From The Johannes Gutenberg University Mainz [Johannes Gutenberg-Universität Mainz] (DE): “New possibilities in the theoretical prediction of particle interactions” 

From The Johannes Gutenberg University Mainz [Johannes Gutenberg-Universität Mainz] (DE)

Professor Dr. Stefan Weinzierl
Theoretical High Energy Physics (THEP)
Institute of Physics and
PRISMA+ Cluster of Excellence
Johannes Gutenberg University Mainz
55099 Mainz
phone: +49 6131 39-25579

How does the world look like at the smallest scales? This is a question scientists are trying to answer in particle collider experiments like the Large Hadron Collider (LHC) at CERN in Switzerland.

To compare the results of these experiments, theoretical physicists need to provide more and more precise predictions based on our current model for the interactions of fundamental particles, the so-called standard model. A key ingredient in these predictions are so called Feynman integrals. Recently, a team of the PRISMA+ Cluster of Excellence at Johannes Gutenberg University Mainz (JGU), consisting of Dr. Sebastian Pögel, Dr. Xing Wang and Prof. Dr. Stefan Weinzierl, developed a method to efficiently compute a new class of these Feynman integrals, associated to Calabi-Yau geometries. This research is now published in the renowned Physical Review Letters [below] and opens the path to high-precision theoretical predictions of particle interactions and to a better understanding of the elegant mathematical structure underpinning the world of particle physics.

“During the interaction of subatomic particles something special happens: Any number of additional particles can temporarily pop in and out of existence”, explained Professor Stefan Weinzierl. “When making theoretical predictions of such interactions, the more of these additional particles are taken into account, the more precise the computation will be to the real result.” Feynman integrals are mathematical objects which describe this effect, summing in effect all possible ways particles can appear and immediately disappear again.

Calabi-Yau geometries: An interplay of mathematics and physics

An important property determining the complexity of a Feynman integral is its geometry. Many of the simplest Feynman integrals have the geometry of a sphere or a torus, which is the mathematical term for a donut shape. Such integrals are nowadays well understood. However, there are entire families of geometries, so-called Calabi-Yau geometries, which are generalizations of the donut case to higher dimensions. These have proven to be a rich field of research in pure mathematics and have found extensive application in string theory in the last decades. In recent years, it was discovered that many Feynman integrals are associated to Calabi-Yau geometries, too. However, due to the complexity of the geometry, the efficient evaluation of such integrals has remained a challenge.

In their recent publication, Dr. Sebastian Pögel, Dr. Xing Wang, and Professor Stefan Weinzierl present a method that allows them to tackle integrals of Calabi-Yau geometries. They studied a simple family of Calabi-Yau Feynman integrals, so-called banana integrals.

Feynman graph of a banana intergral (ill./©: Weinzierl group)

The name is derived from the Feynman graph. Thereby they could find for the first time a so-called “epsilon-factorized form” for these integrals. This form allows to quickly evaluate the integral to nearly arbitrary precision, making them accessible for future experimental predictions predictions.

“It opens the door to a wide variety of hitherto unreachable Feynman integrals,” said Dr. Xing Wang. According to Dr. Sebastian Pögel, this is a nice example of how pure mathematics feeds into phenomenological predictions for high-energy experiments. “We are grateful to our colleagues in mathematics, and in particular to the group of Professor Duco van Straten, as we built on their work and now were able to achieve this exciting result”, Professor Stefan Weinzierl summarized.

Physical Review Letters

See the full article here.

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The The Johannes Gutenberg University Mainz [Johannes Gutenberg-Universität Mainz] (DE) is a public research university in Mainz, Rhineland Palatinate, Germany, named after the printer Johannes Gutenberg since 1946. With approximately 32,000 students (2018) in about 100 schools and clinics, it is among the largest universities in Germany. Starting on 1 January 2005 the university was reorganized into 11 faculties of study.

The university is a member of the German U15, a coalition of fifteen major research-intensive and leading medical universities in Germany. The Johannes Gutenberg University is considered one of the most prestigious universities in Germany.

The university is part of the IT-Cluster Rhine-Main-Neckar. The Johannes Gutenberg University Mainz, The Goethe University Frankfurt(DE) and The Technische Universität Darmstadt(DE) together form the Rhine-Main-Universities [Rhein-Main Universitäten](DE)(RMU).

The first University of Mainz goes back to the Archbishop of Mainz, Prince-elector and Reichserzkanzler Adolf II von Nassau. At the time, establishing a university required papal approval and Adolf II initiated the approval process during his time in office. The university, however, was first opened in 1477 by Adolf’s successor to the bishopric, Diether von Isenburg. In 1784 the University was opened up for Protestants and Jews (curator Anselm Franz von Betzel). It fastly became one of the largest Catholic universities in Europe with ten chairs in theology alone. In the confusion after the establishment of the Mainz Republic of 1792 and its subsequent recapture by the Prussians, academic activity came to a gradual standstill. In 1798 the university became active again under French governance, and lectures in the department of medicine took place until 1823. Only the faculty of theology continued teaching during the 19th century, albeit as a theological Seminary (since 1877 “College of Philosophy and Theology”).

The current Johannes Gutenberg University Mainz was founded in 1946 by the French occupying power. In a decree on 1 March the French military government implied that the University of Mainz would continue to exist: the University shall be “enabled to resume its function”. The remains of anti-aircraft warfare barracks erected in 1938 after the remilitarization of the Rhineland during the Third Reich served as the university’s first buildings and are still in use today.

The continuation of academic activity between the old university and Johannes Gutenberg University Mainz, in spite of an interruption spanning over 100 years, is contested. During the time up to its reopening only a seminary and midwifery college survived.

In 1972, the effect of the 1968 student protests began to take a toll on the University’s structure. The departments (Fakultäten) were dismantled and the University was organized into broad fields of study (Fachbereiche). Finally in 1974 Peter Schneider was elected as the first president of what was now a “constituted group-university” institute of higher education. In 1990 Jürgen Zöllner became University President yet spent only a year in the position after he was appointed Minister for “Science and Advanced Education” for the State of Rhineland-Palatinate. As the coordinator for the SPD’s higher education policy, this furloughed professor from the Institute for Physiological Chemistry played a decisive role in the SPD’s higher education policy and in the development of Study Accounts.