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We investigate the cold nuclear matter (CNM) effects on the productions ofthe isolated prompt photon and $\gamma+$jet in proton-lead collisions at $\rm8.16$ TeV under the next-to-leading order (NLO) perturbative quantumchromodynamics calculations with four parametrizations for nuclear partondistribution functions (nPDFs), i.e. DSSZ, EPPS16, nCTEQ15, nIMParton. Ourtheoretical calculations provide good descriptions of pp baseline in the ATLAScollaboration and make predictions for future experimental results at $\rmp$+$\rm Pb$ collisions. We calculate the dependence of the nuclear modificationfactor of isolated prompt photon on transverse momentum $\rm p_T^{\gamma}$ andpseudo-rapidity $\eta^{\gamma}$ at very forward and backward rapidity regions,and demonstrate that the forward-to-backward yield asymmetries $\rm Y_{\rmpPb}^{\rm asym}$ as a function of $\rm p_T^{\gamma}$ with different nPDFsparametrizations have diverse behaviors. Furthermore, the nuclear modificationfactor of isolated-$\gamma+$jet $\rm R_{\rm pPb}^{\gamma Jet}$ as a function of$\gamma+$jet's pseudo-rapidity $\eta_{\gamma \rmJet}=\frac{1}{2}(\eta_{\gamma}+\eta_{\rm Jet})$ at different average transversemomentum $\rm p_T^{\rm avg}=\frac{1}{2}(\rm p_T^{\gamma}+\rm p_T^{\rm Jet})$has been discussed, which can facilitate a tomography study of CNM effects withprecise locations in a rather wide kinematic region by varying the transversemomenta and rapidities of both isolated photon and jet in p+A collisions.

Probing cold nuclear matter effects with the productions of isolated-$\gamma$ and $\gamma$+jet in p$+$Pb collisions at $\sqrt{s_{NN}}=$ 8.16 TeV