Double parton correlations in mesons within AdS/QCD soft-wall models: a first comparison with lattice data
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Regular Article - Theoretical Physics
Double parton correlations in mesons within AdS/QCD soft-wall models: a first comparison with lattice data Matteo Rinaldia Dipartimento di Fisica e Geologia, Università degli studi di Perugia, INFN Sezione di Perugia, Via A. Pascoli, 06123 Perugia, Italy
Received: 27 March 2020 / Accepted: 14 July 2020 © The Author(s) 2020
Abstract Double parton distribution functions (dPDFs), entering the double parton scattering (DPS) cross section, are unknown fundamental quantities encoding new interesting properties of hadrons. Here, the pion dPDFs are investigated within different holographic QCD quark models in order to access their basic features. Results of the calculations obtained within the AdS/QCD soft-wall approach, have been compared with predictions of lattice QCD evaluations of the pion two-current correlation functions. The present analysis confirms that double parton correlations, affecting dPDFs, are very important and not direct accessible from generalised parton distribution functions and electromagnetic form factors. The comparison between lattice data and quark model calculations unveils the relevance of the contributions of high partonic Fock states in the pion. Nevertheless, by using a complete general procedure, results of lattice QCD have been used, for the first time, to estimate the mean value of the so called σe f f , a relevant experimental observable for DPS processes. In addition, the results of the first calculations of the ρ meson dPDFs are discussed in order to make predictions.
Contents 1 Introduction . . . . . . . . . . . . . . . . . . . . . . 2 Meson double PDF within the light-front approach . . 2.1 Moments of dPDFs . . . . . . . . . . . . . . . . 2.2 An approximation in terms of one body quantities 2.3 The effective cross section . . . . . . . . . . . . 2.3.1 On the geometric interpretation of σ e f f . . 3 Lattice analysis of moments of dPDFs . . . . . . . . . 3.1 The pion form factor . . . . . . . . . . . . . . . 3.2 Effective form factor . . . . . . . . . . . . . . . 3.3 An approximation for the moment of dPDFs in lattice QCD . . . . . . . . . . . . . . . . . . . . 4 The pion dPDF within the holographic QCD . . . . . a e-mail:
[email protected] (corresponding author)
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4.1 Pion in AdS/QCD I: the original version . . . . 4.2 Pion in AdS/QCD II: dynamical spin effects in holographic QCD . . . . . . . . . . . . . . . . 4.3 Pion in AdS/QCD III: a universal wave function 5 Numerical results . . . . . . . . . . . . . . . . . . . 5.1 Calculation of dPDFs . . . . . . . . . . . . . . 5.2 The pion form factor . . . . . . . . . . . . . . 5.3 The effective form factor of the pion . . . . . . 5.4 Calculation of σ e f f . . . . . . . . . . . . . . . 5.5 Comparison between two-body distributions and the product of one-body functions . . . . . 5.6 Parameter dependence of the results . . . . . . 5.6.1 The Original model . . . . . . . . . . . . 5.6.2 The universal model . . . . . . . . . . . 6 The ρ meson within AdS/QCD . . . . . . .
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