arXiv subjects

Tianjun Li

Publications and source records attributed to Tianjun Li.

At least 19 recordsLinked to original sources

arXiv2026

Inverse seesaw and inflation in a supersymmetric 331 model from $SU(6)$

We propose a $N=1$ supersymmetric $SU(6)$ theory with an intermediate $(SU(3)_C\times SU(3)_L\times U(1)_X)$ phase, in which common fields and operators relate the neutrinos, gauge mediation, unification, and symmetry-breaking sectors. The inverse-seesaw Dirac matrix is antisymmetric and thus has rank two, leaving one massless neutrino at leading order. The leading symmetry-allowed correction lifts this zero mode through its projection onto the left and right null vectors of the Dirac matrix, resulting in a quartic suppression by the ratio of the intermediate and ultraviolet scales. The complete unified messenger multiplets preserve the relative one-loop gauge-coupling crossing, while the supersymmetry-breaking spurion entering the messenger sector also determines the scale of lepton-number violation. The coupling governing (331) breaking fixes both the inflationary normalization and the radial mass in the broken vacuum. For the conditional heavy spectrum adopted in the threshold calculations, the gauge couplings remain perturbative. The physical scalar directions transverse to the inflaton are stable within the neutral $((\Phi,\bar\Phi,S))$ subspace. These results provide the analytical scale relations among the inverse seesaw, messenger sector, unified gauge evolution, and inflation, while keeping the assumptions associated with the ultraviolet Higgs and heavy-threshold sectors explicitly.

hep-ph↗

arXiv2026

Penumbral Inflation from Calabi-Yau Boundaries

Mapping Calabi-Yau geometry to early Universe cosmology remains a primary goal in string phenomenology. We present an inflationary mechanism where flux stationarity shifts the field dynamics, driving inflation along the volume-controlling saxion direction near a Hodge boundary. In this region, the internal geometry strictly dictates the scalar potential. This setup stabilizes the field against heavy moduli corrections without consuming extra flux tadpoles. As a result, the properties of the geometric boundary translate directly into primordial tensor perturbations, creating a clear physical link from string compactifications to measurable data. The resulting geometric predictions match current cosmic microwave background limits and provide specific, testable targets for upcoming LiteBIRD and CMB-S4 observations.

hep-ph↗

arXiv2026

Light Neutralino Dark Matter in a Supersymmetric Pati-Salam Framework

We investigate the low-energy phenomenology of the MSSM arising from the supersymmetric $SU(4)_C \times SU(2)_L \times SU(2)_R$ Pati-Salam framework, focusing on neutralino dark matter in bulk annihilation and Higgs/Z-funnel regions. Using a comprehensive parameter scan consistent with radiative electroweak symmetry breaking and a neutralino LSP, we analyze collider, flavor, and dark matter constraints for both signs of {\mu}. To isolate genuine bulk annihilation from coannihilation, we impose the mass-splitting condition $\mathcal{R}_{\tilde{\phi}} \equiv (m_{\tilde{\phi}}-m_{\tilde{\chi}_1^0})/m_{\tilde{\chi}_1^0}\gtrsim 10\%$. We identify a viable bulk region with a bino-like LSP and a light right-handed stau NLSP. These solutions satisfy all experimental constraints, including LHC searches, flavor observables, and the Planck 2018 relic density, predicting upper bounds $m_{\tilde{\chi}_1^0}\lesssim 110~{\rm GeV}$ and $m_{\tilde{\tau}_1}\lesssim 120~{\rm GeV}$. This parameter space lies within the reach of future CEPC and FCC-ee colliders. We also analyze Higgs- and Z-funnel regions. Current direct-detection limits strongly constrain light Higgsino-assisted resonances for {\mu}>0. Conversely, for {\mu}<0, destructive interference in Higgs-mediated scattering suppresses the direct-detection cross section, allowing a viable Z-funnel region to survive below the projected LZ 1000-day sensitivity. These results highlight the negative-{\mu} Pati-Salam framework as a predictive, testable scenario for upcoming dark matter and lepton collider experiments

hep-ph↗

arXiv2026

Determining the Spin Density Matrix via Its Rank and Probing the Quantum Entanglement and Bell Non-Locality at the Lepton Colliders

Considering two-fermion $F_a F_b$ productions and decays via one scalar or photon exchange at the $e^+e^-$ collider, we show that the rank $r_{\rho}$ of spin density matrix $\rho$ is equal to the number of degrees of freedom of the mediator. For one generic scalar exchange, the spin density matrix is rank one for a pure state. With rank-one condition, we can determine the spin analyzing powers for $F_a$ and $F_b$ and their product if the CP symmetry is violated and conserved, respectively, and probe the CP violation. These results can be applied to the $\eta_c \to \Lambda {\bar \Lambda}$ at the BESIII experiment and the Higgs $\to \tau \tau $ at the LHC. For one photon exchange, the spin density matrix is rank two for a mixed state. Considering the $\Lambda \bar \Lambda $ productions and decays at the BESIII experiment as an example, we show that the spin analyzing powers for $F_a$ and $ F_b$ can be determined by the rank-two conditions in details. Therefore, we can reconstruct the spin density matrices, probe the quantum entanglement and Bell non-locality, and evade the no-go theorem. Furthermore, we conjecture that the $N\times N$ spin density matrix with $r_{\rho} \le N-2 $ can be reconstructed at the lepton colliders in general.

hep-ph↗

arXiv2026

Determining the Spin-Analyzing Powers via Invariants of the Spin Correlation Matrices and Probing the Bell Non-Locality at the Lepton Colliders

We consider the two-fermion $F_a F_b$ productions and decays via one mediator exchange at the $e^+e^-$ collider. With the assumption that the spin is defined via the Lorentz symmetry, or considering the implicit symmetry in the spin density matrix, we prove that the trace ${\rm Tr} [C]$ of the spin correlation matrix $C$ is an invariant quantity, and is invariant under basis rotations. Thus, for the exchanges of one mediator such as scalar and gauge boson, we can determine the product of the spin-analyzing powers for $F_a F_b$ via ${\rm Tr} [C]$, and reconstruct the spin correlation matrix. With the CHSH-Horodecki criterion, we can probe the Bell non-locality, and evade the no-go theorem. To be concrete, we study the Bell non-locality for the $\Lambda \bar \Lambda$ productions and decays at the BESIII experiment. In addition, the invariant ${\rm Tr} [C]$ is a new physics observable to probe the new physics beyond the Standard Model (SM) and study the SM precision measurements. Moreover, for the scalar exchanges, we discuss the general invariants of the spin correlation matrices and the related phenomenological consequences.

hep-ph↗

arXiv2026

Controlled Penumbral Inflation from Monodromic Valleys

Realizing controlled, single-clock inflation in string theory is fundamentally obstructed by the backreaction of heavy moduli. We show that in the \emph{penumbra} -- the near-boundary regime of complex-structure moduli space where asymptotic symmetries are partially broken -- this obstruction can be exactly quantified. We derive a covariant control theorem demonstrating that local branch data dictate whether a monodromic valley supports a controlled inflationary plateau, thereby isolating the first controlled penumbral inflationary window. The result turns the penumbra from a geometric regime into a dynamical filter. In the axion-saxion effective theory, a branch-displacing odd term generates a plateau when $\Delta\equiv p+2\nu-q>0$, while covariant single-clock control further requires $p<2$, or $p=2$ with $12A_pm^2/(dV_0)\gg1$ over the observational window. This splits penumbral valleys into no plateau, uncontrolled plateau, and controlled plateau before global completion is attempted. We identify a minimal analytic family with a closed-form valley and an invariant attractor equation for the full two-field dynamics, providing the first exactly solvable penumbral realization that remains predictive under the next penumbral order. The controlled corridor targets $r\sim10^{-3}$ with the correlated running $\alpha_s\simeq-r/2$ for the $d=q=1$ benchmark, providing a falsifiable target for LiteBIRD/CMB-S4.

hep-ph↗

arXiv2026

Dilaton-Flattened Axion Inflation

We present a solvable same-sector effective theory for anomaly-inspired axion inflation, in which a heavy trace-anomaly mode dynamically backreacts on the axion potential. The tree-level elimination of the radial field resums the backreaction into a closed-form Lambert-$W$ potential, naturally flattening the hilltop potential without external plateau operators. By deriving the exact trough metric, we evaluate all the observables on the fully reduced one-field action, bypassing uncontrolled kinetic approximations. Calibrated at $N_\star=56$, reheating-compatible branches yield $r\simeq0.033$--$0.036$ and $\alpha_s\simeq-(4.6$--$4.7)\times10^{-4}$, comfortably satisfying the current ACT/SPT/BICEP constraints. The evolution remains strictly adiabatic ($m_\perp^2/H^2\gtrsim6.1$, $\Omega/H\lesssim7.6\times10^{-4}$) with negligible sound-speed and metric corrections. We provide analytic control over the constant-$w_{\rm eff}$ reheating map, the $N_{\rm re}=0$ boundary, and robustness against vacuum-offset deformations. This Lambert-$W$ backbone establishes a precise, deformable benchmark for confining axion inflation, with microscopic matching and reheating microphysics accessible as systematic EFT refinements.

hep-ph↗

arXiv2026

LHC Run-3, Dark Matter and Supersymmetric Spectra in the Supersymmetric Pati-Salam Model

Driven by the growing agreement between the experimentally measured muon anomalous magnetic moment and its SM prediction, we reexamine phenomenological consequences of the MSSM, which is embedded in the supersymmetric $SU(4)_C \times SU(2)_L \times SU(2)_R$ Pati-Salam model. In contrast to earlier studies that predominantly favored a specific sign for the Higgsino mass parameter, our analysis systematically explores both $\mu > 0$, and $\mu < 0$ scenarios in light of current collider, cosmological, and DM constraints. Within this framework, we identify viable parameter space regions where the observed DM relic density is reproduced through multiple mechanisms: co-annihilations involving sbottom-neutralino, gluino-neutralino, stop-neutralino, stau-neutralino, and chargino-neutralino coannihilation, as well as resonant s-annihilation channel via the pseudoscalar Higgs boson. We demonstrate that all such scenarios are consistent with present bounds from LHC supersymmetry searches, the Planck~2018 DM relic density bound, and current limits from DD DM searches. Our results reveal characteristic mass spectra associated with these mechanisms. In particular, sbottom-neutralino coannihilation typically requires sbottom masses near $2.8~\text{TeV}$, while gluino-neutralino and stop-neutralino coannihilation scenarios allow gluino masses in the range $1$--$3~\text{TeV}$ and stop masses between $1$ and $3.5~\text{TeV}$. In coannihilation-dominated regions, the stau and chargino masses may reach values as high as $3.8~\text{TeV}$, whereas viable $A$ resonance solutions are realized for pseudoscalar Higgs masses spanning approximately $1.6$--$3.8~\text{TeV}$. We anticipate that a portion of the parameter space will be accessible to supersymmetry searches in LHC Run-3 and future runs.

hep-ph↗

arXiv2026

Non-Minimal Dilaton Inflation from the Effective Gluodynamics

We develop a nonminimal dilaton-inflation model in which the inflaton is the lightest scalar excitation of a hidden confining gauge theory. The Migdal--Shifman anomaly-matching action fixes a logarithmic contribution to the scalar potential, $V_{\rm MS}=A\varphi^4[\ln(\varphi/\mu)-1/4]$, with $(A,\mu)$ mapped to the scalar mass and vacuum condensate. Embedding this sector in the leading curved-space EFT introduces the independent Wilson coefficients $\lambda$ and $\xi$, and the resulting Einstein-frame dynamics yields a plateau with a calculable anomaly-induced deformation. We analyze the pure MS limit as a baseline, derive the $\mu$--$\lambda$ reparametrization, state finite-window RG-control conditions, and impose both the nonminimal-gravity cutoff and the intrinsic confining-sector gap. Exact slow-roll scans show that the viable regime combines the usual large-$\xi$ attractor behavior with a logarithmic imprint tied directly to nonperturbative trace-anomaly matching.

hep-ph↗

arXiv2026

Unveiling a Universal Formalism for Quantum Entanglement in Arbitrary Spin Decays

We present a comprehensive theoretical framework for probing quantum entanglement in the decay angular distributions of a spin-$S$ particle-antiparticle pair $A\bar{A}$, where each particle decays sequentially into a two-body final state, $A\to B+C$ and $\bar{A}\to\bar{B}+\bar{C}$, with $B(\bar{B})$ carrying spin $b$ and $C(\bar{C})$ being spinless. Starting from the most general polarized initial state, we derive the fully differential angular distribution $\mathcal{W}(\theta_1,\theta_2,\phi_1,\phi_2)$ and identify observables $\langle\cos(2S(\phi_1\mp\phi_2))\rangle$ whose expectation values directly depend on the entanglement-sensitive coefficients $\text{Re}\left(\alpha_{-S,\mp S}\alpha_{S,\pm S}^*\right)$ of the initial state. The proportionality factor $\mathcal{C}(S,b)$ in these relations is computed explicitly. For bosonic decays ($b=0,1,2,\ldots$), $\mathcal{C}(S,b)$ is universal and independent of decay dynamics; in particular, $\mathcal{C}(S,0)=1/2$ for any $S$, and $\mathcal{C}(1,1)=1/8$, matching known results for $W^+W^-$ decays. For fermionic decays ($b=\frac{1}{2},\frac{3}{2},\frac{5}{2}\ldots$), $\mathcal{C}(S,b)$ depends explicitly on the spin analysis powers $\alpha_{A/\bar{A}}$, making entanglement extraction more decay-dependent. We further demonstrate, within the context of $e^+e^-\to\gamma^*\to A\bar{A}$ production, how $\alpha_{A/\bar{A}}$ can be determined experimentally using specific angular observables restricted to the beam-axis region. Our results highlight the special role of bosonic decays in providing clean, model-independent tests of quantum entanglement at colliders, while outlining a pathway for entanglement measurement in fermionic cases through supplementary polarization information.

hep-ph↗

arXiv2026

Excluding Local Hidden Variables in $\Lambda\bar{\Lambda}$ Production: The Incompatibility with Angular-Momentum Conservation and CPT Invariance

We analyze spin entanglement in $\Lambda\bar{\Lambda}$ pairs produced in the decays of spin-zero particles, contrasting predictions from quantum field theory (QFT) with those of local hidden-variable theories (LHVTs). Using the self-analyzing weak decays $\Lambda \to p\pi^-$ and $\bar{\Lambda} \to \bar{p}\pi^+$, we derive the joint angular distributions within QFT. Our key findings are: For scalar production $h \to \Lambda\bar{\Lambda}$, no LHVT respecting locality and angular-momentum conservation can reproduce the QFT distribution. For pseudoscalar production $a \to \Lambda\bar{\Lambda}$, a CPT-symmetric LHVT is excluded by positivity constraints given the measured analyzing powers; however, if CPT symmetry is relaxed, an explicit LHVT construction -- with uniform hidden-variable measure and response functions satisfying $b_1 c_1 = 3\alpha_{\Lambda}\alpha_{\bar{\Lambda}}$ -- can match the QFT result. For the most general spin-zero decay $s\to \Lambda\bar{\Lambda}$ with arbitrary scalar-pseudoscalar mixing, we, under CPT invariance, identify the regions of parameter space where the QFT joint angular distribution does or does not admit an LHVT realization. These distinct signatures provide clear, experimentally testable criteria to discriminate between QFT and LHVT in $\Lambda\bar{\Lambda}$ systems across different production mechanisms.

hep-ph↗

arXiv2025

Three-Family Supersymmetric Pati-Salam Flux Models from Rigid D-Branes

Intersecting D-brane model building often suffer from the unstabilized open-string moduli, leading to the unwanted massless adjoint scalars. In our previous work arXiv:2505.03664, this issue was resolved by employing the rigid D6-branes on the $\mathbb{T}^6/(\mathbb{Z}_2 \times \mathbb{Z}_2^\prime)$ orientifold with discrete torsion, where fractional cycles eliminate all adjoint scalars. In this paper, we construct new three-family flux models in the Type IIB setup on $\mathbb{T}^6/(\mathbb{Z}_2 \times \mathbb{Z}_2)$, T-dual to the Type IIA rigid D6-brane construction with discrete torsion, by introducing the quantized background $G_3$ flux that stabilizes the closed-string complex structure moduli and axio-dilaton. The resulting Pati-Salam gauge symmetry can be spontaneously broken down to the Standard Model via a supersymmetry-preserving Higgs mechanism. All the consistency conditions, including $\mathcal{N}=1$ supersymmetry, RR tadpole cancellation, and K-theory constraints, are satisfied. We present the complete particle spectra for these models and discuss how exotic states dynamically decouple through strong dynamics in the hidden sector.

hep-th↗

arXiv2025

The ${\cal N}=1$ supersymmetric Pati-Salam models with extra $SU(2)_{L_2/R_2}$ gauge symmetry from intersecting D6-branes

By introducing an extra stack of D6-branes to standard ${\cal N}=1$ supersymmetric Pati-Salam models, we extend the landscape of its complete search. In this construction, the $d$-stack of D6-branes is introduced besides the standard $a,~b,~c$-stacks. More intersections from the extra stacks of D6-branes appear, and thus Higgs/Higgs-like particles arise from more origins. Among these models, we find eight new classes of ${\cal N}=1$ supersymmetric Pati-Salam models with gauge symmetries $SU(4)_C\times SU(2)_L\times SU(2)_{R_1}\times SU(2)_{R_2}$ and $SU(4)_C\times SU(2)_{L_1}\times SU(2)_{R}\times SU(2)_{L_2}$, where $d$-stack of D6-branes carries the gauge symmetries $SU(2)_{R_2}$ and $SU(2)_{L_2}$, respectively. The $SU(2)_{L_1/R_1} \times SU(2)_{L_2/R_2}$ can be broken down to the diagonal $SU(2)_{L/R}$ gauge symmetry via bifundamental Higgs fields. In such a way, we for the first time successfully constructed three-family supersymmetric Pati-Salam models from non-rigid D6-branes with extra $d$-stacks of D6-branes as visible sectors. Interestingly, by introducing extra stack of D6-branes to the standard supersymmetric Pati-Salam models, the number of filler brane reduces in general, and eventually the models without any $USp(N)$ gauge symmetry present. This reduces the exotic particles from filler brane intersection yet provides more vector-like particles from ${\cal N}=2$ subsector that are useful in renormalization group equation evolution as an advantage. Moreover, interesting degeneracy behavior with the same gauge coupling ratio exists in certain class of models.

hep-th↗

arXiv2025

Generalized Three-Family Supersymmetric Pati-Salam Models from Type IIA Intersecting D6-Branes

Generalizing three-family chiral fermion conditions to $I_{ac}=-(3+h)$ and $I_{ac'}=h$, with positive integer $h$, we extend the landscape of three-family ${\cal N}=1$ supersymmetric Pati-Salam models in a broader region. Differing from the former investigation with $I_{ac}=-3$ and $I_{ac'}=0$, we do not restrict that the $a$ stack of D6-branes must be parallel to the orientifold image of the $c$-stack along one of the three two-tori. In this investigation, without the simple parallel construction, we find four new classes of supersymmetric Pati-Salam models that are allowed by the extended three generation condition with $I_{ac}=3, I_{ac'}=-6$ and $I_{ac}=-1, I_{ac'}=-2$ through the intersections of $a$- and $c/c'$-branes. Moreover, with the $SU(2)_{L'}$ gauge coupling realized from $SU(2)_{L_1}\times SU(2)_{L_2}$ symmetry breaking, the canonical normalization requirement of the gauge kinetic term provides an alternative approach that can be imposed before the renormalization group equation evolution for $SU(2)_{L'}$ gauge coupling. This turns out to be an effective mechanism to realize the string-scale gauge coupling relation, especially for the new supersymmetric Pati-Salam models with large $g_b/g_a$ ratio. We show that this symmetry-breaking modified renormalization group evolution can highly suppress $g_b/g_a$, and finally realizes string-scale gauge coupling relations for the extended supersymmetric Pati-Salam models as well.

hep-th↗

arXiv2025

Nuclear Ptychoscopy: A Ptychographic Framework for Nuclear Spectroscopy

Accessing both amplitude and phase of nuclear response functions is central to fully characterizing light-matter interactions in the X-ray-nuclear regime. Recent work has demonstrated phase retrieval in two-dimensional time- and energy-resolved spectra, establishing the feasibility of phase-sensitive nuclear spectroscopy. Here, we introduce Nuclear Ptychoscopy, a ptychographic framework that adapts algorithms from coherent diffractive imaging to nuclear spectroscopy, enabling reconstruction of the complex response function by exploiting redundancy in two-dimensional spectra. We develop three complementary reconstruction schemes tailored to distinct experimental scenarios: reconstruction with a known analyzer response, blind reconstruction, and reconstruction incorporating partial prior information. In parallel, we develop geometric analysis techniques that elucidate algorithmic behavior and contribute new tools to ptychography. The framework is validated through experimental data and simulations, demonstrating its versatility across diverse nuclear spectroscopy scenarios and bridging nuclear spectroscopy with ptychography. Beyond advancing quantitative nuclear spectroscopy, our framework opens new opportunities for metrology, coherent control, and quantum applications in the X-ray-nuclear regime.

physics.ins-det↗

arXiv2025

High-Quality Axion Models with the Anomalous $U(1)_X$ Gauge Symmetry

We propose the generic high-quality axion models with anomalous $U(1)_X$ gauge symmetry and vector-like particles. We briefly review the gauge anomaly cancellations via the Green-Schwarz mechanism, study the breaking of the $U(1)_X$ gauge symmetry, as well as derive the Nambu-Goldstone boson, Peccei-Quinn (PQ) axion, and axion decay constant in general. The high-dimensional operators, which break the $U(1)_{PQ}$ global symmetry, have dimension eleven or higher due to the anomalous $U(1)_X$ gauge symmetry, and thus the axion quality problem is solved. In particular, unlike the high-quality axion models with anomaly free $U(1)$ gauge symmetry, we only need to introduce two pairs of vector-like particles. To be concrete, we present three specific models with two pairs of vector-like particles. We show that gauge anomalies in all three models can be canceled via the Green-Schwarz mechanism. To achieve gauge coupling unification, we need to introduce additional vector-like particles only in Model I. We find that gauge coupling unification is achieved at the unification scale around $10^{16}$ GeV with a relative error of less than 1\%. Notably, gauge coupling unification in Model II is achieved naturally with the smallest relative error of 0.1\%.

hep-ph↗

arXiv2025

Bypassing Spin-Analyzing Power Dependence for Quantum Entanglement at Colliders: A Case Study of $\Lambda\bar{\Lambda}$

We study, as a concrete case study using the $\Lambda(\to p\pi^-)\bar{\Lambda}(\to \bar{p}\pi^+)$ system, whether quantum entanglement in fermion pairs produced at colliders can be certified solely using angular information from final-state decays, while remaining independent of the parity-violating decay parameters $\alpha_\Lambda$ and $\alpha_{\bar{\Lambda}}$. Building on a general decomposition of any angular observable in terms of Wigner d-functions, we show that the expectation value must take the form $\mathcal{O}_0+\mathcal{O}_1\alpha_\Lambda+\mathcal{O}_2\alpha_{\bar{\Lambda}}+\mathcal{O}_3\alpha_\Lambda\alpha_{\bar{\Lambda}}$, with coefficients $\mathcal{O}_i$ ($i=0,1,2,3$) linear in the spin-density matrix elements $\alpha_{k,j}\alpha^*_{m,n}$. We obtain the value ranges of observables over the general and separable spaces of $\alpha_{k,j}$, and demonstrate a sufficient entanglement condition for pure states, extending it to mixed states by convexity. In constructing an $\alpha_\Lambda$- and $\alpha_{\bar{\Lambda}}$-independent witness from angular observables alone, we find that there are obstacles to probe quantum entanglement via the inequality-type and ratio-type ways. In particular, for the ratio-type criterion ${\langle A\rangle}/{\langle B\rangle}$, the presence of zeros of $\langle B\rangle$ in both the general and separable spaces of $\alpha_{k,j}(k,j=\pm\frac{1}{2})$ results in identical value ranges of ${\langle A\rangle}/{\langle B\rangle}$ in the two spaces (covering the entire real line), thereby precluding any effective criterion. Finally, for this specific system, we present the successful constructions with additional spin information.

hep-ph↗

arXiv2025

The Light Neutralino Dark Matter at Future Colliders in the MSSM with the Generalized Minimal Supergravity (GmSUGRA)

We perform a detailed investigation of light right-handed slepton bulk regions, together with the Higgs- and $Z$-resonance regimes, in the Minimal Supersymmetric Standard Model (MSSM) with Generalized Minimal Supergravity (GmSUGRA), focusing on the higgsino mass parameter scenario $\mu < 0$, given that the anomalous magnetic moment of the muon may now be consistent with the Standard Model (SM) prediction. A systematic numerical exploration of the parameter space is carried out, where the bulk region is conservatively defined by the mass-splitting ratio \[ \mathcal{R}_{\tilde{\phi}} = \frac{m_{\tilde{\phi}} - m_{\tilde{\chi}_1^0}}{m_{\tilde{\chi}_1^0}} \gtrsim 10\%. \] In particular, we analyze the case in which the right-handed stau ($\tilde{\tau}_R$) emerges as the Next-to-Lightest Supersymmetric Particle (NLSP). We uncover a sizeable parameter space consistent with current experimental bounds, including limits from LHC supersymmetry searches, the Planck 2018 relic density measurement, and direct detection constraints on neutralino-nucleon scattering. This region naturally accommodates bulk annihilation channels mediated by right-handed sleptons. We obtain robust upper bounds on the masses of the lightest neutralino, $m_{\tilde{\chi}_1^0} \lesssim 143~\text{GeV}$, and the right-handed stau, $m_{\tilde{\tau}_R} \lesssim 158~\text{GeV}$. The identified bulk region lies within the prospective reach of forthcoming dark matter direct detection facilities such as LUX-ZEPLIN, as well as future high-energy $e^+e^-$ colliders including FCC$_{\text{ee}}$ and CEPC. Conversely, scenarios with the right-handed selectron as the NLSP have already been excluded by current LHC data. Furthermore, the parameter space consistent with our findings yields contributions to the anomalous magnetic moment of the muon, $a_\mu = (g_\mu - 2)/2$.

hep-ph↗