2025/09/18 by Babiarz, Izabela, Flett, Chris A., Ozcelik, Melih A. +2 · 1 citation
#FOS: Physical sciences #High Energy Physics - Phenomenology (hep-ph) #Nuclear Theory (nucl-th)
paper · doi:10.48550/arxiv.2509.15310
In this work, we discuss both relativistic and perturbative QCD corrections to the transition form-factor \cal FηQ(t1,t2) for the process γ^*(q1) γ^*(q2) ↔ ηQ(P) with dependencies on the normalised photon virtualities t1=q12/mQ2 and t2=q22/mQ2, where mQ is the heavy quark mass. We resum a class of relativistic corrections to all orders in the relativistic parameter ⟨ v2 ⟩ηQ. In addition, we include perturbative QCD corrections up to Next-to-Next-to-Leading Order (NNLO) in the strong coupling constant αs. This involves the computation of two-loop amplitudes with two off-shell photons. We explore three different phenomenological applications of our transition form-factors for the charmonium case. We first study the ratio \vert \cal Fηc(t1,0) \vert/ \vert \cal Fηc(0,0) \vert for the single space-like photon case and compare our results with the existing ηc measurements from the BaBar collaboration. Secondly, we consider observables for the case of double space-like photons and discuss the impact of the different corrections. The NNLO corrections for this case are presented here for the first time in the literature. Finally, we revisit the decay width Γ[ηc → γγ] and compare it with the existing PDG value.