Minimal supersymmetry confronts R_b, A^b_(FB) and m_h

We study the impact of the measurements of three sets of observables on the parameter space of the constrained minimal supersymmetric Standard Model (cMSSM), its slightly general variant, the non-universal scalar model (NUSM), and some selected benchmark points of the 19-parameter phenomenological MSSM (pMSSM): ($i$) the direct measurement of the Higgs boson mass $m_h \approx 125$ GeV at the CERN Large Hadron Collider (LHC); ($ii$) $Z$ boson decay width in the $b \bar{b}$ channel normalized to its hadronic width ($R_b$), and the forward-backward asymmetry on the $Z$-peak in the same channel $(A_{\rm FB}^b)$; and ($iii$) several $B$-physics observables, along with $(g-2)$ of muon. In addition, there are constraints from non-observation of superparticles from direct searches at the LHC. In view of the recently re-estimated standard model (SM) value of $R_b$ with improved higher order corrections, the measured value of $R_b$ has a 1.2$\sigma$ discrepancy with its SM value, while the corresponding discrepancy in $A_{\rm FB}^b$ is 2.5$\sigma$. MSSM contributions from light superpartners improve the agreement of $R_b$ but worsen that of $A_{\rm FB}^b$. We project this ($R_b$-$A_{\rm FB}^b$) tension {\em vis-\`{a}-vis} the constraints arising from other observables in the parameter space of cMSSM and NUSM. We also consider a few well-motivated pMSSM benchmark points and show that pMSSM does not fare any better than the SM.