Gluon radiation from a classical point particle

We consider an initially at rest colored particle which is struck by an ultrarelativistic nucleus. The particle is treated classically with respect to both its motion and its color charge. The nucleus is treated as a sheet of colored glass within the context of the color glass condensate framework. We compute both the momentum and coordinates of the struck classical particle and the emitted radiation. Our computations generalize the classic electrodynamics computation of the radiation of an accelerated charged particle to include the radiation induced by the charged gluon field. This latter contribution adds to the classic electrodynamics result and produces a gluon rapidity distribution that is roughly constant as a function of rapidity at rapidities far from the fragmentation region of the struck particles. These computations may form the basis of a first principles treatment for the initial conditions for the evolution of matter produced in the fragmentation region of asymptotically high energy collisions.

Figure 1

Longitudinal kinematics of the process. Nucleus A moving along the light cone with color current ${\delta }^{\mu +}\delta (x^{-})\rho (\mathbf{x})$ meets with a stationary quark and is excited into a classical background Yang-Mills configuration $A^{\mu }=(0,0,A^i\theta (-x^{-}))$. In region I, for $x^{-}<0$, the background field is vacuum equivalent transverse field (26) and the fluctuation field $\delta A_i\equiv a_i$ is a gauge rotated Coulomb field of the stationary quark (75). In II and III there are no background fields, and the fluctuation fields contain electrodynamicslike radiation caused by quark acceleration (81) and radiation from the quark-nucleus interaction (108).

Figure 2

Rapidity distribution [bracketed factor in Eq. (90) is plotted] of gluons emitted in an acceleration of a static quark to rapidity $y_p=10$ by the nucleus. The maximum is at $y_p/2=5$ and the curve is symmetric around the maximum value.

Figure 3

Rapidity distribution [bracketed factor in Eq. (126) is plotted] at fixed $k_T$ of gluons emitted in a collision of an initially static quark with nucleus. The IR regulator mass is $k_T/10$, and the curve shows a linear increase as a function of rapidity in the fragmentation region.