Space

Signatures

CP violation Belle-II LHCb

Belle-II & LHCb New b decays

ATLAS & CMS High pT jets and missing energy BaBar/Belle

*Arrows indicate projections for 2025

LHCb

s d FIG. 13. Parameter space for successful baryogenesis and dark matter generation within B-Mesogenesis in the ASL-ASL plane. Similarly to Fig.3, the red bands indicate the minimum Br( B → ψ BM) needed to obtain the observed baryon asymmetry of the Universe. In black we highlight the SM prediction for the semileptonic asymmetries, while in orange we show current experimental constraints. The arrows indicate the upcoming sensitivity from collider experiments on these quantities. The purple arrows highlight the reach on Br(B → ψ BM) from analyses at BaBar or Belle, and from Belle-II and LHCb. With a green arrow we indicate the region of parameter space for which ATLAS and CMS could be sensitive to the colored triplet scalar needed to trigger the new B → ψ BM decay. We see that the upcoming measurements and searches at Belle-II and LHCb have the potential to test the entire B-Mesogenesis parameter space.

B ψ . As we have discussed in Sec.IV, such space of B-Mesogenesis. → BM processes are already constrained in an inclusive way by Additionally, LHCb can also search for decays of the LEP at the Br(B ψ ) < 0.5% level. We stress type B ψ ?, where B? is a resonant baryon. The → BM → B 1 that while B-Mesogenesis is only sensitive to the inclu- sensitivity of LHCb with 15 fb− for decays of this type sive Br(B ψ ) rate, searches for exclusive channels 7 can reach the Br 10− level [43]. From the theoret- like B ψ→+ BMare typically easier to carry out in col- ∼ → B ical point of view, it is not straightforward to translate lider experiments. Indeed, LEP constrains these exclu- a limit on Br(B ψ ?) to Br(B ψ ). How- 4 3 sive modes down to Br(B ψ ) 10− 10− at 95% → B → BM → B . − ever, these modes should represent some fraction of the CL. It is therefore crucial to know the relative exclusive inclusive decay and probing Br(B ψ ?) down to the vs. inclusive branching ratios, which for the simplest case 6 7 → B 10− 10− level would represent an important test of containing no additional mesons in the final state we es- B-Mesogenesis.− timate to be in the 1 10% range following our discussion Given all of the above sensitivity expectations, we con- in Sec.IVD. − clude that Belle-II and LHCb have the capabilities of In light of the current constraints on the semileptonic performing a direct search for the decays predicted by 4 B-Mesogenesis in order to test the its entire parameter asymmetries, we know that Br(B ψ ) > 10− is required for successful baryogenesis.→ WithBM this target in space. The reach of the individual searches are indicated mind, the sensitivity of past and current collider experi- with purple arrows in Fig. 13. ments to these decays is already promising. In particular, An alternative avenue to test B-Mesogenesis is to di- a direct search using old BaBar or Belle data should im- rectly search for the colored particle that mediates the prove upon existing constraints by more than an order B meson decay mode into a visible baryon and a dark 5 of magnitude, reaching Br(B ψ ) 3 10− for antibaryon. This new mediator cannot be too heavy and some of the flavor combinations.→ RegardingB ∼ × upcoming could therefore be produced and searched for at the LHC. experiments, Belle-II is expected to improve this figure In fact, as we have shown in Sec.V, ATLAS and CMS by another order of magnitude and constrain exclusive searches for high pT jets, and jets plus missing energy al- 6 branching fractions down to 3 10− . Given this sensi- ready place relevant constraints on the couplings of this tivity, searches at Belle-II for these× decays together with mediator to quarks and dark sector states. Given that improved measurements of the semileptonic asymmetries Br(B ψ ) is completely determined by these cou- could be enough to probe the entirety of the parameter plings→ and theBM mass of Y (see Eq. (39)), one can use these 26 bounds to place indirect constraints on Br(B ψ ). A. Summary At present, these constraints are particularly→ relevantBM for decay operators involving a charm quark, as Fig. 11 The main results obtained in this work are the following: shows, but with the planned increase in luminosity, the LHC has great potential to discover (or exclude) this me- • Current measurements of the semileptonic asymme- 0 diator. tries in Bq decays imply that baryogenesis and dark matter generation in the early Universe requires (see In summary, we have argued that there is an intimate Fig.3) interplay between (i) direct searches for B ψ de- → BM 4 cays at BaBar, Belle, Belle II and LHCb, (ii) the various Br(B ψ ) & 10− , (49) possible tests of CP violation in the B0 system at Belle → BM q where Br(B ψ ) is the inclusive branching II, LHCb, ATLAS and CMS, and (iii) the searches for → BM color-triplet scalars at ATLAS and CMS in order to test fraction of a B meson decaying into a visible baryon B-Mesogenesis. Not only could it be possible to detect , a dark sector antibaryon ψ, and any number of lightB mesons collectively denoted by . multiple signatures of this scenario at different collider M experiments, but, most importantly, a combination of • The most stringent current constraint on these new measurements has the potential to conclusively confirm decay modes arises from an old search at ALEPH for whether or not this mechanism is responsible for the ori- b decay events with large missing energy [80]. Our gin of the baryon asymmetry and the dark matter of the recast of this search yields constraints at the level of Universe. 4 Br(B ψ ) 10− 0.5% (ALEPH) , (50) → BM . − 4 3 Br(B ψ ) 10− 10− (ALEPH) . (51) → B . − The weakest constraints are for mψ 1 GeV, while VII. CONCLUSIONS the more stringent limit applies for heavier∼ ψ states, see Fig.5 for the precise dependence of the limits on Within the framework of baryogenesis and dark matter mψ. from B mesons—B Mesogenesis [1], the baryon asymme- • Given the above constraints on Br(B ψ ), we try of the Universe is directly proportional to two exper- conclude that at least one of the semileptonic→ BM asym- imental observables: i) the CP asymmetries in neutral metries should be positive and have a magnitude 0 Bq decays, and ii) the branching fraction of a new de- q 4 cay mode of B mesons into dark matter (missing en- ASL > 10− (52) ergy) and a visible baryon, Br(B ψ ) (recall in order to generate a sufficient baryon asymmetry. Eq. (6)). In this work, we have presented→ a detailedBM study of experimental tests that could confirm or refute this • We estimate that B factories should have a sensitiv- mechanism—see Figs.1 and 13 for a summary of these ity to exclusive B meson decays of (see Sec.IVB) 5 possible searches and their implications. We have found Br (B ψ + ) 3 10− (BaBar-Belle) , (53a) → B ∼ × that B-Mesogenesis should be fully testable at current 6 Br (B ψ + ) 3 10− (Belle II) , (53b) and upcoming collider experiments. → B ∼ × In order to asses all possible theoretical uncertainties, which are up to two orders of magnitude better than we have first revisited the calculation of the evolution existing limits. of B meson oscillations in the early Universe using a • Given our (rather primitive) phase space calculation density matrix approach (see AppendixVIIIA for de- of the B ψ decay, we expect the ratio between tails). The corresponding predictions of the mechanism exclusive→ and inclusiveB decays to be (see Fig.6) have then been contrasted against current CP violating measurements in the B0 system in Sec.III. In Sec.IV Br (B ψ ) q → B (1 10) % . (54) we have discussed current constraints and the expected Br(B ψ ) & − sensitivity of possible searches of the B ψ decay → BM at recent and current collider experiments.→ WeBM have also This, together with Eq. (49) and Eq. (53), supports presented a rough phase-space calculation that suggests our expectation that direct searches at B factories that the ratio between the rate of the minimal exclusive have a great potential to test wide regions (if not all) channel B ψ and that of the aforementioned inclu- of parameter space of B-Mesogenesis. → B sive one should be & 1 %, see Fig.6. In Sec.V we have • The LHC has the potential to search for B ψ , ? → B considered the collider implications of the new TeV-scale B ψ , and b ψ¯ decays. In fact, a recent color-triplet scalar Y , needed to mediate the B ψ analysis→ B shows thatB → LHCbM could reach sensitivities → BM 7 5 decay. Finally, in Sec.VI we have presented a global view at the level of Br 10− 10− [43]. We have dis- of the experimental landscape with which the implica- cussed the implications∼ of− irreducible backgrounds tions of B-Mesogenesis for current collider experiments for these searches in Sec.IVC, which need to be have been assessed in an all-encompassing way. carefully analyzed to reach these target sensitivities. 27

• The color-triplet scalar Y needed to mediate the plementarily, dijet and jet+MET searches of TeV-scale B ψ decay has the potential to be discov- color-triplet scalars can indirectly constrain the mecha- ered→ at theBM LHC by ATLAS and CMS. Current dijet nism. and jet+MET searches already represent a power- ful indirect constraint on the parameter space of the mechanism as shown in Fig. 11. In fact, we expect B. Outlook: Future Directions that upcoming squark searches at the HL-LHC will provide an independent probe of relevant and yet In the course of our analysis, the following additional uncharted parameter space of the mechanism, as ar- experimental, phenomenological, and theoretical studies gued in Sec.VE. that remain to be explored have been identified: • While meson-mixing constraints do not directly con- strain the mechanism, they do shape the Y -quark- • Theory: quark and Y -ψ-quark coupling matrices. The fact q – UV models: Across the entire paper, we have that A > 10 4 is needed for successful baryoge- SL − employed a minimal implementation of the particle nesis implies that there should be new physics con- q q content necessary for the mechanism and have tributions to the phases of M or Γ in the B 12 12 q remained agnostic about possible UV completions meson system, which could be probed via meson- that can accommodate B-Mesogenesis. Needless to mixing observables. In fact, the new tree-level b de- say, one would expect additional signals to arise cays enabled by the triplet-scalar mediator could be after an exhaustive UV completion is constructed. directly responsible for such contributions, making For example, in a Supersymmetric version of the the mechanism completely self-contained. mechanism [40], one finds new signals involving • Our analysis of meson-mixing constraints in auxiliary long-lived states and further implications Sec.VIIIE shows that only one of the four oper- for flavor and neutrino physics. It is therefore in- ators highlighted in Sec.II can be sizeable and thus teresting to pursue the construction of UV models responsible for baryogenesis. Namely, we do not ex- of this kind further, as they may help to not only pect any scenarios in which two operators are si- shed light on the origin of baryogenesis and dark multaneously large. However, it is in general not matter, but also more generally on the nature of possible to favor any particular operator above the the physics beyond the Standard Model. others provided that Br(B ψ ) and m lie → BM ψ within the allowed regions depicted in Fig. 11. As – QCD calculations: In Sec.IVD, we have presented a consequence, searches for all possible flavor vari- a very rough calculation that has allowed us to ations of the B ψ are necessary in order to → BM quantify the relative size of exclusive and inclusive fully test the mechanism. B ψ decay modes. Unfortunately and due • In Sec.VI we have presented a global analysis of to→ the purelyBM kinematic nature of our argumenta- the signals of B-Mesogenesis that highlights the re- tion, our predictions in Figs.6 and7 could have markable complementarity between recent, current, uncertainties of up to an order of magnitude. We and upcoming collider experiments in testing the pa- would like to remark that a lattice or a sum-rule rameter space of B-Mesogenesis. In particular, we calculation of the exclusive decay rates required for have shown that it is possible that simultaneously i) baryogenesis and dark matter production would be BaBar, Belle and Belle II could discover the new de- highly desirable to provide more accurate estimates. cay mode B ψ , ii) LHCb, ATLAS & CMS could Similarly, we have calculated the inclusive missing → B measure the relevant CP violation in the B0 B¯0 energy spectrum of B mesons decays at the parton s − s system, and iii) ATLAS and CMS could discover level in order to contrast it with a search performed a TeV scale color-triplet scalar responsible for the at ALEPH [80]. This is clearly a rough estimation B ψ decay. of the actual inclusive spectrum, and a robust con- → BM straint can only be obtained after properly account- In summary, we have presented an exhaustive and ing for the relevant QCD corrections and for the ef- global study of the experimental signals of baryogene- fect of the b quark momentum inside the B meson. sis and dark matter from B mesons. Importantly, if the mechanism of [1] is at play in the early Universe, there • Phenomenology: should be clear signals at B factories of B mesons decay- ing into a baryon and missing energy at rates that are – Flavor Structures: In Sec.VE, we have assessed within the reach of current data from BaBar and Belle what structures of the Y -quark-quark and Y -ψ- and certainly from upcoming data at Belle II. In addi- quark coupling matrices are needed in order to ac- tion, upcoming measurements of the CP violation in the commodate baryogenesis while satisfying all known 0 ¯0 Bq Bq system will play a key role in constraining the pa- collider and meson-mixing constraints on color- rameter− space of the mechanism. This is relevant for mea- triplet scalars. Although we have not aimed to surements at Belle II, LHCb, ATLAS and CMS. Com- provide a theoretical explanation of the particular 28

shapes of the resulting coupling matrices, we be- Uncovering the mechanism responsible for generating lieve that such a study would be very relevant as it an asymmetry of matter over antimatter in the early Uni- could yield indirect constraints on viable UV com- verse is key to explaining our very existence. That such a pletions of the mechanism. Finally, given that the process may also be at the origin of dark matter, thereby models aimed to explain the anomalous measure- explaining the nature of the component that dominates ments in B K`` decays [133] modify the mixing the matter density of the Universe, is particularly ap- →0 ¯0 pattern of Bs Bs oscillations [134] and thus lead pealing. B-Mesogenesis is such a mechanism, and in this s s − to ASL = ASL SM, it would be very interesting to work we have shown it to be fully testable at current explore6 connections| between the mechanism of [1] hadron colliders and B factories. This scenario resurrects and these current anomalies in b s`` transitions. the dream that discovering baryogenesis can be a physics q → goal of B factories and hadron colliders. In fact, we are – CP violation in Γ12: The new tree-level b decays present in our model generically contribute to the looking forward to forthcoming results from searches and 0 studies already underway at BaBar, Belle, Belle II and width mixing in Bd,s mesons. We have not analyzed the sizes and phases of couplings of the triplet scalar LHCb. By providing a roadmap towards the discovery of d s baryogenesis and dark matter from B mesons, it is our that could result in an enhancement of ASL and ASL with respect to their SM values, as such calculation hope that many more experimental programs will be set requires non-trivial QCD matching and a careful forth to discover or refute this mechanism. analysis of many tree-level decays, which is beyond the scope of this work. Given that current global Acknowledgments fits including some of the operators [66, 67] present in our model highlight that these modes can lead to q We are forever thankful to Ann Nelson, our collaborator, large values of A , we believe that it would be par- SL mentor, and friend who pioneered the ideas that this pa- ticularly interesting to systematically consider the q per is based on. We would also like to thank David McK- possible modifications to Γ from new tree-level de- 12 een for collaboration during the early stages of this work. cays. We are grateful to Zoltan Ligeti, Jorge Martin-Camalich – LHC simulations: In Sec.VB we have presented and Dean Robinson for useful discussions regarding the an analysis of dijet and jet+MET signals involv- use of the vacuum insertion approximation for our de- ing color-triplet scalars at the LHC. It would cays, to Alexander Lenz for useful discussions regard- be interesting to re-evaluate these analyses at q ing tree-level decays effects in Γ12, to Ville Vaskonen next-to-leading order in QCD and foregoing the for helpful discussions on neutron star bounds, to Chris- narrow width approximation, in a similar fashion tos Hadjivasiliou, Jan Strube, and the whole Belle/Belle to [135, 136] but in the context of a singly-produced II team at PNNL for useful discussions regarding miss- color-triplet scalar. ing energy searches at B factories, to Xabier Cid Vidal for helpful discussions on the LHCb capabilities to miss- ing energy final states, and to Veronika Chobanova and • Experiment: Diego Mart´ınez Santos for useful discussions regarding ccs¯ – LHC searches: In Sec.IVC, we have commented φs measurements and analyses. Finally, we are grate- on the opportunities and difficulties when searching ful to Veronika Chobanova, Xabier Cid Vidal, Bertrand for the new decay modes of B mesons and b-flavored Echenard, Diego Mart´ınez Santos and Jan Strube for baryons at the LHC. Although recent ideas to target their very useful comments and suggestions on a prelim- these decays have been put forward [43, 101, 103], inary version of this manuscript. GA acknowledges sup- evaluating the full impact of direct LHC searches port by a “la Caixa” postgraduate fellowship from the on the parameter space of B-Mesogenesis remains Fundaci´on“la Caixa”, by a McGill Trottier Chair Astro- an exciting avenue to explore. physics Postdoctoral Fellowship, and by NSERC (Natu- ral Sciences and Engineering Research Council, Canada). – Searches at BaBar, Belle and Belle II: In Sec.IVB GE is supported by the U.S. Department of Energy, un- we have estimated that upcoming measurements at der grant number DE-SC0011637. GE thanks the Berke- B factories have the potential to test wide regions of ley Center for Theoretical Physics and Lawrence Berkeley parameter space for baryogenesis and dark matter National Laboratory for their hospitality during the com- from B mesons as originally proposed in [1]. In pletion of this work. ME is supported by a Fellowship of fact, searches are currently ongoing for B0 ψ Λ d the Alexander von Humboldt Foundation. decays [41, 42] at BaBar, Belle and Belle II. We→ look forward to the results of upcoming searches which we expect will significantly test B-Mesogenesis. 29

VIII. APPENDICES the successful predictions of Big Bang Nucleosynthesis. In this way, the b quarks produced via the decay of 0 0 A. B Meson Oscillations in the Early Universe Φ hadronize into B±, Bd, Bs mesons and b-baryons. Among those, the neutral B mesons undergo CP violat- In this appendix we describe the set of Boltzmann ing oscillations and subsequently decay. If the oscillation equations that characterize the evolution of the popu- process is coherent, i.e. it is not damped by interactions lation of B mesons and their decay products in the early with the plasma, then the resulting chain of events can Universe in order to establish the benchmarks for the ex- lead to the generation of a net particle-antiparticle asym- perimental searches proposed in the main body of this metry in the Universe. work. Although our discussion is based on that of [1] The most accurate framework to study these processes and [38], we have updated the numerical results and iden- in the early Universe is the density-matrix formalism. tified and quantified the main sources of uncertainty in This formalism has been applied to study similar set ups the calculation. Compared to [1] and as was done in [38], in [140–143] and was specifically described in [38] for B- we use a density-matrix approach to track the evolution Mesogenesis. We therefore follow closely the notations of the number densities, thus consistently taking into ac- and equations [38]. In terms of the density matrix count decoherence effects in the neutral B meson oscilla- n n ¯ tions. It is important to note that the results originally n = BB BB , (58) n ¯ n ¯ ¯ obtained in [38] show some discrepancies with the one  BB BB in [1] in the limit of vanishing decoherence, where both approaches should agree. Crucially and thanks to our up- the Boltzmann equations that govern the oscillations can dated numerical treatment, we resolve this discrepancy be compactly written as and fully agree with [1] in this limiting case. We therefore dn 1 strongly advise to use the numerical results presented in + 3Hn = i( n n †) Γe±B [O , [O , n]] this appendix rather than the ones in [1, 38]. dt − H − H − 2 − − 1 At times well before the relevant dynamics take place + ΓΦnΦBrΦ BO+ . (59) 2 → (i.e. at times much shorter than 1/ΓΦ), the Universe is assumed to be dominated by an admixture of radiation Here, O diag(1, 1) discriminates between flavor- and non-relativistic Φ particles. The Hubble parameter blind and± flavor-sensitive≡ ± interactions. The first term can thus be expressed as describes oscillations and decays in terms of the ∆F = 2 effective Hamiltonian = M iΓ/2. The second 8π ρr + ρΦ H2 = , (55) one describes elastic scatteringsH with− the electrons and 3 M 2 pl positrons in the plasma, which occur due to the non- trivial charge distribution in the neutral mesons. These in terms of the energy densities, ρΦ = MΦnΦ, and 2 4 interactions are flavor-sensitive and therefore act to de- ρr = (π /30)g?(T )T , where g?(T ) are the number of cohere the B0 B¯0 oscillations via the quantum Zeno relativistic degrees of freedom as a function of tempera- − ture which we take from [137]. effect [144]. We use the estimation of the scattering rate The evolution of the energy and number densities of computed in [1], radiation and the decaying Φ particles is given by the 5 2 2 following Boltzmann equations 11 T rB Γe±B 10− GeV h i , (60) ' 20 MeV 0.187 fm2 dn     Φ + 3Hn = Γ n , (56) dt Φ − Φ Φ that depends on the charge radius of neutral B mesons dρ which can only be estimated theoretically and for which r + 4Hρ = Γ M n . (57) dt r Φ Φ Φ we have taken the value obtained in [70]. The particle-antiparticle asymmetry ∆B = nBB nB¯B¯ Note that although the decay of Φ is assumed to be pre- that is generated through the coherent oscillations− is dominantly into non-relativistic b quarks, these hadronize translated into a baryon-antibaryon asymmetry through and decay into radiation in a timescale much shorter than 1 the new B meson decay into a baryon ( ) and a dark that of the Universe expansion, H− . This justifies ne- antibaryon (ψ): B ψ . In this manner,B the visible glecting the brief existence of B mesons in (56) to only positive baryon asymmetry→ BM is compensated by a negative include the final relativistic products of the decay chain one that is stored in the dark matter. Thus, dark mat- of Φ. ter is antibaryonic in our set up. The baryon asymmetry Instead of using the lifetime of Φ as a parameter, in the visible sector, which we denote by n , is there- we use the “reheat temperature” to which it leads, B fore sourced by the B meson asymmetry ∆B. The time i.e. 3H(T ) Γ . Physically, this temperature must R ≡ Φ evolution of n is given by be below the hadronization scale Λ 200 MeV B QCD ∼ (otherwise B mesons do not hadronize) but above dn ∼ B + 3Hn = BrB ΓB∆B , (61) 4 MeV [138, 139] so that the decays of Φ do not spoil dt B →B 30

Z decays Tevatron Υ(5S) αd 1.25 fu 0.408 0.344 0.379 αs fd 0.408 0.344 0.379 1.00 fs 0.100 0.115 0.199

0.75 fbaryon 0.084 0.198 0.045

coefficients TABLE III. Experimentally measured values for the fragmen- q 0.50 ± 0 0 α tation ratios of b quarks into B , Bd, Bs , and b-baryons as compiled by [64]. In addition, ATLAS has measured a value 0.25 fs/fd = 0.252 [145] in pp collisions at 7 TeV. 0.00 0 20 40 60 If the decay of Φ happens at low temperatures, the rate Reheating temperature T [MeV] R at which electrons and positrons scatter with the neutral B mesons, given in (60), is small and the oscillations can FIG. 14. Functions describing the dependence of the gen- proceed unimpeded. In this limit, the asymmetry scales erated baryon asymmetry on the reheat temperature, as proportionally to the number of B mesons produced in parametrized in (6) and (63). The severe suppression of the the decay of Φ relative to the number of photons, which baryon yield at high temperatures is caused by the decoher- grows as TR. 0 ¯0 ∝ ence of the B − B oscillations due to interactions with elec- At higher reheat temperatures, scatterings with e± trons and positrons in the plasma. The shaded regions repre- become more frequent and decohere the system once sent the uncertainty in our calculation arising from the lack their rate overcomes the frequency at which the neu- of precise knowledge of the charge radius of the neutral B tral mesons oscillate. This results in a sharp decline mesons. in the generated asymmetry, which happens earlier for 0 Bd mesons given that their oscillation frequency ∆Md = 1 0 from which the baryon-to-entropy ratio 0.5065 0.0019 ps− is smaller than that of Bs mesons, ± 1 ∆M = 17.757 0.021 ps− . n d ± Y = 2 B , (62) The overall conclusion is that the generation of the B 2π 3 g?,S(T )T 0 45 asymmetry is maximally efficient at TR 5 MeV for Bd mesons and T 10 MeV for B0 mesons.∼ Given that can be obtained. R ∼ s Owing to the fact that both the oscillation frequency current experimental data favor a negative value of the d 0 and the lifetime of neutral B mesons are much smaller semileptonic asymmetry ASL of Bd mesons, these are ex- 1 pected to contribute negatively to the baryon asymmetry. than H− at the relevant temperatures, the system described by (59) reaches equilibrium in a very short Under this assumption, the production of the observed 0 timescale. This allows us to solve (59) algebraically for positive baryon asymmetry is driven by Bs mesons and the fixed point of ∆ as a function of time, once (56) is occurs most favorably at temperatures TR 10 20 MeV, B s ∼ −d solved numerically. With this, one can numerically inte- depending on the exact magnitude of ASL and ASL, which 0 are currently not well-determined experimentally. grate (61), including the contributions from both Bd and 0 The uncertainty of the numerical calculation of c is Bs , to obtain the baryon asymmetry. d,s The resulting asymmetry can be parametrized as in (6) shown as shaded regions in Fig. 14 and is dominated by in terms of the functions αd,s(TR,MΦ), which encompass the lack of precise knowledge of the charge radius of neu- the dependence of the result on the cosmological param- tral B mesons. A larger (smaller) value of the charge eters. In turn, these functions can be written as radius results in more (less) efficient scatterings with the e± in the plasma and reduces (increases) the generated 11 GeV BrΦ B0/B¯0 → d d asymmetry. For our benchmark calculation we use the αd(TR,MΦ) = cd(TR) , (63a) 2 2 MΦ 0.4 value rB = 0.187 fm , which was estimated in [70].     However,h i given− the dispersion in its determination by 11 GeV BrΦ B0/B¯0 α (T ,M ) = → s s c (T ) , (63b) different authors [70–72], we choose to conservatively al- s R Φ M 0.1 s R  Φ    low for a factor of 2 uncertainty in this parameter, which where the functions cs,d enclose the dependence on the leads to the upper and lower bands for cd,s depicted in reheat temperature and have to be obtained numeri- Fig. 14. cally. The reheat temperature is ultimately controlled by Aside from this, the functions αd,s depend on the mass the lifetime of Φ, and it determines the precise moment of Φ, which has to be MΦ > 2mb, and on its branching 0 0 when the out-of-equilibrium population of B mesons is fraction to Bd and Bs . Assuming for simplicity that injected. Keeping this in mind, the functional form of the decay of Φ always produces b quarks, the important αs,d(TR), which is displayed in Fig. 14, can be under- quantity is the fragmentation ratio of b quarks into the stood as follows. different b-hadrons. These fractions are usually denoted 31

0 0 fu (for B±), fd (for Bd), fs (for Bs ), and fbaryon (for b- Exclusive Missing Energy Spectrum: baryons). These ratios are challenging to compute from 2-body hadronic decays first principles and have experimentally been found to be very process dependent, as can be seen in TableIII. We study the missing energy spectrum in exclusive Clearly, the fragmentation ratios for Φ decays are com- two-body decays of the type B ψ . For these de- pletely unknown. For concreteness, in Fig. 14 we choose cays, the kinematics is fixed in the→B mesonB rest frame, a benchmark ratio 4 : 4 : 1 : 1, consistent with mea- and the energy of the dark antibaryon ψ simply reads surements from Z decays into b¯b [64]. However, the ac- 2 2 2 tual value for Φ decays could significantly deviate from B frame mB + mψ m 0 0 Eψ− = − B . (65) this benchmark as, for example, the Bd to Bs ratio is 2mB measured to be closer to 3 : 1 in pp¯ collisions [64]. For- tunately, it is straightforward to use Eqs. (63) to scale This energy can be easily boosted to the laboratory our results for different values of these ratios. For the frame, predictions presented in the main text, we choose to ac- LEP B frame B frame count for the uncertainty in the fragmentation fractions EMiss = γ Eψ− βpψ− cos θ , (66) by allowing the ratio f /f to vary over the range of ex- − s d   perimentally measured values given in TableIII, which 2 2 2 amounts to f /f [0.22, 0.37]. where pψ = Eψ mψ, β = γ 1/γ and γ = s d ∈ − − EB/mb, and whereq EB = xb√s/p2. In addition, θ is a random angle that characterizes the direction of the B. Missing energy spectrum from b-decays at emitted ψ with respect to the direction of flight of the B ALEPH meson. By choosing √s = MZ = 91.2 GeV and generat- ing random samples of θ, the missing energy spectrum at This appendix contains supplementary material to our LEP can be easily simulated. recast of the ALEPH search for events with large missing energy at LEP [80]. In particular, we provide the relevant Inclusive Missing Energy Spectrum: formulas needed to calculate the missing energy spectrum 3-body parton decays of the decays predicted in B-Mesogenesis as produced at the Z peak in Z b¯b processes. We first comment We also calculate the missing energy of inclusive decays on the relationship between→ the center of mass energy at the parton level, ¯b ψud, where u and d stand for → (√s = MZ ) and the energy of the decaying b-quark as quarks of any generation. In the b-frame the differential encoded in the b-quark fragmentation function. Then decay rate can be written as we discuss how to calculate the missing energy spectrum in exclusive 2-body B decays and for inclusive decays, 1 1 2 dΓ = 3 dEudEψ . (67) b ψuidj. We finish by showing some representative (2π) 8mb |M| results→ for each of the cases. Given the purely right-handed nature of the triplet scalar The b-fragmentation function at LEP couplings, the matrix elements can be expressed as

A relevant quantity to calculate the missing energy = (ψb)(ud) 2 (p p )(p p ), (68) spectrum at ALEPH is the fragmentation function of O → |M| ∝ b · ψ u · d = (ψd)(ub) 2 (p p )(p p ), (69) b hadrons at the Z peak. This essentially represents O → |M| ∝ b · u ψ · d 2 the fraction of the center-of-mass energy that the de- = (ψu)(db) (pb pd)(pψ pu) . (70) caying b quark carries, xb = Eb/(√s/2). The distribu- O → |M| ∝ · · tion of xb values is dependent upon the hadronization of Taking into account the relevant 3-body decay phase the b-quark and is typically characterized using theoret- space (see e.g. the PDG review for kinematics) one can ical models which are then fitted to b-quark decay data. rewrite these momentum products in terms of Eu and Eψ In [80], the Peterson model [146] is used, which gives and integrate over Eu. The formulas that we obtain for 2 the differential decay rate dΓ/dEψ are not particularly dN N 1  − b = 1 b , (64) insightful and we do not explicitly reproduce them here. dx x − x − 1 x b b  b − b  In any case, this yields dΓ/dEψ, the differential missing energy spectrum in the b-quark rest frame as a function where N is a normalization constant, and b must be obtained from a fit to kinematic decay data and is found of the ψ mass for each type of operator. The last ingredient in order to calculate the missing to be b = 0.0032 0.0017 [147]. We note that the used fragmentation function± does lead to a relevant 20 40% energy spectrum is to know the kinematic regions for the ∼ − min effect on the resulting missing energy spectrum at high decay. Clearly, these correspond to Eψ = mψ (ψ at max 2 2 2 energy as relevant for the ALEPH analysis. In order rest) and E = (m + m (mu + md) )/2mb (ud ψ b ψ − to derive our constraints, and as is done in [80], we use diquark at rest). Finally, the shift to the LAB frame b = 0.0032 + 0.0017 in order to remain conservative. is done by performing boost similar to that described 32

√ FIG. 15. Missing energy spectrum from the decays predicted by B-Mesogenesis at s = MZ arising from Z → ¯bb processes. Left panel: exclusive two body decays, B → ψ B. Right panel: inclusive decays (calculated here at the parton level as a 3-body decay without any QCD corrections). We also highlight the signal region targeted in the ALEPH [80] search. Note that the region with Emiss < 30 GeV suffers from the presence of substantially large backgrounds. in Eq. (66). For our numerical evaluation, we use the heavy quark corrections to the missing energy spectrum following values for the quark masses: are expected to lead to an even smaller fraction of events in this window—in a similar way to what happens with pole m = 4.8 GeV, mc = 1.275 GeV , ms = 0.093 GeV , b sνν¯ decays, see the erratum of [88] for a discussion. b → md = 0.0047 GeV , mu = 0.0022 GeV . (71)

0 Simulation C. Exclusive vs. Inclusive decays: Bs and Λb

0 We generate 20000 random events for every value of Figs. 16 and 17 show the fraction of Bs and Λb decays mψ for each of the 4 different operators. The 3 random that are not expected to contain hadrons other than the variables are ones listed in TableI in the final state, as a function of the mass of the dark fermion ψ. These fractions are 1. x , which is generated with the Peterson probabil- b obtained based on the phase-space arguments detailed ity distribution and ranging between 0 x 1. ≤ b ≤ in Sec.IVD, and in particular using Eq. (37) with the 2. θ, which is generated randomly over an uniform appropriate flavor content for each case. From the right distribution in the range 0 θ π. panel of Fig. 15 we can appreciate that the missing energy ≤ ≤ spectrum is not very large in the signal region, Emiss > 3. For 3-body decays, Eψ, which is generated ran- 30 GeV, with only a fraction of 10 15 % of the events domly given the probability distribution dictated in such kinematic region. This∼ is simply− because the 3- 2 by dΓ/dEψ and in the region mψ Eψ (mb + body kinematics imply typically lead to less energetic ψ 2 2 ≤ ≤ mψ (mu + md) )/2mb. particles in the b-quark rest frame (as compared to the − exclusive 2-body decay). The missing energy spectrum from exclusive (B → ψ ) and inclusive (¯b ψ ui dj) decays is shown in Fig.B 15. In the left panel,→ we can appreciate that the exclusive missing-energy spectrum significantly depends upon the ψ mass and upon the mass of the resulting baryon in the final state. Heavier baryons in the fi- nal state naturally lead to a smaller missing energy. In the right panel of Fig. 15, we show the missing energy spectrum for inclusive decays for operators of the type (ψb)(ud) (similar results are obtained for the others). In this case, the number of events with large missing energy is substantially smaller than for exclusive 2-body decays. This is simply because in the 3-body decay the ψ particle carries less energy than in the exclusive decays in the b rest frame. It is important to highlight that QCD and 33

0 1 Bs decays through ij = (ψb)(uidj) 0 2 3 Bs decays through ij = (ψdj)(uib) or ij = (ψui)(djb) 0 0 O 0 0 Bs Λ + ψ ( = ψbud) Bs Ξc + ψ ( = ψbcd) 0 0 O 0 O0 → O → O Bs Λ + ψ ( = ψbud) Bs Ξc + ψ ( = ψbcd) 0 0 0 0 → O → O Bs Ξ + ψ ( = ψbus) Bs Ωc + ψ ( = ψbcs) 0 0 0 0 → O → O Bs Ξ + ψ ( = ψbus) Bs Ωc + ψ ( = ψbcs) 0 → O → O

) 10 0

) 10 M M ψ ψ ij ij → B → B 0 s 0 s

B 1

B 1 10− 10− Br( Br( / / ) ) ψ ψ ij ij → B → B 0 s 0 2 s 2 B 10− B 10− Br( Br( 1.0 1.5 2.0 2.5 3.0 3.5 4.0 1.0 1.5 2.0 2.5 3.0 3.5 4.0 mψ [GeV] mψ [GeV] 0 FIG. 16. Same as Fig.6 but for Bs → ψ BM decays.

Λ decays through 1 = (ψb)(u d ) 2 3 b Oij i j Λb decays through ij = (ψdj)(uib) or ij = (ψui)(djb) 0 ¯ ¯ 0 ¯ O O Λb π + ψ ( = ψbud) Λb D + ψ ( = ψbcd) Λ π0 + ψ¯ ( = ψbud) Λ D¯ 0 + ψ¯ ( = ψbcd) → O → O b → O b → O 0 ¯ + ¯ 0 + Λb K + ψ ( = ψbus) Λb D− + K + ψ ( = ψbcs) Λ K + ψ¯ ( = ψbus) Λ D− + K + ψ¯ ( = ψbcs) → O → O b → O b → O

) 0 10 ) 100 M M ¯ ¯ ψ 1 ψ 1 ij 10− ij 10−

2 2 → M 10− → M 10− b b

3 3 Br(Λ 10− Br(Λ 10− / / ) ) ¯ ¯ ψ 4 ψ ij 4 10− ij 10−

→ M 5 → M 5 10− 10− b b

6 6 Br(Λ 10− Br(Λ 10− 1.0 1.5 2.0 2.5 3.0 3.5 4.0 1.0 1.5 2.0 2.5 3.0 3.5 4.0 mψ [GeV] mψ [GeV]

FIG. 17. Same as Fig.6 but for Λ b → ψ M decays.

D. LHC Bounds on Color-Triplet Scalars and ∆m in Eq. (40) becomes smaller. As a result, the band shifts to larger couplings as compared to the cases involving only u, d, and s quarks. This is the reason why For the hypercharge 1/3 case, the combined limits we distinguish between yψu and yψc in the hypercharge − on the yud vs. yψd parameter space are shown in Fig 19 2/3 case shown in Fig. 20, where we plot the limits in the for three benchmark values of MY = 1.5, 3, and 5 TeV ydd0 vs. yψu planes. and each of the quark flavor variations in yud (given that no flavor-tagging techniques are employed in the analyses, the limits are insensitive to the quark flavor of the yψd coupling). Each of the panels in Fig. 19 shows E. New physics in neutral meson mixing the dijet exclusion in green and the jet+MET limits in blue, and the thin dotted line indicates where the nar- row width approximation ΓY MY is expected to break The mass difference of neutral mesons is modified by down. The red band corresponds to the range in which the presence of a color-triplet scalar with the couplings B-Mesogenesis is possible. The position of this band in given in (38). As a consequence, the flavor structure of each panel depends on the quark flavors involved: in the the coupling constants yuidj / ydidj and yψdk / yψuk can presence of a c quark, the B decays into a charmed baryon be constrained with neutral meson mixing data. The new 34

qj /ψ q q q j 1 2 q1 q1

Y Y Y W, H

q q 2 1 q2 q2 qi/ψ qi

FIG. 18. Box diagrams involving the heavy colored scalar Y and contributing to the neutral meson oscillations. The one involving the dark baryon ψ is only possible for down-type external quarks. contributions to the mass difference can be expressed as while the one with the internal dark fermion ψ results in

5 3 NP ∆M = 2 CiMi + C˜iM˜ i , (72) i=1 i=1 ! X X where we have split the contributions into a partonic am- 1 1 2 C˜ = y∗ y S˜ (x , x ). (77) 1 2 2 ψq1 ψq2 1 ψ ψ plitude Ci and a hadronic matrix element Mi. Our la- 128π mY belling follows the conventions of [148]. The Y particle 2 2 Here, xf = m /m and we have defined
can mediate the two new kinds of box diagrams depicted f Y in Fig. 18, which yield contributions to C˜1, C4, and C5. The corresponding matrix elements can be expressed as

1 M˜ M = f 2 m BM , (73) S˜ (x , x ) = I (x , x , 1, 1), (78) 1 3 M M 1 1 qi qj 4 qi qj 2 S˜5(xq , xq ) = xq xq I2(xq , xq , xW , 1) M 1 1 mM 2 M i j √ i j i j M4 = + fM mM B4 , 24 4 mq + mq 1 "  1 2  # + I (x , x , x , 1) , (79) 4x 4 qi qj W 1 1 m 2 W M M = + M f 2 m BM ,  5 8 12 m + m M M 5 "  q1 q2  # In terms of the masses of the meson M and its constituent quarks q1, q2, the decay constant fM , and the bag pa- M with the loop integrals rameters Bi . The partonic amplitudes for the diagrams involving internal SM quarks read 1 1 C˜ = y∗ y y∗ y S˜ (x , x ), 1 128π2 m2 qiq1 qiq2 qj q1 qj q2 1 qi qj Y i,j X n/2 (74) ∞ t dt In(x, y, w, z) = . (80) 0 (t + x)(t + y)(t + w)(t + z) C4 = C5, (75) Z − 1 g2 C = y y∗ V V ∗ S˜ (x , x ), 5 128π2 m2 qiq2 qj q1 qj q1 qiq2 5 qi qj Y i,j X (76)

[1] G. Elor, M. Escudero, and A. Nelson, Phys. Rev. D99, [3] G. Bertone and D. Hooper, Rev. Mod. Phys. 90, 045002 035031 (2019), arXiv:1810.00880 [hep-ph]. (2018), arXiv:1605.04909 [astro-ph.CO]. [2] N. Aghanim et al. (Planck), Astron. Astrophys. 641, A6 [4] P. Peebles, Nat. Astron. 1, 0057 (2017), (2020), arXiv:1807.06209 [astro-ph.CO]. arXiv:1701.05837 [astro-ph.CO]. [5] E. W. Kolb and M. S. Turner, Front. Phys. 69, 1 (1990). 35

[6] V. A. Rubakov and D. S. Gorbunov, Introduction to [38] A. E. Nelson and H. Xiao, Phys. Rev. D100, 075002 the Theory of the Early Universe: Hot big bang theory (2019), arXiv:1901.08141 [hep-ph]. (World Scientific, Singapore, 2017). [39] G. Elor and R. McGehee, (2020), arXiv:2011.06115 [7] V. C. Rubin and J. Ford, W.Kent, Astrophys. J. 159, [hep-ph]. 379 (1970). [40] G. Alonso-Alvarez,´ G. Elor, A. E. Nelson, and H. Xiao, [8] K. Freeman, Astrophys. J. 160, 811 (1970). JHEP 03, 046 (2020), arXiv:1907.10612 [hep-ph]. [9] G. Jungman, M. Kamionkowski, and K. Griest, Phys. [41] P. communication: Bertrand Echenard (on behalf of the Rept. 267, 195 (1996), arXiv:hep-ph/9506380. BaBar collaboration), . [10] G. Bertone, D. Hooper, and J. Silk, Phys. Rept. 405, [42] P. communication: Jan Strube (on behalf of the Belle- 279 (2005), arXiv:hep-ph/0404175. (I&II) collaborations), . [11] J. Preskill, M. B. Wise, and F. Wilczek, Phys. Lett. B [43] A. B. Rodr´ıguez, V. Chobanova, X. Cid Vidal, S. L. 120, 127 (1983). Soli˜no, D. M. Santos, T. Momb¨acher, C. Prouv´e, [12] M. Dine and W. Fischler, Phys. Lett. B 120, 137 (1983). E. X. R. Fern´andez, and C. V´azquezSierra, (2021), [13] L. Abbott and P. Sikivie, Phys. Lett. B 120, 133 (1983). arXiv:2106.12870 [hep-ph]. [14] S. Dodelson and L. M. Widrow, Phys. Rev. Lett. 72, 17 [44] M. Artuso, G. Borissov, and A. Lenz, Rev. Mod. Phys. (1994), arXiv:hep-ph/9303287. 88, 045002 (2016), arXiv:1511.09466 [hep-ph]. [15] X.-D. Shi and G. M. Fuller, Phys. Rev. Lett. 82, 2832 [45] H. P. Nilles, Phys. Rept. 110, 1 (1984). (1999), arXiv:astro-ph/9810076. [46] H. Davoudiasl, D. E. Morrissey, K. Sigurdson, and [16] M. Drewes et al., JCAP 01, 025 (2017), S. Tulin, Phys. Rev. Lett. 105, 211304 (2010), arXiv:1602.04816 [hep-ph]. arXiv:1008.2399 [hep-ph]. [17] B. Carr, F. Kuhnel, and M. Sandstad, Phys. Rev. D [47] J. R. Ellis, M. K. Gaillard, and D. V. Nanopoulos, 94, 083504 (2016), arXiv:1607.06077 [astro-ph.CO]. Phys. Lett. B 80, 360 (1979), [Erratum: Phys.Lett.B [18] V. Mossa et al., Nature 587, 210 (2020). 82, 464 (1979)]. [19] A. D. Sakharov, Pisma Zh. Eksp. Teor. Fiz. 5, 32 (1967), [48] S. M. Barr, G. Segre, and H. Weldon, Phys. Rev. D 20, [Usp. Fiz. Nauk161,61(1991)]. 2494 (1979). [20] A. Dolgov, Phys. Rept. 222, 309 (1992). [49] D. McKeen, A. E. Nelson, S. Reddy, and D. Zhou, [21] A. G. Cohen, D. Kaplan, and A. Nelson, Ann. Rev. Phys. Rev. Lett. 121, 061802 (2018), arXiv:1802.08244 Nucl. Part. Sci. 43, 27 (1993), arXiv:hep-ph/9302210. [hep-ph]. [22] D. E. Morrissey and M. J. Ramsey-Musolf, New J. Phys. [50] D. McKeen, M. Pospelov, and N. Raj, (2020), 14, 125003 (2012), arXiv:1206.2942 [hep-ph]. arXiv:2012.09865 [hep-ph]. [23] J. M. Cline, in Les Houches Summer School - Session [51] Z. Berezhiani, R. Biondi, M. Mannarelli, and F. Tonelli, 86: Particle Physics and Cosmology: The Fabric of (2020), arXiv:2012.15233 [astro-ph.HE]. Spacetime (2006) arXiv:hep-ph/0609145. [52] J. Ellis, G. H¨utsi,K. Kannike, L. Marzola, M. Raidal, [24] A. Riotto and M. Trodden, Ann. Rev. Nucl. Part. Sci. and V. Vaskonen, Phys. Rev. D 97, 123007 (2018), 49, 35 (1999), arXiv:hep-ph/9901362. arXiv:1804.01418 [astro-ph.CO]. [25] M. Dine and A. Kusenko, Rev. Mod. Phys. 76, 1 (2003), [53] T. Motta, P. Guichon, and A. Thomas, J. Phys. G 45, arXiv:hep-ph/0303065. 05LT01 (2018), arXiv:1802.08427 [nucl-th]. [26] S. Davidson, E. Nardi, and Y. Nir, Phys. Rept. 466, [54] G. Baym, D. Beck, P. Geltenbort, and J. Shelton, Phys. 105 (2008), arXiv:0802.2962 [hep-ph]. Rev. Lett. 121, 061801 (2018), arXiv:1802.08282 [hep- [27] M. Drewes, B. Garbrecht, P. Hernandez, M. Kekic, ph]. J. Lopez-Pavon, J. Racker, N. Rius, J. Salvado, and [55] I. Goldman, R. Mohapatra, S. Nussinov, D. Rosen- D. Teresi, Int. J. Mod. Phys. A 33, 1842002 (2018), baum, and V. Teplitz, Phys. Lett. B 725, 200 (2013), arXiv:1711.02862 [hep-ph]. arXiv:1305.6908 [astro-ph.CO]. [28] S. Dimopoulos and L. Susskind, Phys. Rev. D 18, 4500 [56] K. Frankiewicz (Super-Kamiokande), J. Phys. Conf. (1978). Ser. 888, 012210 (2017). [29] S. Weinberg, Phys. Rev. Lett. 42, 850 (1979). [57] A. Olivares-Del Campo, C. Bœhm, S. Palomares-Ruiz, [30] I. Affleck and M. Dine, Nucl. Phys. B 249, 361 (1985). and S. Pascoli, Phys. Rev. D 97, 075039 (2018), [31] M. Fukugita and T. Yanagida, Phys. Lett. B 174, 45 arXiv:1711.05283 [hep-ph]. (1986). [58] N. F. Bell, M. J. Dolan, and S. Robles, JCAP 09, 019 [32] E. K. Akhmedov, V. Rubakov, and A. Smirnov, Phys. (2020), arXiv:2005.01950 [hep-ph]. Rev. Lett. 81, 1359 (1998), arXiv:hep-ph/9803255. [59] C. A. Arg¨uelles,A. Diaz, A. Kheirandish, A. Olivares- [33] T. Asaka and M. Shaposhnikov, Phys. Lett. B 620, 17 Del-Campo, I. Safa, and A. C. Vincent, (2019), (2005), arXiv:hep-ph/0505013. arXiv:1912.09486 [hep-ph]. [34] T. Asaka, S. Blanchet, and M. Shaposhnikov, Phys. [60] M. Escudero, N. Rius, and V. Sanz, Eur. Phys. J. C Lett. B 631, 151 (2005), arXiv:hep-ph/0503065. 77, 397 (2017), arXiv:1607.02373 [hep-ph]. [35] K. Babu, R. Mohapatra, and S. Nasri, Phys. Rev. Lett. [61] M. Escudero, N. Rius, and V. Sanz, JHEP 02, 045 97, 131301 (2006), arXiv:hep-ph/0606144. (2017), arXiv:1606.01258 [hep-ph]. [36] K. Babu, P. Bhupal Dev, E. C. Fortes, and R. Mohap- [62] H. Davoudiasl, D. E. Morrissey, K. Sigurdson, atra, Phys. Rev. D 87, 115019 (2013), arXiv:1303.6918 and S. Tulin, Phys. Rev. D 84, 096008 (2011), [hep-ph]. arXiv:1106.4320 [hep-ph]. [37] K. Aitken, D. McKeen, T. Neder, and A. E. Nelson, [63] G. Steigman, JCAP 10, 016 (2006), arXiv:astro- Phys. Rev. D96, 075009 (2017), arXiv:1708.01259 [hep- ph/0606206. ph]. 36

[64] P. Zyla et al. (Particle Data Group), PTEP 2020, [94] F. Abudin´en et al. (Belle-II), (2021), arXiv:2104.12624 083C01 (2020). [hep-ex]. [65] Y. S. Amhis et al. (HFLAV), (2019), arXiv:1909.12524 [95] J. Lees et al. (BaBar), Phys. Rev. D 100, 111101 (2019), [hep-ex]. arXiv:1908.07425 [hep-ex]. [66] A. Lenz and G. Tetlalmatzi-Xolocotzi, JHEP 07, 177 [96] R. Aaij et al. (LHCb), JHEP 08, 117 (2013), (2020), arXiv:1912.07621 [hep-ph]. arXiv:1306.3663 [hep-ex]. [67] A. Lenz, M. L. Piscopo, and C. Vlahos, Phys. Rev. D [97] M. Aaboud et al. (ATLAS), JHEP 11, 062 (2017), 102, 093002 (2020), arXiv:2007.03022 [hep-ph]. arXiv:1705.03374 [hep-ex]. [68] M. Z. Barel, K. De Bruyn, R. Fleischer, and E. Malami, [98] V. Khachatryan et al. (CMS), Phys. Rev. Lett. 106, J. Phys. G 48, 065002 (2021), arXiv:2010.14423 [hep- 112001 (2011), arXiv:1101.0131 [hep-ex]. ph]. [99] H.-Y. Cheng, Int. J. Mod. Phys. A 21, 4209 (2006), [69] S. J¨ager,M. Kirk, A. Lenz, and K. Leslie, JHEP 03, arXiv:hep-ph/0603003. 122 (2020), arXiv:1910.12924 [hep-ph]. [100] M. Borsato et al., (2021), arXiv:2105.12668 [hep-ph]. [70] C.-W. Hwang, Eur. Phys. J. C 23, 585 (2002), [101] S. Stone and L. Zhang, Adv. High Energy Phys. 2014, arXiv:hep-ph/0112237. 931257 (2014), arXiv:1402.4205 [hep-ex]. [71] D. Becirevic, E. Chang, and A. Le Yaouanc, Phys. Rev. [102] R. Aaij et al. (LHCb), JHEP 06, 129 (2020), D 80, 034504 (2009), arXiv:0905.3352 [hep-lat]. arXiv:2003.04352 [hep-ex]. [72] T. Das, D. K. Choudhury, and N. S. Bordoloi, (2016), [103] A. Poluektov and A. Morris, JHEP 02, 163 (2020), arXiv:1608.06896 [hep-ph]. arXiv:1911.12729 [hep-ph]. [73] A. Cerri et al., CERN Yellow Rep. Monogr. 7, 867 [104] V. Chobanova, D. M. Santos, C. Prouve, and (2019), arXiv:1812.07638 [hep-ph]. M. Romero Lamas, (2020), arXiv:2012.02692 [hep-ex]. [74] R. Aaij et al. (LHCb), Physics case for an LHCb [105] M. Gaillard and B. W. Lee, Phys. Rev. Lett. 33, 108 Upgrade II - Opportunities in flavour physics, and (1974). beyond, in the HL-LHC era, Other thesis (2016), [106] I. I. Bigi, Phys. Lett. B 106, 510 (1981). arXiv:1808.08865 [hep-ex]. [107] I. Dunietz, (1996), arXiv:hep-ph/9606247. [75] P. communication: Bostjan Golob (on behalf of the [108] I. Dunietz, Phys. Rev. D 58, 094010 (1998), arXiv:hep- Belle-II collaboration), . ph/9805287. [76] W. Altmannshofer et al. (Belle-II), PTEP 2019, [109] I. I. Bigi, (1995), arXiv:hep-ph/9508408. 123C01 (2019), [Erratum: PTEP 2020, 029201 (2020)], [110] A. M. Sirunyan et al. (CMS), JHEP 08, 130 (2018), arXiv:1808.10567 [hep-ex]. arXiv:1806.00843 [hep-ex]. [77] M. Gavela, P. Hernandez, J. Orloff, and O. Pene, Mod. [111] M. Aaboud et al. (ATLAS), JHEP 01, 126 (2018), Phys. Lett. A 9, 795 (1994), arXiv:hep-ph/9312215. arXiv:1711.03301 [hep-ex]. [78] M. Gavela, P. Hernandez, J. Orloff, O. Pene, and [112] M. Aaboud et al. (ATLAS), Eur. Phys. J. C78, 250 C. Quimbay, Nucl. Phys. B 430, 382 (1994), arXiv:hep- (2018), arXiv:1710.07171 [hep-ex]. ph/9406289. [113] G. Aad et al. (ATLAS), (2020), arXiv:2010.14293 [hep- [79] F. Krinner, A. Lenz, and T. Rauh, Nucl. Phys. B876, ex]. 31 (2013), arXiv:1305.5390 [hep-ph]. [114] A. M. Sirunyan et al. (CMS), JHEP 10, 244 (2019), [80] R. Barate et al. (ALEPH), Eur. Phys. J. C 19, 213 arXiv:1908.04722 [hep-ex]. (2001), arXiv:hep-ex/0010022. [115] B. A. Dobrescu, (2019), arXiv:1912.13155 [hep-ph]. [81] H. Albrecht et al. (ARGUS), Z. Phys. C 42, 519 (1989). [116] B. Pascual-Dias, P. Saha, and D. London, JHEP 07, [82] G. D. Crawford et al. (CLEO), Phys. Rev. D 45, 752 144 (2020), arXiv:2006.13385 [hep-ph]. (1992). [117] A. Alloul, N. D. Christensen, C. Degrande, C. Duhr, [83] B. Aubert et al. (BaBar), Phys. Rev. D 75, 012003 and B. Fuks, Comput. Phys. Commun. 185, 2250 (2007), arXiv:hep-ex/0609004. (2014), arXiv:1310.1921 [hep-ph]. [84] B. Aubert et al. (BaBar), Phys. Rev. Lett. 95, 142003 [118] J. Alwall, R. Frederix, S. Frixione, V. Hirschi, F. Mal- (2005), arXiv:hep-ex/0504014. toni, O. Mattelaer, H. S. Shao, T. Stelzer, P. Torrielli, [85] Y. Li et al. (Belle), Phys. Rev. Lett. 122, 082001 (2019), and M. Zaro, JHEP 07, 079 (2014), arXiv:1405.0301 arXiv:1811.09738 [hep-ex]. [hep-ph]. [86] D. Buskulic et al. (ALEPH), Phys. Lett. B 298, 479 [119] X. Cid Vidal et al., CERN Yellow Rep. Monogr. 7, 585 (1993). (2019), arXiv:1812.07831 [hep-ph]. [87] D. Buskulic et al. (ALEPH), Phys. Lett. B 343, 444 [120] E. Conte, B. Fuks, and G. Serret, Comput. Phys. Com- (1995). mun. 184, 222 (2013), arXiv:1206.1599 [hep-ph]. [88] Y. Grossman, Z. Ligeti, and E. Nardi, Nucl. Phys. B [121] E. Conte, B. Dumont, B. Fuks, and C. Wymant, Eur. 465, 369 (1996), [Erratum: Nucl.Phys.B 480, 753–754 Phys. J. C 74, 3103 (2014), arXiv:1405.3982 [hep-ph]. (1996)], arXiv:hep-ph/9510378. [122] E. Conte and B. Fuks, Int. J. Mod. Phys. A 33, 1830027 [89] D. Buskulic et al. (ALEPH), Phys. Lett. B 313, 535 (2018), arXiv:1808.00480 [hep-ph]. (1993). [123] D. Sengupta, (2018), 10.7484/INSPIRE- [90] A. Abada et al. (FCC), Eur. Phys. J. C 79, 474 (2019). HEP.DATA.HUH5.239F. [91] L. B. Rizzuto, PoS Beauty2019, 063 (2020). [124] T. Sj¨ostrand, S. Ask, J. R. Christiansen, R. Corke, [92] J. Lees et al. (BaBar), Phys. Rev. D 87, 112005 (2013), N. Desai, P. Ilten, S. Mrenna, S. Prestel, C. O. Ras- arXiv:1303.7465 [hep-ex]. mussen, and P. Z. Skands, Comput. Phys. Commun. [93] O. Lutz et al. (Belle), Phys. Rev. D 87, 111103 (2013), 191, 159 (2015), arXiv:1410.3012 [hep-ph]. arXiv:1303.3719 [hep-ex]. [125] J. de Favereau, C. Delaere, P. Demin, A. Giammanco, V. Lemaˆıtre,A. Mertens, and M. Selvaggi (DELPHES 37

3), JHEP 02, 057 (2014), arXiv:1307.6346 [hep-ex]. [138] P. de Salas, M. Lattanzi, G. Mangano, G. Miele, S. Pas- [126] S. Davidson, D. C. Bailey, and B. A. Campbell, Z. Phys. tor, and O. Pisanti, Phys. Rev. D 92, 123534 (2015), C 61, 613 (1994), arXiv:hep-ph/9309310. arXiv:1511.00672 [astro-ph.CO]. [127] G. F. Giudice, B. Gripaios, and R. Sundrum, JHEP [139] T. Hasegawa, N. Hiroshima, K. Kohri, R. S. Hansen, 08, 055 (2011), arXiv:1105.3161 [hep-ph]. T. Tram, and S. Hannestad, JCAP 12, 012 (2019), [128] P. Agrawal, M. Blanke, and K. Gemmler, JHEP 10, arXiv:1908.10189 [hep-ph]. 072 (2014), arXiv:1405.6709 [hep-ph]. [140] J. P. Kneller and G. Steigman, New J. Phys. 6, 117 [129] S. Fajfer and D. Susiˇc, (2020), arXiv:2010.08367 [hep- (2004), arXiv:astro-ph/0406320. ph]. [141] M. Cirelli, P. Panci, G. Servant, and G. Zaharijas, [130] J. Brod, M. Gorbahn, and E. Stamou, Phys. Rev. Lett. JCAP 03, 015 (2012), arXiv:1110.3809 [hep-ph]. 125, 171803 (2020), arXiv:1911.06822 [hep-ph]. [142] S. Tulin, H.-B. Yu, and K. M. Zurek, JCAP 05, 013 [131] M. Bona et al. (UTfit), JHEP 03, 049 (2008), (2012), arXiv:1202.0283 [hep-ph]. arXiv:0707.0636 [hep-ph]. [143] S. Ipek and J. March-Russell, Phys. Rev. D 93, 123528 [132] J. F. Nieves and P. B. Pal, Am. J. Phys. 72, 1100 (2004), (2016), arXiv:1604.00009 [hep-ph]. arXiv:hep-ph/0306087. [144] B. Misra and E. Sudarshan, J. Math. Phys. 18, 756 [133] J. Aebischer, W. Altmannshofer, D. Guadagnoli, M. Re- (1977). boud, P. Stangl, and D. M. Straub, Eur. Phys. J. C 80, [145] G. Aad et al. (ATLAS), Phys. Rev. Lett. 115, 262001 252 (2020), arXiv:1903.10434 [hep-ph]. (2015), arXiv:1507.08925 [hep-ex]. [134] L. Di Luzio, M. Kirk, and A. Lenz, Phys. Rev. D97, [146] C. Peterson, D. Schlatter, I. Schmitt, and P. M. Zerwas, 095035 (2018), arXiv:1712.06572 [hep-ph]. Phys. Rev. D 27, 105 (1983). [135] A. Albert et al., Phys. Dark Univ. 26, 100377 (2019), [147] D. Buskulic et al. (ALEPH), Z. Phys. C 62, 179 (1994). arXiv:1703.05703 [hep-ex]. [148] J. A. Bagger, K. T. Matchev, and R.-J. Zhang, Phys. [136] C. Arina, B. Fuks, L. Mantani, H. Mies, L. Panizzi, Lett. B 412, 77 (1997), arXiv:hep-ph/9707225. and J. Salko, Phys. Lett. B 813, 136038 (2021), arXiv:2010.07559 [hep-ph]. [137] M. Laine and M. Meyer, JCAP 07, 035 (2015), arXiv:1503.04935 [hep-ph]. 38

yud, MY = 1.5 TeV yud, MY = 3.0 TeV yud, MY = 5.0 TeV 10 10 −2 −3 10 10 10 −1 −3 −4 0 0 0 10 10 10 10 10 −2 −4

10 −3 ud ud ud

y 10 y y 1 −4 1 1 10− 10− 10−

Br(B ψ ) Br(B ψ ) Br(B ψ ) → B M → B M → B M dijet dijet dijet

jet+MET ΓY /MY < 0.1 jet+MET ΓY /MY < 0.1 jet+MET ΓY /MY < 0.1 2 2 2 10− 2 1 0 10− 2 1 0 10− 2 1 0 10− 10− 10 10− 10− 10 10− 10− 10 yψb yψb yψb

yus, MY = 1.5 TeV yus, MY = 3.0 TeV10 yus, MY = 5.0 TeV 10 −3 10 10 −4 −2 −3 10 10 −2 −1 0 0 0 10 10 10 10 −3 10 10 −4 −4 us us us y y y 1 1 1 10− 10− 10−

Br(B ψ ) Br(B ψ ) Br(B ψ ) → B M → B M → B M dijet dijet dijet

jet+MET ΓY /MY < 0.1 jet+MET ΓY /MY < 0.1 jet+MET ΓY /MY < 0.1 2 2 2 10− 2 1 0 10− 2 1 0 10− 2 1 0 10− 10− 10 10− 10− 10 10− 10− 10 yψb yψb yψb

yub, MY = 1.5 TeV yub, MY = 3.0 TeV yub, MY = 5.0 TeV 10 10 −2 −3 10 10 10 −1 −3 −4 0 0 0 10 10 10 10 10 −2 −4

10 −3 ub ub ub

y 10 y y 1 −4 1 1 10− 10− 10−

Br(B ψ ) Br(B ψ ) Br(B ψ ) → B M → B M → B M dijet dijet dijet

jet+MET ΓY /MY < 0.1 jet+MET ΓY /MY < 0.1 jet+MET ΓY /MY < 0.1 2 2 2 10− 2 1 0 10− 2 1 0 10− 2 1 0 10− 10− 10 10− 10− 10 10− 10− 10 yψd yψd yψd

ycd, MY = 1.5 TeV ycd, MY = 3.0 TeV ycd, MY = 5.0 TeV 10 10 −2 −3 10 −4 0 0 0 10 10 10 10 10 −4 −4 10 −3 cd cd cd y y y 1 1 1 10− 10− 10−

Br(B ψ ) Br(B ψ ) Br(B ψ ) → B M → B M → B M dijet dijet dijet

jet+MET ΓY /MY < 0.1 jet+MET ΓY /MY < 0.1 jet+MET ΓY /MY < 0.1 2 2 2 10− 2 1 0 10− 2 1 0 10− 2 1 0 10− 10− 10 10− 10− 10 10− 10− 10 yψb yψb yψb

ycs, MY = 1.5 TeV 10 ycs, MY = 3.0 TeV ycs, MY = 5.0 TeV −2 10 10 10 −4 −3 −4

0 0 0 10 10 10 10 10 −4 −3 cs cs cs y y y 1 1 1 10− 10− 10−

Br(B ψ ) Br(B ψ ) Br(B ψ ) → B M → B M → B M dijet dijet dijet

jet+MET ΓY /MY < 0.1 jet+MET ΓY /MY < 0.1 jet+MET ΓY /MY < 0.1 2 2 2 10− 2 1 0 10− 2 1 0 10− 2 1 0 10− 10− 10 10− 10− 10 10− 10− 10 yψb yψb yψb

ycb, MY = 1.5 TeV ycb, MY = 3.0 TeV ycb, MY = 5.0 TeV 10 10 −2 −3 10 −4 0 0 0 10 10 10 10 10 −4 −4 10 −3 cb cb cb y y y 1 1 1 10− 10− 10−

Br(B ψ ) Br(B ψ ) Br(B ψ ) → B M → B M → B M dijet dijet dijet

jet+MET ΓY /MY < 0.1 jet+MET ΓY /MY < 0.1 jet+MET ΓY /MY < 0.1 2 2 2 10− 2 1 0 10− 2 1 0 10− 2 1 0 10− 10− 10 10− 10− 10 10− 10− 10 yψd yψd yψd

FIG. 19. LHC limits on the couplings of the color-triplet scalar defined in Eq. (38). The green (blue) region is excluded by dijet (jet+MET) searches. The red band band corresponds to successful baryogenesis and encompasses 0.1 > Br(B → ψ BM) > 10−4 for mψ = 1.5 GeV. In black dashed we show the region of parameter space in which√ ΓY /MY = 0.1. In blue dashed line we show the reach of the high luminosity LHC. We have restricted the couplings to be < 4π. 39

ydb, MY = 1.5 TeV ydb, MY = 3.0 TeV ydb, MY = 5.0 TeV 10 10 −2 −3 10 10 10 −1 −3 −4 0 0 0 10 10 10 10 10 −2 −4

10 −3 db db db

y 10 y y 1 −4 1 1 10− 10− 10−

Br(B ψ ) Br(B ψ ) Br(B ψ ) → B M → B M → B M dijet dijet dijet

jet+MET ΓY /MY < 0.1 jet+MET ΓY /MY < 0.1 jet+MET ΓY /MY < 0.1 2 2 2 10− 2 1 0 10− 2 1 0 10− 2 1 0 10− 10− 10 10− 10− 10 10− 10− 10 yψu yψu yψu

ydb, MY = 1.5 TeV ydb, MY = 3.0 TeV ydb, MY = 5.0 TeV 10 10 −2 −3 10 −4 0 0 0 10 10 10 10 10 −4 −4 10 −3 db db db y y y 1 1 1 10− 10− 10−

Br(B ψ ) Br(B ψ ) Br(B ψ ) → B M → B M → B M dijet dijet dijet

jet+MET ΓY /MY < 0.1 jet+MET ΓY /MY < 0.1 jet+MET ΓY /MY < 0.1 2 2 2 10− 2 1 0 10− 2 1 0 10− 2 1 0 10− 10− 10 10− 10− 10 10− 10− 10 yψc yψc yψc

ysb, MY = 1.5 TeV ysb, MY = 3 TeV10 ysb, MY = 5.0 TeV 10 −3 10 10 −4 −2 −3 10 10 −2 −1 0 0 0 10 10 10 10 −3 10 10 −4 −4 sb sb sb y y y 1 1 1 10− 10− 10−

Br(B ψ ) Br(B ψ ) Br(B ψ ) → B M → B M → B M dijet dijet dijet

jet+MET ΓY /MY < 0.1 jet+MET ΓY /MY < 0.1 jet+MET ΓY /MY < 0.1 2 2 2 10− 2 1 0 10− 2 1 0 10− 2 1 0 10− 10− 10 10− 10− 10 10− 10− 10 yψu yψu yψu

ysb, MY = 1.5 TeV 10 ysb, MY = 3.0 TeV ysb, MY = 5.0 TeV −2 10 10 10 −4 −3 −4

0 0 0 10 10 10 10 10 −4 −3 sb sb sb y y y 1 1 1 10− 10− 10−

Br(B ψ ) Br(B ψ ) Br(B ψ ) → B M → B M → B M dijet dijet dijet

jet+MET ΓY /MY < 0.1 jet+MET ΓY /MY < 0.1 jet+MET ΓY /MY < 0.1 2 2 2 10− 2 1 0 10− 2 1 0 10− 2 1 0 10− 10− 10 10− 10− 10 10− 10− 10 yψc yψc yψc

FIG. 20. Same as Fig. 19 but for a color-triplet scalar with SM gauge quantum numbers Y ∼ (3, 1, +2/3) described by Lagrangian (38b).