2021/08/03 by Kumano, S., Song, Qin-Tao
#FOS: Physical sciences #High Energy Physics - Experiment (hep-ex) #High Energy Physics - Lattice (hep-lat) #High Energy Physics - Phenomenology (hep-ph) #Nuclear Theory (nucl-th)
paper · doi:10.48550/arxiv.2108.01381
We show transverse-momentum-dependent parton distribution functions (TMDs) for spin-1 hadrons including twist-3 and 4 functions by taking the decomposition of a quark correlation function in the Lorentz-invariant way with the conditions of Hermiticity and parity invariance. We found 30 new TMDs in the tensor-polarized spin-1 hadron at twists 3 and 4 in addition to 10 TMDs at twist 2. Since time-reversal-odd terms of the collinear correlation function should vanish after integrals over the partonic transverse momentum, we obtained new sum rules for the time-reversal-odd structure functions, \bm∫ d2 kT gLT = ∫ d2 kT hLL = ∫ d2 kT h3LL\bm=0, at twists 3 and 4. We also indicated that transverse-momentum-dependent fragmentation functions exist in tensor-polarized spin-1 hadrons. The TMDs can probe color degrees of freedom, so that they are valuable in providing unique opportunities for creating interdisciplinary physics fields such as gluon condensate, color Aharonov-Bohm effect, and color entanglement. We also found three new collinear PDFs at twists 3 and 4, and a twist-2 relation and a sum rule were derived in analogy to the Wandzura-Wilczek relation and the Burkhardt-Cottingham sum rule on the structure function \bmg2.