New findings in gluon TMD physics

We revisit the model-independent decomposition of the gluon correlator, producing T-even and T-odd gluon transverse momentum distributions (TMDs), at leading twist. We propose an expansion of the gluon correlator, using a basis of four tensors (one antisymmetric and three symmetric), which are expressed through generators of the U(2) group acting in the two-dimensional transverse plane. One can do clear interpretations of the two transversity T-odd TMDs with linear polarization of gluons: symmetric and asymmetric under permutation of the transverse spin of the nucleon and the transverse momentum of the gluon. Using light-front wave function (LFWF) representation, we also derive T-even and T-odd gluon TMDs in the nucleon at leading twist. The gluon–three-quark Fock commponent in the nucleon is considered as bound state of gluon and three-quark core (spectator). The TMDs are constructed as factorized product of two LFWFs and gluonic matrix encoding information about both T-even and T-odd TMDs. In particular, T-odd TMDs arise due to gluon rescattering between the gluon and three-quark spectator. Gluon rescattering effects are parametrized by unknown scalar functions depending on the x and k⊥ variables. Our gluon TMDs obey the model-independent Mulders-Rodrigues inequalities. We also derive new sum rules (SRs) involving T-even TMDs. One of the SRs states that the square of the unpolarized TMD is equal to a sum of the squares of three polarized TMDs. Based on the SR derived for T-even gluon TMDs, we make a conjecture that there should two additional SRs involving T-odd gluon TMDs, valid at orders αs and α2s. Then, we check these SRs at small and large values of x. We think that our study could serve as useful input for future phenomenological studies of TMDs.