{"arxiv_id":"2003.03037","incoming":{"papers":14,"sentences":28,"groups":[{"kind":"extends","label":"Builds on it","papers":1,"sentences":1,"quotes":[{"arxiv_id":"2108.10625","title":"Ground state pseudoscalar mesons on the light front: from the light to heavy sector","url":"/paper/2108.10625","section":"INTRODUCTION","sentence":"In this work, based on the study of the pion at physical mass in [ref] , we will predict LF-LFWFs of fictitious pion at masses of 310 MeV and 690 MeV which are directly accessible by lattice QCD, as well as $η_c$ and $η_b$ from the heavy sector.","intent_p":0.97,"contests_p":null}]},{"kind":"method_or_tool","label":"Uses its method or tool","papers":3,"sentences":4,"quotes":[{"arxiv_id":"2101.09910","title":"The light front wave functions and diffractive electroproduction of vector mesons","url":"/paper/2101.09910","section":"From vector meson Bethe-Salpeter wave functions to LF-LFWFs.","sentence":"To compute the $J/ψ$ LFWFs, we adopt the technique used in [ref] : by fitting the meson BS amplitude with Nakanishi-like representation [ref] and the quark propagator with pairs of complex conjugate poles form which is particularly accurate in heavy sector [ref] , we are able to compute point-wisely accurate LFWFs.","intent_p":1.0,"contests_p":null},{"arxiv_id":"2110.06463","title":"Regularization dependence of pion generalised parton distributions","url":"/paper/2110.06463","section":"The definition and calculation of pion GPDs","sentence":"Ref. [ref] has showed the process in their appendix, the inhomogeneous BSE in Fig. [ref], on the right side, the first diagram is the bare vertex corresponds to the bare vector GPD $H^a(x,ξ,t)$, the second term corresponds to the dressed GPD term $H^c(x,ξ,t)$ which is plotted in Fig. [ref], after some calculation, we get the final form of $H^c$","intent_p":0.89,"contests_p":null},{"arxiv_id":"2108.10625","title":"Ground state pseudoscalar mesons on the light front: from the light to heavy sector","url":"/paper/2108.10625","section":"From Bethe-Salpeter wave functions to LF-LFWFs","sentence":"Using Eqs.([ref]-[ref]) and Eqs.([ref],[ref]), one can reproduce the pointwise behavior of $ψ(x,k_T^2)$ with very high precision, using same method explained in section II of [ref] .","intent_p":0.86,"contests_p":null}]},{"kind":"comparison","label":"Compares with it","papers":4,"sentences":8,"quotes":[{"arxiv_id":"2301.11599","title":"Unpolarized transverse-momentum dependent distribution functions of a quark in a pion with Minkowskian dynamics","url":"/paper/2301.11599","section":"Transverse degree of freedom","sentence":"A more detailed view of the fall-off can be gained from the right panel of Fig. [ref], where $f^S⊥(γ,ξ=0.5)$ is compared with the results obtained by using i) the LF constituent quark model of Ref. [ref] (cf. the second line in Eq. [ref], without the gluonic term). ii) the LF wave function from DSE calculations [ref] and iii) the NJL model [ref] .","intent_p":1.0,"contests_p":null},{"arxiv_id":"2409.05098","title":"Heavy flavor-asymmetric pseudoscalar mesons on the light front","url":"/paper/2409.05098","section":"Three-dimensional Parton distribution functions of the heavy-light pseudoscalar mesons.","sentence":"Defining their mean squared impact parameter $⟨b_T^2 ⟩^q= ∫d b_T^2 b_T^2 ρ^q,(0)(b_T^2)$ as a measure for their spatial extension, we find $⟨b_T^2 ⟩^c_D=(0.13 fm)^2$, $⟨b_T^2 ⟩^u̅_D=(0.40 fm)^2$, $⟨b_T^2 ⟩^b_B=(0.056 fm)^2$, $⟨b_T^2 ⟩^u̅_B=(0.47 fm)^2$ and $⟨b_T^2 ⟩^b_B_c=(0.077 fm)^2$, $⟨b_T^2 ⟩^c̅_B_c=(0.22 fm)^2$, in comparison with our results in pion and heavy quarkonium $⟨b_T^2 ⟩^u_π=(0.33 fm)^2$ [ref] , $⟨b_T^2 ⟩^c_η_c=(0.16 fm)^2$ and $⟨b_T^2 ⟩^b_η_b=(0.092 fm)^2$ [ref] .","intent_p":0.95,"contests_p":null},{"arxiv_id":"2108.10625","title":"Ground state pseudoscalar mesons on the light front: from the light to heavy sector","url":"/paper/2108.10625","section":"Spatial and Momentum Tomography of the heavy pseudoscalar mesons.","sentence":"Comparing with our results on pion and kaon $⟨b_T^2 ⟩^u_π=(0.332 fm)^2$, $⟨b_T^2 ⟩^u_K=(0.361 fm)^2$ and $⟨b_T^2 ⟩^s_K=(0.283 fm)^2$ from [ref] , one finds the heavy mesons are considerably more compact in the transverse plane on the light front.","intent_p":0.93,"contests_p":null},{"arxiv_id":"2205.04714","title":"Transverse momentum structure of proton within the basis light-front quantization framework","url":"/paper/2205.04714","section":"TMDs within the BLFQ framework","sentence":"We note that the qualitative behaviors of our TMDs are similar to those of other theoretical calculations in [ref] .","intent_p":0.99,"contests_p":null}]},{"kind":"background","label":"Cites it as background","papers":3,"sentences":4,"quotes":[{"arxiv_id":"2301.11599","title":"Unpolarized transverse-momentum dependent distribution functions of a quark in a pion with Minkowskian dynamics","url":"/paper/2301.11599","section":"Introduction","sentence":"In view of our study, one has to separately mention the approaches developed within the so-called continuum-QCD, that are based on solutions (actually in Euclidean space) of dynamical equations like the homogeneous 4D Bethe-Salpeter equation (BSE) [ref] in combination or not with the quark gap-equation (see, e.g. Refs. [ref] ).","intent_p":0.82,"contests_p":null},{"arxiv_id":"2205.04714","title":"Transverse momentum structure of proton within the basis light-front quantization framework","url":"/paper/2205.04714","section":"Introduction","sentence":"Meanwhile, promising theoretical frameworks for accessing TMDs also include the discretized space-time Euclidean lattice [ref] and the Dyson–Schwinger equations approach [ref] .","intent_p":0.93,"contests_p":null},{"arxiv_id":"2010.12498","title":"Transverse structure of electron in momentum space in basis light-front quantization","url":"/paper/2010.12498","section":"Introduction","sentence":"Meanwhile, promising theoretical frameworks for illuminating TMDs also include the Dyson–Schwinger equations approach [ref] and the discretized space-time euclidean lattice [ref] .","intent_p":0.91,"contests_p":null}]}],"unlabelled_sentences":11},"outgoing":{"papers":61,"sentences":89,"groups":[{"kind":"method_or_tool","label":"Uses the method or tool of","papers":3,"sentences":3,"quotes":[{"arxiv_id":"1009.3458","title":"Dressed-quark anomalous magnetic moments","url":"/paper/1009.3458","section":"Parameterization of $S(k)$ and $Γ(k;P)$","sentence":"To aid the calculation of the moments $< x^m >_l_z$ we use an accurate parametrization of numerical solutions to the gap and BSEs in the DCSB-improved truncation to the DSEs [ref] .","intent_p":0.88,"contests_p":null},{"arxiv_id":"1301.0324","title":"Imaging dynamical chiral symmetry breaking: pion wave function on the light front","url":"/paper/1301.0324","section":"Parameterization of $S(k)$ and $Γ(k;P)$","sentence":"To aid the calculation of the moments $< x^m >_l_z$ we use an accurate parametrization of numerical solutions to the gap and BSEs in the DCSB-improved truncation to the DSEs [ref] .","intent_p":0.88,"contests_p":null},{"arxiv_id":"1907.08256","title":"Impact of DCSB and dynamical diquark correlations on proton GPDs","url":"/paper/1907.08256","section":"ELECTROMAGNETIC AND GRAVITATIONAL FORM FACTORS","sentence":"Using a dressed operator that defines the GPD from the NJL model [ref] , we find in the impulse approximation that our leading Fock state DSE result is modified such that","intent_p":0.8,"contests_p":null}]},{"kind":"data_used","label":"Uses data or values from","papers":4,"sentences":5,"quotes":[{"arxiv_id":"1806.04799","title":"Intrinsic Transverse Motion of the Pion's Valence Quarks","url":"/paper/1806.04799","section":"PION AND KAON LIGHT FRONT WAVE FUNCTIONS","sentence":"This approximation to the full valence quark distribution function is best at a low hadronic scale $μ_0$, which in Ref. [ref] was determined to be $μ_0 = 520$MeV.","intent_p":0.95,"contests_p":null},{"arxiv_id":"hep-lat/0303015","title":"Parton distribution functions in the pion from lattice QCD","url":"/paper/hep-lat/0303015","section":"GPDS AT ZERO SKEWNESS","sentence":"The initial scale $μ_0$ is determined as follows (see Ref. [ref] ): At the scale of $Q^2 = 4$GeV$^2$, the $πN$ Drell-Yan analysis gives averaged momentum fraction of valence quark distribution in pion as $2 ⟨x ⟩_v = 0.47(2)$ [ref] and the lattice QCD gives $2 ⟨x ⟩_v = 0.48(4)$ [ref] .","intent_p":0.97,"contests_p":null},{"arxiv_id":"hep-ph/9903288","title":"Pionic Parton Distributions Revisited","url":"/paper/hep-ph/9903288","section":"GPDS AT ZERO SKEWNESS","sentence":"The initial scale $μ_0$ is determined as follows (see Ref. [ref] ): At the scale of $Q^2 = 4$GeV$^2$, the $πN$ Drell-Yan analysis gives averaged momentum fraction of valence quark distribution in pion as $2 ⟨x ⟩_v = 0.47(2)$ [ref] and the lattice QCD gives $2 ⟨x ⟩_v = 0.48(4)$ [ref] .","intent_p":0.97,"contests_p":null},{"arxiv_id":"1405.5542","title":"Role of diquark correlations and the pion cloud in nucleon elastic form factors","url":"/paper/1405.5542","section":"Dressed GPD operator at zero skewness in NJL model","sentence":"Here the proper time regularization is used, with parameters determined by hadron mass spectrum and decay constant from Table 1 in Ref. [ref] , i.e., $Λ_IR=0.24$ GeV, $Λ_UV=0.645$ GeV, $M=0.4$ GeV and $G_ρ=11.0$ GeV$^-2$.","intent_p":0.94,"contests_p":null}]},{"kind":"comparison","label":"Compares with","papers":3,"sentences":3,"quotes":[{"arxiv_id":"nucl-th/0005015","title":"The $\\pi$, $K^+$, and $K^0$ electromagnetic form factors","url":"/paper/nucl-th/0005015","section":"ELECTROMAGNETIC AND GRAVITATIONAL FORM FACTORS","sentence":"In general we find that our result overshoots the data for all $Q^2$, and also the full DSE calculation that uses the Bethe-Salpeter wave function and a dressed quark-photon vertex to directly calculate the pion's form factor [ref] .","intent_p":0.99,"contests_p":null},{"arxiv_id":"nucl-th/9405014","title":"Hard Constituent Quarks and Electroweak Properties of Pseudoscalar Mesons","url":"/paper/nucl-th/9405014","section":"ELECTROMAGNETIC AND GRAVITATIONAL FORM FACTORS","sentence":"A similar result was also found using a relativistic constituent quark model based on an effective $qq̅$ Hamiltonian [ref] , where a pion charge radius of $r_c = 0.45$ fm was found [ref] .","intent_p":0.87,"contests_p":null},{"arxiv_id":"0809.1744","title":"Gravitational and higher-order form factors of the pion in chiral quark models","url":"/paper/0809.1744","section":"ELECTROMAGNETIC AND GRAVITATIONAL FORM FACTORS","sentence":"It is closer to the NJL model result (blue dashed) [ref] than to the spectral quark model [ref] .","intent_p":1.0,"contests_p":null}]},{"kind":"supports_this_paper","label":"Cites as support","papers":1,"sentences":1,"quotes":[{"arxiv_id":"nucl-th/9707003","title":"Pion mass and decay constant","url":"/paper/nucl-th/9707003","section":"PION AND KAON LIGHT FRONT WAVE FUNCTIONS","sentence":"The strong support of the LFWFs at infrared $k_T^2$ originates from the strength of the covariant Bethe-Salpeter wave functions at low $|k_T|$, which is closely connected to DCSB, as illustrated model-independently in Ref. [ref] .","intent_p":0.99,"contests_p":null}]},{"kind":"background","label":"Cites as background","papers":11,"sentences":16,"quotes":[{"arxiv_id":"hep-ph/0005108","title":"Impact Parameter Dependent Parton Distributions and Off-Forward Parton Distributions for $\\zeta\\to 0$","url":"/paper/hep-ph/0005108","section":"GPDS AT ZERO SKEWNESS","sentence":"The IPDs have the interpretation of parton distributions in the transverse plane [ref] , with $x$ the light-cone momentum fraction and $b_T$ the transverse separation between the active parton and the origin of transverse center of momentum $R_T$.","intent_p":0.91,"contests_p":null},{"arxiv_id":"hep-ph/0207047","title":"Impact Parameter Space Interpretation for Generalized Parton Distributions","url":"/paper/hep-ph/0207047","section":"GPDS AT ZERO SKEWNESS","sentence":"The IPDs have the interpretation of parton distributions in the transverse plane [ref] , with $x$ the light-cone momentum fraction and $b_T$ the transverse separation between the active parton and the origin of transverse center of momentum $R_T$.","intent_p":0.91,"contests_p":null},{"arxiv_id":"hep-ph/0307382","title":"Generalized Parton Distributions","url":"/paper/hep-ph/0307382","section":"GPDS AT ZERO SKEWNESS","sentence":"where the gauge link is unity [ref] , $x$ denotes the parton's averaged light-cone momentum fraction, the skewness parameter is $ξ=-Δ^+/2 P^+$, and the momentum transfer $t = Δ^2 = -4ξ^2 m_M^2+Δ_T^2/1-ξ^2$.","intent_p":0.85,"contests_p":null},{"arxiv_id":"hep-ph/9609381","title":"Deeply Virtual Compton Scattering","url":"/paper/hep-ph/9609381","section":"GPDS AT ZERO SKEWNESS","sentence":"where the gauge link is unity [ref] , $x$ denotes the parton's averaged light-cone momentum fraction, the skewness parameter is $ξ=-Δ^+/2 P^+$, and the momentum transfer $t = Δ^2 = -4ξ^2 m_M^2+Δ_T^2/1-ξ^2$.","intent_p":0.85,"contests_p":null},{"arxiv_id":"1310.2651","title":"Explanation and Prediction of Observables using Continuum Strong QCD","url":"/paper/1310.2651","section":"INTRODUCTION","sentence":"In the past few decades the DSE framework has been applied extensively to hadron physics [ref] .","intent_p":1.0,"contests_p":null}]}],"unlabelled_sentences":61},"claims":[],"thresholds":{"intent_p":0.8,"supports_p":0.95,"contests_p":0.7},"method":"Citing sentences come from each paper's LaTeX source; every \\cite marks the sentence and the works it cites. Pith's classifier typed each sentence. A label is shown at intent probability 0.8 or more (0.95 for support), a contest at 0.7 or more. Measured accuracy against two blind model families is at https://pith.science/accuracy. The quoted sentences are the citing authors' own.","held_up":null,"_links":{"html":"https://pith.science/paper/2003.03037"}}