Alexei Prokudin

We present the first simultaneous global QCD analysis of unpolarized transverse momentum dependent (TMD) and collinear parton distribution functions (PDFs) in the proton. Our Letter 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.

We assess the impact of future measurements of dihadron production in semi-inclusive deep-inelastic scattering from the CLAS12 and proposed SoLID experiments at Jefferson Lab, as well as from the ePIC experiment at the future Electron-Ion Collider (EIC), on the transversity parton distribution functions (PDFs) and the corresponding tensor charges of the nucleon. To this end, we generate pseudodata for these experiments for a proton target (CLAS12 and ePIC) and a He 3 target (SoLID and ePIC), and we include these pseudodata in the JAMDiFF global analysis of existing experimental dihadron data. We find that future data from Jefferson Lab will significantly reduce uncertainties in the transversity PDFs in the region of intermediate-to-large quark momentum fractions x , while the EIC will provide strong constraints across the entire range of x , allowing for the first experimental test of the predicted small- x behavior of the transversity PDFs. In discussing the reduction of uncertainties in the tensor charges, we also compare the results from the data analyses with those from lattice QCD, highlighting scenarios in which compatibility or tension between the two would arise.

We make several comments on the recent work in Rogers [] while also reaffirming and adding to the work in Pitonyak []. We show that the factorization formula for e + e − → ( h 1 ⋯ h n ) X in Rogers is equivalent to a version one can derive using the definition of a n -hadron fragmentation function (FF) introduced in Pitonyak . 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 should be considered the standard one while the definition in Rogers has no clear interpretation. We also emphasize that the evolution equations for dihadron FFs (DiFFs) in Pitonyak have the same splitting functions as those for single-hadron FFs. Therefore, the DiFF (and n -hadron FF) definitions in Pitonyak have a natural number density interpretation and, contrary to what is stated in Rogers , are consistent with collinear factorization using the standard hard factors and evolution kernels.

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.

We investigate the collinear matching of transverse momentum dependent (TMD) distributions at large values of x, computing and resumming the leading large-x asymptotics for matching coefficients. The large-x resummation is done directly within TMD distributions, ensuring the process-independence of the result. The derived resummation formulas are valid for all TMD distributions (except the pretzelosity). Their application improves perturbative convergence, provides practical estimation for unknown higher-order contributions, and sets restrictions for the nonperturbative part of models. Using the known anomalous dimensions, resummation can reach N³LL, often exceeding the accuracy of known coefficient functions.