In-plane transverse polarization in heavy-ion collisions

We give an analytical expression for the in-plane polarization $P^x$, in heavy-ion collisions that has, to our knowledge, not been measured in heavy-ion collision experiments. We also carry out a numerical study of $P^x$ using a hydrodynamic model simulation as a cross-check for the analytical formula. It is found that if the temperature-gradient contribution is neglected the simulation result for $P^x$ qualitatively agrees with the analytical one. The prediction of $P^x$ can be tested in experiments and will contribute to provide a complete and consistent picture of spin phenomena in heavy-ion collisions.