Sgoldstino Phenomenology at SND@HL-LHC

Technical Summary: Sgoldstino Phenomenology at SND@HL-LHC

Problem Statement
The Standard Model (SM) leaves open questions regarding the origin of the electroweak scale and the nature of dark matter. Supersymmetry (SUSY) offers a solution by relating bosonic and fermionic degrees of freedom, requiring a hidden sector for SUSY breaking. This breaking generates a Goldstone fermion (goldstino) and its scalar superpartners, the scalar and pseudoscalar sgoldstinos. While heavy sgoldstinos are typically searched for at high-$p_T$ colliders, light sgoldstinos (masses from the dimuon threshold up to a few GeV) may be produced in rare meson decays. The SND@LHC and its high-luminosity upgrade, SND@HL-LHC, are forward detectors designed to capture long-lived particles produced at small angles. However, a clean signature for light sgoldstinos decaying into muon–antimuon pairs ($S \to \mu^+\mu^-$) requires the experimental separation of the two tracks. If the muons are highly collimated due to the high boost of the parent sgoldstino, they may appear as a single track, mimicking background events from neutrino interactions. This paper investigates the phenomenology of light scalar sgoldstinos at SND@HL-LHC, specifically quantifying how the detector's magnetic field and spatial resolution impact the ability to resolve dimuon pairs and the resulting sensitivity to SUSY-breaking parameters.

Methodology
The authors employ an effective field theory approach to describe sgoldstino interactions with SM particles below the electroweak scale. The analysis proceeds through the following steps:

1. Interaction and Decay Modeling:

   • The effective Lagrangian includes couplings to photons, gluons, quarks, and leptons, parameterized by the SUSY-breaking scale $\sqrt{F}$, gaugino masses ($M_1, M_2, M_3$), and trilinear couplings ($A_q, A_l$).
   • Decay widths are calculated for $S \to \ell^+\ell^-$, $S \to \gamma\gamma$, and hadronic modes. Hadronic decays are treated using Chiral Perturbation Theory ($\chi$PT) for $m_S < 1$ GeV (dominated by $\pi\pi$ and $K\bar{K}$) and a gluonic description for $m_S > 1$ GeV.
   • Two representative SUSY-breaking parameter sets are analyzed:
     • Set 1: Natural scaling where $M_3 = M_{\gamma\gamma} = A_q = A_l = 0.3\sqrt{F}$.
     • Set 2: A scenario with heavy gauginos ($M_3=3$ TeV, $M_{\gamma\gamma}=1$ TeV) and $A_{q,l} = 0.5\sqrt{F}$, chosen to enhance the muon branching fraction while maintaining a lifetime sufficient for the sgoldstino to reach the detector.

2. Production Mechanisms:

   • The primary production channels considered are flavor-conserving and flavor-violating meson decays ($B, K, D, \eta$).
   • Flavor-conserving production proceeds via one-loop diagrams involving top quarks or Higgs mixing.
   • Flavor-violating production is modeled via off-diagonal squark mass terms ($\tilde{m}_{LR}$), specifically considering $\tilde{m}_{LR} = 30$ GeV to open D-meson decay channels.
   • Direct gluon fusion production is noted but excluded from the quantitative analysis due to uncertainties in parton distribution functions at low masses and the harder momentum spectrum it produces.

3. Detector Simulation and Kinematics:

   • The study utilizes the proposed SND@HL-LHC geometry: a 480 m distance from the interaction point, a 2.9 m long detector with a 40 cm square cross-section, and a magnetized hadronic calorimeter (HCAL) with $B=1.75$ T.
   • Meson production spectra are generated using EPOS-LHC/CRMC (light mesons) and PYTHIA 8 (B mesons).
   • A critical component is the calculation of the muon–antimuon separation factor ($A_\mu$). The authors numerically propagate muons through the detector to determine the transverse distance $\Delta r$ between tracks.
   • Events are accepted only if the tracks remain separated by a distance $\Delta r > \Delta_\mu$ over a path length $d_\mu = 15$ cm (three HCAL layers). Two criteria are tested: an optimistic $\Delta_\mu = 1$ mm and a conservative $\Delta_\mu = 1$ cm.

4. Sensitivity Calculation:

   • The expected number of signal events ($N_S$) is computed by integrating over parent meson distributions, sgoldstino branching ratios, decay probabilities within the detector volume, and the separation factor $A_\mu$.
   • Sensitivity is defined by the 95% Confidence Level (CL) criterion $N_S > 3$, assuming a background-free environment after veto and vertex requirements.

Key Contributions

• Quantification of Separation Efficiency: The paper provides a detailed numerical evaluation of the muon–antimuon separation efficiency as a function of sgoldstino mass ($m_S$) and momentum ($p_S$). It demonstrates that for high-momentum sgoldstinos (particularly from B-meson decays), the dimuon pair is highly collimated, making separation difficult without magnetic bending.
• Impact of Magnetic Field: The study explicitly compares sensitivity with and without the HCAL magnetic field. It shows that for light sgoldstinos where the intrinsic opening angle is small, the magnetic field is crucial for restoring sensitivity, particularly under conservative separation criteria. For heavier sgoldstinos, the intrinsic opening angle is larger, and spatial resolution alone often suffices.
• Parameter Space Exploration: The authors map the exclusion and sensitivity regions in the $(m_S, \sqrt{F})$ plane for both flavor-conserving and flavor-violating scenarios, incorporating existing constraints from meson decay limits (Table 1).

Results

• Flavor-Conserving Scenarios:
  • For Set 1, the sensitivity is limited by the large hadronic decay widths which reduce the sgoldstino lifetime, causing most particles to decay before reaching the detector.
  • For Set 2, the sensitivity extends to $\sqrt{F} \approx 2000$ TeV for $m_S \approx 0.3$ GeV and up to $\sqrt{F} \approx 4000$ TeV for heavier masses ($m_S \sim 2.5$ GeV).
  • The "muon separation" requirement significantly reduces the projected reach. Under the conservative criterion ($\Delta_\mu = 1$ cm), sensitivity to B-meson produced sgoldstinos is nearly lost without the magnetic field. The magnetic field ($B=1.75$ T) recovers a substantial portion of this sensitivity.
• Flavor-Violating Scenarios ($\tilde{m}_{LR} = 30$ GeV):
  • D-meson decays become a dominant source. The softer momentum spectrum of sgoldstinos from D-mesons compared to B-mesons makes them easier to separate.
  • In this scenario, the magnetic field significantly extends the sensitivity region for lighter sgoldstinos ($m_S \approx 0.5$ GeV) under the conservative separation criterion, allowing the experiment to probe $\sqrt{F} \approx 1000$ TeV.
• Mass Dependence: For heavier sgoldstinos ($m_S > 1$ GeV), the intrinsic opening angle of the muon pair increases, reducing the reliance on the magnetic field for track separation.

Significance and Claims
The paper claims that the SND@HL-LHC experiment has the potential to probe scalar sgoldstinos with masses from the dimuon threshold up to $\approx 2.5$ GeV and SUSY-breaking scales up to $\sqrt{F} \approx 4000$ TeV. A central claim is that the muon–antimuon separation efficiency is a critical, non-negligible factor in these searches. The authors emphasize that for light, highly boosted sgoldstinos, the assumption of a background-free dimuon signature is only valid if the detector can resolve the two tracks.

The study concludes that the magnetized calorimeter configuration is not merely an auxiliary feature but a necessary component for maximizing sensitivity in the low-mass, high-momentum regime. Without the magnetic field, the conservative spatial resolution requirements would exclude a large fraction of the parameter space accessible to flavor-conserving and flavor-violating models. The authors modestly note that their results are specific to the scalar sgoldstino and the proposed detector configuration, and that pseudoscalar sgoldstinos would exhibit similar phenomenology regarding track separation, though with different hadronic decay patterns.