Abstract
We determine the leading Fock state light front wave functions (LFWFs) of the pion and kaon via light front projections of the covariant Bethe-Salpeter wave function. Using these LFWFs we study the multi-dimensional images of the valence quarks in the pion and kaon that are provided by their generalized parton distribution functions (GPDs) and transverse momentum dependent parton distribution functions (TMDs). Moments of the GPDs are taken to obtain the electromagnetic and gravitational form factors of the pion and kaon, and comparisons to available experimental and lattice data are made. Highlights from this study include predictions that the mean-squared impact parameter for the quarks in the pion and kaon are: $\langle \vec{b}_T^2\rangle_{u}^\pi=0.11$fm$^2$, $\langle \vec{b}_T^2\rangle_{s}^K=0.08$fm$^2$, and $\langle \vec{b}_T^2\rangle_{u}^K=0.13$fm$^2$, and therefore the $s$ quark in the kaon is much closer to the center of transverse momentum than the $u$ quark. From the electromagnetic and gravitational form factors we find that the light-cone energy radii are about 60\% smaller than the light-cone charge radii for each quark sector in the pion and kaon. A quantitative measure of the importance of the leading Fock state is obtained via comparison with a full DSE calculation (containing an infinite tower of Fock states) for the pion form factor.
Highlights
Multidimensional images of the partonic structure of hadrons are provided by the generalized parton distribution functions (GPDs) [1,2,3] and transverse momentum dependent parton distributions functions (TMDs) [4]
In this paper we extend this work to the kaon light front wave functions (LFWFs) and TMDs, and the study of pion and kaon GPDs
The kaon’s LFWFs based on a DysonSchwinger equations (DSE) approach are given for the first time. These LFWFs are significantly enhanced at low jkTj and exhibit the perturbative quantum chromodynamics (QCD) power law behavior at large jkTj
Summary
Multidimensional images of the partonic structure of hadrons are provided by the generalized parton distribution functions (GPDs) [1,2,3] and transverse momentum dependent parton distributions functions (TMDs) [4]. Lattice QCD has typically been limited to certain aspects of GPDs and TMDs, such as low x-weighted moments, together with their k2T-dependence for TMDs or t-dependence [8,9,10] for GPDs [11,12,13] New approaches, such as large-momentum effective theory (LaMET) [14,15,16,17], enable lattice QCD to reveal much richer information on GPDs and TMDs. Model calculations are crucial, as they can help provide an intuitive picture of the GPDs and TMDs. For instance, using the Nambu–Jona-Lasinio model or the spectral quark model one can calculate the full pion GPD over the entire kinematic range jxj < 1, jξj < 1 [18]. In a recent work the pion’s leading Fock state LFWFs were obtained from its Bethe-Salpeter wave function provided by a DSE calculation [33], and used to study the pion TMD.
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