Forward trijet production in proton-nucleus collisions

Abstract

Using the formalism of the light-cone wave function in perturbative QCD together with the hybrid factorization, we compute the cross-section for three particle production at forward rapidities in proton-nucleus collisions. We focus on the quark channel, in which the three produced partons -- a quark accompanied by a gluon pair, or two quarks plus one antiquark -- are all generated via two successive splittings starting with a quark that was originally collinear with the proton. The three partons are put on-shell by their scattering off the nuclear target, described as a Lorentz-contracted "shockwave". The three-parton component of the quark light-cone wave function that we compute on this occasion is also an ingredient for other interesting calculations, like the next-to-leading order correction to the cross-section for the production of a pair of jets.

Figures (31)

• Figure 1: Left: One "real" gluon emission with 3-momentum $(k^+,\bm{k})=(\vartheta q^{+},\,\vartheta\bm{q}+\bm{\widetilde{k}})$ from an initial quark with 3-momentum $\left(q^{+},\,\bm{q}\right)$. We are using a non-eikonal vertex, in which the recoil of the quark will not be neglected. Right: One "virtual" gluon emission contributing to the normalization of the WF.
• Figure 2: The quark-gluon component of the outgoing wave-function for an incoming quark. There are two ways to insert the shockwave, before and after the gluons emission, represented in Fig. a and b, respectively. The transverse position of the quark is deflected by the emission of the gluon, from $\bm{w}$ to $\bm{x}=\frac{\bm{w}-\vartheta\bm{z}}{1-\vartheta}$.
• Figure 3: The quark-antiquark contributions to the gluon outgoing state.
• Figure 4: The two-gluon contributions to the gluon outgoing state.
• Figure 5: One of the contributions (the one proportional to $S_{q\bar{q}g}\left(\overline{\bm{w}},\,\bm{x},\,\bm{z}\right)$) to the quark-gluon production cross section in Eq. (\ref{['LOfinal']}). There are four such contributions, in which the shockwave can be located either before or after the gluon emission, in both the direct amplitude and the complex conjugate amplitude. The dashed line represents the final state at $x^{+}\rightarrow\infty$.