Results on the resummation of non-power-series expansions of the Adler function of a scalar,
D
S
, and a vector,
D
V
, correlator are presented within fractional analytic perturbation theory (FAPT). ...The first observable can be used to determine the decay width
of a scalar Higgs boson to a bottom-antibottom pair, while the second one is relevant for the
e
+
e
−
annihilation cross section. The obtained estimates are compared with those from fixed-order (FOPT) and contour-improved perturbation theory (CIPT), working out the differences. We prove that although FAPT and CIPT are conceptually different, they yield identical results. The convergence properties of these expansions are discussed and predictions are extracted for the resummed series of
R
S
and
D
V
using oneand two-loop coupling running, and making use of appropriate generating functions for the coefficients of the perturbative series.
The aim of this topical article is to outline the fundamental ideas underlying the recently developed Fractional Analytic Perturbation Theory (FAPT) of QCD and present its main calculational tools ...together with key applications. For this, it is first necessary to review previous methods to apply QCD perturbation theory at low spacelike momentum scales, where the influence of the Landau singularities becomes inevitable. Several concepts are considered and their limitations are pointed out. The usefulness of FAPT is discussed in terms of two characteristic hadronic quantities: the perturbatively calculable part of the pion’s electromagnetic form factor in the spacelike region and the Higgs-boson decay into a
b
pair in the timelike region. In the first case, the focus is on the optimization of the prediction with respect to the choice of the renormalization scheme and the dependence on the renormalization and the factorization scales. The second case serves to show that the application of FAPT to this reaction reaches already at the four-loop level an accuracy of the order of 1%, avoiding difficulties inherent in the standard perturbative expansion. The obtained results are compared with estimates from fixed-order and contour-improved QCD perturbation theory. Using the brand-new Higgs mass value of about 125 GeV, measured at the Large Hadron Collider (CERN), a prediction for
= 2.4 ± 0.15 MeV is extracted.
The renormalization-group properties of gauge-invariant transverse-momentum dependent (TMD) parton distribution functions (PDF) in QCD are addressed. We perform an analysis of their leading-order ...anomalous dimensions, which are local quantities, making use of the renormalization properties of contour-dependent composite operators in QCD. We argue that attaching individual gauge links with transverse segments to quark fields in the light-cone gauge, the associated gauge contours are joined at light-cone infinity through a cusp-like junction point. We find that the renormalization effect on the junction point creates an anomalous dimension which has to be compensated in order to recover the results in a covariant gauge. To this end, we include in the definition of the TMD PDF an additional soft counter term (gauge link) along that cusped contour. We show that the eikonal factors entering this counter term are peculiar to the Mandelstam field formalism and are absent when one uses a direct gauge contour.
The leading-twist distribution amplitude for the longitudinal rho-meson was studied using QCD Sum Rules with nonlocal condensates and a spectral density which includes next-to-leading order radiative ...corrections. The obtained profile is compared with results from standard QCD sum rules, lattice QCD, holographic QCD, a light-front quark model, and the instanton liquid model. Preliminary estimates for the first two moments of the transverse ρ-meson distribution amplitude are also given.
We highlight the progress, current status, and open challenges of QCD-driven physics, in theory and in experiment. We discuss how the strong interaction is intimately connected to a broad sweep of ...physical problems, in settings ranging from astrophysics and cosmology to strongly coupled, complex systems in particle and condensed-matter physics, as well as to searches for physics beyond the Standard Model. We also discuss how success in describing the strong interaction impacts other fields, and, in turn, how such subjects can impact studies of the strong interaction. In the course of the work we offer a perspective on the many research streams which flow into and out of QCD, as well as a vision for future developments.
The transition pion–photon form factor is studied within the framework of light-cone QCD sum rules. The spectral density for the next-to-leading order corrections is calculated for any Gegenbauer ...harmonic. At the level of the next-to-next-to-leading order (NNLO) radiative corrections, only that part of the hard-scattering amplitude is included that is proportional to the
β-function, taking into account the leading zeroth-order harmonic. The relative size of the NNLO contribution in the prediction for the form factor
F
γ
∗
γ
π
(
Q
2
)
has been analyzed, making use of the BLM scale-setting procedure. In addition, predictions for the form factor
F
γ
∗
ρ
π
are obtained that turn out to be sensitive to the endpoint behavior of the pion distribution amplitude, thus providing in connection with experimental data an additional adjudicator for the pion distribution amplitude. In a note added, we comment on the preliminary high-
Q
2
BaBar data on
F
γ
∗
γ
π
arguing that the significant growth of the form factor between 10 and
40
GeV
2
cannot be explained in terms of higher-order perturbative corrections at the NNLO.
We use QCD sum rules with non-local condensates to recalculate more accurately the moments and their confidence intervals of the twist-2 pion distribution amplitude including radiative corrections. ...We are thus able to construct an admissible set of pion distribution amplitudes which define a reliability region in the
a
2,
a
4 plane of the Gegenbauer polynomial expansion coefficients. We emphasize that models like that of Chernyak and Zhitnitsky, as well as the asymptotic solution, are excluded from this set. We show that the determined
a
2,
a
4 region strongly overlaps with that extracted from the CLEO data by Schmedding and Yakovlev and that this region is also not far from the results of the first direct measurement of the pion valence quark momentum distribution by the Fermilab E791 Collaboration. Comparisons with recent lattice calculations and instanton-based models are briefly discussed.
The CLEO experimental data on the πγ transition are analyzed to next-to-leading order accuracy in QCD perturbation theory using light-cone QCD sum rules. By processing these data along the lines ...proposed by Schmedding and Yakovlev, and recently revised by us, we obtain new constraints for the Gegenbauer coefficients a2 and a4, as well as for the inverse moment 〈x−1〉π of the pion distribution amplitude (DA). The former determine the pion DA at low momentum scale, the latter is crucial in calculating pion form factors. From the results of our analysis we conclude that the data confirm the end-point suppressed shape of the pion DA we previously obtained with QCD sum rules and nonlocal condensates, while the exclusion of both the asymptotic and the Chernyak–Zhitnitsky DAs is reinforced at the 3σ- and 4σ-level, respectively. The reliability of the main results of our updated CLEO data analysis is demonstrated. Our pion DA is checked against the di-jets data from the E791 experiment, providing credible evidence for our results far more broadly.
A survey is presented on the current status of 3D nucleon tomography. Several research frontiers are addressed that dominate modern physics from theory to current and future experiments. We have now ...a much more detailed spatial image of the nucleon thanks to various theoretical concepts and methods to describe its charge distribution and spin decomposition which are highlighted here. The progress of lattice computations of these quantities is reported and the prospects of what we can come to expect in the near future are discussed. Multi-dimensional maps of the nucleon’s partonic structure appear now within reach of forthcoming experiments.
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