Solar wind test of the de Broglie-Proca's massive photon with Cluster multi-spacecraft data

Our understanding of the universe at large and small scales relies largely on electromagnetic observations. As photons are the messengers, fundamental physics has a concern in testing their properties, including the absence of mass. We use Cluster four spacecraft data in the solar wind at 1 AU to estimate the mass upper limit for the photon. We look for deviations from Amp`ere’s law, through the curlometer technique for the computation of the magnetic field, and through the measurements of ion and electron velocities for the computation of the current. We show that the upper bound for $m_{\gamma }$ lies between $1.4\times {10}^{-49}$ and $3.4\times {10}^{-51}$ kg, and thereby discuss the currently accepted lower limits in the solar wind.