We explore the low-scale implications of the Pati-Salam Model including the TeV scale right-handed neutrinos interacting and mixing with the MSSM fields through the inverse seesaw (IS) mechanism in light of the muon anomalous magnetic moment (muon $g-2$) resolution and highlight the solutions which are compatible with the quasi-Yukawa unification condition (QYU). We find that the presence of the right-handed neutrinos causes heavy smuons as $m_{\tilde{\mu }}\gtrsim 800\mathrm{GeV}$ in order to avoid tachyonic staus at the low scale. On the other hand, the sneutrinos can be as light as about 100 GeV, and along with the light charginos of mass $\lesssim 400\mathrm{GeV}$, they can yield such large contributions to muon $g-2$ that the discrepancy between the experiment and the theory can be resolved. These solutions also require $m_{{\tilde{\chi }}_1^{\pm }}\lesssim 400\mathrm{GeV}$ and $m_{{\tilde{\chi }}_1^0}\lesssim 200$. We also discuss such light chargino and neutralino along with the light stau ($m_{\tilde{\tau }}\gtrsim 200\mathrm{GeV}$) in the light of current LHC results. Besides, the gluino mass lies in a range $\sim [2.5–3.5]\mathrm{TeV}$, which is tested in near future experiments. In addition, the model predicts relatively light Higgsinos ($\mu \lesssim 700\mathrm{GeV}$); hence, the second chargino mass is also light enough ($\lesssim 700\mathrm{GeV}$) to contribute to muon $g-2$. Light Higgsinos also yield less fine-tuning at the electroweak scale, and the regions compatible with muon $g-2$ restrict ${\mathrm{\Delta }}_{\mathrm{EW}}\lesssim 100$ strictly, and this region also satisfies the QYU condition. In addition, the ratios among the Yukawa couplings should be $1.8\lesssim y_t/y_b\lesssim 2.6$, $y_{\tau }/y_b\sim 1.3$ to yield correct fermion masses. Even though the right-handed neutrino Yukawa coupling can be varied freely, the solutions bound its range to $0.8\lesssim y_{\nu }/y_b\lesssim 1.7$.

• Received 23 June 2017

DOI:https://doi.org/10.1103/PhysRevD.97.055007

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

Published by the American Physical Society