Exclusive <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>J</mml:mi> <mml:mo>/</mml:mo> <mml:mi>ψ</mml:mi> </mml:math> production off a dilute proton within a refined hotspot description

We revisit the calculation of exclusive <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>J</a:mi> <a:mo>/</a:mo> <a:mi>ψ</a:mi> </a:math> production in electron-proton scattering within the QCD dipole model, employing a refined description of the proton in terms of gluonic hot spots in the dilute regime. In contrast to earlier studies, we incorporate key missing elements; the event-by-event fluctuations in both the number of hot spots and their local saturation scales, as well as the first relativistic corrections to the <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mi>J</c:mi> <c:mo>/</c:mo> <c:mi>ψ</c:mi> </c:math> wave function. We perform a Bayesian analysis to constrain the model parameters using HERA data. These enhancements significantly improve the agreement with HERA data. Saturation scale fluctuations are found to be more important than fluctuations in the number of hot spots. Including the first relativistic correction is found to be important, especially in order to describe the observed power-law behavior in the incoherent cross section at large <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mi>t</e:mi> </e:math> .