Bootstrap Equations for String-Like Amplitude

One of the ways to check the consistency of our effective field theory (EFT) approach (explained by A.Vereshagin and V.Vereshagin at this conference) is to perform the numerical testing of those sum rules for hadron resonance parameters which follow from the system of bootstrap constrains. In this talk we discuss the peculiar features of this procedure for the case of exactly solvable bootstrap model based on Veneziano string amplitude. This allows us to simulate different situations that may encounter in realistic EFT models. We also make a short review of the technique that may be useful for further analysis of various bootstrap systems.Comment: 7 pages, talk given at QFTHEP 2004, Russia, June 2004, to be published in Proceeding

On the equivalence of GPD representations

Phenomenological representations of generalized parton distributions (GPDs) implementing the non-trivial field theoretical requirements are employed in the present day strategies for extracting of hadron structure information encoded in GPDs from the observables of hard exclusive reactions. Showing out the equivalence of various GPD representations can help to get more insight into GPD properties and allow to build up flexible GPD models capable of satisfactory description of the whole set of available experimental data. We review the mathematical aspects of establishing equivalence between the the double partial wave expansion of GPDs in the conformal partial waves and in the $t$-channel ${\rm SO}(3)$ partial waves and the double distribution representation of GPDs.Comment: A contribution into the Proceedings of QUARKS-2016 19th International Seminar on High Energy Physics, Pushkin, Russia, 29 May - 4 June, 201

A spectral representation for baryon to meson transition distribution amplitudes

We construct a spectral representation for the baron to meson transition distribution amplitudes (TDAs), i.e. matrix elements involving three quark correlators which arise in the description of baryon to meson transitions within the factorization approach to hard exclusive reactions. We generalize for these quantities the notion of double distributions introduced in the context of generalized parton distributions. We propose the generalization of A.Radyushkin's factorized Ansatz for the case of baryon to meson TDAs. Our construction opens the way to modeling of baryon to meson TDAs in their complete domain of definition and quantitative estimates of cross-sections for various hard exclusive reactions.Comment: This is the second version of the paper. Important changes were made in the text and many errors in the formulas were corrected. 37 pages, 8 figure

Baryon to meson transition distribution amplitudes and their spectral representation

We consider the problem of construction of a spectral representation for nucleon to meson transition distribution amplitudes (TDAs), non-diagonal matrix elements of nonlocal three quark light-cone operators between a nucleon and a meson states. We introduce the notion of quadruple distributions and generalize Radyshkin's factorized Ansatz for this issue. Modelling of baryon to meson TDAs in the complete domain of their definition opens the way to quantitative estimates of cross-sections for various hard exclusive reactions.Comment: Talk presented at International Workshop on Diffraction in High-Energy Physics DIFFRACTION 2010, September 10 - 15, 2010 Otranto (Lecce), Italy. 4 page

Dual parametrization of GPDs versus the double distribution Ansatz

We establish a link between the dual parametrization of GPDs and a popular parametrization based on the double distribution Ansatz, which is in prevalent use in phenomenological applications. We compute several first forward-like functions that express the double distribution Ansatz for GPDs in the framework of the dual parametrization and show that these forward-like functions make the dominant contribution into the GPD quintessence function. We also argue that the forward-like functions $Q_{2 \nu}(x)$ with $\nu \ge 1$ contribute to the leading singular small-$x_{Bj}$ behavior of the imaginary part of DVCS amplitude. This makes the small-$x_{Bj}$ behavior of \im A^{DVCS} independent of the asymptotic behavior of PDFs. Assuming analyticity of Mellin moments of GPDs in the Mellin space we are able to fix the value of the $D$-form factor in terms of the GPD quintessence function $N(x,t)$ and the forward-like function $Q_0(x,t)$.Comment: 18 pages, 5 figures. A version that appeared in Eur. Phys. J. A. Some of the statements were refined and misprints in the formulas were correcte

Dual parametrization of generalized parton distributions in two equivalent representations

The dual parametrization and the Mellin-Barnes integral approach represent two frameworks for handling the double partial wave expansion of generalized parton distributions (GPDs) in the conformal partial waves and in the $t$-channel ${\rm SO}(3)$ partial waves. Within the dual parametrization framework, GPDs are represented as integral convolutions of forward-like functions whose Mellin moments generate the conformal moments of GPDs. The Mellin-Barnes integral approach is based on the analytic continuation of the GPD conformal moments to the complex values of the conformal spin. GPDs are then represented as the Mellin-Barnes-type integrals in the complex conformal spin plane. In this paper we explicitly show the equivalence of these two independently developed GPD representations. Furthermore, we clarify the notions of the $J=0$ fixed pole and the $D$-form factor. We also provide some insight into GPD modeling and map the phenomenologically successful Kumeri\v{c}ki-M\"uller GPD model to the dual parametrization framework by presenting the set of the corresponding forward-like functions. We also build up the reparametrization procedure allowing to recast the double distribution representation of GPDs in the Mellin-Barnes integral framework and present the explicit formula for mapping double distributions into the space of double partial wave amplitudes with complex conformal spin.Comment: 56 pages, 3 figure

Pion and photon beam initiated backward charmonium or lepton pair production

Hard exclusive reactions initiated by pion or photon beams within the near-backward kinematical regime specified by the small Mandelstam variable $-u$ can be studied to access pion-to-nucleon and photon-to-nucleon Transition Distribution Amplitudes (TDAs). Checking the validity of collinear factorized description of pion and photon induced reactions in terms of TDAs allows to test the universality of TDAs between the space-like and time-like regimes that is the indispensable feature of the QCD collinear factorization approach. In this short review we consider the exclusive pion- and photo-production off nucleon of a highly virtual lepton pair (or heavy quarkonium) in the near-backward region. We first employ a simplistic cross channel nucleon exchange model of pion-to-nucleon TDAs to estimate the magnitude of the corresponding cross sections for the kinematical conditions of J-PARC. We then illustrate the flexibility of our approach by building a two parameter model for the photon-to-nucleon TDAs based on preliminary results for near threshold $J/\psi$ photoproduction at JLab and provide our estimates for near-backward $J/\psi$ photoproduction and Timelike Compton Scattering cross sections for the kinematical conditions of JLab and of future EIC and EicC.Comment: 22 pages, 9 figures; The paper is extended by adding in Sec. 7 a discussion on the near-backward charmonium photoproduction employing the photon-to-nucleon TDA model driven by the recent GlueX data on the $J/\psi$ photoproduction in arXiv:2304.0384

Exact summation of leading infrared logarithms in 2D effective field theories

A method of exact all-order summation of leading infrared logarithms in two dimensional massless $\Phi^4$-type non-renormalizable effective field theories (EFTs) is developed. The method is applied to the ${\rm O}(N)$-symmetric EFT, which is a two-dimensional sibling of the four dimensional ${\rm O}(N+1)/{\rm O}(N)$ sigma-model. For the first time the exact all-order summation of the $\left(E^{2} \ln(1/E)\right)^n$ contributions (chiral logarithms) for the $2 \to 2$ scattering amplitudes is performed in closed analytical form. The cases when the resulting amplitudes turn to be meromorphic functions with an infinite number of poles (Landau poles) are identified. This provides the first explicit example of quasi-renormalizable field theories.Comment: 22 pages, 2 figure