Joint Mass-Radius and Magnetic-Geometry Inference of PSR J0740+6620

X-ray pulse-profile modeling can measure neutron-star radii, but its physical interpretation remains limited by the largely phenomenological description of the surface hotspots. Here we connect the X-ray hotspots directly to the pulsar magnetospheric structure and jointly infer the mass, radius, and magnetic geometry of the massive millisecond pulsar PSR J0740+6620 from \emph{NICER} and \emph{XMM-Newton} observations. Using a GPU-accelerated implementation, we compare two low-dimensional magnetic configurations that can produce non-antipodal emission: a centered axisymmetric dipole–quadrupole and a shifted dipole. The shifted-dipole model is decisively favored under the adopted priors, with $\mathrm{\Delta }\ln Z=5.65$ (Bayes factor $\sim 285$), and yields $M=2.059_{-0.069}^{+0.068}{M}_{\odot }$ and $R=13.28_{-1.07}^{+1.47}\mathrm{k}\mathrm{m}$, broadly consistent with previous phenomenological analyses, while requiring nearly symmetric heating of the two polar caps. Both the marginalized shifted-dipole posterior and the timing-compatible representative require an effective X-ray-emitting footprint much smaller than the nominal force-free polar cap calibrated for a centered dipole. This compact footprint is not reproduced by our exploratory photon-conversion estimates and instead points to missing physics in the mapping from magnetospheric currents to observable X-ray emission. Our results show that physically motivated hotspots can preserve the mass–radius inference while turning hotspot morphology into a probe of pulsar magnetospheric structure and emission physics.