Abstract
We study forward dijet production in dilute-dense hadronic collisions. By considering the appropriate limits, we show that both the transverse-momentum-dependent (TMD) and the high-energy factorization formulas can be derived from the Color Glass Condensate framework. Respectively, this happens when the transverse momentum imbalance of the dijet system, $k_t$, is of the order of either the saturation scale, or the hard jet momenta, the former being always much smaller than the latter. We propose a new formula for forward dijets that encompasses both situations and is therefore applicable regardless of the magnitude of $k_t$. That involves generalizing the TMD factorization formula for dijet production to the case where the incoming small-$x$ gluon is off-shell. The derivation is performed in two independent ways, using either Feynman diagram techniques, or color-ordered amplitudes.
Highlights
Projectile is used as a probe to investigate a small-x target, are sometimes called dilutedense collisions
By considering the appropriate limits, we show that both the transverse-momentum-dependent (TMD) and the high-energy factorization formulas can be derived from the Color Glass Condensate framework
We note that the Color Glass Condensate (CGC) approach has been very successful in describing forward di-hadron production at RHIC [4,5,6], in particular it predicted the suppression of azimuthal correlations in d+Au collisions compared to p+p collisions [7], which was observed later experimentally [8, 9]
Summary
The hard factors accompanying the gluon densities Fa(ig) were calculated from the squared diagrams presented in figures 3–6 This procedure has certain drawbacks, especially when one would like to consider more complicated processes. The color decompositions and helicity method [26, 49] are considered as the most effective ways to deal with them It is not obvious how the gauge invariance comes into play for the separate diagrams from figures 3–6 contributing to the hard factors. In view of the above, and to cross-check the results from section 5, we will give an alternative procedure to obtain the factorization formulas with off-shell gluon To this end, we shall need TMD gluon densities corresponding to color decomposition of amplitudes and the color-ordered amplitudes themselves
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