Are Subleading Effects Really Subleading? $B$-Meson Decays in Mesogenesis

TL;DR

We study inclusive $B$-meson decays in the Mesogenesis framework using the Heavy Quark Expansion up to the dimension-six two-quark Darwin term to assess subleading contributions. We find regions of parameter space where subleading terms exceed the leading free-$b$-quark decay, signaling a breakdown of the HQE and illustrating how the HQE can resemble SM behavior only under artificially large charm masses. We update exclusive bounds on $\mathrm{Br}(B^+ \to p^+ \psi)$ by incorporating the HQE-corrected inclusive width and examine lifetime ratios $\tau(B_s)/\tau(B_d)$ and $\tau(B^+)/\tau(B_d)$, finding no new constraints beyond collider bounds and only small NP effects in the lifetime ratio. Overall, the HQE hierarchy in Mesogenesis is highly operator-dependent, underscoring the need for NLO QCD and higher-power calculations and motivating a combined program with LCSR-based exclusive predictions for a robust phenomenological probe of the model.

Abstract

We calculate inclusive $B$-meson decay rates in the Mesogenesis framework, a model explaining baryogenesis and the existence of dark matter, using the Heavy Quark Expansion (HQE), up to the dimension-six two-quark Darwin term. By systematically studying the power-suppressed contributions, we identify regions of parameter space where subleading terms exceed the leading contribution, i.e., the free $b$-quark decay, highlighting the limits of the HQE in this BSM scenario. This behavior is reminiscent of the Standard Model only under artificially heavy charm masses, and can be used to study the HQE close to its breakdown. We further update the lower bounds on the exclusive decay mode $B^+ \to p^+ ψ$ by incorporating the fully HQE-corrected inclusive width in the ratio $Γ_{\mathrm{excl}}/Γ_{\mathrm{incl}}$. Extending the analysis from total decay rates to the lifetime ratio $τ(B_s)/τ(B_d)$, we find no additional constraints on the couplings beyond existing collider bounds, consistent with analogous results for $τ(B^+)/τ(B_d)$. We further compare the sensitivity of both lifetime ratios.

Figures (19)

• Figure 1: Schematic representation of the HQE of the $B$-meson. The two-quark contribution arises from two loops, whereas the four-quark contribution involves a single loop. Crossed vertices indicate insertions of operators from the effective $\Delta B=1$ Hamiltonian. The vertical dotted line indicates taking the imaginary part of the diagrams, and $f_1$, $f_2$, $f_3$ represent general fermions into which the $b$ quark can decay.
• Figure 2: Diagram illustrating the mixing of the four-quark operator with the Darwin operator.
• Figure 3: Total decay width $\Gamma(B^+)$ arising purely from the Mesogenesis operators as a function of $\rho_f= (m_f/m_b)^2$. The left column displays individual HQE contributions, and the right column shows the ratio $R_d=|\Gamma_d/\Gamma_3|$, where $\Gamma_d$ is the subleading term indicated. Vertical lines mark the $\rho_f$ values where the subleading contribution exceeds the leading dimension-three term $\Gamma_3$ (the corresponding $m_f$ values are also indicated).
• Figure 4: Total decay width of $\Gamma(B^+)$ arising purely from the Mesogenesis operators as a function of $\rho_f= (m_f/m_b)^2$. The figure displays the cumulative sum of all terms up to the indicated dimension. The vertical lines indicate the value of $\rho_f$, where the contribution exceeds the leading dimension-three $\Gamma_3$ term (the corresponding $m_f$ values are also indicated).
• Figure 5: Topologies of the four-quark contributions to the total decay width $\Gamma(B^+)$ for the Mesogenesis operators: $\mathcal{O}=(b\,u)(\psi \,d)$ (left, $\overline{\text{PI}}$) and $\mathcal{O}=(d\,u)(\psi\,b)$ (right, $\text{PI}$).