Characterizing Dark Bosons at Chiral Belle

Abstract

We explore the advantages of a polarized electron beam at Belle II, as proposed for ``Chiral Belle'', in the search for invisibly decaying (dark) bosons that weakly couple to the Standard Model. By measuring the polarization dependence of the production cross section of dark bosons in association with a photon, the dark boson's spin and Lorentz structure of its couplings can potentially be determined. We analyze the mono-photon channel, $e^+ e^- \rightarrow γ+ \text{invisible}$, in detail, focusing on the production of an on-shell spin-1 boson. We explore this in the context of three separate scenarios for a new dark vector: a dark photon, a mass-mixed ``dark $Z$'', and a vector that couples to right-handed electrons, and estimate how well the couplings of such bosons to electrons can be constrained in the event of a positive signal.

Figures (3)

• Figure 1: Truth-level (left) and smeared (right) distribution of the mono-photon SM background for 20 fb$^{-1}$ of data as a function of the center-of-mass energy of the measured single photon $E_\gamma^\ast$, and the photon lab-frame angle $\theta_\gamma^\text{lab}$ relative to the electron beam, with the ECL geometry information included. The arch shapes are a consequence of the endcap gaps (which are visible in the histogram) that give a significantly higher probability of missing a particle there and still measuring a photon in the ECL. The concentration of events at high energies comes from $\gamma \gamma$ events where one photon is missed inside the main barrel of the ECL.
• Figure 2: Left: Estimated Belle II 95% CL upper limits on $\epsilon_{\rm eff}$ as a function of $m_V$ given the analysis described in the text, for both unpolarized and polarized beams with a luminosity 20 fb$^{-1}$ (black curve), a polarized electron beam with $P = 0.7$ and a luminosity of 20 ab$^{-1}$ (blue curve), and a polarized electron beam with $P=-0.7$ and a luminosity of 20 ab$^{-1}$ (orange curve). The bound from polarized beams should be interpreted as being on $\epsilon_{\rm eff}$ as defined in Eq. (\ref{['eq:sigmaP']}). Existing limits for invisible dark photon searches from E787/E949 Essig:2013vhaE787:2001urh*BNL-E949:2009dza*Davoudiasl:2014kua, BaBar BaBar:2017tiz, NA62 NA62:2019meo, BESIII BESIII:2022oww, NA64 NA64:2023wbi, and the electron anomalous magnetic moment $a_e$Fan:2022eto (assuming a vector coupling and the measurement of $\alpha$ in Ref. Morel:2020dww---taking an axial-vector coupling and the larger $\alpha$ in Ref. Parker:2018vye does not change the bound substantially). The gray-dashed curves are thermal DM targets with $m_V = 3 m_{\rm DM}$ and $\alpha_D = 0.5$ for scalar, Majorana, and pseudo-Dirac DM candidates Berlin:2018bsc. Right: The 95% CL limits in the $g_V$ vs $g_A$ plane at Chiral Belle for $m_V = 100$ MeV, assuming 20 ab$^{-1}$ of $70\%$ left-handed (orange) or $70\%$ right-handed (blue) polarized electron beams (regions outside the ellipses are excluded). We also show the Belle II reach for unpolarized beams with 40 ab$^{-1}$ of data (black). The dashed green lines indicate the relationship between $g_A$ and $g_V$ for a dark photon, a dark $Z$ boson, and a right-handed vector as labeled.
• Figure 3: Example of the discriminatory power from $e^-$ beam polarization for the three different models we consider. In these plots, we assume a future $5\sigma$ discovery with $40~{\rm ab}^{-1}$ of unpolarized data for $m_V=3.67~\rm GeV$, which carves out the gray circular $1\sigma$ preferred coupling regions. The $20~{\rm ab}^{-1}$ of $P=0.7$ and $P=-0.7$ (orange) data in this sample then require at $1\sigma$ that the couplings are in the blue and orange regions respectively, (partially) breaking the degeneracy in the $g_V$ and $g_A$ plane. The dashed green lines are the coupling relationships for each scenario. The red shaded regions show the couplings preferred at the $1\sigma$ level from measurements of $A_{LR}$ defined in Eq. (\ref{['eq:ALR']}), which is less subject to systematic errors. Note that there is a degeneracy in the $A^\prime$ and $Z_d$ cases between (nearly) purely vector or axial-vector couplings so that the cross sections for left- or right-polarized $e^-$ beams are nearly the same. In the $Z_R$ case, the chiral nature of the couplings breaks this degeneracy.