Revisiting the realistic intersecting D6-brane model with positive and negative <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>μ</mml:mi></mml:mrow></mml:math> terms

In light of current constraints from supersymmetry (SUSY) searches within the LHC as well as findings from direct dark matter detection experiments such as LUX-ZEPLIN (LZ), we revisit the three-family Pati-Salam model derived from intersecting D6-branes in type IIA string theory compactified on the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msup><a:mi>T</a:mi><a:mn>6</a:mn></a:msup><a:mo>/</a:mo><a:mo stretchy="false">(</a:mo><a:msub><a:mi mathvariant="double-struck">Z</a:mi><a:mn>2</a:mn></a:msub><a:mo>×</a:mo><a:msub><a:mi mathvariant="double-struck">Z</a:mi><a:mn>2</a:mn></a:msub><a:mo stretchy="false">)</a:mo></a:math> orientifold, known for its realistic low-energy phenomenology. Because the muon anomalous magnetic moment might be in accordance with the Standard Model prediction, we conduct a comprehensive scan over the model’s parameter space for each sign of the Higgsino mass parameter, <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi>μ</g:mi><g:mo>&lt;</g:mo><g:mn>0</g:mn></g:math> and <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi>μ</i:mi><i:mo>&gt;</i:mo><i:mn>0</i:mn></i:math>. We found that a gravitino mass is typically greater than 1.5 TeV in both scenarios while simultaneously satisfying the LHC SUSY bounds, B-physics observables, along with the Higgs mass constraint. Within the experimentally viable region of the parameter space, the mass spectra of sparticles are found to fall within the following ranges: Gluinos lie in the range of 2–18 TeV, the first- and second-generation squarks and sleptons span 3–16 TeV and 1–6 TeV, respectively. For third-generation sfermions, the lightest stop, which can satisfy the dark matter relic density through neutralino-stop coannihilation consistent with the Planck <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mrow><k:mn>5</k:mn><k:mi>σ</k:mi></k:mrow></k:math> bounds, has a mass in the range of 0.5–1.2 TeV. Note that the lightest neutralino will be as heavy as 2.9 TeV. Additionally, the lightest stau could be as light as 200 GeV, as well as heavy up to 5.2 TeV. We further identify several viable mechanisms, including multiple coannihilation channels and resonance mechanisms, and the observed dark matter relic abundance is successfully realized.