Unified description of Sivers and Boer-Mulders asymmetries from twist-3 correlations

Abstract

We present the first calculation of the Efremov-Teryaev-Qiu-Sterman functions and associated twist-3 quark-gluon correlation functions for both the proton and pion. These functions are determined using the light-front wave functions obtained by diagonalizing a light-front effective Hamiltonian within a Fock space truncated to include a dynamical gluon. We compute the twist-3 correlations in the hard-pole region and extrapolate them to the soft-gluon pole limit. After the scale evolutions, our predictions demonstrate quantitative consistency with recent experimental extractions, providing a unified description of the Sivers and Boer-Mulders asymmetries from a light-front Hamiltonian approach.

Figures (6)

• Figure 1: The proton ETQS function $T_F(x,x)$ for $u$ (left) and $d$ (right) quarks at $\mu^2 = 100\; \mathrm{GeV}^2$. The black curves with bands represent the BLFQ results with uncertainty estimates. Color bands represent experimental extractions from JAM20 Cammarota:2020qcw, EKT20 Echevarria:2020hpy, and PV20 Bacchetta:2020gko.
• Figure 2: The first transverse moment of the proton Sivers function, $x f_{1T}^{\perp(1)}(x)$. BLFQ predictions (black curves) are compared with extractions from JAM22 Gamberg:2022kdb, EIKV Echevarria:2014xaa, TC Boglione:2018dqd, and PV11 Bacchetta:2011gx.
• Figure 3: Comparison of $T_{F}^{(\sigma)}(x,x)$ and $xh_{1}^{\perp(1)}(x)$ for the proton and pion. Left: The associated twist-3 function $T_{F}^{(\sigma)}(x,x)$ at $\mu^2 = 100\; \mathrm{GeV}^2$. Right: The first transverse moment of the Boer-Mulders function $x h_{1}^{\perp(1)}(x)$ at $\mu^2 = 4\; \mathrm{GeV}^2$. Blue and red curves denote the $u$ and $d$ quarks in the proton, respectively; orange curves denote the light quark in the pion.
• Figure 4: Three-dimensional plots of the proton twist-3 functions at the initial scale for the $u$ quark (left column) and the $d$ quark (right column).
• Figure 5: Three-dimensional plot of the pion twist-3 function $T_F^{(\sigma)}$ at the initial scale.