Detecting new fundamental fields with Pulsar Timing Arrays

Strong evidence of the existence of the Stochastic Gravitational-Wave Background (SGWB) has been reported by the NANOGrav, PPTA, EPTA and CPTA collaborations. The Bayesian posteriors of the Gravitational-Wave Background (GWB) amplitude and spectrum are compatible with current astrophysical predictions for the GWB from the population of supermassive black hole binaries (SMBHBs). In this paper, we discuss the corrections arising from the extra scalar or vector radiation to the characteristic dimensionless strain in PTA experiments and explore the possibility to detect charges surrounding massive black holes, which could give rise to SGWB with vector or scalar polarizations. The parametrized frequency-dependent characteristic dimensionless strain is used to take a Bayesian analysis and the Bayes factor is also computed for charged and neutral SMBHBs. The Bayesian posterior of GWB tensor amplitude is $\log_{10} A_T=-14.85^{+0.26}_{-0.38}$ and spectral exponent $\alpha=-0.60^{+0.32}_{-0.36}$. The Bayesian posterior for vector or scalar amplitude $A_{V, S}$ is nearly flat and there is nearly no constraint from the current observation data. The Bayesian factor is $0.71$ far less than 100, so the current observation can not support the existence of the charged SMBHB.