Contact interaction analysis of pion GTMDs

Abstract

A contact interaction is used to calculate an array of pion twist-two, -three and -four generalised transverse light-front momentum dependent parton distribution functions (GTMDs). Despite the interaction’s simplicity, many of the results are physically relevant, amongst them a statement that GTMD size and shape are largely prescribed by the scale of emergent hadronic mass. Moreover, proceeding from GTMDs to generalised parton distributions, it is found that the pion’s mass distribution form factor is harder than its electromagnetic form factor, which is harder than the gravitational pressure distribution form factor; the pressure in the neighbourhood of the pion’s core is commensurate with that at the centre of a neutron star; the shear pressure is maximal when confinement forces become dominant within the pion; and the spatial distribution of transversely polarised quarks within the pion is asymmetric. Regarding transverse momentum dependent distribution functions, their magnitude and domain of material support decrease with increasing twist. The simplest Wigner distribution associated with the pion’s twist-two dressed-quark GTMD is sharply peaked on the kinematic domain associated with valence-quark dominance; has a domain of negative support; and broadens as the transverse position variable increases in magnitude.

Concerning pion parton distributions

“…(3) expresses intrinsic properties of the pion LFWF. This fact is expressed in all existing calculations, as highlighted elsewhere [59][60][61][62][63][64][65][66][67][68][69][70][71][72]. Indeed, working in the chiral limit and assuming that chiral symmetry is dynamically broken, so m 2 π = 0 in the presence of a dynamically generated dressed-quark mass [13][14][15][16][17][18], one can show algebraically [10, Sec.…”

“…To elucidate, we consider the valence-quark DF for a m π = 0.14 GeV pion obtained using a symmetry-preserving regularisation of a vector × vector contact interaction (SCI) [68]:…”

“…Since it provides a largely algebraic framework, the SCI has been widely used [68,[84][85][86][87] to set benchmarks for more complex studies using QCD-kindred interactions. Comparisons with such calculations [86,[88][89][90] and also data [91][92][93] show that SCI results are typically a reliable guide for long-wavelength properties of hadrons, such as masses and decay constants, but, unsurprisingly, fail in applications that are sensitive to and/or reveal structural properties.…”

Kaon generalized parton distributions and light-front wave functions in the Nambu–Jona-Lasinio model

“…Thus, several modeling frameworks have been used in the last few decades, each one having its advantages. For instance, we have the Nambu-Jona-Lasinio (NJL) model [63][64][65][66][67][68], the constituent quark model [69][70][71], the light-front holographic model [72][73][74], the light-front quark-diquark model [75][76][77], the AdS/QCD model [78][79][80], the chiral quark model [81,82] and the Dyson-Schwinger equations (DSEs) [7,8,83]. The NJL model has an effective Lagrangian of relativistic fermions interacting through local fermion-fermion couplings, and especially, it preserves one of the most important fundamental symmetries of QCD, namely, chiral symmetry.…”

“…We also give the light-cone energy radius for the quarks of the kaon from the mass distribution θ 2 : r u,K E,LC = 0.187 fm, r s,K E,LC = 0.167 fm, and the light-cone charge radius from quark form factors of the kaon: r u,K c,LC = 0.390 fm, r s,K c,LC = 0.296 fm, which means that the s quark has a smaller extent than the u quark. Generalized parton distributions (GPDs) [1][2][3][4][5][6][7][8][9] were proposed in the 1990s to describe the multi-dimensional pictures of hadrons. GPDs include a mass of inaccessible information about the partonic structure of hadrons; therefore, GPDs have been under thorough theoretical and experimental studies ever since.…”