The bremsstrahlung-like production of the massive spin-2 dark matter mediator

Abstract The link between Standard Model (SM) particles and dark matter (DM) can be introduced via spin-2 massive mediator, $$ {\text {G}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mtext>G</mml:mtext> </mml:math> , that couples to photon and charged leptons. Moreover, in a mediator mass range from sub-MeV to sub-GeV, fixed-target facilities such as NA64e, LDMX, NA64 $$\mu $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>μ</mml:mi> </mml:math> , $$\hbox {M}^3$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mtext>M</mml:mtext> <mml:mn>3</mml:mn> </mml:msup> </mml:math> , and E137, can potentially probe such particle of the hidden sector via the signatures that are described by the bremsstrahlung-like process involving tensor mediator. We compare numerically the Weizsaker–Williams (WW) approximation and the exact tree-level (ETL) method for the bremsstrahlung-like mediator production cross section by choosing various parameters of the fixed-target experiments. To be more specific, the determination of WW validity region (in the parameter space of spin-2 DM mediator scenario, that can be examined in the laboratory facilities) is of particular interest of the present manuscript. In addition, we derive novel constraints on spin-2 DM mediator parameter space from the data of the E137 fixed-target experiment. In particular, we demonstrate that the E137 experiment has been ruled out the couplings of the spin-2 mediator at the level of $$8~\times ~10^{-8}~\text{ GeV}^{-1}~\lesssim ~c^{\text {G}}_{ee}~\lesssim ~10^{-5}~\text{ GeV}^{-1}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>8</mml:mn> <mml:mspace/> <mml:mo>×</mml:mo> <mml:mspace/> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>8</mml:mn> </mml:mrow> </mml:msup> <mml:mspace/> <mml:mspace/> <mml:msup> <mml:mtext>GeV</mml:mtext> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> <mml:mspace/> <mml:mo>≲</mml:mo> <mml:mspace/> <mml:msubsup> <mml:mi>c</mml:mi> <mml:mrow> <mml:mi>ee</mml:mi> </mml:mrow> <mml:mtext>G</mml:mtext> </mml:msubsup> <mml:mspace/> <mml:mo>≲</mml:mo> <mml:mspace/> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>5</mml:mn> </mml:mrow> </mml:msup> <mml:mspace/> <mml:mspace/> <mml:msup> <mml:mtext>GeV</mml:mtext> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> for the typical masses in the range $$100~\text{ MeV }~\lesssim ~m_{\text {G}}~\lesssim 800~\text{ MeV }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>100</mml:mn> <mml:mspace/> <mml:mspace/> <mml:mtext>MeV</mml:mtext> <mml:mspace/> <mml:mspace/> <mml:mo>≲</mml:mo> <mml:mspace/> <mml:msub> <mml:mi>m</mml:mi> <mml:mtext>G</mml:mtext> </mml:msub> <mml:mspace/> <mml:mo>≲</mml:mo> <mml:mn>800</mml:mn> <mml:mspace/> <mml:mspace/> <mml:mtext>MeV</mml:mtext> <mml:mspace/> </mml:mrow> </mml:math> , that corresponds to the statistics of $$1.87~\times ~10^{20}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>1.87</mml:mn> <mml:mspace/> <mml:mo>×</mml:mo> <mml:mspace/> <mml:msup> <mml:mn>10</mml:mn> <mml:mn>20</mml:mn> </mml:msup> </mml:mrow> </mml:math> electrons accumulated on target. The latter implies its universal coupling to photons and electrons, $$c^{\textrm{G}}_{\gamma \gamma }~=~c^{\textrm{G}}_{ee}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msubsup> <mml:mi>c</mml:mi> <mml:mrow> <mml:mi>γ</mml:mi> <mml:mi>γ</mml:mi> </mml:mrow> <mml:mtext>G</mml:mtext> </mml:msubsup> <mml:mspace/> <mml:mo>=</mml:mo> <mml:mspace/> <mml:msubsup> <mml:mi>c</mml:mi> <mml:mrow> <mml:mi>ee</mml:mi> </mml:mrow> <mml:mtext>G</mml:mtext> </mml:msubsup> </mml:mrow> </mml:math> .