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A<sc>bstract</sc> The production cross sections of$$ {\textrm{B}}_{\textrm{s}}^0 $$ $B_s^0$and B⁺mesons are reported in proton-proton (pp) collisions recorded by the CMS experiment at the CERN LHC with a center-of-mass energy of 5.02 TeV. The data sample corresponds to an integrated luminosity of 302 pb⁻¹. The cross sections are based on measurements of the$$ {\textrm{B}}_{\textrm{s}}^0 $$ $B_s^0$→J/ψ(μ⁺μ⁻)ϕ(1020)(K⁺K⁻) and B⁺→J/ψ(μ⁺μ⁻)K⁺decay channels. Results are presented in the transverse momentum (p_T) range 7–50 GeV/cand the rapidity interval |y|<2.4 for the B mesons. The measuredp_T-differential cross sections of B⁺and$$ {\textrm{B}}_{\textrm{s}}^0 $$ $B_s^0$in pp collisions are well described by fixed-order plus next-to-leading logarithm perturbative quantum chromodynamics calculations. Using previous PbPb collision measurements at the same nucleon-nucleon center-of-mass energy, the nuclear modification factors,R_AA, of the B mesons are determined. Forp_T>10 GeV/c, both mesons are found to be suppressed in PbPb collisions (withR_AAvalues significantly below unity), with less suppression observed for the$$ {\textrm{B}}_{\textrm{s}}^0 $$ $B_s^0$mesons. In thisp_Trange, theR_AAvalues for the B⁺mesons are consistent with those for inclusive charged hadrons and D⁰mesons. Below 10 GeV/c, both B⁺and$$ {\textrm{B}}_{\textrm{s}}^0 $$ $B_s^0$are found to be less suppressed than either inclusive charged hadrons or D⁰mesons, with the$$ {\textrm{B}}_{\textrm{s}}^0 $$ $B_s^0$R_AAvalue consistent with unity. TheR_AAvalues found for the B⁺and$$ {\textrm{B}}_{\textrm{s}}^0 $$ $B_s^0$are compared to theoretical calculations, providing constraints on the mechanism of bottom quark energy loss and hadronization in the quark-gluon plasma, the hot and dense matter created in ultrarelativistic heavy ion collisions.