Search for synchrotron emission from secondary electrons of proton-proton interaction in Galactic PeVatron candidate HESS J1641$-$463

HESS J1641-463 is an unidentified gamma-ray source with a hard TeV gamma-ray spectrum, and thus it has been proposed to be a possible candidate for cosmic ray (CR) accelerators up to PeV energies (a PeVatron candidate). The source spatially coincides with the radio supernova remnant (SNR) G338.5+0.1, but has not yet been fully explored in the X-ray band. We analyzed newly taken NuSTAR data, pointing at HESS J1641-463, with 82 ks effective exposure time. There is no apparent X-ray counterpart of HESS J1641-463, while nearby stellar cluster, Mercer 81, and stray-light X-rays are detected. Combined with the archival Chandra data, partially covering the source, we derived an upper limit of ~ 6× 10⁻¹³ erg cm⁻² s⁻¹ in 2-10 keV (~ 3× 10⁻¹³ erg cm⁻² s⁻¹ in 10-20 keV). If the gamma-ray emission is originated from decay of π⁰ mesons produced in interactions between CR protons and ambient materials, secondary electrons in the proton-proton interactions can potentially emit synchrotron photons in the X-ray band, which can be tested by our X-ray observations. Although the obtained X-ray upper limits cannot place a constraint on the primary proton spectrum, it will be possible with a future hard X-ray mission.