On spatial variations of the electron-to-proton mass ratio in the Milky Way

(Abridged) Radio-astronomical observations of molecular cores in lines of NH3 (J,K)=(1,1), CCS J_N=2_1-1_0, HC3N J=5-4, and N2H+ J=1-0 are used to measure the relative radial velocity offsets, Delta V, between the NH3 (1,1) and other molecular transitions. Robust statistical analysis is applied to the n=207 individual measurements in the Perseus molecular cloud (PC), the Pipe Nebula (PN), and the infrared dark clouds (IRDCs) to deduce the mean value of Delta V and its uncertainty. The measured values of Delta V from the PC, PN, and IRDCs show statistically significant positive velocity shifts between the line centers of NH3 and other molecules. The most accurate estimates are obtained from subsamples of the NH3/CCS pairs observed in the PC (n=21) and the PN (n=8), Delta V = 36+/-7_stat+/-13.5_sys} m/s and 53+/-11_stat+/-13.5_sys m/s, respectively, and from the n=36 NH3/N2H+ and n=27 NH3/HC3N pairs observed in the IRDCs, Delta V = 148+/-32_stat+/-13.6_sys m/s and 115+/-37_stat+/-31_sys m/s, respectively. Being interpreted in terms of the electron-to-proton mass ratio variation, this gives Delta mu/mu = (4-14)10^{-8}, which is an order of magnitude more sensitive than previous astronomical constraints on this quantity.