Transverse Structure of the Kaon: A light-front Hamiltonian Approach

Abstract

We employ the Basis Light-Front Quantization (BLFQ) framework to compute the leading-twist (twist-2) and subleading-twist (twist-3) transverse-momentum-dependent parton distribution functions (TMDs) of the kaon. The light-front wave functions are obtained by diagonalizing a light-front QCD Hamiltonian that includes quark-antiquark (|q\bar{q}\rangle) and quark-antiquark-gluon (|q\bar{q}g\rangle) Fock components together with a three-dimensional confinement. Using the QCD equations of motion, the twist-3 TMDs are decomposed into twist-2 constributions and genuine twist-3 terms, the latter encoding quark-quark-gluon correlations beyond the probabilistic picture. These genuine twist-3 constributions arise from the interference between the |q\bar{q}\rangle and |q\bar{q}g\rangle sectors, which are usually negelected in the Wandzura-Wilczek approximation. This work provides the first theoretical predictions of kaon subleading-twist TMDs that explicitly account for Fock-sector interference. In addition, we present results for the kaon's twist-2 and twist-3 collinear parton distribution functions (PDFs). The twist-2 PDFs are found to be in good agreement with the recent global analysis by the JAM collaboration.

Figures (12)

• Figure 1: 3D plots of the BLFQ results for the twist-2 TMD $f_1(x,k_\perp)$ of the kaon. The left, middle, and right panels correspond to the $\bar{s}$ quark, $u$ quark, and gluon, respectively. As described in the text, all results are obtained by averaging over BLFQ calculations with $N_{\mathrm{max}}=\{12,14,16\}$ and $K=15$.
• Figure 2: Contributions from the $|q\bar{q}\rangle$ (red lines) and $|q\bar{q}g\rangle$ (blue lines) Fock sectors to the total (black lines) twist-2 TMD $f_1(x,k_\perp)$ of the kaon. The left, middle, and right panels correspond to the $\bar{s}$ quark, $u$ quark, and gluon, respectively. In the upper panels, the TMDs are shown as functions of $x$ at fixed $k_\perp = 0.22~\mathrm{GeV}$. In the lower panels, the TMDs are shown as functions of $k_\perp$ at fixed $x = 2.5/15$ for a quark and $x = 3/15$ for a gluon. As described in the text, all results are obtained by averaging over BLFQ calculations with $N_{\mathrm{max}}=\{12,14,16\}$ and $K=15$.
• Figure 3: 3D plots of the BLFQ results for the twist-3 TMDs $e(x,k_{\perp})$ (left panels) and $f^{\perp}(x,k_{\perp})$ (right panels). The upper panels correspond to the $\bar{s}$ quark, while the lower panels correspond to the $u$ quark. As described in the text, all results are obtained by averaging over BLFQ calculations with $N_{\mathrm{max}}=\{12,14,16\}$ and $K=15$. Note the differences in the vertical scales.
• Figure 4: 3D plots of the BLFQ results for the genuine twist-3 TMDs $\tilde{e}(x,k_{\perp})$ (left panels) and $\tilde{f}^{\perp}(x,k_{\perp})$ (right panels). The upper panels correspond to the $\bar{s}$ quark, while the lower panels correspond to the $u$ quark. As described in the text, all results are obtained by averaging over BLFQ calculations with $N_{\mathrm{max}}=\{12,14,16\}$ and $K=15$.
• Figure 5: 2D slices of the 3D BLFQ results for the genuine twist-3 TMDs $\tilde{e}(x,k_\perp)$ (left panels) and $\tilde{f}^{\perp}(x,k_\perp)$ (right panels). In the upper panels, the TMDs are shown as functions of $x$ at fixed $k_\perp = 0.22~\mathrm{GeV}$. In the middle panel, the TMDs $x\tilde{e}(x,k_{\perp})$ and $x\tilde{f}(x,k_{\perp})$ are shown as functions of $x$ with the same fixed $k_{\perp}$. In the lower panels, the TMDs are shown as functions of $k_\perp$ at fixed $x = 2.5/15$. The red and blue curves correspond to the $\bar{s}$ and $u$ quarks, respectively. As described in the text, all results are obtained by averaging over BLFQ calculations with $N_{\mathrm{max}}=\{12,14,16\}$ and $K=15$.