Unwinding the rare $Ω$ sector: Fragmentation of fully charmed baryons from HL-LHC to FCC

Abstract

By adopting a hadron-structure-oriented approach, we present and discuss the release of the novel OMG3Q1.0 set of collinear fragmentation functions for fully charmed, rare $Ω$ baryons. Our methodology combines diquark-like proxy model inputs for both charm-quark and gluon channels, calculated at the initial energy scales, with a DGLAP evolution that ensures a consistent treatment of heavy-quark thresholds, following directly from the HF-NRevo scheme. We complement our work with a phenomenological study of NLL/NLO$^+$ resummed $Ω_{3c}$ plus jet distributions using (sym)JETHAD at the HL-LHC and the future FCC. Unraveling the production mechanisms of rare, yet-unobserved hadrons, as provided by the OMG3Q1.0 functions, stands as a key asset for deepening our understanding of QCD at future high-energy hadron colliders.

Figures (7)

• Figure 1: Representative leading diagrams for the diquarklike proxy model of the initial-scale collinear fragmentation of a constituent heavy quark (left) or a gluon (right) into a color-singlet $S$-wave ${\rm \Omega}_{3Q}$ baryon. Double lines stand for ${\@fontswitch\mathcal{D}}$ or $\bar{{\@fontswitch\mathcal{D}}}$ diquark states, while orange blobs represent the nonperturbative hadronization component of corresponding FFs. Black bullet vertices denote scalar diquark form-factor couplings.
• Figure 2: Initial-scale charm (left) and gluon (right) channels to ${\rm \Omega}_{3c}$ for our OMG3Q1.0 FFs. The shaded bands represent the effect of DGLAP evolution within the range $4 m_c < \mu_F < 6 m_c$ for the charm quark and $5 m_c < \mu_F < 7 m_c$ for the gluon.
• Figure 3: Factorization-scale dependence of the OMG3Q1.0 FFs describing the VFNS fragmentation of the ${\rm \Omega}_{3c}$ baryon (left), compared with the corresponding TQ4Q1.1 FFs Celiberto:2024begCeliberto:2025dfeCeliberto:2025ziy portraying the $T_{4c}(2^{++})$ tetraquark (right), evaluated at $z = 0.5 \simeq \langle z \rangle$.
• Figure 4: Pictorial representation of semi-inclusive hadroproduction of a ${\rm \Omega}_{3Q}$ baryon plus a jet within the hybrid factorization. Red blobs depict collinear PDFs. The singly off-shell coefficient function embodied in the hadron (jet) emission function is portrayed by the green (violet) oval. The orange composite arrow represents the inclusive formation of a ${\rm \Omega}_{3Q}$ baryon. The large blue oval blob stands for the high-energy Green's function resumming secondary gluon emissions in the $t$-channel. Diagram was realized with the JaxoDraw 2.0 code Binosi:2008ig.
• Figure 5: $\Delta Y$ differential distribution for semi-inclusive ${\rm \Omega}_{3c}$ plus jet detections at $\sqrt{s} = 14$ TeV (HL-LHC, left) and $100$ TeV (nominal FCC, right). NNPDF4.0 NLO proton PDFs NNPDF:2021uiqNNPDF:2021njg are used in combination with OMG3Q1.0 NLO heavy-baryon FFs Celiberto:2025_OMG3Q10. Ancillary panels below the main plots show the ratio of ${\rm LL/LO}$ and ${\rm HE}\hbox{-}{\rm NLO^+}$ predictions to ${\rm NLL/NLO^+}$. Uncertainty bands account for the combined effects of MHOUs and numerical phase-space integration.