Long-lived particle decays at the proposed MATHUSLA experiment

We carefully study the decay and reconstruction of long-lived particle (LLP) decays in the proposed MATHUSLA LLP detector for the HL-LHC. Our investigations are focused on three LLP benchmark models. MATHUSLA’s primary physics target is represented by hadronically decaying LLPs with mass above $\sim 10\mathrm{GeV}$, produced in exotic Higgs decays. We also investigate GeV-scale scalar and right-handed neutrino LLPs, which are the target of many other proposed experiments. We first introduce a public mathusla fastsim code to allow for efficient signal-only studies of LLP decays in MATHUSLA and general external LLP detectors. For each of our benchmark scenarios, we carefully simulate LLP production and decay, and make our simulation library publicly accessible for future investigations and comparisons with other experiments. We then systematically study the geometric acceptance of MATHUSLA for LLP decays in these scenarios, and present updated sensitivity projections that include these acceptances. Our results show that the idealized reach of MATHUSLA computed in earlier studies is mostly realized. We also investigate possible ways of increasing the signal acceptance using the inherent geometric flexibility of the FastSim, which will provide useful inputs for realistic experimental and engineering optimization of the detector in the future.

Figure 1

(a) MATHUSLA geometry relative to the CMS collision point, illustrating how LLPs can decay in the detector and be reconstructed as displaced vertices by the ceiling trackers. For clarity, the modular structure of the MATHUSLA detector is not shown. (b) Vertical structure of the $9\mathrm{m}\times 9\mathrm{m}$ footprint detector modules, which are arranged in a square grid with 1m gaps to make up the $100\mathrm{m}\times 100\mathrm{m}$ detector footprint.

Figure 2

Top: The fraction of LLP decays with $\ge 2$, 4, 6 (solid, dashed, dot-dashed) detector-stable charged particles in our simulations of the $\mathrm{SM}+\mathrm{S}$ model. Bottom: The same for the three right-handed neutrino benchmark models with electron, muon and tau neutrino mixing dominance (red, blue, green). $\mathrm{Br}(N_{\text{charged}}\ge 2)$ corresponds to Br(vis) in Eq. (1).

Figure 3

Geometric acceptances ${\xi }_{\mathrm{geo},i}^{\text{decay}}$, see Eq. (1), for visible LLP decays in the MATHUSLA baseline detector geometry of Fig. 1 to satisfy the $i=\mathrm{DV}2$ (solid) and DV3 (dashed) criteria in Table 1 for reconstruction of 2- and 3-pronged displaced vertices in the long-lifetime limit. Top: Exotic Higgs decays to LLPs that decay to either $\overline{b}b$ (red), $gg$ (blue) or ${\ell }^{+}{\ell }^{-}$ (gray). Middle: LLP in the $\mathrm{SM}+\mathrm{S}$ model (red). For comparison, we show the acceptance for a simplified S-LLP scenario produced only in $B$, $D$-decays and decaying only to $e^{+}{e}^{-}$ (black). Bottom: LLPs in the three RHN scenarios with single-coupling dominance (red, blue, green). For comparison, we show acceptance for a simplified RHN-LLP produced only in $B$ decays and decaying only to $e^{+}{e}^{-}\nu$ (black).

Figure 4

Sensitivity of the MATHUSLA baseline geometry of Fig. 1 to hadronically decaying LLPs produced in exotic Higgs decays. The red curve shows the exclusion reach from a search for DVs with $3+$ prongs, which is very close to the idealized estimate of four decays in the decay volume (black dashed). For comparison, we show the current $\mathrm{Br}(h\to \text{invis})$ limit from ATLAS [54] (purple shading) and the HL-LHC projection [55] (purple line); current ATLAS constraints from searches for 1 or 2 DVs (blue shading) and 2 DVs (green shading) in the muon system [56, 57]; projections for an ATLAS 1DV search in the muon system at the HL-LHC [3] (blue dashed), and the idealized sensitivity of CODEX-b for $m_{\mathrm{LLP}}=10\mathrm{GeV}$ [8] (orange dashed).

Figure 5

Top: the sensitivity of the MATHUSLA baseline geometry in Fig. 1 to scalar LLPs in the $\mathrm{SM}+\mathrm{S}$ model. Black dashed, thick black solid, thin black solid contours; four visible decays in decay volume, reconstructable as 2-pronged DVs, reconstructable as 3-pronged DVs. Hadronization uncertainties mostly affect the near-vertical left boundary of the thin $N_{\mathrm{DV}3}$ contour at the $\mathcal{O}(0.1\mathrm{GeV})$ level. Colored contours show how DV2 signal scales in the parameter space. Shaded areas are bounds from CHARM [58, 59], SN1987 [60], BBN [61], NA62 ($K$-decay) [62, 63, 64], and LHCb [65, 66]. Bottom: MATHUSLA’s sensitivity compared to projections for NA62 (${10}^{18}$ Protons-on-Target beam dump mode) [28], FASER2 [13], LHCb [8], SHADOWS2 [67], CODEX-b [8], and SHiP [28].

Figure 6

Left: the sensitivity of the MATHUSLA baseline geometry in Fig. 1 to scalar LLPs in the RHN benchmark models with electron (top), muon (middle) and tau (bottom) coupling dominance. Black dashed, thick black solid, thin black solid contours; four visible decays in decay volume, reconstructable as 2-pronged DVs, reconstructable as 3-pronged DVs. [For RHN ($U_{\tau }$), the $N_{\mathrm{DV}3}=4$ contour for $m_N<0.75\mathrm{GeV}$ is based on an extrapolation of ${\xi }_{\mathrm{geo}m,\mathrm{DV}3}^{\text{decay}}(m_N)·\mathrm{Br}(\mathrm{vis})$ from higher masses, indicated by the pink dashed contour, see text details.] Hadronization uncertainties mostly affect the lower boundary of the thin $N_{\mathrm{DV}3}$ contour near a GeV, at most at the $\mathcal{O}(1)$ level. Colored contours show how DV2 signal scales in the parameter space. Shaded areas are bounds from BBN [68], DELPHI [69], Charm [59], Belle [70], CMS [71], PS191 [72], NA62 ($K$-decay) [73, 74], DUNE near detector, and T2K [75]. Right: MATHUSLA’s sensitivity compared to projections for LHCb and CMS [76], FASER2 [13], SHADOWS2 [67], CODEX-b [8], SHiP [28], DarkQuest [77], NA62 ($K$-decay, $5\times {10}^9$ Protons-on-Target) [73, 74, 78], NA62 (${10}^{18}$ Protons-on-Target beam dump mode) [79], and the DUNE near detector [80].

Figure 7

Spatial distributions of reconstructed decay vertices (DV2 criterion) in the MATHUSLA baseline geometry of Fig. 1 for representative examples of the exotic Higgs decay, $\mathrm{SM}+\mathrm{S}$ and RHN ($U_e$) benchmark models in the long lifetime limit, projected onto the vertical plane that intersects the LHC beamline. (The IP is situated at the origin of this coordinate system.) The red solid, dashed, dotted, dot-dashed lines represent optimized choices of volume cuts below lines starting on the floor and ending on the rear wall, which are constrained to reduce the detector volume by 5%, 10%, 20%, and 30% respectively while minimizing the fraction of “lost” reconstructed decays below the line.

Figure 8

Geometric acceptances for visible LLP decays, ${\xi }_{\mathrm{geo},i}^{\text{decay}}$, for LLP decays in the exotic Higgs decay, $\mathrm{SM}+\mathrm{S}$ and RHN benchmark models, comparing the baseline MATHUSLA geometry of Fig. 1(black) to the same geometry with a full-wall tracker (magenta), a back-wall tracker only (dark cyan) and no gaps between modules (orange).

Figure 9

Comparing the sensitivity of the MATHUSLA baseline geometry in Fig. 1 to the same geometry with a full-wall tracker (magenta), a back-wall tracker only (dark cyan) and no gaps between modules (orange) for the $\mathrm{SM}+\mathrm{S}$ and RHN benchmark models. We do not show the corresponding comparison for hadronically decaying LLPs produced in exotic Higgs decays, since full and back wall tracker geometries essentially fully recover the ideal $N_{\text{decay}}=4$ sensitivity in Fig. 4, and the geometry without module gaps performs identically to the baseline.

Figure 10

Purple curve: number of LLP decays in the decay volume vs area of a MATHUSLA-like detector in the long lifetime limit, normalized to the ($100\mathrm{m}\times 100\mathrm{m}$) benchmark of Fig. 1. The dashed line indicates linear scaling. This is for a 15 GeV LLP produced in exotic Higgs decays, but similar scalings are observed for the other benchmark models across their parameter space.

Figure 11

Comparing the idealized reach of the MATHUSLA baseline geometry in Fig. 1 to similarly situated versions of MATHUSLA with smaller area.