<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>J</mml:mi> <mml:mo>/</mml:mo> <mml:mi>ψ</mml:mi> </mml:mrow> </mml:math> production in proton-proton collisions at Spin Physics Detector energies of the JINR Nuclotron-based Ion Collider fAcility

We investigate inclusive <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:mi>J</a:mi> <a:mo>/</a:mo> <a:mi>ψ</a:mi> </a:mrow> </a:math> production in proton-proton collisions at tens of GeV <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:msqrt> <b:mi>s</b:mi> </b:msqrt> </b:math> energy, relevant for forthcoming measurements with the Spin Physics Detector (SPD) at NICA. Simulations are performed using the PEGASUS event generator with transverse-momentum-dependent (TMD) gluon densities, comparing the recent KMR-based <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mrow> <c:msup> <c:mrow> <c:mi>KL</c:mi> </c:mrow> <c:mo>′</c:mo> </c:msup> <c:mn>2025</c:mn> </c:mrow> </c:math> and CCFM-based <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"> <d:mrow> <d:msup> <d:mrow> <d:mi>LLM</d:mi> </d:mrow> <d:mo>′</d:mo> </d:msup> <d:mn>2024</d:mn> </d:mrow> </d:math> parametrizations. Differential cross sections in rapidity and transverse momentum exhibit smooth, stable behavior under renormalization-scale variation. Normalized <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"> <e:msub> <e:mi>p</e:mi> <e:mi>T</e:mi> </e:msub> </e:math> spectra reveal distinct hardening patterns linked to the underlying gluon <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"> <f:msub> <f:mi>k</f:mi> <f:mi>T</f:mi> </f:msub> </f:math> broadening in each model. The relative contributions of color-singlet and color-octet channels are also quantified, demonstrating the dominance of color-octet mechanisms in the SPD energy regime. These results provide the first detailed assessment of quarkonium production sensitivity to gluon TMDs near threshold, offering timely theoretical guidance for upcoming <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"> <g:mrow> <g:mi>J</g:mi> <g:mo>/</g:mo> <g:mi>ψ</g:mi> </g:mrow> </g:math> measurements at SPD/NICA.