Probing Graviton Mass with MeerKAT PTA and SKA--PTA Forecasts

We present constraints on the graviton mass using the 4.5-year data release from the MeerKAT Pulsar Timing Array (MPTA) and provide forecasts for the upcoming Square Kilometre Array PTA (SKA--PTA). By modeling the modified dispersion relation and the corresponding tensor correlation function for massive gravitons, we perform Bayesian inference on the angular-correlation measurements under three noise configurations (DATA, ER, ALT). Our 90\% credible upper limits on the graviton mass are $m_g < 2.10 \times 10^{-23}\,\mathrm{eV}/c^{2}$ (DATA), $m_g < 2.58 \times 10^{-23}\,\mathrm{eV}/c^{2}$ (ER), and $m_g < 2.25 \times 10^{-23}\,\mathrm{eV}/c^{2}$ (ALT). Including monopolar and dipolar contributions does not significantly alter these bounds, confirming that the constraints are driven by the quadrupolar tensor correlation. All results remain fully consistent with general relativity. For SKA--PTA, we forecast sensitivities down to $m_g \sim 10^{-24}\,\mathrm{eV}/c^{2}$ with a 10-year observing baseline and $m_g \sim 10^{-25}\,\mathrm{eV}/c^{2}$ with a 50-year observing baseline, representing order-of-magnitude improvements over current limits. This work demonstrates the power of current and future PTA observations to test fundamental aspects of gravity in the nanohertz band.