Dark Photon Searches with Initial-State Radiation at Fixed-Target Configurations

TL;DR

This work analyzes initial-state radiation (ISR) in $e^+e^- \to \gamma A'$ production to improve invisible dark photon searches at fixed-target experiments. Using an electron-PDF radiator formalism, the authors show ISR can distort the $A'$ resonance and enhance sensitivity to the kinetic mixing parameter $\epsilon$, especially for narrow $A'$ widths, with notable gains around $m_{A'} \lesssim 65$ MeV at Belle II and around $m_{A'} \sim 200$ MeV at NA64. They implement a multi-bin analysis at Belle II to exploit spectral information and demonstrate up to ~30% additional improvement beyond ISR effects alone. The framework, applicable to future facilities, highlights the importance of ISR in resonant dark photon searches and provides concrete sensitivity projections across measured mass ranges.

Abstract

In this work, we investigate the contribution of the annihilation process with initial-state radiation ($e^+ e^- \to γA'$) to the invisible dark photon ($A'$) searches at the electron fixed-target configurations. For illustration, we consider both the disappearing positron track signature at Belle II and the large missing energy search at NA64. When the dark photon has a narrow decay width, the effect of the initial-state radiation to the annihilation process can dominate over its $s$-channel and bremsstrahlung counterparts around $m_{A'} \simeq 60\,\rm{MeV}$ ($m_{A'} \simeq 200\,\rm{MeV}$) for Belle II (NA64), to enhance the corresponding sensitivity on the kinetic mixing parameter $ε$ by a factor of up to approximately 2.7 (1.3). For Belle II, we further perform a multi-bin analysis with the spectrum information to better separate the background and signal channels for significant improvement of the sensitivity.

Figures (9)

• Figure 1: Feynman diagrams of $e^+e^- \rightarrow \gamma A'$ processes considering the $s$-channel with an initial-state radiation for the dark photon production.
• Figure 2: The expected signal event number of the disappearing positron track signature at Belle II for the $s$-channel (red), $s$-channel with ISR (blue) and bremsstrahlung process (black), respectively, in which $m_\chi = m_{A'}/3$, $\epsilon = 10^{-3}$, and $L = 50 \, {\rm ab}^{-1}$. The $\alpha_D$ dependence of each contribution is illustrated with $\alpha_D = 10^{-1}$ (solid) and $\alpha_D = 10^{-3}$ (dashed). The inset plot around the resonance peaks shows zoomed-in view of the the dark photon mass regions of ($65 \sim 70$) MeV.
• Figure 3: Weighting factor for the signal event number given by convoluting the positron track-length distribution $T_e(E_{e^+}, E_i, L_T)$ and the differential Bhabha scattering cross section $d \sigma_{\rm B} / d E_i$ over the outgoing positron energy range, $4.35\,{\rm GeV} \leq E_i \leq 6.62\,{\rm GeV}$, from the Bhabha scattering at Belle II.
• Figure 4: The expected signal (colorful lines) and background (black lines) event rates at Belle II with an integrated luminosity $L = 50 \, {\rm ab}^{-1}$. The analysis takes two fixed dark photon masses, $m_{A'} = 40 \, {\rm MeV}$ (red lines) and $m_{A'} = 67 \, {\rm MeV}$ (blue lines). To show the signal and background with similar size, the signal event rates have been scaled by tuning the dark photon kinetic mixing parameter $\epsilon = 10^{-3}$ for $m_{A'} = 40$ MeV and $\epsilon = 5\times 10^{-5}$ for $m_{A'} = 67$ MeV. The solid lines denote the event numbers estimated for the binning with a size of $2\%$ for the missing energy fraction $x = E_{\rm miss}/E_i$, ranging from $90\%$ to $100\%$. For the dashed lines, however, the event numbers are obtained within a single bin covering the missing energy fraction from $95\%$ to $100\%$.
• Figure 5: The expected sensitivity contribution as a function of missing energy fraction, normalized by $\epsilon^2$ at Belle II with an integrated luminosity $L = 50 \, {\rm ab}^{-1}$. The analysis takes two fixed dark photon masses, $m_{A'} = 40 \, {\rm MeV}$ (red lines) and $m_{A'} = 67 \, {\rm MeV}$ (blue lines). For the solid lines, the sensitivity is estimated for each bin with a bin size of $2\%$ for the missing energy fraction $x = E_{\rm miss}/E_i$, ranging from $90\%$ to $100\%$. For the dashed lines, however, the sensitivity contribution is obtained within a single bin covering the missing energy fraction from $95\%$ to $100\%$.