Collider signals of baryogenesis and dark matter from $B$ mesons: A roadmap to discovery

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, Phys. Rev. D 99, 035031 (2019)], 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, which we scrutinize in this paper. We study $CP$-violating observables in the $B_q^0-{\overline{B}}_q^0$ 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.

Figure 1

Summary of the collider implications of baryogenesis and dark matter from $B$ mesons [39], i.e., B-Mesogenesis. The distinctive signals of the mechanism are (i) the requirement that at least one of the semileptonic ($CP$) asymmetries in $B_q^0$ decays is $A_{\mathrm{SL}}^q>{10}^{-4}$, (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 $\mathrm{Br}(B\to \psi \mathcal{B}\mathcal{M})>{10}^{-4}$, and (iii) that $b$-flavored baryons should decay into light mesons and missing energy at a rate $\mathrm{Br}({\mathcal{B}}_b\to \overline{\psi }\mathcal{M})>{10}^{-4}$. In addition, we include as indirect signals the various oscillation observables in the $B_q^0-{\overline{B}}_q^0$ system as they are linked to $A_{\mathrm{SL}}^q$, and the presence of a new TeV-scale color-triplet scalar $Y$ that is needed to trigger the $B\to \psi \mathcal{B}\mathcal{M}$ decay. We also highlight the existing experiments that can probe each corresponding signal. Notation: $B$, $B$ meson; $\mathcal{B}$, SM baryon; $\mathcal{M}$, any number of light mesons; $\psi$, dark sector antibaryon (ME in the detector).

Figure 2

Summary of the mechanism of baryogenesis and dark matter from $B$ mesons [39], i.e., B-Mesogenesis. Adapted from Fig. 1 in [39].

Figure 3

Contour lines for the minimum $\mathrm{Br}(B\to \psi \mathcal{B}\mathcal{M})$ required for baryogenesis and dark matter generation as a function of the semileptonic asymmetries in $B_q^0$-meson decays, $A_{\mathrm{SL}}^q$. In red, we show the relevant parameter space in which baryogenesis can successfully occur. The dashed lines delineate the cosmological uncertainties of our predictions (see text for more details). The black rectangle corresponds to the SM prediction for the semileptonic asymmetries [66], while the orange contour corresponds to the current world averages for experimental measurements of these quantities [64]. The gray line highlights the region of parameter space corresponding to $\mathrm{Br}(B\to \psi \mathcal{B}\mathcal{M})>0.5\%$, which is disfavored by an ALEPH search as discussed in Sec. 4a2. All contours are shown at 95% C.L. This figure showcases that, given current measurements of the semileptonic asymmetries, a branching ratio $\mathrm{Br}(B\to \psi \mathcal{B}\mathcal{M})\gtrsim {10}^{-4}$ is required for successful baryogenesis. Similarly, in light of the ALEPH constraint, $A_{\mathrm{SL}}^q>{10}^{-4}$ is necessary in order to explain the observed baryon asymmetry of the Universe.

Figure 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 $\psi$ would appear as missing energy in the detector, and $Y$ is a heavy color-triplet scalar mediator with $M_Y>1.2\mathrm{TeV}$ (see Sec. 5).

Figure 5

Constraints on $B$-mesons decays into a dark sector antibaryon $\psi$ and a baryon $\mathcal{B}$. 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 $\mathrm{Br}<10\%$ 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 $50{\mathrm{ab}}^{-1}$ of data, as well as that of LHCb with $15{\mathrm{fb}}^{-1}$ [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.

Figure 6

Fraction of $B^{+}\to \psi \mathcal{B}\mathcal{M}$ decays that are not expected to contain hadrons other than $\mathcal{B}$ in the final state, as a function of the mass of the dark fermion $\psi$. Different colors correspond to decays induced by the different operators listed in Table 1. Each panel corresponds to a different kinematic structure of the effective four-fermion operator as listed in Table 2. The width of the band represents an estimation of the uncertainty in our computations and is obtained by varying the $b$-quark mass used in the calculation between ${\overline{m}}_b(\mu ={\overline{m}}_b)$, $m_b^{\mathrm{pole}}$ (solid line), and $m_{B_d^0}$.

Figure 7

Same as Fig. 6 but for $B_d^0\to \psi \mathcal{B}\mathcal{M}$ decays.

Figure 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.

Figure 9

Left panel: constraints on $y_{q_i{q}_j}^2\mathrm{Br}(Y\to jj)$ from dijet searches. Bounds are based on a recast of the CMS search of [115] that used $36{\mathrm{fb}}^{-1}$ of data at 13 TeV. We have assumed ${\mathrm{\Gamma }}_Y/M_Y=0.04$ and, as discussed in [115], an acceptance of $A=0.56$. Right panel: constraints on $y_{q_i{q}_j}^2\mathrm{Br}(Y\to j\psi )$ from jet plus missing-energy signals. Bounds have been recasted from the analysis of ATLAS [119] that used $36{\mathrm{fb}}^{-1}$ of data at 13 TeV. We have assumed ${\mathrm{\Gamma }}_Y/M_Y=0.06$ and performed a fit without correlating errors to the exclusive signal regions of [119].

Figure 10

Maximum possible exotic branching ratio of $B$-meson decays mediated by a hypercharge $-1/3$ or $2/3$ color-triplet scalar, in view of the LHC constraints displayed in Fig. 9. The value of $\mathrm{Br}(B\to \psi \mathcal{B}\mathcal{M})$ is obtained using Eq. (39) with a fixed value of $m_{\psi }=1.5\mathrm{GeV}$ (larger branching ratios are possible for a lighter $\psi$). The red band highlights the values of $\mathrm{Br}(B\to \psi \mathcal{B}\mathcal{M})$ where $B$-Mesogenesis can proceed, while the gray line shows the lower limit of the ALEPH bound on $\mathrm{Br}(B\to \psi \mathcal{B}\mathcal{M})$ as found in Sec. 4a2.

Figure 11

Maximum inclusive $\mathrm{Br}(B\to \psi \mathcal{B}\mathcal{M})$ as a function of $m_{\psi }$ as directly constrained by an ALEPH search [80] for $b$ decays with large missing energy (see Fig. 5), and indirectly by ATLAS and CMS searches for TeV-scale color-triplet scalars. In red we highlight the region of parameter space compatible with baryogenesis and dark matter production. Each line represents the constraints on each of the four possible $b$ decay operators in Table 1.

Figure 12

Two examples of flavor structure of the couplings of the color-triplet scalar $Y$ that can produce the observed baryon asymmetry and the dark matter abundance while satisfying all current constraints. The heavy scalar mass here is fixed to $M_Y=1.5\mathrm{TeV}$, but masses up to 20 TeV are possible with the subsequent relaxation of experimental constraints. The couplings controlling the $B\to \psi \mathcal{B}\mathcal{M}$ decay as relevant for baryogenesis are shown in green. Note that $y_{bt}$ and $y_{\psi t}$ are largely unconstrained.

Figure 13

Parameter space for successful baryogenesis and dark matter generation within $B$-Mesogenesis in the $A_{\mathrm{SL}}^s-A_{\mathrm{SL}}^d$ plane. Similar to Fig. 3, the red bands indicate the minimum $\mathrm{Br}(B\to \psi \mathcal{B}\mathcal{M})$ 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 $\mathrm{Br}(B\to \psi \mathcal{B}\mathcal{M})$ 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 $B\to \psi \mathcal{B}\mathcal{M}$ 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.

Figure 14

Functions describing the dependence of the generated baryon asymmetry on the reheat temperature, as parametrized in (6) and (a9). The severe suppression of the baryon yield at high temperatures is caused by the decoherence of the $B^0-{\overline{B}}^0$ oscillations due to interactions with electrons and positrons in the plasma. The shaded regions represent the uncertainty in our calculation arising from the lack of precise knowledge of the charge radius of the neutral $B$ mesons.

Figure 15

Missing-energy spectrum from the decays predicted by $B$-Mesogenesis at $\sqrt{s}=M_Z$ arising from $Z\to \overline{b}b$ processes. Left panel: exclusive two body decays, $B\to \psi \mathcal{B}$. Right panel: inclusive decays (calculated here at the parton level as a three-body decay without any QCD corrections). We also highlight the signal region targeted in the ALEPH [80] search. Note that the region with $E_{\mathrm{miss}}<30\mathrm{GeV}$ suffers from the presence of substantially large backgrounds.

Figure 16

Same as Fig. 6 but for $B_s^0\to \psi \mathcal{B}\mathcal{M}$ decays.

Figure 17

Same as Fig. 6 but for ${\mathrm{\Lambda }}_b\to \psi \mathcal{M}$ decays.

Figure 18

LHC limits on the couplings of the color-triplet scalar defined in Eq. (38). The green (blue) region is excluded by dijet ($\text{jet}+\mathrm{MET}$) searches. The red band band corresponds to successful baryogenesis and encompasses $0.1>\mathrm{Br}(B\to \psi \mathcal{B}\mathcal{M})>{10}^{-4}$ for $m_{\psi }=1.5\mathrm{GeV}$. In black dashed, we show the region of parameter space in which ${\mathrm{\Gamma }}_Y/M_Y=0.1$. In blue dashed line, we show the reach of the high-luminosity LHC. We have restricted the couplings to be $<\sqrt{4\pi }$.

Figure 19

Same as Fig. 18 but for a color-triplet scalar with SM gauge quantum numbers $Y\sim (3,1,+2/3)$ described by Lagrangian (38b).

Figure 20

Box diagrams involving the heavy colored scalar $Y$ and contributing to the neutral meson oscillations. The one involving the dark baryon $\psi$ is only possible for down-type external quarks.