Nonperturbative features of the axial current

Kopeliovich, B. Z.; Schmidt, Iván; Siddikov, Marat

doi:10.1016/j.nuclphysa.2013.09.009

Cited by 12 publications

(16 citation statements)

References 46 publications

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“…Within the domain upon which perturbation theory is valid, evolution to another scale ζ is described by the ERBL equations [30,31] for |x| < ξ and the DGLAP equations [32][33][34][35] [36,37]: it is a fixed point of the renormalisation group; and a covariant gauge, which is readily implemented in numerical simulations of lattice-QCD. It is therefore significant that W[−z/2, z/2] is not quantitatively important in the calculation of the leading-twist contributions to numerous matrix elements [38].…”

Section: General Features Of Pion Gpdsmentioning

confidence: 99%

Sketching the pion's valence-quark generalised parton distribution

et al. 2015

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International audienceIn order to learn effectively from measurements of generalised parton distributions (GPDs), it is desirable to compute them using a framework that can potentially connect empirical information with basic features of the Standard Model. We sketch an approach to such computations, based upon a rainbow-ladder (RL) truncation of QCD's Dyson–Schwinger equations and exemplified via the pion's valence dressed-quark GPD, Hπv(x,ξ,t) . Our analysis focuses primarily on ξ=0 , although we also capitalise on the symmetry-preserving nature of the RL truncation by connecting Hπv(x,ξ=±1,t) with the pion's valence-quark parton distribution amplitude. We explain that the impulse-approximation used hitherto to define the pion's valence dressed-quark GPD is generally invalid owing to omission of contributions from the gluons which bind dressed-quarks into the pion. A simple correction enables us to identify a practicable improvement to the approximation for Hπv(x,0,t) , expressed as the Radon transform of a single amplitude. Therewith we obtain results for Hπv(x,0,t) and the associated impact-parameter dependent distribution, qπv(x,|b→⊥|) , which provide a qualitatively sound picture of the pion's dressed-quark structure at a hadronic scale. We evolve the distributions to a scale ζ=2 GeV , so as to facilitate comparisons in future with results from experiment or other nonperturbative methods

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Section: General Features Of Pion Gpdsmentioning

confidence: 99%

Sketching the pion's valence-quark generalised parton distribution

et al. 2015

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“…The reader may find this a bold approximation, but it has been argued in Ref. [149] that the gauge link in twist-two operators along the lightcone brings only numerically negligible contributions. The overall normalisation of the triangle diagram is controlled by the local twist-two operator.…”

Section: Local Impulse Approximationmentioning

confidence: 99%

From Bethe–Salpeter Wave functions to Generalised Parton Distributions

2016

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We review recent works on the modelling of Generalised Parton Distributions within the Dyson-Schwinger formalism. We highlight how covariant computations, using the impulse approximation, allows one to fulfil most of the theoretical constraints of the GPDs. Specific attention is brought to chiral properties and especially the so-called soft pion theorem, and its link with the Axial-Vector Ward-Takahashi identity. The limitation of the impulse approximation are also explained. Beyond impulse approximation computations are reviewed in the forward case. Finally, we stress the advantages of the overlap of lightcone wave functions, and possible ways to construct covariant GPD models within this framework, in a two-body approximation.

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“…We will consider only the two-parton DAs. For the pion case, the corresponding DAs are defined as [72,73] 0 ψ (y) γ µ γ 5 ψ (x) π(q) = if πˆ1 0 dα e i(αp·y+ᾱp·x) × × p µ φ 2;π (α) + 1 2 z µ (p · z) ψ 4;π (α) ,…”

Section: A Meson Distribution Amplitudesmentioning

confidence: 99%

Generalized parton distributions from charged current meson production

Siddikov

Schmidt

2019

Phys. Rev. D

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In this paper we prove that the simultaneous study of both ρ-and π-meson production by charged currents in Bjorken kinematics allows for a very clean extraction of the leading twist Generalized Parton Distributions of the target, with inherent control of the contribution of higher-twist corrections. Also, it might provide target-independent constraints on the distribution amplitudes of the produced mesons. We expect that such processes might be studied either in neutrino-induced or in electron-induced processes. According to our numerical estimates, the cross-sections of these processes are within the reach of JLab and EIC experiments. I. INTRODUCTIONThe structure of the hadrons remains up to now a challenging puzzle, which attracts a lot of attention from both theoretical and experimental viewpoints. Nowadays, this structure is parametrized in terms of the so-called generalized parton distributions (GPDs), which are directly related to amplitudes of physical processes in Bjorken kinematics [1,2]. The early analyses of GPDs were mostly based on experimental data on deeply virtual Compton scattering (DVCS) [3] and deeply virtual meson production (DVMP) [4][5][6][7][8][9][10][11][12][13][14][15][16][17], yet very soon it was realized that in view of the rich structure of GPDs, the poorly known wave functions of the produced mesons, as well as the sizable higher twist contributions [17][18][19][20][21], additional channels are needed. Since the amplitudes of physical processes typically include contributions of GPDs of several flavors and helicity states (sometimes convoluted with distribution amplitudes of other hadrons), the GPDs could be extracted only from self-consistent global fits of all available experimental data. Currently the list of processes which might be used for the extraction of GPDs include: ρ-meson photoproduction [22][23][24][25][26], timelike Compton Scattering [27][28][29], exclusive pion-or photon-induced lepton pair production [30,31], heavy charmonia photoproduction [32,33] (for gluon GPDs), as well as a few other channels [34,35]. Hopefully the forthcoming experimental data from upgraded JLab [17], COMPASS [36][37][38][39][40][41] and J-PARC [31,42], will enrich and enhance the early data from HERA and 6 GeV JLab experiments, as well as improve our understanding of the GPDs of the proton [43][44][45][46][47][48][49][50][51][52][53][54].Some of the experimentally studied channels suffer from well-understood theoretical complications. For example, as was found recently from theoretical analysis of pion DVMP [55], the dominant contribution in JLab kinematics (and possibly at the planned Electron Ion Collider [35]) stems from transversely polarized virtual photons, which implies dominance of twist-three effects. A careful Rosenbluth separation might help to single out contributions of the longitudinal photons. However, even in this case the longitudinal cross-sections might still include various other sources of higher-twist contributions [22]. Recently it was suggested that a test of the Q 2 -...

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Nonperturbative features of the axial current

Cited by 12 publications

References 46 publications

Sketching the pion's valence-quark generalised parton distribution

Sketching the pion's valence-quark generalised parton distribution

From Bethe–Salpeter Wave functions to Generalised Parton Distributions

Generalized parton distributions from charged current meson production

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