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We investigate the transverse energy-energy correlator (TEEC) event-shape observable for back-to-back $\gamma +h$and $Z+h$production in both $pp$and $pA$collisions. Our study incorporates nuclear modifications into the transverse-momentum dependent (TMD) factorization framework, with resummation up to next-to-leading logarithmic accuracy, for TEEC as a function of the variable $\tau =(1+\cos \varphi )/2$, where $\varphi$is the azimuthal angle between the vector boson and the final hadron. We analyze the nuclear modification factor $R_{pA}$in $p\mathrm{Au}$collisions at Relativistic Heavy Ion Collider and $p\mathrm{Pb}$collisions at the Large Hadron Collider. Our results demonstrate that the TEEC observable is a sensitive probe for nuclear modifications in TMD physics. Specifically, the changes in the $\tau$-distribution shape provide insights into transverse momentum broadening effects in large nuclei, while measurements at different rapidities allow us to explore nuclear modifications in the collinear component of the TMD parton distribution functions in nuclei. 

We investigate the transverse energy-energy correlators (TEEC) in the small- $x$regime at the upcoming Electron-Ion Collider (EIC). Focusing on the back-to-back production of electron-hadron pairs in both $ep$and $eA$collisions, we establish a factorization formula given in terms of the hard function, quark distributions, soft functions, and TEEC jet functions, where the gluon saturation effect is incorporated. Numerical results for TEEC in both $ep$and $eA$collisions are presented, together with the nuclear modification factor $R_A$. Our analysis reveals that TEEC observables in deep inelastic scattering provide a valuable approach for probing gluon saturation phenomena. Our findings underscore the significance of measuring TEEC at the EIC, emphasizing its efficacy in advancing our understanding of gluon saturation and nuclear modifications in high-energy collisions. Published by the American Physical Society2024 

A<sc>bstract</sc> In this work, we present a complete theoretical framework for analyzing the distribution of polarized hadrons within jets, with and without measuring the transverse momentum relative to the standard jet axis. Using soft-collinear effective theory (SCET), we derive the factorization and provide the theoretical calculation of both semi-inclusive and exclusive fragmenting jet functions (FJFs) under longitudinal and transverse polarization. With the polarized FJFs, one gains access to a variety of new observables that can be used for extracting both collinear and transverse momentum dependent parton distribution functions (PDFs) and fragmentation functions (FFs). As examples, we provide numerical results for the spin asymmetry$$ {A}_{TU,T}^{\cos \left({\phi}_S-{\hat{\phi}}_{S_h}\right)} $$ $A_{\mathrm{TU},T}^{cos\left({\varphi }_S-{\hat{\varphi }}_{S_h}\right)}$from polarized semi-inclusive hadron-in-jet production in polarizedppcollisions at RHIC kinematics, where a transversely polarized quark would lead to the transverse spin of the final-state hadron inside the jet and is thus sensitive to the transversity fragmentation functions. Similarly, another spin asymmetry,$$ {A}_{TU,L}^{\cos \left({\phi}_q-{\phi}_S\right)} $$ $A_{\mathrm{TU},L}^{cos\left({\varphi }_q-{\varphi }_S\right)}$from polarized exclusive hadron-in-jet production in polarizedepcollisions at EIC kinematics would allow us to access the helicity fragmentation functions. These observables demonstrate promising potential in investigating transverse momentum dependent PDFs and FFs and are worthwhile for further measurements. 

A recent global QCD analysis of jet production and other polarized scattering data has found the presence of negative solutions for the gluon helicity distribution in the proton, Δ⁢𝑔, along with the traditional Δ⁢𝑔>0 solutions. We consider polarized semi-inclusive deep-inelastic scattering for hadrons produced with large transverse momentum as a means of constraining the dependence of Δ⁢𝑔 on the parton momentum fraction, 𝑥. Focusing on the double longitudinal spin asymmetry, we identify the kinematics relevant for future experiments at Jefferson Lab and the Electron-Ion Collider that are particularly sensitive to the polarized gluon channel and could discriminate between the different Δ⁢𝑔 behaviors. We find that a ∼20  GeV beam at the high luminosity Jefferson Lab may be especially well-suited for discriminating between the positive and negative solutions.