Search for a scalar partner of the X(3872) via ψ(3770) decays into γηη′ and γπ+π−J/ψ

Using a data sample corresponding to an integrated luminosity of 2.93 fb−1 collected at a center-of-mass energy of 3.773 GeV with the BESIII detector at the BEPCII collider, we search for a scalar partner of the X(3872), denoted as X(3700), via ψ(3770) → γηη0 and γπ+π−J/ψ processes. No significant signals are observed and the upper limits of the product branching fractions B(ψ(3770) → γX(3700)) · B(X(3700) → ηη0) and B(ψ(3770) → γX(3700)) · B(X(3700) → π+π−J/ψ) are determined at the 90% confidence level, for the narrow X(3700) with a mass ranging from 3710 to 3740 MeV/c2, which are from 0.9 to 1.9(×10−5) and 0.9 to 3.4(×10−5), respectively.