Subleading Asymptotic Charges in Massless Scalar QED

We study subleading asymptotic charges of a U(1) gauge field coupled to a charged massless scalar field in Minkowski spacetime. We consider a phase space for which the scalar-field initial data on null infinity have compact support, while the gauge-field initial data admit an asymptotic expansion with inverse-power tails in retarded (advanced) time, which we refer to as initial-data tails. We identify three finite charges at the null infinities which are conserved under scattering. One is a renormalized version of the standard subleading soft charge. The second is a logarithmic charge which is the difference of the coefficients of the leading order tails at the future and past ends of null infinity. The third is a new charge that probes the average of the tail coefficients. We conjecture that the third charge is associated with a new class of large gauge transformations which diverge linearly in retarded time.