Hadron Properties from QCD Sum Rules

In elementary particle physics theory, all fundamental interactions - apart from gravity - are described in terms of (relativistic) quantum field theories based on certain gauge symmetries. Strong interactions, in particular, are described by quantum chromodynamics (QCD), with quarks and gluons as its fundamental degrees of freedom constituting the basic building blocks of any kind of strongly interacting matter. QCD exhibits two very peculiar properties: "confinement" - a phenomenon according to which neither quarks nor gluons exist as free particles and only their bound states, called "hadrons," may be observed in nature - and dynamical breakdown of chiral symmetry. Both of these distinct features of QCD are of definitely nonperturbative origin: they cannot be revealed by perturbative considerations. Accordingly, these effects may be properly taken into account exclusively within appropriate nonperturbative approaches to QCD. At present, one of the most important nonperturbative theoretical tools for the study of hadron properties in QCD is the method of QCD sum rules. This project aims at the theoretical analysis of nonperturbative QCD effects in hadron form factors with the help of QCD sum rules. The crucial feature of this project is the application of new ideas, proposed and developed within a preceding project, on the extraction of the ground-state parameters from sum rules. In a recent study, we took advantage of the exact solvability of a quantum-mechanical model incorporating confinement: in this framework the bound-state parameters can be calculated from the bound-state equation and then compared with the results of applying the standard extraction procedures adopted in the sum-rule method. This unambiguously showed that these procedures have grave shortcomings and limitations and, generally, do not predict hadron parameters to the accuracy expected. These observations, however, allowed to identify the modifications of the technique necessary for improving its predictions. In the exactly solvable model, these changes entailed a dramatic increase of the accuracy of the bound-state parameters obtained. Continuing the earlier studies, this project will implement such modifications in the sum-rule approach to the realistic case of QCD, in order to find improved and more reliable predictions for hadron parameters, specifically, for heavy-meson decay constants, for the form factors of heavy-to-heavy and heavy-to-light transitions, and for elastic form factors at intermediate momentum transfers. Beyond doubt, such analysis will lead to a significant improvement of the accuracy of theoretical predictions for hadron parameters.

Elementary particle physics studies the fundamental building blocks of matter and the (non-gravitational) forces or, more precisely, interactions experienced by these constituents. All insights produced by these investigations are subsumed by the so-called standard model of elementary particle physics, which is a mathematical theory compatible with any requirements imposed by special relativity or quantum physics. Any elementary particle that is subject to the strong interactions and that may be observed in nature as a free particle is called a hadron; this class of particles encompasses the well-known constituents of nuclei (the proton and the neutron), particles that either do not carry spin at all (such as the pion) or carry spins that are integer multiples of the Planck constant and a significant number of heavier representatives with similar features. Hadrons do not belong to the class of fundamental particles (the members of which are characterized by having no discernible extension or substructure) but are complex composites of quarks, antiquarks, and gluons, which are the fundamental particles that constitute the basic degrees of freedom of quantum chromodynamics (QCD), the relativistic quantum field theory that governs strong interactions and, therefore, is responsible for the formation of hadrons and their internal structure and characteristics. However, so far the inherent mathematical complexity of QCD, determined by symmetry considerations, prevents us from inferring any of its exact solutions. Of course, approximate solutions may be found by application of methods of perturbation theory. However, gaining true insight into the relationship between the parameters of QCD as the underlying fundamental theory, on the one hand, and features of hadrons observed by experiment, on the other hand, beyond mere intuition requires nonperturbative approaches.QCD sum rules provide one of the most promising tools for establishing the desired relationship between hadronic properties and QCD. The idea behind this formalism is rather simple: certain quantum-theoretic expressions are evaluated both at the experimentally accessible level of hadrons and at the theoretically well-founded level of QCD; equating the two results emerging thereby, derived along different routes but expected to be equivalent, then yields the QCD sum rule appropriate for the system under consideration.Within the framework of the present research project, various formulations of QCD sum rules have been used in order to investigate for the particular class of spinless hadrons that contains also the pion and its more massive counterparts some of the (apart from their masses) most important properties of hadrons: their decay constants, which determine the lifetimes of unstable hadrons, and some of their form factors, quantities which prove crucial for our understanding of various transition reactions of such hadrons. In all cases, the sum-rule approach allowed for a very successful description of the hadronic bound states and enabled us to offer some explanation to still existing puzzles of both experimental and theoretical nature, for instance, with regard to predictions for the electromagnetic form factor of the electrically charged pion that are in obvious conflict with fundamental theoretical statements, or to rather doubtful outcomes of an experimental measurement of the form factor for the transition of the electrically neutral pion to photons.