Research

One of the currently best ways to access QCD at low energies while taking into account its non-perturbative nature is the lattice gauge theory. In the nutshell it is based on the discretization of the 4D-spacetime by an Euclidean 4D discrete lattice in a finite volume. Quarks are allowed to live only on the intersections of the lattice sites while gluons are associated with the links between the intersections. Through a series of well-defined steps (see fig. to the right for an excerpt) physical information can be accessed in a numerical calculation performed in supercomputing facilities. For an introductory lecture on the techniques as well as historical details see, e.g., [ LectureNotes ].

I am interested in relating the results of lattice QCD to the phenomenological ones based on experimental observations. A central object of study hereby is the so-called quantization condition which relates real energy eigenvalues of a multi-particle system in a finite volume with complex-valued scattering amplitudes. Based on continuum Quantum Field Theory principles we have derived few years ago the Finite-Volume-Unitarity (FVU) approach which extends to up to three interacting particles. See figure to the left and [ Review ].

What can truly evoke a shiver of awe is seeing numerical lattice QCD techniques and analytical techniques of continuum Quantum Field Theory now weaving into a common thread allowing us to study (excited) states of matter. With no explicit input from observations we can predict new configurations or study their properties. Hypothetical gedanken-experiment-worlds with, e.g., heavier than physical quarks or other experimentally unrealizable scenarios can be studied now in a controlled fashion.

A powerful and systematically improvable access to QCD at low energies can be gained through the so-called Effective Field Theories. In a nutshell, the idea is to replace (integrate out) degrees of freedom which are irrelevant at the energies of interest by the effective ones. Typically, this is guided by studying the symmetries of the underlying theory and their potential breaking. In the case of QCD at low energies, the effective theory is called Chiral Perturbation Theory, see e.g. [ Review , Lectures ].

I have worked on developing various theoretical tools based on Chiral Perturbation Theory, particularly to study properties of the excited hadrons (strongly interacting particles). In this, S-matrix principles become another important guiding tool which are based on very fundamental symmetries of nature. For example (for more details see, e.g., "Theory of resonances" ):

• In quantum field theories particles can be related to antiparticles . This relates various transition amplitudes.
• Because of the causality , these transition amplitudes are meromorphic in the kinematic variables promoted to complex values
• In any fundamental process, the probability to measure anything is per definition unity. This translates to the unitarity constraint of the transition amplitudes

One consequence of this is that transition amplitudes (objects encoding everything there is to know about a physical process) become meromorphic functions on, in general, multi-sheeted complex Riemann surface. They are bound by an observation on the real-valued boundary of a physical Riemann sheet, and can have poles on further unphysical Riemann sheets. Poles on unphysical Riemann sheets are associated with unstable states (e.g., excited hadrons). See figure to the right for a pictorial example.

The complex-valued positions of these poles do not depend on a particular process but are rather universal, encoding a unique signature of nature. The summary of humanity's knowledge in this regard is compiled by the [ Particle Data Group ].

Physics is an experimental science. Hadron spectroscopy is not different from that driven historically mostly by experimental observations. Plenty of modern experiments around the globe (at CERN, GSI, ELSA, Jefferson laboratory, BES, ...) provide us these days with an abundance of new high precision data, driven by multiple systemic and technological factors.

The question is then, what can one do with these data? Can one for example build a global hadronic model describing that data, filling in possible gaps in the measurement, remove possible misidentified results and ultimately allow us to extract universal parameters of excited states of matter? These are some of the bird's view questions we are aiming to answer in the JBW collaboration .

Data driven approaches run a danger of over-fitting or under-fitting the provided data. Another issue is the treatment of outliers and model misspecifications or other biases. Such problems are well known beyond physics and plenty of modern statistical or machine learning tools exists to mitigate them. One example of Neural Network based approach is shown in the right figure from a recent talk: "Denoising and sharpening the hadron spectrum through machine learning" at the recent dedicated workshop[ link ] in Thessaloniki.