The search for non-baryonic dark matter, particularly the weakly interacting massive particle (WIMP), can be approached through a direct detection method. According to the super-symmetry (SUSY) theory, the neutralino, formed in the early Universe, is the prime candidate for WIMPs[1]. The previous researches estimate that these WIMPs, present near the Sun's orbit, have a density of 0.3GeV/cm³[2] and move with average speed of 270 km/s relative to the Sun. Using a xenon nucleus in detection experiments, it is observed that the average recoil energy, as a result of elastic scattering, lies in the range of tens of keV for WIMP masses between 10.0GeV and several 100.0GeV[1, 3, 4, 5, 6]. Although xenon detectors can detect of 0.01 to 0.1 events/day/kg[7, 8, 9]. The signal strengths, both primary and secondary, from these detectors are too weak for definitive WIMP identification. To enhance the performance of these detectors, researches suggest amplifying the primary scintillation signal and employing the electroluminescence method for the secondary signal, especially xenon detectors. Given these conditions, we will continue to study the characteristics of xenon detectors using protons.

Xenon WIMP detectors offer a advantage in differentiating between heavy ionization

particles (HIPs), such as neutrons, alphas, and WIMPs, and minimum ionization particles

(MIPs) like gamma rays. The purity of xenon can be substantially enhanced using a outstanding separation method[8, 9, 10, 11], leading to improved detection efficiency. The interaction between WIMPs and a xenon nucleus results in two process sugnals: excitation and ionizaition.

1. Excitation process:

This reaction produces a scintillation photon with λ=175 nm.

2. Ionization process:

Here, a fraction of the ionized electrons recombine and yield a UV photon of 175 nm[10, 12], while

the remaining electrons produce electroluminescence photons in a high electric field. HIPs and MIPs produce distinct primary-to-secondary signal proportions, simplifying the process of particle identification. Two-phase xenon detectors are particularly adept at distinguishing between gamma rays and alpha particles, etc.,[14, 13]. The behavior of the primary and secondary signals is influenced by the applied electric field.

In the main of interaction of WIMP Xenon nucleus scattering, primary signals are directly transmitted to the photomultiplier tube (PMT), while secondary signals go through a photon-producing process. These detectors exhibit the excellence in separating HIPs from MIPs, based on distinct primary-to-secondary signal ratios for different sources. Gamma background can be minimized using specialized underground laboratories and shielding. The primary and secondary scintillations have behaviors in relation to the applied voltage, with the latter being dependent on drift electrons.

Using thorough GEANT4 simulations helps in making Xenon WIMP detectors better. The GEANT4 simulation is key for accurately designing the detector's shape and choosing the right materials. It also helps in improving how signals are processed and in cutting down unwanted noise. Furthermore, the GEANT4 simulation provides important insights into how well the detector works and how efficient it is. This assists in making better designs and in predicting the results of experiments, especially in areas like dark matter and neutrino studies, where detecting faint signals is important.

In our simulation with GEANT4, we design a Xenon WIMP detector that is combined with distinct materials and geometric configurations to optimize the detection efficiency and minimize potential background signals. Simulation can contribute to the improvement of a Xenon WIMP detector by optimizing the detector design, understanding the detector response, developing new detection techniques, and guiding data analysis.

1. Materials Configuration

• Vacuum (G4 Galactic): In our simulation, we set the main environment as a vacuum to describe an absence of matter. This space, commonly referred to as the `world' in GEANT4, offers a defined area for placing the detector and related parts. We retained the default G4 Galactic setting without any modifications.

• Liquid Xenon: In the GEANT4 simulation, the primary detector is constructed as a liquid Xenon sphere with a radius of 11.0 cm, centrally positioned at the origin. The chosen material for this detector is liquid Xenon, characterized by its atomic number of 54, atomic mass of 135.91 g/mole, and a density of 3.0 g/cm³. This spherical detector is optimized the simulation environment and designed as a multi-functional sensitive detector for data simulation.

• Stainless Steel (304 grade): In the computational simulation, 304 stainless steel was employed, characterized by a density of 7.999g/cm3. This alloy's composition encompasses manganese (2%), silicon (1%), chromium (19%), nickel (1%), iron (67.92%), and carbon (0.08%). Notably, this material was selected for the construction of a protective cover in the detector apparatus.

2. Geometric Configuration

• World Volume: In our study, we used a big cube called as `world' for our simulations. This cube has dimension as 4.0 meters long on all sides and filled with a vacuum. This space allows us to fit the detector and other parts, and track how particles move.

• Stainless Steel Protective Cover: Protecting the sensitive core of the detector is a designed stainless steel cover. This cover is not only protect a Xenon detector but also reject low energy background particles. a Xenon detector has three primary components:

• Top Half-Sphere (cover1): This domed segment caps the top of the detector and thickness is 0.5 cm.

• Central Cylindrical Shell (cover2): This cylinder forms positioned centrally the main body of the protective cover and thickness is 0.5 cm.

• Base Disc (cover3): A flat, disc-shaped segment provides a stable base for the detector and thickness is 0.5 cm.

The GEANT4 simulation process produces a detailed and methodical procedure. It begins with the `Action Initialization' that sets the stage by organizing all the required actions for the simulation. In the next step, the `Detector Construction' phase sets up the materials and design of the detector, influencing how particles will interact in the simulation. The `Primary Generator Action' then determines the starting conditions, specifying the primary particles. Each event in the simulation, managed by the Event Action, is like a distinct story segment with its own start and finish. The Run Action manages the whole simulation, making sure it works smoothly and records results correctly. Figure 1(b) provides an overview of the simulation process.

In our experimental setup, we specifically configured the primary proton beam in the simulation to operate at two distinct energy levels: 2.0 GeV and 50.0 GeV. This approach was taken to evaluate the Xenon WIMP detector's sensitivity and response characteristics. The PrimaryGeneratorAction class in the GEANT4 was modified accordingly, where the SetParticleDefinition method was used to define protons as the incident particles, and the SetParticleEnergy method was employed to assign the proton beam energies of 2.0 GeV and 50.0 GeV in separate simulation runs. This dual-energy setup enabled a comprehensive analysis of the detector's performance in detecting and measuring energy depositions within its operational range.

Overall, the GEANT4 simulation provides the perfect fusion of scientific precision and creative representation, illustrating particle behaviors in different scenarios.

Using the GEANT4 simulation, we studied the detector response of protons behavior in our detector for searching xenon wimp dark matter. Protons are used in WIMP detection simulations because they have a high scattering cross-section, are easy to detect, and well-understand. For this reason, protons are a valuable tool for simulating WIMP interactions. Figure 2 shows that the secondary signals produced by interaction between a wimp and xenon nucleus. In Fig. 2, the arrow indicates the direction of the WIMP particle propagation. When a WIMP strikes the xenon nucleus, it transfers energy and generate electrons in the process. One of these electrons generated a photon and electrons in the process, while the remaining two of third produced signals.

Figure 2. (Color online) Schematic view of the working principle of a dual-phase on Xenon Detector.

Figure 3 illustrates the detector performance ability to distinguish between initial photon signals (below 27.0 ns) and subsequent electric signals resulting from proton impacts. The initial burst of photons appears when the proton first strikes and may be followed by more intense photon signals. This categorization effectively utilizes the distinct timing and informational characteristics of each signal type, enhancing the detection and analysis capabilities of this Xenon WIMP detector. This dual-signal methodology enables detectors to accurately measure the energy of events, determine their spatial location, and differentiate between signal types, which is particularly crucial in the search for rare events like those involving WIMPs. a proton beam interacting with a Xenon-based detector can generate neutrons and gamma rays as secondary particles as well. Since it has a complicated signals in a Xenon WIMP detector, which are dominant background, its analysis requires pulse shape discrimination (PSD) method. In Fig. 3, the dotted circle represents the primary signals below 27.0 ns[15], while the lined circle indicates the secondary photon signals, as illustrated in Fig. 2. Figure 3 shows the primary signals, which are the direct scintillations resulting from the incident particle-Xe interactions. The primary signals are generated photons from the recombination of electrons. The secondary signals, which are the ionization electrons. The primary signals were left about 0.01%–0.06% below 27 ns from excitation and recombination process, while most of the secondary signals were left electrons from ionization process.

Figure 3. (Color online) Our simulations showed that the depth information deposited by a proton in a Xenon WIMP detector, it shows clearly primary signal and secondary signal as well.

In Fig. 4(a)–(b), we observe how protons interact with our a Xenon WIMP detector in two different scenarios relate to the incident proton beam energies 2.0 GeV and 50.0 GeV. A consistent observation was the energy left behind by the protons, always around 20.0MeV/c2, regardless of the proton strength. A Xenon WIMP detector is designed to detect energies within certain limits, meaning it might not register events below a specific energy threshold. Moreover, the quenching factor indicates the proportion of kinetic energy from a recoiling nucleus that is transformed into observable signals, such as light or an electrical charge. As a result, only a part of the kinetic energy deposited in the xenon atoms is actually measurable by the detector. This consistent energy deposition suggests the reliable behavior of our Xenon WIMP detector.

Figure 4. (Color online) Our simulations showed that the energy deposited by a proton in a Xenon WIMP detector is approximately 20MeV/c2, regardless of the incident proton energy.

The primary signals below 27.0 ns is crucial for a Xenon WIMP detectors. our study shows that within 27 ns interval aids in determining the exact location of impacted by proton in the Xenon WIMP detector and in identifying the most significant signals to focus on impact by proton.

In this study, we used the GEANT4 software to see how well Xenon detectors can detect

WIMPs. Our tests showed that protons always deposit the same amount of energy in the Xenon WIMP detectors, no matter how strong they are when they hit it. This provides us important information because it helps us tell the difference between signals from WIMPs and noise from protons.

The Xenon WIMP detector provides outstanding advantages that they can discriminate the unwanted signals and give clear results. This Xenon detector using GEANT4 simulation provides us a great tool for trying to find WIMPs. But there is more to the learn and improve. In the future, we want to fine-tune the detector and maybe combine it with other tools to get even clearer results. Our work provides a good starting point for making the Xenon WIMP detectors effective in detecting WIMPs.

This work was supported by the grant of NRF-(2021R1F1A1061174).