Using 2917 pb−1 of data accumulated at 3.773~GeV,
44.5~pb−1 of data accumulated at 3.65~GeV and data accumulated
during a ψ(3770) line-shape scan with the BESIII detector, the reaction
e+e−→ppˉ is studied considering a possible interference
between resonant and continuum amplitudes. The cross section of
e+e−→ψ(3770)→ppˉ,
σ(e+e−→ψ(3770)→ppˉ), is found to have two
solutions, determined to be (0.059±0.032±0.012) pb with the phase angle
ϕ=(255.8±37.9±4.8)∘ (<0.11 pb at the 90% confidence level),
or σ(e+e−→ψ(3770)→ppˉ)=(2.57±0.12±0.12) pb with ϕ=(266.9±6.1±0.9)∘ both of which
agree with a destructive interference. Using the obtained cross section of
ψ(3770)→ppˉ, the cross section of ppˉ→ψ(3770), which is useful information for the future PANDA experiment, is
estimated to be either (9.8±5.7) nb (<17.2 nb at 90% C.L.) or
(425.6±42.9) nb