Abstract
Considering forward dijet production in the q → qg partonic process, we derive the spectrum of accompanying soft gluon radiation induced by rescatterings in a nuclear target. The spectrum is obtained to logarithmic accuracy for an arbitrary energy sharing between the final quark and gluon, and for final transverse momenta as well as momentum imbalance being large as compared to transverse momentum nuclear broadening. In the case of equal energy sharing and for approximately back-to-back quark and gluon transverse momenta, we reproduce a previous result of Liou and Mueller. Interpreting our result, we conjecture a simple formula for the medium-induced radiation spectrum associated to hard forward 1 → n processes, which we explicitly check in the case of the g → gg process.
Highlights
Interpreting our result, we conjecture a simple formula for the medium-induced radiation spectrum associated to hard forward 1 → n processes, which we explicitly check in the case of the g → gg process
In this kinematical setup, which we will choose in the present study, the average medium-induced energy loss ∆E turns out to scale as E, and the behavior ∆E ∝ E arises from soft gluon radiation with formation time tf scaling as E, being fully coherent over the medium size at asymptotically large E [5]
We derive the coherent radiation spectrum associated to the q → qg process already studied in [9], but using slightly more general kinematics
Summary
The definition of the induced spectrum as it stands in (2.1) represents the conditional probability of having gluon radiation provided a given final state with specific kinematics is produced in a hard process. [5] the medium-induced coherent radiation spectrum dI/dx associated to the g → g process (with the final ‘gluon’ being a compact color octet QQpair of mass M ) was derived by modeling the transverse momentum broadening ∆q⊥ across the medium by a single rescattering l⊥, and identifying l2⊥ = ∆q⊥2 (L) = qL, where q = μ2/λg, with μ the typical transverse momentum exchange in a single scattering and λg the gluon mean free path in the medium. (iii) At each order in opacity, and to leading logarithmic accuracy (as defined after (2.4)) considered throughout our study, the contribution to (2.5) of purely initial state radiation can be checked to be negligible. The result is proportional to E and power-suppressed (as 1/q⊥) in the hard scale,
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