[O III]λλ4960,5008 doublet are often the strongest narrow
emission lines in starburst galaxies and quasi-stellar objects (QSOs), and thus
are a promising probe to possible variation of the fine-structure constant
α over cosmic time. Previous such studies using QSOs optical spectra
were limited to z<1. In this work, we constructed a sample of 40 spectra of
Lyα emitting galaxies (LAEs) and a sample of 46 spectra of QSOs at
1.09<z<3.73 using the VLT/X-Shooter near-infrared spectra publicly available.
We measured the wavelength ratios of the two components of the spin-orbit
doublet and accordingly calculated α(z) using two methods. Analysis on
all of the 86 spectra yielded Δα/α=(−3±6)×10−5 with
respect to the laboratory α measurements, consistent with no variation
over the explored time interval. If assuming a uniform variation rate, we
obtained α−1dα/dt=(−3±6)×10−15 yr−1
within the last 12 Gyrs. Extensive tests indicate that α variation could
be better constrained using starburst galaxies' spectra than using QSO spectra
in future studies.Comment: 24 pages, 22 figures. Accepted for publication in MNRA