Transverse momentum spectra of fermions and bosons produced in strong Abelian fields

We study the transverse momentum spectra of fermions and bosons produced in a strong, time-dependent Abelian field. The transverse size of the Abelian field is finite, similarly to color strings and ropes. Different time-dependent field strengths are investigated in a kinetic model, and transverse momentum spectra are calculated for fermions and bosons. These spectra display exponential or polynomial behavior at high $p_T$, depending on the given time dependence. We compare our spectra to the lattice result for a classical gluon field and obtain surprisingly good agreement in certain cases.

Figure 1

The time dependence of external field $E(t)$ in three physical scenarios: (a) pulse (dotted line); (b) constant field, $E_0$ (dashed line); (c) scaled decrease (solid line).

Figure 2

The transverse momentum spectra for bosons in the three physical scenarios (see Fig. 1 and text for explanation).

Figure 3

The transverse momentum spectra for fermions in the three physical scenarios (see Fig. 1 and text for explanation).

Figure 4

Longitudinal momentum spectra for fermions (thick line) and bosons (thin line) at $k_T/E_0^{1/2}=1$ and $t=2/E_0^{1/2}$.

Figure 5

Transverse momentum spectra for fermions (thick solid line) and bosons (thin solid line) from our calculation with scaled time evolution, $E_{\mathrm{scaled}}(t)$, and gluon production (diamonds) from the SU(3) lattice-QCD calculation [13].