Modification of $Z^0$ leptonic invariant mass in ultrarelativistic heavy ion collisions as a measure of the electromagnetic field

An extraordinary strong magnetic field, $eB_0 \approx 10^{18}$ Gauss, is expected to be generated in non-central ultrarelativistic heavy ion collisions and it is envisaged to induce several effects on hot QCD matter including the possibility of local parity and local parity and charge conjugation symmetry violations. A direct signature of such e.m. fields and a first quantitative measurement of its strength and lifetime are still missing. We point out that both the mean value of leptonic invariant mass of $Z^0$ boson, reconstructed by its decaying lepton pairs, and the relative width are modified in relativistic heavy ion collisions due to the presence of strong initial e.m. fields. We propose a measurement of the leptonic invariant mass of $Z^0$ as a novel probe of the strength of the $B_y$. Both shifts could be up to about few hundred MeV and are found to depend on the integral of $B_y$ over the time duration quadratically (approximate). Hence it provides a novel and clear probe of electromagnetic fields, which can be tested experimentally.