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Abstract
Motivated by recent experimental LHC measurements on the forward inclusive jet productions and based on our previous calculations on forward hadron productions, we calculate a single inclusive jet cross section in $pA$ collisions at forward rapidity within the color glass condensate framework up to the next-to-leading order. Moreover, with the application of a jet algorithm and proper subtraction of the rapidity and collinear divergences, we further demonstrate that the resulting next-to-leading-order hard coefficients are finite. In addition, in order to deal with the large logarithms that can potentially spoil the convergence of the perturbative expansion and improve the reliability of the numerical predictions, we introduce the collinear jet function and the threshold jet function and resum these large logarithms hidden in the hard coefficients.
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