arXiv subjects

Imtiaz Khan

Publications and source records attributed to Imtiaz Khan.

At least 19 recordsLinked to original sources

arXiv2026

Flip-Flop Shocks and Tori in Bondi-Hoyle-Lyttleton Accretion onto Rotating Kerr-Weyl Black Holes and Their Quasi-Periodic Variability

We present GRHD simulations of Bondi-Hoyle-Lyttleton accretion onto a rotating black hole in Weyl conformal gravity, described by the Kerr-Weyl metric. The equatorial flow is evolved for spins a=0.9M and a=0.5M and several Weyl coefficients, which enter through an effective curvature parameter k, and is compared with Kerr runs sharing the same setup. For the k considered, the horizon, ISCO and test-particle frequencies differ from Kerr by at most ~2%. However, the curvature term grows as kr^2 and acts at the accretion radius R_acc. The flow is controlled by one quantity, eta=|k|R_acc^3/M, the ratio of curvature-induced to Newtonian acceleration at R_acc. For eta<~0.03 a stable shock cone forms, indistinguishable from Kerr. For eta~0.2-0.3 the anti-de Sitter-like term traps shocked gas behind the black hole and drives persistent flip-flop oscillations. For eta>~1.6 the cone is destroyed and an oscillating torus forms. Spin modifies only the inner few gravitational radii and does not change the regime. In strongly deviating models the mean accretion rate is 1.7-3 times the Kerr value and varies by 20-60% rms, versus 0.1-1% in Kerr-like flows. The power spectra show global QPOs with fundamentals at 2.9-4.8 Hz for a 10 Msun black hole, with harmonic ladders whose 3:2 and 2:1 ratios come from one non-sinusoidal oscillation, not resonances. These lie in the low-frequency QPO band and are unrelated to test-particle frequencies (~70-200 Hz). They scale as f_0=xi f_K(R_acc), with xi~0.7-1.1 for stable cones and xi~0.23-0.38 for flip-flop and torus regimes. Strong oscillations would be detectable within seconds for a bright Galactic source. The required |k| exceeds galactic-rotation-curve values by 18-36 orders of magnitude, so a detected shock-driven QPO would measure a local deviation from Kerr, and its absence would constrain |k|.

astro-ph.HE↗

arXiv2026

Primordial black holes and scalar-induced gravitational waves in the supersymmetric 331 model from SU(6)

We study primordial black holes and scalar-induced gravitational waves in the supersymmetric 331 model based on SU(6). The inflaton continues to be the D-flat radial combination of the 331 symmetry-breaking fields Phi and Phi-bar, fields which are already accountable for the CMB branch. A gauge-invariant contribution that is localised in the Kaehler frame function causes the force in the Einstein frame to decrease over a finite range of the field and results in a temporary nonattractor phase. We calculate the supergravity potential and the radial metric, evolve the background and the Mukhanov-Sasaki modes, and assess the neutral covariant Hessian along the local region. The CMB trajectory is still in agreement with the present observational constraints while the curvature spectrum attains a value of P_zeta ~ 5.38 x 10^-3 when k ~ 1.88 x 10^13 Mpc^-1. The enhanced spectrum leads to a primordial black hole distribution with a mass comparable to that of an asteroid and to a maximum in the scalar-induced gravitational wave signal at a frequency of 3.17 x 10^-2 Hz with Omega_GW,0 h^2 ~ 9.41 x 10^-11. The local geometry also results in a clear hierarchy of sensitivities. The gravitational wave spectrum changes smoothly as one moves along nearby trajectories whereas the Gaussian tail of the primordial black hole distribution changes much more rapidly. The positive eigenvalues of the neutral transverse Hessian remain throughout the reference trajectory. A Gaussian critical collapse calculation yields a reference integrated primordial black hole fraction of near 9.08 x 10^-3, while recent nonlinear studies suggest significant corrections to the statistics of rare collapses at the scalar power achieved here.

hep-ph↗

arXiv2026

The compressed bino--wino dark matter in the GmSUGRA and the LHC soft-lepton searches

The search for electroweak supersymmetric particles remains an important part of the LHC program since neutralinos and charginos with masses around a few hundred GeV are still compatible with the present constraints in compressed spectra. Run-2 searches for the ``golden channel'', $pp\to\widetildeχ_2^0\widetildeχ_1^\pm\to\widetildeχ_1^0 Z^{(*)}\widetildeχ_1^0 W^{\pm(*)}$, have reported mild excesses in parts of the soft two- and three-lepton data, with the corresponding simplified-model interpretations emphasizing $m_{\widetildeχ_2^0}\simeq m_{\widetildeχ_1^\pm}\gtrsim200$~GeV and a neutralino mass difference near $20$~GeV. We study this configuration in the Minimal Supersymmetric Standard Model (MSSM) with the Generalized minimal Supergravity (GmSUGRA) boundary conditions, imposing the Higgs, flavor, collider, relic-density and direct-detection constraints relevant to the spectrum. For both signs of $μ$, the solutions compatible with the Planck experiment contain an almost pure bino $\widetildeχ_1^0$ with mass about $260$--$266$~GeV and a nearly degenerate wino-like $\widetildeχ_2^0/\widetildeχ_1^\pm$ pair near $280$~GeV. The resulting splitting, $Δm_{21}\simeq18.5$--$19.1$~GeV, lies in the mass-difference region probed by the ATLAS and CMS soft-lepton searches and places the $Z^{(*)}/W^{(*)}$ decays below the on-shell gauge-boson thresholds. The same compressed hierarchy keeps the wino states thermally populated during freeze-out, so bino-wino coannihilation yields a neutralino relic abundance consistent with the Planck experiment while the surviving solutions remain compatible with the direct-detection experimental bounds. Thus, the GmSUGRA boundary conditions provide a high-scale realization of the compressed bino-wino spectrum relevant to the LHC soft-lepton channel.

hep-ph↗

arXiv2026

Thermal Higgsino Dark Matter in GmSUGRA for the LZ Event and Solar-Neutrino Constraint

We study the thermal Higgsino dark matter in the Minimal Supersymmetric Standard Model (MSSM) with Generalized Minimal Supergravity (GmSUGRA) boundary conditions after the high-recoil event reported by the LUX--ZEPLIN experiment and the subsequent solar-neutrino limits inferred from IceCube data. The Higgs sector is implemented in a NUHM2-type parametrization with $μ$ and $m_A$ as inputs, while the supersymmetry breaking soft terms obey the non-universal GmSUGRA relations. The numerical scan contains a Planck-compatible Higgsino branch near the thermal mass, with the neutral-state splitting extending continuously from the few-hundred-keV region to the MeV scale. The part of this branch with $\dmchi\simeq0.3$--$0.4$ MeV overlaps the kinematic interval relevant to the LZ event, but is disfavored by the current solar-capture reinterpretations for a full-density thermal Higgsino. The same high-scale branch persists at larger splittings, including representative spectra with $\dmchi\simeq0.85$, $1.10$, and $1.34$ MeV, beyond the quoted solar-capture limits. Our results demonstrate that the mass and sub-MeV splitting favored by the LZ high-recoil interpretation can be realized dynamically within a GUT-motivated supersymmetric construction, without imposing the neutralino compression as a weak-scale input. The combined data therefore select different parts of a common GmSUGRA Higgsino branch rather than excluding the thermal Higgsino construction itself.

hep-ph↗

arXiv2026

LZ-Motivated Pseudo-Dirac Higgsinos in the Supersymmetric 331 Model from the Supersymmetric \texorpdfstring{$SU(6)$}{SU(6)} GUT Model

The high-recoil event reported by LUX--ZEPLIN motivates a neutral electroweak state with an inelastic splitting in the sub-MeV range. We propose supersymmetric 331 model from the supersymmetric $SU(6)$ GUT model, and we study the electroweakino sector relevant to this recoil. Above the $331$-breaking scale hypercharge is not an independent gauge factor, and the leading bino--wino cancellation is replaced by a relation between the physical $U(1)_X$ and $SU(3)_L$ gaugino invariants, $I_X=-I_L$. A singlet--adjoint gauge-kinetic source also correlates the colored invariant. We diagonalize the neutral gauge--Higgs fermion sector of the renormalizable model and determine the tree-level Higgsino splitting without introducing an effective bino mass by hand. The required solutions form a continuous locus in the gaugino and $331$-breaking parameters. At the reference point, the solution lies close to the leading sum rule, while variation of the $331$-breaking coupling moves the locus continuously. The same calculation tests the ordering of the additional neutral states, the gauge/gaugino contribution to the $331$-breaking scalar mass, and the gravitino ordering. We compare this construction with recent $SU(5)$, singlino-assisted, electroweak-multiplet, nuclear-response and solar-capture analyses of the LZ event.

hep-ph↗

arXiv2026

Elastic toroidal vector dark matter through a dark photon in the LUX-ZEPLIN high recoil window

The 2026 LUX-ZEPLIN search reports one nuclear recoil candidate at $248\pm23_{\rm stat}\pm23_{\rm sys}~\mathrm{keV}$ in an extended window reaching about $270~\mathrm{keV}$. We consider elastic scattering of neutral complex vector dark matter through its dimension-six toroidal electromagnetic moment and find appreciable spectral weight in this recoil region. The nonrelativistic reduction correlates $\mathcal O_{17}$ and $\mathcal O_{20}$, relating a coherent charge branch to a transverse spin tensor branch. For $m_X=1~\mathrm{TeV}$, natural xenon exhibits a broad high recoil maximum at $204.8$ to $206.6~\mathrm{keV}$ and retains $80.4$ to $85.4\%$ of this maximum at $248~\mathrm{keV}$. Resolving the interaction through a dark photon relates the high-to-low recoil ratio to the mediator mass. A renormalizable $SU(2)_X\times U(1)_D$ realization stabilizes the complex vector by a residual $Z_3$ gauge symmetry and generates the toroidal current through vectorlike messengers carrying a physical CP phase. For a benchmark with $m_X=0.998~\mathrm{TeV}$ and $m_{A'}=0.450~\mathrm{GeV}$, $R(248)/R(50)=1.43$ for GCN and $1.21$ for JJ55, while the odd $A$ xenon fraction remains above $99.9\%$. The response level ratio between the $350$ to $590~\mathrm{keV}$ and $100$ to $270~\mathrm{keV}$ intervals is about $0.46$ at this benchmark. The tensor branch is absent for spin zero argon, whereas annual modulation remains at the few percent level. The resulting spectral, isotope, target, timing, mediator, and high energy dependences give correlated tests of an elastic tensor interpretation of the LZ recoil.

hep-ph↗

arXiv2026

Floquet-spin-orbit compensation and flat- and quadratic-band contact in the $α$-$T_3$ lattice

We investigate Floquet--spin-orbit compensation in the three-band $α$-$T_3$ system, which interpolates between graphene at $α=0$ and the dice lattice at $α=1$. By tuning the interplay between an off-resonant circularly polarized optical field and intrinsic spin--orbit coupling, we identify three distinct pairwise band-degeneracy conditions in the quasienergy spectrum: (i) valley--spin degeneracy, (ii) spin--band degeneracy, and (iii) flat--dispersive band degeneracy. The flat band is not an artifact of a two-band reduction but rather an exact property of the continuum Hamiltonian at this compensation point, where the complete three-band Hamiltonian supports a momentum-independent dark state. A winding-two low-energy Hamiltonian and a finite-momentum Berry-curvature maximum, whose radius scales as the square root of the detuning, emerge from detuning this contact. We further show that the intrinsic transverse thermoelectric response encodes these spectrum patterns. The flat- and quadratic-band degeneracy can be predicted for $0<α<1/2$ because the two response scales linked to the linear contacts have a monotonic ratio independent of the common spin--orbit energy scale. This allows an inverse determination of $α$ and of the common spectral scale. The analytical results are confirmed by full three-band Kubo calculations, which also define the regime in which this inverse characterization is still observable. These results connect an experimentally accessible, Berry-curvature-sensitive thermoelectric response to tunable Floquet--spin--orbit band geometry.

cond-mat.mes-hall↗

arXiv2026

Nuclear interference versus dark sector excitation in the 248 keV LUX-ZEPLIN recoil candidate

The 2026 LUX-ZEPLIN (LZ) high energy nuclear recoil search reports one event at $248\pm23_{\rm stat}\pm23_{\rm sys}~\mathrm{keV}$ and finds the elastic isovector interaction $\mathcal L_6^v$ locally favored at about $3.3σ$ in the heavy dark matter regime. We examine whether this recoil scale can arise from resolved nuclear response within the elastic interaction and compare its spectral, target, and annual modulation behavior with endothermic dark sector excitation. Covariant matching correlates four Galilean operators, removes the longitudinal spin response algebraically, and fixes interference between density and orbital spin orbit amplitudes. The GCN and JJ55 xenon shell model calculations give a second natural xenon cancellation at $211$ and $214~\mathrm{keV}$. In the heavy mass regime, its position changes by less than $0.01~\mathrm{keV}$ from a dark matter mass of $200~\mathrm{GeV}$ to the asymptotic limit. A curvature weighted isotope centroid reproduces the position and residual depth of the natural xenon minimum. Direct $^{40}$Ar calculations shift the nuclear feature to about $350$ and $425~\mathrm{keV}$, whereas endothermic excitation follows reduced mass scaling set by the dark state splitting. At a dark matter mass of $1~\mathrm{TeV}$, the endothermic Ar to Xe scale ratio is $1.082$, compared with $1.63$ to $2.01$ for the nuclear calculations. Elastic scattering gives a few percent annual modulation in the adopted halo model, while endothermic solutions near the maximum laboratory halo speed show much larger seasonal variation. These scaling and timing behaviors provide tests of a target-dependent nuclear cancellation against an excitation energy set by dark sector kinematics.

hep-ph↗

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 $((Φ,\barΦ,S))$ 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

Finite-duration non-slow-roll effects in inflationary production of ultralight vector dark matter

Inflationary production of ultralight vector dark matter can be amplified by a brief non-slow-roll phase, yet instantaneous mass transitions generate ultraviolet ringing and leave finite-time predictions unresolved. We replace the sharp transition with a smooth profile and derive the momentum-response kernel of the longitudinal mode. Finite duration preserves the infrared enhancement, suppresses modes that resolve the transition, and introduces a profile-dependent correction to the relic abundance. After fixing the dark matter abundance, the induced gravitational-wave signal retains an independent transverse-traceless source dependence, so abundance rescaling alone leaves residual profile information. Numerical mode evolution and radiation-era tensor integration support the finite-width treatment. Transition duration therefore links microscopic inflationary dynamics to ultralight vector abundance and its low-frequency gravitational-wave signal.

hep-ph↗

arXiv2026

CMB Test of the Higgs Origin of Dark-Photon Dark Matter

Laboratory searches determine the mass and kinetic mixing of dark-photon dark matter. The CMB isocurvature probes how its abundance depends on inflationary initial conditions. We formulate this dependence through the logarithmic response $q_{\rm eff}=\partial\ln n_{A'}/\partial\ln r_i$ of the final vector number to the primordial dark-Higgs displacement. For a smooth local abundance map, the separate-universe relation connects $q_{\rm eff}$ to the CDM isocurvature. The uncorrelated Planck limit applies when the dark Higgs is a light and energetically subdominant spectator with weak inflaton mixing. In the quadratic conserved-number branch displacement-independent transfer gives $q_{\rm eff}=2$. The all-dark-matter bound then requires $r_i/H_*>3.5\times10^4$. We calculate the dynamical map by evolving the radial mode and its tangent response through a smooth Abelian-Higgs crossover. The post-transition orbit gives the comoving action. The map contains positive, negative, and near-zero responses at finite transferred action. Tanh and error-function crossovers retain these branches. A thermal-mass profile and finite inflationary quartics shift their locations continuously. Stochastic duration and radiative stability then determine realization regions. Early symmetry breaking and momentum redshift add the remaining conditions. Low-energy measurements and the CMB response can distinguish Higgsed-vector cosmologies with identical present-day $(m_{A'},ε)$ and relic abundance.

hep-ph↗

arXiv2026

Post-Inflationary Quenched Production of Axion SU(2) Dark Matter

The relic abundance of vector dark matter originating from an inherited axion-$SU(2)$ condensate is typically determined by implementing an adiabatic matching procedure across the symmetry-breaking transition. We demonstrate that this outcome does not arise in the generic case. The post-inflationary crossover can instead be formulated as a dynamical quantum quench problem, in which the residual coherent component of the field is characterized by a survival factor that induces an $\mathcal{O}(1)$ renormalization of the standard abundance relation. Expressed in conformal time, the spatially homogeneous condensate dynamics reduce to those of a canonical oscillator with quartic and quadratic self-interactions. This representation enables an analytic determination of the matching conditions across the symmetry-breaking transition, the derivation of the corresponding quench work and excess energy relations, and a quantitative validation of the coherent sector description via numerical simulations in both Minkowski and Friedmann--Robertson--Walker backgrounds. We also formulate the homogeneous fluctuation theory via the diagonal-$SO(3)$ $1 \oplus 3 \oplus 5$ decomposition and isolate a soft traceless-symmetric quintet with a $k=0$ vacuum obstruction, a regulated ultraviolet adiabatic bound, and a positive quartic stabilization term. Collectively, these results refine the theoretical description of inherited non-Abelian dark matter production and establish the necessary infrared framework for subsequent investigations of finite-$k$ gauge--Higgs transfer dynamics.

hep-ph↗

arXiv2026

Thermal Alignment as a Pathway to Axion Dark Matter

Thermal alignment cannot be inferred from the axion mean alone because the dissipative bath that erases the initial displacement also prepares field and momentum fluctuations. We derive a phase space covariance bound that quantifies this memory and noise relation in the full inertial Langevin system. A renormalizable finite temperature gauge theory then links the temporary susceptibility, the Chern-Simons bath, bath termination, and the stable late potential through one scalar transition. Solving the coupled mean and covariance evolution demonstrates erasure of the incoming state, release of a causal infrared spectrum, and capture of the full phase space distribution as axion dark matter across the transition interval. Thermal alignment therefore determines a calculable late axion state rather than a homogeneous displacement alone.

hep-ph↗

arXiv2026

Conformal dark matter and MHz gravitational waves

A localized enhancement of the primordial curvature spectrum can leave two distinct relics: gravitationally produced conformal-fermion dark matter and a scalar-induced stochastic gravitational-wave background. We show that the dark-matter abundance fixes the scalar normalization through the cubic moment of the curvature spectrum, while the induced tensor signal probes its quadratic convolution. This closes the usual normalization freedom in scalar-induced gravitational-wave templates and ties the MHz signal directly to the dark-matter mass, peak scale, and spectral width. A concrete single-field realization demonstrates this mechanism: a Mukhanov--Sasaki evolution produces a broad MHz background that sits safely below the Gaussian primordial-black-hole threshold. In this construction, a null high-frequency search becomes a lower bound on the conformal-fermion mass, while a detection has to reproduce the relic abundance, peak frequency, amplitude, and width from one primordial feature. The result is a testable link between small-scale inflationary structure, superheavy dark matter, and laboratory MHz gravitational-wave searches

astro-ph.CO↗

arXiv2026

Parametric Resonance of Higgsed Vector Dark Matter: Inflationary Initial Conditions and Sourced Displacements

Parametric resonance in a Higgsed Abelian sector provides an efficient mechanism for producing vector dark matter, but its viability depends crucially on the origin of the initial dark-Higgs displacement that seeds the resonance. In this work, we investigate this initial-condition problem in a weakly coupled Abelian-Higgs theory with potential $V=λ_4(ϕ^2-v^2)^2/4$, using the calibrated nonlinear broad-resonance relic map together with a stochastic inflationary analysis of the dark-Higgs condensate. We show that a minimal light-spectator realization fails under standard inflationary duration: while broad resonance and isocurvature constraints require $ ϕ_0/H_I \gtrsim 3.3\times10^4, $ the stochastic equilibrium and finite-duration random walk produce only $ ϕ/H_I=\mathcal O(1). $ This large displacement mismatch is robust against order-of-magnitude variations in the resonance efficiency and broadness threshold, establishing a model-independent obstruction to the stochastic branch. We then identify a distinct classically sourced branch, generated by a negative Hubble-induced mass, in which the condensate tracks a time-dependent minimum, $ ϕ_0=κH_*/\sqrt{λ_4}, $ and the radial fluctuation remains heavy during inflation. In this case, the fixed-$e/λ_D$ relic scaling shifts from $ m_X\propto λ_4^{5/8}H_I^{-3/2} $ to $ m_X\propto κ^{-3/2}λ_4 H_*^{-3/2}. $ We derive the simultaneous consistency conditions for this sourced branch, including broad resonance, adiabatic tracking, perturbativity, sub-Planckian displacement, thermal non-erasure, spectator backreaction, and control of inflationary vector fluctuations. Our results establish that Higgsed-vector resonance is not merely a dark-matter production mechanism, but a sensitive probe of the inflationary and reheating dynamics that determine its initial conditions.

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, $V_{\rm MS}=Aφ^4[\ln(φ/μ)-1/4]$, with $(A,μ)$ mapped to the scalar mass and vacuum condensate. Embedding this sector in the leading curved-space EFT introduces the independent Wilson coefficients $λ$ and $ξ$, 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 $μ$--$λ$ 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-$ξ$ attractor behavior with a logarithmic imprint tied directly to nonperturbative trace-anomaly matching.

hep-ph↗

arXiv2026

Nonlinear Hall effect in Floquet-driven monolayer 1T$'$-MoS$_2$

We study the nonlinear Hall effect in Floquet-driven monolayer $1T'$-MoS$_2$, a low-symmetry quantum spin Hall material whose tilted Dirac bands sustain an intrinsic Berry-curvature dipole without the need for strain or trigonal warping. We show that off-resonant circularly polarized light offers a way to control both the sign and the magnitude of the nonlinear Hall response through optically induced topological phase transitions using a Floquet effective Hamiltonian and nonlinear semiclassical transport theory. We show that the anisotropic crystal symmetry enforces a selection rule in which the Berry-curvature dipole elements satisfy $D_x\equiv0$, while a finite $D_y$ originates from the intrinsic band tilt. The Berry curvature is recreated in momentum space as the Floquet drive successively inverts individual spin-valley sectors, resulting in an identical sign reversal of the nonlinear Hall conductivity and the Berry-curvature dipole at each bulk gap closing. In contrast, tuning the band tilt modifies only the magnitude of the response without changing its sign, establishing the observed sign reversal as an unambiguous transport signature of genuine Floquet topological phase transitions. We further show that the nonlinear Hall response can be controlled by the driving strength, perpendicular electric field, Fermi energy, and temperature, providing multiple experimental knobs for observation. Our findings establish the sign of the nonlinear Hall response as a universal transport fingerprint of Floquet-engineered topology and point to monolayer $1T'$-MoS$_2$ as a viable platform for all-electrical detection of nonequilibrium topological phases.

cond-mat.mes-hall↗

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 μ. To isolate genuine bulk annihilation from coannihilation, we impose the mass-splitting condition $\mathcal{R}_{\tildeϕ} \equiv (m_{\tildeϕ}-m_{\tildeχ_1^0})/m_{\tildeχ_1^0}\gtrsim 10\%$. 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 $m_{\tildeχ_1^0}\lesssim 110~{\rm GeV}$ and $m_{\tildeτ_1}\lesssim 120~{\rm GeV}$. 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 μ>0. Conversely, for μ<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-μ Pati-Salam framework as a predictive, testable scenario for upcoming dark matter and lepton collider experiments

hep-ph↗