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Light-cone sum rules with $B$-meson distribution amplitudes for the $B\to p$ form factors in $B$-mesogenesis models

Aritra Biswas, Alexander Khodjamirian, Ali Mohamed

Abstract

New decay modes of $B$-meson into a baryon and invisible dark antibaryon $Ψ$ are among the most distinctive signatures of the $B$-mesogenesis scenario. We concentrate on the proton mode and consider two versions of the underlying interaction of $Ψ$ with quarks, the so-called models $(d)$ and $(b)$. To estimate the width of the $B^+\to p Ψ$ decay, we obtain the $B^+\to p$ transition form factors, applying QCD light-cone sum rules (LCSRs) with $B$-meson distribution amplitudes with an accuracy up to twist-5, while interpolating the proton with a current. This method is independent of the previously applied one, which was based on the nucleon distribution amplitudes. We estimate the partial width of the $B^+\to p Ψ$ decay as a function of the dark antibaryon mass. Furthermore, we use the ratio of this width to the inclusive $B\to X_N Ψ$ width, the latter predicted earlier using the heavy quark expansion method. This ratio, which is independent of the effective coupling, when combined with the minimal inclusive branching fraction of $O(10^{-4})$, necessary for the feasibility of $B$-mesogenesis, yields lower limits on the $B^+\to p Ψ$ branching fraction. We confront these limits with the most recent upper bounds obtained from BaBar and Belle/Belle II searches for the decays of $B^+$-meson into a proton and missing energy. The comparison indicates that experimental upper bounds on the branching fraction of $B\to p Ψ$ at the level of $10^{-8}-10^{-7}$ are needed for a decisive probe of this invisible mode of $B$ decays.

Light-cone sum rules with $B$-meson distribution amplitudes for the $B\to p$ form factors in $B$-mesogenesis models

Abstract

New decay modes of -meson into a baryon and invisible dark antibaryon are among the most distinctive signatures of the -mesogenesis scenario. We concentrate on the proton mode and consider two versions of the underlying interaction of with quarks, the so-called models and . To estimate the width of the decay, we obtain the transition form factors, applying QCD light-cone sum rules (LCSRs) with -meson distribution amplitudes with an accuracy up to twist-5, while interpolating the proton with a current. This method is independent of the previously applied one, which was based on the nucleon distribution amplitudes. We estimate the partial width of the decay as a function of the dark antibaryon mass. Furthermore, we use the ratio of this width to the inclusive width, the latter predicted earlier using the heavy quark expansion method. This ratio, which is independent of the effective coupling, when combined with the minimal inclusive branching fraction of , necessary for the feasibility of -mesogenesis, yields lower limits on the branching fraction. We confront these limits with the most recent upper bounds obtained from BaBar and Belle/Belle II searches for the decays of -meson into a proton and missing energy. The comparison indicates that experimental upper bounds on the branching fraction of at the level of are needed for a decisive probe of this invisible mode of decays.
Paper Structure (16 sections, 83 equations, 5 figures, 3 tables)

This paper contains 16 sections, 83 equations, 5 figures, 3 tables.

Table of Contents

  1. Introduction
  2. The effective couplings and $B^+\to p \Psi$ decay amplitude
  3. LCSR with $B$-meson distribution amplitudes
  4. OPE for the correlation function
  5. Contribution of two-particle DAs
  6. Contribution of three-particle DAs
  7. Numerical results
  8. Inputs
  9. Numerical analysis of LCSRs
  10. Branching fraction of the $B^+\to p\Psi$ decay
  11. Ratio of the $B^+\to p \Psi$ width to inclusive width
  12. Conclusion
  13. $B$-meson distribution amplitudes
  14. Two-particle DAs
  15. Three-particle DAs
  16. ...and 1 more sections

Figures (5)

  • Figure 1: Diagram corresponding to the contribution of two-particle $B$-meson DAs to the correlation function (\ref{['eq:corr']}). The wavy (dashed) line represents the interpolating current of the proton (the dark antibaryon).
  • Figure 2: Diagram describing the contributions of three-particle (quark-antiquark-gluon) $B$-meson DAs to the correlation function (\ref{['eq:corr']}). The curly line represents a gluon component of the DA. The cross indicates the second diagram, where the gluon is attached to the $d$-quark.
  • Figure 3: The form factors $F^{(d)}_{B\to P_R}$ (left panel) and $\widetilde{F}^{(d)}_{B\to P_L}$ (right panel) in the spacelike region and at central input, shown with the red solid lines. The blue dashed (green solid) lines represent the sum of the twist-2 and twist-3 (twist-4 and twist-5) contributions, and the black dashed line represents the twist-4 contribution.
  • Figure 4: Branching fraction predicted for the $B^+ \to p \Psi$ decay in the model $(d)$ (left panel) and model $(b)$ (right panel). The blue bands represent the results of this work obtained with the LCSR-$B$ method. For comparison, the orange bands show the results obtained using the method with nucleon DAs (LCSR-$N$).
  • Figure 5: Branching fraction $\mathrm{BR}(B^+ \to p \Psi)$ as a function of $m_\Psi$ for model $(d)$ (left panel) and model $(b)$ (right panel). The solid green lines present the predicted lower limit (\ref{['eq:lowlim']}), and the dashed green lines indicate maximal value of this limit within estimated uncertainties; orange and blue shaded regions display experimental upper limits set by, respectively, BaBar BaBar:2023dtq and Belle/Belle II Belle-II:2026tyb measurements of the $B\to p+invisible$ decays. The white areas indicate the parameter space allowed by current experimental data.