Doubling NIRSpec/IFS capability to calibrate the single-epoch black hole mass relation at high redshifts

The recent discovery of a large population of overmassive black holes (BHs) in the early Universe challenges the validity of the BH-host galaxy coevolution framework. However, the reliability of the estimated BH masses (M BH) is being questioned, as these are typically derived using single-epoch (SE) relations calibrated locally. Calibrating SE relations at high redshift would therefore enable more accurate M BH estimates and help identify potential biases. In this work, we release a data-reduction technique for JWST/NIRSpec IFU observations that doubles the effective wavelength coverage, enabling detection of otherwise inaccessible emission. Whenever adjacent dispersers are required, observers should carefully evaluate the tradeoff between integrating longer in the bluer configuration alone versus distributing the exposure time across two dispersers. We apply this pipeline to a sample of 5 quasars at z~2 with M BH independently measured through reverberation mapping (RM). This enables a joint analysis of both H β and H α; the latter lying beyond the nominal wavelength range. We assess the reliability of the most widely adopted SE calibrations, finding that Hβ yields the closest agreement with RM-based M BH estimates, whereas Hα-based estimators exhibit a larger scatter. For the least massive BH in our sample (MBH,RM ~ 10^7.5M⊙), which is accreting at a rate close to the Eddington limit ( λEdd=0.8), all SE calibrators overestimate M BH,RM by one order of magnitude. This may indicate a systematic overestimation of M BH for highly accreting BHs at high redshift. Finally, we provide the first high-redshift SE calibration based on Hα and Hβ. Although a larger sample is needed to reduce the uncertainties, our calibration can already be applied to the newly discovered BH population in the early Universe.