Abstract
We predict the twist-2 Transverse Momentum Dependent parton distribution functions (TMDs) of the pion, namely the unpolarized quark TMD, $f_{1}(x, k_\perp)$, and the transversely polarized quark TMD, also known as the Boer-Mulders function, $h^\perp_{1}(x, k_\perp)$, using a holographic light-front pion wavefunction with dynamical spin effects. These spin effects, in conjunction with gluon rescattering, are crucial to predict a non-zero holographic Boer-Mulders function. We investigate the use of a non-perturbative SU(3) gluon rescattering kernel, thus going beyond the usual approximation of perturbative U(1) gluons. We find that the non-perturbative color dynamics offer a more promising way to describe the available lattice data on the generalized Boer-Mulders shifts.
Highlights
Transverse momentum dependent parton distributions functions (TMDs) contain important information on the three-dimensional internal structure of hadrons, especially the spin-orbit correlations of quarks within them [1]
The Boer-Mulders function is naively a T-odd distribution and such distributions were initially thought to vanish due to the time reversal invariance of QCD [4] but later it became apparent that they can be dynamically generated by initial or final state interactions [5,6]
A string theory in the higher dimensional anti-de Sitter (AdS) space. In this gauge/gravity duality, the radial lightfront variable ζ maps onto the fifth dimension in AdS space and the mass scale κ emerging from the dAFF mechanism governs simultaneously the strength of the confining harmonic potential in physical spacetime and that of the dilaton field which breaks conformal invariance in AdS space
Summary
Transverse momentum dependent parton distributions functions (TMDs) contain important information on the three-dimensional internal structure of hadrons, especially the spin-orbit correlations of quarks within them [1]. F1ðx; k⊥Þ describes the momentum distribution of unpolarized quarks within the pion while h⊥1 ðx; k⊥Þ describes the spin-orbit correlations of transversely polarized quarks within the pion. The gauge link makes these distributions process-dependent, flipping their sign from semi-inclusive deep inelastic scattering (SIDIS) to DrellYan (DY) scattering. In conjunction with their nucleon counterparts, the pion unpolarized TMD and the Boer-Mulders function are inputs in the theoretical predictions of the cross sections and azimuthal asymmetries for unpolarized pion-induced DY scattering [10,11] which have both been measured [12,13,14]. We shall predict the so-called generalized Boer-Mulders shifts in order to compare with the lattice data of Ref. [26]
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