  In this paper, we investigate the Kibble-Zurek scaling of the sigma field and
net-protons within the framework of Langevin dynamics of model A. After
determining the characteristic scales $\tau_{kz},l_{kz}$ and $\theta_{kz}$ and
properly rescaling the traditional cumulants, we construct universal functions
for the sigma field and approximate universal functions for net-protons in the
critical regime, which are insensitive to the relaxation time and the chosen
evolving trajectory. Besides, the oscillating behavior for the higher order
cumulants of net-protons near the critical point is also drastically
suppressed, which converge into approximate universal curves with these
constructed Kibble-Zurek functions.
