Reassessing the constraints from SH0ES extragalactic Cepheid amplitudes on systematic blending bias

The SH0ES collaboration Hubble constant determination is in a similar to 5 sigma difference with the Planck value, known as the Hubble tension. The accuracy of the Hubble constant measured with extragalactic Cepheids depends on robust stellar-crowding background estimation. Riess et al. (R20) compared the light-curve amplitudes of extragalactic and MW Cepheids to constrain an unaccounted systematic blending bias, gamma=-0.029 +/- 0.037mag, which cannot explain the required, gamma=0.24 +/- 0.05mag, to resolve the Hubble tension. Further checks by Riess et al. demonstrate that a possible blending is not likely related to the size of the crowding correction. We repeat the R20 analysis, with the following main differences: (1) we limit the extragalactic and MW Cepheids comparison to periods gamma less than or similar to 50d, since the number of MW Cepheids with longer periods is minimal; (2) we use publicly available data to recalibrate amplitude ratios of MW Cepheids in standard passbands; (3) we remeasure the amplitudes of Cepheids in NGC 5584 and NGC 4258 in two Hubble Space Telescope filters (F555W and F350LP) to improve the empirical constraint on their amplitude ratio A(555)/A(350). We show that the filter transformations introduce an approximate to 0.04mag uncertainty in determining gamma, not included by R20. While our final estimate, gamma=0.013 +/- 0.057mag, is consistent with the value derived by R20 and is consistent with no bias, the error is somewhat larger, and the best-fitting value is shifted by approximate to 0.04mag and closer to zero. Future observations, especially with JWST, would allow better calibration of gamma