Photoproduction and detection of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mi>ρ</mml:mi> <mml:mo>′</mml:mo> </mml:msup> <mml:mo>→</mml:mo> <mml:msup> <mml:mi>π</mml:mi> <mml:mo>+</mml:mo> </mml:msup> <mml:ms

Vector meson photoproduction is an important probe of nuclear structure. Light vector mesons are most sensitive to <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:mi>low</a:mi> <a:mtext>−</a:mtext> <a:mi>x</a:mi> </a:mrow> </a:math> structure, as long as they are not too light for perturbative QCD calculations. The <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:msup> <b:mi>ρ</b:mi> <b:mo>′</b:mo> </b:msup> </b:math> is of interest as an intermediate mass state (between the <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mi>ρ</c:mi> </c:math> and <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"> <d:mrow> <d:mi>J</d:mi> <d:mo>/</d:mo> <d:mi>ψ</d:mi> </d:mrow> </d:math> ) that is easier to detect than the <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"> <e:mi>ϕ</e:mi> </e:math> . Using HERA data on proton targets, we make projections for lead/gold targets in ultraperipheral collisions (UPCs) at the CERN Large Hadron Collider and the BNL Relativistic Heavy Ion Collider, and for <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"> <f:mrow> <f:mi>e</f:mi> <f:mi>p</f:mi> </f:mrow> </f:math> and <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"> <g:mrow> <g:mi>e</g:mi> <g:mi>A</g:mi> </g:mrow> </g:math> collisions at a future electron-ion collider (EIC). We compare the UPC projections with ALICE data, and constrain the branching ratio divided by the square of the photon- <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"> <h:msup> <h:mi>ρ</h:mi> <h:mo>′</h:mo> </h:msup> </h:math> coupling. The data prefer large couplings and small branching ratio, probably less than 25%. The photon-meson coupling predicted by generalized vector meson dominance does not fit the data. The HERA <i:math xmlns:i="http://www.w3.org/1998/Math/MathML"> <i:mrow> <i:mi>e</i:mi> <i:mi>p</i:mi> </i:mrow> </i:math> and ALICE UPC <j:math xmlns:j="http://www.w3.org/1998/Math/MathML"> <j:mrow> <j:mi>e</j:mi> <j:mi>Pb</j:mi> </j:mrow> </j:math> data exhibit very similar <k:math xmlns:k="http://www.w3.org/1998/Math/MathML"> <k:mrow> <k:mn>4</k:mn> <k:mi>π</k:mi> </k:mrow> </k:math> mass spectra, indicating that, if the system is composed of two resonances, the products of their photon couplings with their four-pion branching ratios are similar. The predicted rates are high for both UPCs and the EIC. The <l:math xmlns:l="http://www.w3.org/1998/Math/MathML"> <l:mrow> <l:msup> <l:mi>ρ</l:mi> <l:mo>′</l:mo> </l:msup> <l:mo>→</l:mo> <l:msup> <l:mi>π</l:mi> <l:mo>+</l:mo> </l:msup> <l:msup> <l:mi>π</l:mi> <l:mo>−</l:mo> </l:msup> <l:msup> <l:mi>π</l:mi> <l:mo>+</l:mo> </l:msup> <l:msup> <l:mi>π</l:mi> <l:mo>−</l:mo> </l:msup> </l:mrow> </l:math> decay can be observed at the EIC with high efficiency. In <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mi>e</m:mi> <m:mi>p</m:mi> </m:mrow> </m:math> collisions at the highest energy, the forward B0 detector is needed to observe this channel down to the lowest achievable <n:math xmlns:n="http://www.w3.org/1998/Math/MathML"> <n:mrow> <n:mi>Bjorken</n:mi> <n:mtext>−</n:mtext> <n:mi>x</n:mi> </n:mrow> </n:math> values.