Measurement of exclusive $${{{\uprho _{}^{}} _{}^{}}{{\left( {770}\right) }{}_{}^{}}} ^{0}$$ photoproduction in ultraperipheral pPb collisions at $$\sqrt{\smash [b]{s_{_{\mathrm {NN}}}}} = 5.02\,\text {Te}\text {V} $$

Exclusive $${{{\uprho _{}^{}} _{}^{}}{{\left( {770}\right) }{}_{}^{}}} ^{0}$$photoproduction is measured for the first time in ultraperipheral pPb collisions at $$\sqrt{\smash [b]{s_{_{\mathrm {NN}}}}} = 5.02\,\text {Te}\text {V} $$with the CMS detector. The cross section $$\sigma ({\upgamma _{}^{}} \mathrm{p}\rightarrow {{{\uprho _{}^{}} _{}^{}}{{\left( {770}\right) }{}_{}^{}}} ^{0}\mathrm{p})$$is $$11.0 \pm 1.4\,\text {(stat)} \pm 1.0\,\text {(syst)} $$$$\mu $$b at $$\langle W_{{\upgamma _{}^{}} \mathrm{p}}\rangle = 92.6\,\text {Ge}\text {V} $$for photon–proton centre-of-mass energies $$W_{{\upgamma _{}^{}} \mathrm{p}}$$between 29 and $$213\,\text {Ge}\text {V} $$. The differential cross section $$\mathrm {d}\sigma /\mathrm {d}|t |$$is measured in the interval $$0.025< |t | < 1\,\text {Ge}\text {V} ^{2}$$as a function of $$W_{{\upgamma _{}^{}} \mathrm{p}}$$, where t is the squared four-momentum transfer at the proton vertex. The results are compared with previous measurements and theoretical predictions. The measured cross section $$\sigma ({\upgamma _{}^{}} \mathrm{p}\rightarrow {{{\uprho _{}^{}} _{}^{}}{{\left( {770}\right) }{}_{}^{}}} ^{0}\mathrm{p})$$has a power-law dependence on the photon–proton centre-of-mass, consistent with electron–proton collision measurements performed at HERA. The $$W_{{\upgamma _{}^{}} \mathrm{p}}$$dependence of the exponential slope of the differential cross section $$\mathrm {d}\sigma /\mathrm {d}|t |$$is also measured.