Improved calculation of the γ*γ → π process at low Q2 using LCSR’s and renormalization-group summation

We study two versions of lightcone sum rules to calculate the γ*γ → π0 transition form factor (TFF) within QCD. While the standard version is based on fixed-order perturbation theory by means of a power-series expansion in the strong coupling, the new method incorporates radiative corrections by renormalization-group summation and generates an expansion within a generalized fractional analytic perturbation theory involving only analytic couplings. Using this scheme, we determine the relative nonperturbative parameters and the first two Gegenbauer coefficients of the pion distribution amplitude (DA) to obtain TFF predictions in good agreement with the preliminary BESIII data, while the best-fit pion DA satisfies the most recent lattice constraints on the second moment of the pion DA at the three-loop level.

Eigenvalues, absolute continuity and localizations for periodic unitary transition operators

The localization phenomenon for periodic unitary transition operators on a Hilbert space consisting of square summable functions on an integer lattice with values in a finite-dimensional Hilbert space, which is a generalization of the discrete-time quantum walks with constant coin matrices, is discussed. It is proved that a periodic unitary transition operator has an eigenvalue if and only if the corresponding unitary matrix-valued function on a torus has an eigenvalue which does not depend on the points on the torus. It is also proved that the continuous spectrum of a periodic unitary transition operator is absolutely continuous. As a result, it is shown that the localization happens if and only if there exists an eigenvalue, and when there exists only one eigenvalue, the long-time limit of transition probabilities coincides with the point-wise norm of the projection of the initial state to the eigenspace. The results can be applied to certain unitary operators on a Hilbert space on a covering graph, called a topological crystal, over a finite graph. An analytic perturbation theory for matrices in several complex variables is employed to show the result about absolute continuity for periodic unitary transition operators.

Coulomb scattering in the massless Nelson model II. Regularity of ground states

For the massless Nelson model, we provide detailed information about the dependence of the normalized ground states [Formula: see text] of the fiber single-electron Hamiltonians [Formula: see text] on the total momentum [Formula: see text] and the infrared cut-off [Formula: see text]. This information is obtained with the help of the iterative analytic perturbation theory. In particular, we derive bounds of the form [Formula: see text] for some constant [Formula: see text] and a function of the maximal admissible coupling constant [Formula: see text] such that [Formula: see text]. These results hold both in the infrared-regular and infrared-singular cases. They are exploited in part I of this series to construct the two-electron scattering states in the infrared-regular massless Nelson model (in the absence of an infrared cut-off) along the lines of the Haag–Ruelle scattering theory. They should also be relevant to the problem of scattering of two infraparticles in the infrared-singular Nelson model, whose solution is the goal of this series of papers. Although a part of a larger investigation, the present work is written in a self-contained fashion.

Form factor π0γ*γ in lightcone sum rules combined with renormalization-group summation vs experimental data.

We consider the lightcone sum-rule (LCSR) description of the pionphoton transition form factor in combination with the renormalization group of QCD. The emerging scheme represents a certain version of Fractional Analytic Perturbation Theory and significantly extends the applicability domain of perturbation theory towards lower momenta Q2 ≲ 1 GeV2. We show that the predictions calculated herewith agree very well with the released preliminary data of the BESIII experiment, which have very small errors just in this region, while the agreement with other data at higher Q2 is compatible with the LCSR predictions obtained recently by one of us using fixed-order perturbation theory.

Bjorken sum rule in QCD frameworks with analytic (holomorphic) coupling

We investigate the polarized Bjorken sum rule (BSR) in three approaches to QCD with analytic (holomorphic) coupling: Analytic Perturbation Theory (APT), Two-delta analytic QCD (2[Formula: see text]anQCD) and Three-delta lattice-motivated analytic QCD in the three-loop and four-loop MOM scheme (3l3[Formula: see text]anQCD, 4l3[Formula: see text]anQCD). These couplings do not have unphysical (Landau) singularities, and have finite values when the transferred momentum goes to zero, which allows us to explore the infrared regime. With the exception of APT, these theories at high momenta practically coincide with the underlying perturbative QCD (pQCD) in the same scheme. We apply them in order to verify the Bjorken sum rule within the range of energies available in the data collected by the experimental JLAB collaboration, i.e. [Formula: see text] and compare the results with those obtained by using the perturbative QCD coupling. The results of the new frameworks with respective couplings (2[Formula: see text] and 3[Formula: see text]) are in good agreement with the experimental data for [Formula: see text] already when only one higher-twist term is used. In the low-[Formula: see text] regime [Formula: see text], we use [Formula: see text]PT-motivated expression or an expression motivated by the light-front holography (LFH) QCD used earlier in the literature.

The QCD analysis of the combined set for the F3 structure function data based on the analytic approach

We apply analytic perturbation theory (APT) to the QCD analysis of the xF3(x, Q2) structure function considering a combined set of deep inelastic scattering data presented by several collaborations, and extract values of the scale parameter Λ QCD , the parameters of the form of the xF3 structure function, and the x-shape of the higher twist (HT) contribution. We study the difference between the results obtained within the standard perturbative and analytic approaches in comparison with the experimental errors and state that the greatest difference occurs for large x.