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We make several comments on the recent work in Rogers et al. [Phys. Rev. D 111, 056001 (2025)] while also reaffirming and adding to the work in Pitonyak et al. [Phys. Rev. Lett. 132, 011902 (2024)]. We show that the factorization formula for e+e- --> (h1...hn)X in Rogers et al. is equivalent to a version one can derive using the definition of a n-hadron fragmentation function (FF) introduced in Pitonyak et al.. In addition, we scrutinize how to generalize the number density definition of a single-hadron FF to a n-hadron FF, arguing that the definition given in Pitonyak et al. should be considered the standard one while the definition in Rogers et al. has no clear interpretation. We also emphasize that the evolution equations for dihadron FFs (DiFFs) in Pitonyak et al. have the same splitting functions as those for single-hadron FFs. Therefore, the DiFF (and n-hadron FF) definitions in Pitonyak et al. have a natural number density interpretation and, contrary to what is stated in Rogers et al., are consistent with collinear factorization using the standard hard factors and evolution kernels. 

We establish an approach to analyze the free hadron and transition (nonperturbative) regions of near- side energy-energy correlators (EECs) based on dihadron fragmentation functions (DiFFs). We introduce a (nonperturbative) function we call the “EEC DiFF” and explicitly show that expanding it for large relative transverse momentum between the two hadrons gives the O(alphaS) expression for the “EEC jet” function used in the quark-gluon (perturbative) region. This connection indicates that a formal theoretical matching will be able to bridge the free-hadron region, transition, and quark-gluon regions and allow all of them to be analyzed simultaneously. We further derive a result valid for near- side EECs in the free hadron and transition regions of e+e- annihilation in terms of the EEC DiFF. Using a simple model for the function, we perform the first fit within the dihadron framework to experimental data in this regime. We find reasonable agreement with the measurements and reproduce the salient features of near-side EECs in the free hadron and transition regions. 

We perform a phenomenological study of helicity-dependent parton distribution functions (PDFs) using small-x helicity evolution equations, incorporating for the first time single-inclusive jet production data in polarized proton-proton (pp) scattering at parton momentum fractions x < 0.1. We also simultaneously include double-longitudinal spin asymmetries in inclusive and semi-inclusive deep-inelastic scattering probing x < 0.1. Employing the polarized small-x pure-glue calculation of pp → gX for the jet production cross section, we modify the large-Nc&Nf KPS-CTT evolution equations by setting Nf = 0 to replicate the large-Nc (pure-glue) limit, while retaining external quark flavors for the spinor field operators. We find that the pp data have a considerable impact on the helicity PDFs at small x, reducing their uncertainties and leading to a total quark and gluon helicity in the proton for x < 0.1 of −0.04 +/-0.23. Combining our analysis with a recent JAM helicity PDF analysis of the world polarized data, which includes x > 0.1, we find a total quark and gluon helicity contribution for x > 10−7 of between 0.02 and 0.51. 

We present the first simultaneous global QCD analysis of unpolarized transverse momentum dependent (TMD) and collinear parton distribution functions (PDFs) in the proton. Our study incorporates data from deep-inelastic scattering, Drell-Yan, inclusive weak boson, W+charm, and jet production involving PDFs, as well as TMD Drell-Yan and Z-boson production data from fixed target and collider experiments sensitive to both TMD and collinear distributions. The analysis is performed at next-to-next-to-leading logarithmic accuracy for QCD resummation in TMD observables and next-to-leading order for observables described in collinear factorization. The combined analysis improves knowledge of both TMD and collinear PDFs, particularly in the sea-quark sector, providing a consistent simultaneous description of the aforementioned observables. 

Transverse single-spin asymmetries in the semi-inclusive deep-inelastic production of isolated photons (𝛾SIDIS), 𝐴𝛾SIDIS𝑈𝑇 , provide an unprecedented opportunity to extract the quark-gluon-quark correlators 𝐹𝐹𝑇(𝑥,𝑥′ ) and 𝐺𝐹𝑇(𝑥,𝑥′ ) point-by-point in their full support 𝑥,𝑥′. We utilize realistic models for these functions, based on input from the Sivers transverse momentum dependent parton distribution function and imposing constraints from the 𝑑2 matrix element calculated in lattice QCD, in order to provide numerical estimates for 𝐴𝛾SIDIS𝑈𝑇 at the Electron-Ion Collider (EIC). We thoroughly explore the EIC phase space in order to isolate in which regions the asymmetry can be sizable, finding it can be as much as 10 % or larger for certain kinematics. Given that 𝐹𝐹𝑇(𝑥,𝑥′ ) and 𝐺𝐹𝑇(𝑥,𝑥′ ) are basically unknown, 𝐴𝛾SIDIS𝑈𝑇 will be an important future measurement to learn about multi-parton correlations in the nucleon. 

The goal of the LHCspin project is to develop innovative solutions for measuring the 3D structure of nucleons in high-energy polarized fixed-target collisions at LHC, exploring new processes and exploiting new probes in a unique, previously unexplored, kinematic regime. A precise multi-dimensional description of the hadron structure has, in fact, the potential to deepen our understanding of the strong interactions and to provide a much more precise framework for measuring both Standard Model and Beyond Standard Model observables. This ambitious task poses its basis on the recent experience with the successful installation and operation of the SMOG2 unpolarized gas target in front of the LHCb spectrometer. Besides allowing for interest- ing physics studies ranging from astrophysics to heavy-ion physics, SMOG2 provides an ideal benchmark for studying beam-target dynamics at the LHC and demonstrates the feasibility of simultaneous operation with beam-beam collisions. With the installation of the proposed polarized target system, LHCb will become the first experiment to simultaneously collect data from unpolarized beam-beam collisions at √s=14 TeV and polarized and unpolar- ized beam-target collisions at √sNN ∼100 GeV. LHCspin has the potential to open new frontiers in physics by exploiting the capabilities of the world’s most powerful collider and one of the most advanced spectrometers. This document also highlights the need to perform an R&D campaign and the commissioning of the apparatus at the LHC Interaction Region 4 during the Run 4, before its final installation in LHCb. This opportunity could also allow to undertake preliminary physics measurements with unprecedented conditions.