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

In this manuscript we study the exclusive photoproduction of <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 in the collinear factorization framework. We found the coefficient functions for all possible spins and helicity projections of <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msub><c:mi>χ</c:mi><c:mi>c</c:mi></c:msub></c:math> mesons and final-state photons in the leading order in the 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>. In our analysis we focused on the contribution of the leading twist chiral-even generalized parton distributions (GPDs) and found that for all spin states 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> the suggested process is largely determined by the behavior of the gluon GPDs <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:msub><i:mi>H</i:mi><i:mi>g</i:mi></i:msub></i:math>. Using the phenomenological parametrizations of the GPDs from the literature, we estimated numerically the photoproduction cross sections and the expected counting rates in the kinematics of medium-energy photoproduction experiments that could be realized at the Electron-Ion Collider. We observed that the <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:msub><k:mi>χ</k:mi><k:mrow><k:mi>c</k:mi><k:mn>1</k:mn></k:mrow></k:msub></k:math>, <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:msub><m:mi>χ</m:mi><m:mrow><m:mi>c</m:mi><m:mn>2</m:mn></m:mrow></m:msub></m:math> mesons are produced predominantly with the same polarization as the incoming photon, and the expected counting rates of <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:msub><o:mi>χ</o:mi><o:mrow><o:mi>c</o:mi><o:mn>1</o:mn></o:mrow></o:msub><o:mi>γ</o:mi></o:math> and <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:msub><q:mi>χ</q:mi><q:mrow><q:mi>c</q:mi><q:mn>2</q:mn></q:mrow></q:msub><q:mi>γ</q:mi></q:math> pairs are sufficiently large for their experimental study. We also analyzed the angular distribution of <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:msub><s:mi>χ</s:mi><s:mi>c</s:mi></s:msub></s:math> mesons in electroproduction experiments and noticed that for some helicity components there are sizable angular asymmetries, which can be used as complementary observables for experimental study. Finally, we estimated the role of this process as a potential background to <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:msub><u:mi>χ</u:mi><u:mi>c</u:mi></u:msub></u:math> photoproduction, which has been recently suggested as a tool for studies of odderons. We found that the contribution of <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"><w:msub><w:mi>χ</w:mi><w:mi>c</w:mi></w:msub><w:mi>γ</w:mi></w:math> (with undetected photon) is on par with expected contributions of odderons and Primakoff mechanisms in the kinematics of small momentum transfer <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"><y:mo stretchy="false">|</y:mo><y:mi>t</y:mi><y:mo stretchy="false">|</y:mo><y:mo>≲</y:mo><y:mn>1</y:mn><y:mtext> </y:mtext><y:mtext> </y:mtext><y:msup><y:mrow><y:mi>GeV</y:mi></y:mrow><y:mrow><y:mn>2</y:mn></y:mrow></y:msup></y:math>, but becomes negligible at larger <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"><cb:mo stretchy="false">|</cb:mo><cb:mi>t</cb:mi><cb:mo stretchy="false">|</cb:mo></cb:math>.