Realistic neutron stars in the constant-Q branch of f(Q) gravity

We investigate the hydrostatic equilibrium and global structure of neutron stars within symmetric teleparallel gravity, where gravitational interactions are mediated by the non-metricity scalar $Q$. Working within the metric-affine formulation, we adopt the regular, constant-$Q$ branch ($Q = Q_*$) of $f(Q)$ gravity, which preserves regularity at the stellar centre while maintaining explicit dependence on the non-linear functional form through $f(Q_*)$ and its derivatives. We propose three novel non-linear $f(Q)$ extensions: (i) a Born-Infeld-inspired model, (ii) a Hu--Sawicki analogue, and (iii) a Tsujikawa-inspired model. Incorporating state-of-the-art realistic unified equations of state, namely GPPVA(DD2) and SLy4, we numerically solve the modified Tolman-Oppenheimer-Volkoff equations and evaluate stellar stability via the Harrison-Zel'dovich-Novikov criterion. The Born-Infeld and Hu-Sawicki analogues smoothly recover the general relativistic limit as their control parameters increase, predicting stellar radii for low-mass objects ($M < 2.0\,M_\odot$) that match observational constraints from X-ray binaries and GW170817; however, their maximum masses remain capped below $2.43\,M_\odot$ (DD2) and $2.06\,M_\odot$ (SLy4). Conversely, the Tsujikawa-inspired model significantly stiffens the effective gravitational coupling, accommodating massive compact objects up to $\sim 3.36\,M_\odot$ and offering a viable physical origin for the $2.59_{-0.09}^{+0.08}\,M_\odot$ secondary object in GW190814, albeit at the expense of overpredicting radii for typical low-mass neutron stars. These contrasting behaviours demonstrate a key phenomenological complementarity between maximum mass and radius bounds within the constant-$Q$ framework, highlighting the utility of multimessenger observations in constraining non-linear non-metricity gravity.