QCD Sum Rules and Hadronic Matrix Elements

• Antragsteller: Professor Dr. Alexander Khodjamirian
• Fachliche Zuordnung: Kern- und Elementarteilchenphysik, Quantenmechanik, Relativitätstheorie, Felder
• Förderung: Förderung von 2012 bis 2020
• Projektkennung: Deutsche Forschungsgemeinschaft (DFG) - Projektnummer 214254430

A transparent way to study transitions between the elementary particles of the matter - the quarks and leptons of different flavours - is provided by the electroweak decays of hadrons, the bound states of quarks and antiquarks. In the recent years, prolific measurements of these decays with fixed, exclusive final states were carried out al the Large Hadron Collider and at other particle accelerators. The accumulated data are being intensively used to test and substantiate the theory of flavour within Standard Model of elementary particles and within its extensions involving new physics phenomena. Theoretical description of the exclusive electroweak decays is not possible without the knowledge of hadronic matrix elements. These quantum amplitudes accumulate long-distance interactions of the quarks confined within hadrons and comprise all hadronic effects accompanying the elementary quark-flavour transitions. The major goal of this project is to develop new methods of calculating hadronic matrix elements, abased on the theory of quark-gluon interactions - quantum chromodynamics (QCD) - and to apply these methods to a set of important electroweak decays of hadrons. The approach of sum rules in QCD will prevail as the major working tool. This approach is based on a twofold way of treating process-specific correlation functions of composite quark-antiquark operators. Firstly, one calculate the correlation function in terms of QCD perturbation theory and universal input parameters characterizing quark-gluon interactions beyond perturbation theory. Secondly, one directly relates the same correlation functions to the hadronic matrix elements via dispersion relations. Mutually connected versions of QCD sum rules for different types of hadronic matrix elements will be used including the light-cone sum rules for hadronic form factors and two-point sum rules of the decay constants of hadrons. One employs two different types of correlation functions with, respectively, distribution amplitudes of hadrons and vacuum condensates used as universal nonperturbative parameters. The accomplishment of the tasks planned within this project will further strengthen and diversify the methodology of QCD sum rules, including, e.g., the new calculations of the hadronic matrix elements for semiieptonic decays of heavy mesons with two pseudoscalar mesons in the final states. Extensions of QCD sum rules to the affective theories such as heavy-quark effective theory and soft-collinear effective theory will also be explored. Furthermore, the analysis of correlations between various sum rules will be carried out to reduce inherent theoretical uncertainties. The project as a whole will result in a mutually correlated set of various QCD sum rule techniques with improve i accuracy, updated inputs and with new applications to the hadronic matrix elements relevant for the quark-flavour transitions.

• DFG-Verfahren: Forschungsgruppen
• Teilprojekt zu: FOR 1873: Quark-Flavour-Physik und effektive Feldtheorien