Characterizing dark matter signals with missing momentum experiments

Fixed target missing-momentum experiments such as LDMX and ${\mathrm{M}}^3$ are powerful probes of light dark matter and other light, weakly coupled particles beyond the Standard Model (SM). Such experiments involve $\sim 10\mathrm{GeV}$ beam particles whose energy and momentum are individually measured before and after passing through a suitably thin target. If new states are radiatively produced in the target, the recoiling beam particle loses a large fraction of its initial momentum, and no SM particles are observed in a downstream veto detector. We explore how such experiments can use kinematic variables and experimental parameters, such as beam energy and polarization, to measure properties of the radiated particles and discriminate between models if a signal is discovered. In particular, the transverse momentum of recoiling particles is shown to be a powerful tool to measure the masses of new radiated states, offering significantly better discriminating ability compared to the recoil energy alone. We further illustrate how variations in beam energy, polarization, and lepton flavor (i.e., electron or muon) can be used to disentangle the possible the Lorentz structure of the new interactions.

Figure 1

Schematic diagrams depicting the signal topologies outlined in Sec. 2. Left: two-step DM production via $2\to 3$ scattering in which a massive mediator particle $X$ is produced on shell and subsequently decays invisibly via $X\to \overline{\chi }\chi$. Middle: direct DM production through virtual light mediator exchange corresponding to the $(\overline{e}e)(\overline{\chi }\chi )/q^2$ “millicharge” interaction in Eq. (4). Right: direct DM production through a contact $(\overline{e}e)(\overline{\chi }\chi )/{\mathrm{\Lambda }}^2$ interaction from Eq. (4) represented by the black circle.

Figure 2

Fixed target production cross sections for a representative subset of scenarios in Eqs. (2)–(4) for 4 (solid lines) and 8 (dashed lines) GeV electron beams on a tungsten target. The horizontal axis represents the mediator mass $m_{A^{\prime }}$ for the radiative production of $A^{\prime }$ vector mediators through the interaction in Eq. (2) (top) and $2m_{\chi }$ for the DM pair production through the interactions in Eq. (4). The heavy mediator case corresponds to $m_{A^{\prime }}=10\mathrm{GeV}$ and exhibits a systematic increase in the cross section as the beam energy is increased. This behavior reflects the higher dimensionality of the operator mediating this interaction [first line of Eq. (4)].

Figure 3

Kinematic distributions for the recoiling electron in on shell production of a massive mediator particle in $eN\to eNX$ fixed target reactions. The models considered in the left, center, and right panels correspond to the vector, axial vector, and chiral vector interactions in Eq. (2), respectively. The top row shows the outgoing electron’s recoil energy for the three interaction types for various choices of $m_{\chi }$, and the bottom row shows the corresponding electron $p_{T,e}$ distributions. In all cases, the incident electron beam energy of 4 GeV and a tungsten target are chosen to match projections for LDMX Phase 1 [34].

Figure 4

Kinematic distributions for the recoiling electron in radiative scalar and pseudoscalar emission in $eN\to eNs/a$ fixed target reactions that utilize the interactions in Eq. (3). The top row shows the outgoing electron’s recoil energy for the two interaction types for various choices of $m_{\chi }$, and the bottom row shows the corresponding electron $p_{T,e}$ distributions. In all cases, the incident electron beam energy of 4 GeV and a tungsten target are chosen to match projections for LDMX Phase 1 [34].

Figure 5

Kinematic distributions for the recoiling electron in direct pair-production of Dirac fermions in $eN\to eN\chi \overline{\chi }$ fixed target reactions. The models considered in the left and right columns correspond to the contact (heavy mediator) and millicharge (light mediator) interactions in Eq. (4). The top row shows the outgoing electron’s recoil energy for the two interaction types for various choices of $m_{\chi }$, and the bottom row shows the corresponding electron $p_{T,e}$ distributions. In all cases, the incident electron beam energy of 4 GeV and a tungsten target are chosen to match projections for LDMX Phase 1 [34].

Figure 6

Kinematic distributions for on-shell vector mediator (solid curves), off shell vector mediator with $m_{A^{\prime }}=10\mathrm{GeV}$ (dashed curves), and off-shell massless vector mediator (dotted curves) for different masses. All distributions are for a 4 GeV electron beam colliding with a tungsten target.

Figure 7

Mass discrimination sensitivity for vector mediators using electron transverse momentum $(p_{T,e})$ and electron recoil energy $(E_e)$ distributions. Top left: $p_{T,e}$ distributions for representative test hypotheses for different mass values (colored curves) plotted alongside a mock data set with $N_{\mathrm{sig}}=100$ signal events drawn from a distribution of $m_{A^{\prime }}=100\mathrm{MeV}$; the gray shaded band surrounding the black histogram represents the statistical uncertainty of the mock data set. Top right: two-dimensional histogram of the number of signal events required to distinguish a given test mass hypothesis on the vertical axis from the true mass on the horizontal axis (the one used to generate the mock data set) at 95% confidence level assuming only statistical errors. Darker colors correspond to more signal events needed. This result makes use of the $p_{T,e}$ spectral information only. Bottom left: same as top left, but showing the electron recoil energy $(E_e)$ instead of transverse momentum $(p_{T,e})$. Bottom right: comparison of recoil energy-only versus transverse momentum-only analyses to discriminate between different mass hypotheses. The density plot shows the difference between the number of signal events required to distinguish a test model from the “true” scenario using only $E_e$ and $p_{T,e}$ information. This difference is strictly positive, implying that transverse momentum enables superior model discrimination with a much smaller number of signal events. This improvement is particularly pronounced for models with similar masses where the recoil energy spectra are nearly identical.

Figure 8

Differential left/right asymmetry $A_{\mathrm{LR}}(E_e)$ from Eq. (10) for the (left-handed) chiral vector model plotted against electron recoil energy $E_e$ for a beam energy of 4 GeV. Also shown are the MC statistical uncertainties for each energy bin.

Figure 9

Energy distributions for the recoiling muon in on-shell production of a massive mediator particle in $\mu N\to \mu NX$ fixed target reactions. The top row shows the outgoing muon’s recoil energy for vector (left) and axial vector (right) interactions and the bottom row for scalar (left) and pseudoscalar (right) interactions. In all cases, the incident muon beam energy of 15 GeV is chosen to match projections for ${\mathrm{M}}^3$ Phase 1 [16].

Figure 10

Number of events required to discriminate between axial and vector interactions at a muon beam experiment described in Sec. 5. The solid and dashed lines correspond to two binnings of the kinematic variables (beam muon recoil energy and transverse momentum), representing different experimental resolutions. Higher resolution enables model discrimination with fewer signal events.