Test of the vector portal with dark fermions in the charge-exchange reactions in the NA64 experiment at CERN SPS

We consider an experiment to search for dark sector particles in invisible (or semi-invisible) decays of neutral mesons $M^0={\pi }^0$, $\eta$, ${\eta }^{\prime }$, $\omega$, $f_2(1270)$, which produced the charge-exchange reactions ${\pi }^{-}+(A,Z)\to M^0+(A,Z-1);M^0\to$ invisible of high-energy pions (or kaons) on a nuclei target in the NA64 experiment at the CERN SPS. This reaction chain would lead to a striking signature of the signal event—the complete disappearance of the beam energy in the setup [Phys. Rev. D 91, 015004 (2015)]. Using data obtained from the measurements at IHEP (Protvino) and Fermilab (Batavia) we show that the integral cross sections $\sigma$ for the production of the $M^0\mathrm{s}$ slightly deviate from the phenomenological formula $\sigma \sim Z^{2/3}$, where $Z$ is the nuclei charge. In particular, we present the formulas for the differential and integral cross sections that explicitly depend on the Mandelstam and $Z$ variables. Derived formulas are used to predict the $M^0$ yield as a function of beam energy for several target nuclei, and to estimate the projection sensitivity for the proposed search in the dark vector portal model. Sensitivity to different decay modes of $M^0\mathrm{s}$ is explored.

Figure 1

Fit of the parameters for the $\omega$, $f_2(1270)$, and ${\eta }^{\prime }$ mesons using IHEP data for the differential cross section of their production at $P=39.1\mathrm{GeV}$ beam [59].

Figure 2

Results for the integral cross section of the ${\pi }^0$ production ${\pi }^{-}+(A,Z)\to {\pi }^0(\to 2\gamma )+(A,Z-1)$: comparison of parametrization (5) and (6) with data for the beam momentum $P=40\mathrm{GeV}$ [58] (left), predictions for $P=50\mathrm{GeV}$ (right).

Figure 3

Results for the integral cross section of the $\eta$ production ${\pi }^{-}+(A,Z)\to \eta (\to 2\gamma )+(A,Z-1)$: comparison of parametrization (5) and (6) with data for the beam momentum $P=40\mathrm{GeV}$ [58] (left), predictions for $P=50\mathrm{GeV}$ (right).

Figure 4

Results for the integral cross section of the ${\eta }^{\prime }$ production ${\pi }^{-}+(A,Z)\to {\eta }^{\prime }(\to 2\gamma )+(A,Z-1)$: comparison of parametrization (5) and (6) with data for the beam momentum $P=39.1\mathrm{GeV}$ [59] (left), predictions for $P=50\mathrm{GeV}$ (right).

Figure 5

Results for the integral cross section of the $\omega$ production ${\pi }^{-}+(A,Z)\to \omega (\to {\pi }^0\gamma )+(A,Z-1)$: comparison of parametrization (5) and (6) with data for the beam momentum $P=39.1\mathrm{GeV}$ [59] (left), predictions for $P=50\mathrm{GeV}$ (right).

Figure 6

Results for the integral cross section of the $f_2(1270)$ production ${\pi }^{-}+(A,Z)\to f_2(1270)(\to 2{\pi }^0)+(A,Z-1)$: comparison of parametrization (5) and (6) with data for the beam momentum $P=39.1\mathrm{GeV}$ [59] (left), predictions for $P=50\mathrm{GeV}$ (right).

Figure 7

Bounds for dark photon $\epsilon$ parameter mixing obtained for 90% C.L. and for case where $m_{A^{\prime }}=3m_{\chi }$ and ${\alpha }_D=0.5$. In these panels, we show existed limit from current data of ${\mathrm{NA}64}_e$ experiment [61] and constraints from production of DM in $e^{+}{e}^{-}$ collision at BABAR [37]. In the top panel we plot the bounds from semi-invisible mode of neutral pion decays ${\pi }^0\to \gamma A^{\prime }$ and ${\pi }^0\to \gamma \overline{\chi }\chi$. In the central panel we depict the bounds from semi-invisible mode of $\eta$ meson decays $\eta \to \gamma A^{\prime }$, $\eta \to \gamma \overline{\chi }\chi$ and $\eta \to \gamma {\rho }^{*}\to \gamma \overline{\chi }\chi$. In the bottom panel we show the bounds from semi-invisible mode of ${\eta }^{\prime }$ meson decays ${\eta }^{\prime }\to \gamma A^{\prime }$, ${\eta }^{\prime }\to \gamma \overline{\chi }\chi$, ${\eta }^{\prime }\to \gamma ({\rho }^0\to A^{\prime })\to \gamma \overline{\chi }\chi$ and ${\eta }^{\prime }\to {\rho }^0{A}^{\prime }$, ${\eta }^{\prime }\to {\rho }^0\overline{\chi }\chi$. All constraints are presented for proposal statistics $5\times {10}^{12}\pi \mathrm{OT}$ of NA64 experiment.

Figure 8

Bounds for dark photon $\epsilon$ parameter mixing obtained for 90% C.L. and for case where $m_{A^{\prime }}=3m_{\chi }$ and ${\alpha }_D=0.5$. In both panels, we show existed limit from current data of ${\mathrm{NA}64}_e$ experiment [61] and constraints from production of DM in $e^{+}{e}^{-}$ collision at BABAR [37]. Top: bounds from semi-invisible pseudoscalar decays (${\pi }^0\to \gamma \chi \overline{\chi }$, $\eta \to \gamma \chi \overline{\chi }$, ${\eta }^{\prime }\to semi\text{−}inv$) and invisible decay ($\omega \to \chi \overline{\chi }$) for statistics $3\times {10}^9\pi \mathrm{OT}$ (few days of data taking) and for $5\times {10}^{12}\pi \mathrm{OT}$ as proposal statistics for ${\mathrm{NA}64}_h$ experiment. Bottom: bounds from semi-invisible pseudoscalar decays (${\pi }^0\to \gamma \chi \overline{\chi }$, $\eta \to \gamma \chi \overline{\chi }$, ${\eta }^{\prime }\to \gamma \chi \overline{\chi }$) for proposal/projected statistics of ${\mathrm{NA}64}_h$, REDTOP [40] and HIAF [42] experiments. The dot-dashed lines show limit of neutrino floor from decay light pseudoscalar mesons to $\gamma \nu \overline{\nu }$ predicted in the framework of SM [96].

Figure 9

The projected 90% C.L. exclusion limits for benchmark scenarios of invisible and semi-invisible neutral meson decays to dark matter in dark photon mediator portal model. The constrains are shown for the benchmark values $m_{A^{\prime }}=3m_{\chi }$ and ${\alpha }_D=0.5$. In both panels, we show existed limit from last data of ${\mathrm{NA}64}_e$ experiment [61] and constraints from production of DM in $e^{+}{e}^{-}$ collision at BABAR [37]. Top: Limits from semi-invisible pseudoscalar decays (${\pi }^0\to \gamma \chi \overline{\chi }$, $\eta \to \gamma \chi \overline{\chi }$, ${\eta }^{\prime }\to semi\text{−}inv$) and invisible decay ($\omega \to \chi \overline{\chi }$) using statistics $3\times {10}^9\pi \mathrm{OT}$. Bottom: Limits for the same decays for $5\times {10}^{12}\pi \mathrm{OT}$ of ${\mathrm{NA}64}_h$ experiment in comparison with bound from invisible vector meson decays obtained for ${\mathrm{NA}64}_e$ and LDMX experiments [51].

Figure 10

The projected 90% C.L. exclusion for benchmark scenarios of invisible and semi-invisible neutral meson decays to dark matter in dark photon mediator portal model. In both panels, we show existed limit from last data of ${\mathrm{NA}64}_e$ experiment [61] and constraints from production of DM in $e^{+}{e}^{-}$ collision at BABAR [37] and limits from invisible pseudoscalar decays (${\pi }^0\to \gamma \chi \overline{\chi }$, $\eta \to \gamma \chi \overline{\chi }$, ${\eta }^{\prime }\to semi\text{−}inv$) and invisible decay ($\omega \to \chi \overline{\chi }$) using statistics $5\times {10}^{12}\pi \mathrm{OT}$. Top: for parameter ${\alpha }_D=0.1$ and $m_{A^{\prime }}=3m_{\chi }$. Bottom: for parameter ${\alpha }_D=0.5$ and $m_{A^{\prime }}=5m_{\chi }$.