Exclusive photoproduction of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>χ</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>c</mml:mi> </mml:mrow> </mml:msub> <mml:mi>γ</mml:mi> </mml:mro

In this manuscript we extend our previous analysis of the exclusive photoproduction of the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:msub> <a:mi>χ</a:mi> <a:mi>c</a:mi> </a:msub> <a:mi>γ</a:mi> </a:math> pairs to the high-energy (small- <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mi>x</c:mi> </c:math> ) kinematics, evaluate in detail the cross section in the color glass condensate framework, and discuss the potential of this channel as a novel complementary probe of the hadronic interactions. In the leading order in strong coupling <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:msub> <e:mi>α</e:mi> <e:mi>s</e:mi> </e:msub> </e:math> , the cross section is controlled by the dipole scattering amplitude. Using available phenomenological parametrizations of the latter, we estimated numerically the cross sections for different polarizations of <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:msub> <g:mi>χ</g:mi> <g:mi>c</g:mi> </g:msub> </g:math> mesons and final-state photons in the kinematics of the ultraperipheral collisions at LHC and the future Electron Ion Collider. We found that the expected number of produced and detected events is significant for experimental study. We suggest that the ratio of the cross sections with different spins <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:msub> <i:mi>σ</i:mi> <i:mrow> <i:mi>γ</i:mi> <i:msub> <i:mi>χ</i:mi> <i:mrow> <i:mi>c</i:mi> <i:mn>1</i:mn> </i:mrow> </i:msub> </i:mrow> </i:msub> <i:mo>/</i:mo> <i:msub> <i:mi>σ</i:mi> <i:mrow> <i:mi>γ</i:mi> <i:msub> <i:mi>χ</i:mi> <i:mrow> <i:mi>c</i:mi> <i:mn>2</i:mn> </i:mrow> </i:msub> </i:mrow> </i:msub> </i:math> can be used to test the validity of the heavy quark spin symmetry relations for <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:msub> <k:mi>χ</k:mi> <k:mi>c</k:mi> </k:msub> </k:math> , and in this way resolve a long-standing ambiguity observed in hadroproduction of <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:msub> <m:mi>χ</m:mi> <m:mi>c</m:mi> </m:msub> </m:math> mesons. Finally, we also analyzed the role of this process as a potential background to exclusive <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"> <o:msub> <o:mi>χ</o:mi> <o:mi>c</o:mi> </o:msub> </o:math> photoproduction, which has been recently suggested as an alternative channel for studies of odderons.