Analytic calculation of the energy-momentum tensor in heavy ion collisions from color glass condensate

We generalize calculations of the energy-momentum tensor for classical gluon fields in the boost-invariant McLerran-Venugopalan model using the small-$\tau$ power series expansion method. Results to all orders for the energy density and pressures are given in the leading $Q^2$ approximation and with the inclusion of estimated running coupling effects. The energy density and transverse pressure decrease monotonically with time while the longitudinal pressure starts from a negative value and increases towards zero.

Figure 1

Energy density $\varepsilon /{\varepsilon }_0$ as a function of $Q\tau$ with different calculated accuracy. The black dotted line, green dot-dashed line, blue dashed line, and the red solid line represent approximations of ${\mathsf{G}}_A\left(Q\tau \right)$ and ${\mathsf{G}}_B\left(Q\tau \right)$ to the order of ${\left(Q\tau \right)}^{10}$, ${\left(Q\tau \right)}^{30}$, ${\left(Q\tau \right)}^{50}$, and ${\left(Q\tau \right)}^{100}$, respectively.

Figure 2

Transverse pressure $P_T/{\varepsilon }_0$ as a function of $Q\tau$ with different calculated accuracy. The notation is the same as in Fig. 1.

Figure 3

Longitudinal pressure $P_L/{\varepsilon }_0$ as a function of $Q\tau$ with different calculated accuracy. The notation is the same as in Fig. 1.

Figure 4

The pressures $P_T/\varepsilon$ and $P_L/\varepsilon$ as functions of $Q\tau$. The lines in the upper half-plane represent $P_T/\varepsilon$ while lines on the lower half-plane represent $P_L/\varepsilon$.