Christopher Körber

Ph.D. Student: Physics

The Standard Model (SM) of particle physics is currently the most precise theory describing fundamental physics and drives research at a global level. As the discovery of the Higgs particle further confirms the SM's range of application, it also denied the existence of new physics – physics Beyond the Standard Model (BSM) – up to the TeV scale. This is challenging as current theories can not explain macroscopic observations like the existence of Dark Matter or the asymmetry between matter and antimatter. The essential question is therefore: where does one expect signals beyond the standard model on a microscopic level and how can one describe this?

Complementary to the collider investigations of BSM signatures that take place at the high-energy frontier, it is also possible to probe for these signals with experiments at low energy via precision measurements. Indeed, it can be argued that such indirect searches may have greater reach, with sensitivities in some cases approaching the Grand Unified scale. Examples for such sensitive low-energy tests of BSM physics include searches for nucleon, electron, and atomic Electric Dipole Moments; efforts to directly detect Dark Matter through its scattering off atomic nuclei; measurements of lepton number violating processes like the neutrinoless double beta decay; and sensitive tests for new sources of flavor violation through the conversion of a muon to an electron in the nuclear field. Though there is a variety of ideas on how to detect such signals, the common ground of these low-energy experiments is the measurement of BSM signals on a nuclear level – ranging from large nuclear cores such as Xenon to planned experiments on light nuclei like Helium.

The variety of possible BSM theories hereby answers these questions differently and leads to distinctive beyond-the-SM phenomena. Thus, linking these experiments to the fundamental level is of relevance for two reasons:

• Identification of BSM sources

While a non-vanishing signal would confirm the existence of BSM structures, to identify the sources of these signals, one needs to propagate the signal from the target (nuclear many-body level) to the level of the fundamental theory.

• Experimental guidance

Once one is able to propagate possible BSM interactions to the level of nuclear cores, it might be possible to identify special nuclei which feature a coherent enhancement or suppression of such structures and thus guide experimental efforts.

Theoretical descriptions of such phenomena still suffer from large uncontrolled uncertainties – mostly associated with the nuclear many-body methods or an insufficient treatment or relevant interactions. In some cases, the method-dependent extrinsic uncertainties have improved by several factors but still can be as big as 100%. Since expected signals are supposed to be small, an accurate and precise description is needed to discriminate between different BSM structures. Therefore it is essential to understand the effects of all relevant uncertainties associated with the propagation of scales.

As the main objective of my current research, I intend to set up a consistent and accurate framework for analyzing BSM effects on a nuclear level, which can be systematically improved in order to increase the desired precision of the description.

Sampling General N-Body Interactions with Auxiliary Fields

– Published in Europhysics Letters

We present a general auxiliary field transformation which generates effective interactions containing all possible N-body contact terms. The strength of the induced terms can analytically be described in terms of general coefficients associated with the transformation and thus are controllable. This transformation provides a novel way for sampling 3- and 4-body (and higher) contact interactions non-perturbatively in lattice quantum monte-carlo simulations. We show that our method reproduces the exact solution for a two-site quantum mechanical problem.

Extracting the Single-Particle Gap in Carbon Nanotubes with Lattice Quantum Monte Carlo

We show how lattice Quantum Monte Carlo simulations can be used to calculate electronic properties of carbon nanotubes in the presence of strong electron-electron correlations. We employ the path integral formalism and use methods developed within the lattice QCD community for our numerical work and compare our results to empirical data of the Anti-Ferromagnetic Mott Insulating gap in large diameter tubes.

Hubbard-Stratonovich-Like Transformations for Few-Body Interactions

Through the development of many-body methodology and algorithms, it has become possible to describe quantum systems composed of a large number of particles with great accuracy. Essential to all these methods is the application of auxiliary fields via the Hubbard-Stratonovich transformation. This transformation effectively reduces two-body interactions to interactions of one particle with the auxiliary field, thereby improving the computational scaling of the respective algorithms. The relevance of collective phenomena and interactions grows with the number of particles. For many theories, e.g. Chiral Perturbation Theory, the inclusion of three-body forces has become essential in order to further increase the accuracy on the many-body level. In this proceeding, the analytical framework for establishing a Hubbard-Stratonovich-like transformation, which allows for the systematic and controlled inclusion of contact three- and more-body interactions, is presented.

First-principle calculations of Dark Matter scattering off light nuclei

– Published in Phys. Rev. C 96, 035805

We study the scattering of Dark Matter particles off various light nuclei within the framework of chiral effective field theory. We focus on scalar interactions and include one- and two-nucleon scattering processes whose form and strength are dictated by chiral symmetry. The nuclear wave functions are calculated from chiral effective field theory interactions as well and we investigate the convergence pattern of the chiral expansion in the nuclear potential and the Dark Matter-nucleus currents. This allows us to provide a systematic un- certainty estimate of our calculations. We provide results for $^2$H, $^3$H, and $^3$He nuclei which are theoretically interesting and the latter is a potential target for experiments. We show that two-nucleon currents can be systematically included but are generally smaller than predicted by power counting and suffer from significant theoretical uncertainties even in light nuclei. We demonstrate that accurate high-order wave functions are necessary in order to incorporate two-nucleon currents. We discuss scenarios in which one-nucleon contributions are suppressed such that higher-order currents become dominant.

Applying twisted boundary conditions for few-body nuclear systems

– Published in Phys. Rev. C 93, 054002

We describe and implement twisted boundary conditions for the deuteron and triton systems within finite volumes using the nuclear lattice EFT formalism. We investigate the finite-volume dependence of these systems with different twist angles. We demonstrate how various finite-volume information can be used to improve calculations of binding energies in such a framework. Our results suggest that with the appropriate twisting of boundaries, infinite-volume binding energies can be reliably extracted from calculations using modest volume sizes with cubic length $L \approx 8–14$ fm. Of particular importance is our derivation and numerical verification of three-body analogs of “i-periodic” twist angles that eliminate the leading-order finite-volume effects to the three-body binding energy.

Large-Nc Consistency of Chiral Nuclear Forces

– Published in Ruhr-Universität Bochum (Master thesis)

The work tests the consistency of nucleon-nucleon forces derived by two different approximation schemes of Quantum Chromodynamics (QCD)—the chiral perturbation theory ($\chi$PT) and large-Nc QCD. The approximation schemes and the derivation of the potential are demonstrated in this work. The consistency of the chiral potential, derived using the method of unitary transformation, is verified for chiral orders $Q^\nu$ for $\nu = 0,2,4$. Used methods, as well as possible extensions for higher orders, are presented.

Bringing Light into the Darkness — About Dark Matter Scattering off Light Nuclei

, Seminar at TP2, Ruhr-Universität Bochum

What do we know about Dark Matter and how can we possibly describe it on a fundamental scale? In this talk, I present the scattering of Dark Matter particles off various light nuclei within the framework of chiral effective field theory. I focus on scalar interactions and include one- and two-nucleon scattering processes whose form and strength are dictated by chiral symmetry. The nuclear wave functions are calculated from chiral effective field theory interactions as well. The convergence pattern of the chiral expansion in the nuclear potential and the Dark Matter-nucleus currents is investigated. This allows to provide a systematic uncertainty estimate of the calculations. Results for ${}^2$H, ${}^3$H, and ${}^3$He nuclei, which are theoretically interesting and the latter is a potential target for experiments, are provided.

Bringing Light into the Darkness (Poster)

, Poster at BCGS Poster Session 2017

What do we know about Dark Matter and how can we possibly describe it on a fundamental scale? In this session, I present the scattering of Dark Matter particles off various light nuclei within the framework of chiral effective field theory. I focus on scalar interactions and include one- and two-nucleon scattering processes whose form and strength are dictated by chiral symmetry. The nuclear wave functions are calculated from chiral effective field theory interactions as well. The convergence pattern of the chiral expansion in the nuclear potential and the Dark Matter-nucleus currents is investigated. This allows to provide a systematic uncertainty estimate of the calculations. Results for ${}^2$H, ${}^3$H, and ${}^3$He nuclei, which are theoretically interesting and the latter is a potential target for experiments, are provided.

Hubbard-Stratonovich like Transformations for Few-Body Interactions

, Parallel Session Talk at Lattice 2017, Granada

Through the development of many-body methodology and algorithms, it has become possible to describe quantum systems composed of a large number of particles with great accuracy. Essential to all these methods is the application of auxiliary fields via the Hubbard-Stratonovich transformation. This transformation effectively reduces two-body interactions to interactions of one particle with the auxiliary field, thereby improving the computational scaling of the respective algorithms. With the increasing size of involved particles, the relevance of collective phenomena and interactions grows as well. For many theories, e.g. Chiral Perturbation Theory, the inclusion of three-body forces has become essential in order to further increase the accuracy on the many-body level. In this seminar, the analytical framework for establishing a Hubbard-Stratonovich-like transformation, which allows for the systematic and controlled inclusion of contact three- and more-body interactions, is presented.

Nuclear Lattice Effective Field Theory

, Seminar at IKP

Nuclear Lattice Effective Field Theory (NLEFT) has proven to be a valuable candidate for pushing the borders of nuclear physics in the regime of nuclei as Carbon-12 and has enabled the computation of nuclear matrix elements for larger systems. The applicability of NLEFT to such systems is enabled through the utilization of lattice stochastic approaches as Hybrid Monte Carlo (HMC) algorithms. In this seminar, I briefly present the underlying principles and strategy behind modern algorithms.

dark_matter@JURECA

, Conference Talk at IAS-Symposium, Jülich

As there are several indications for the existence of so-called "Dark Matter" (DM) from an astrophysical point of view, direct detection of a candidate particle in a lab has not been successful this far. A set of direct detection experiments, which use different targets, could potentially test the various types of DM interactions with different properties of nuclei. To connect possible future measurements of DM signals to a candidate DM particle, these DM experimental signals must be propagated through nuclear cores — composed of many protons and neutrons — to the fundamental level of the DM theory. Due to the complexity in describing the many-body nucleus, this propagation has historically been done in a model- dependent fashion. As a candidate for propagating possible experimental data to the level of protons and neutrons, Nuclear Lattice Effective Field Theory (NLEFT) provides an approach which systematically enables the reduction of uncertainties.

Non-Stochastic Approaches for NLEFT

, Seminar at IKP, Jülich

Recently nuclear lattice effective field theory (NLEFT) has proven to be a valuable candidate for pushing the borders of nuclear physics in the regime of nuclei as Carbon-12 and has enabled the computation of nuclear matrix elements for larger systems. The applicability of NLEFT to such systems is enabled through the utilization of lattice stochastic approaches as Hybrid Monte Carlo (HMC) algorithms. As it is common for effective field theories, low energy coefficients (LECs) which describe the strength of effective interactions, need to be determined before one is able to describe and predict physical systems. In this process, it is essential to understand the effect of lattice artifacts as a discrete lattice spacing and the finite volume – independent of stochastic artifacts. Therefore non-stochastic approaches for smaller systems are employed to estimate LECs. In this seminar, such a non-stochastic approach for extracting nuclear energy levels on the lattice will be presented.

Applying Twisted Boundary Conditions for Few-Body Nuclear Systems

, Invited Talk at INT, Seattle

In this talk, I describe twisted boundary conditions for the deuteron and triton systems within finite volumes using the nuclear lattice EFT formalism. The finite-volume dependence of these systems with different twist angles is presented. Various finite-volume information can be used to improve calculations of binding energies in such a framework. The results suggest that with the appropriate twisting of boundaries, infinite-volume binding energies can be reliably extracted from calculations using modest volume sizes with cubic length $L \approx 8–14$ fm. Of particular importance is the derivation and numerical verification of three-body analogs of “i-periodic” twist angles that eliminate the leading-order finite-volume effects to the three-body binding energy.

Lattice Nuclear Physics Investigations of Fundamental Symmetries

, Seminar at ECT$^*$, Trento

One of the greatest unsolved problems in physics is the asymmetry of observed matter – the amount of baryonic matter greatly exceeds the amount of antibaryonic matter. Based on the assumption that at some point in time the universe contained the same amount of particles and antiparticles, a possible explanation for this observation requires the existence of physical processes which violate charge-parity (CP). Though it is known that CP-violating processes exist in nature, the effects by the CP-violating contributions of the standard model (SM) of particle physics are not sufficient to explain the current asymmetry of matter. Therefore there must be additional sources of CP violation that come from beyond the standard model (BSM). A quantity for probing the magnitude of such CP violating processes is the electric dipole moment (EDM) of nuclei. In this talk, a strategy for creating a link between a possible future measurement and the fundamental interpretation is presented.

Consistency of Nuclear Forces in the Limit of Large-Nc

, Conference Talk at Students Exchange Week in Bad Honnef

Conference talk on the consistency of nucleon-nucleon forces derived by two different approximation schemes of Quantum Chromodynamics (QCD)—the chiral perturbation theory ($\chi$PT) and large-Nc QCD. The approximation schemes and the derivation of the potential are demonstrated. The consistency of the chiral potential, derived using the method of unitary transformation, is verified for chiral orders $Q^\nu$ for $\nu = 0,2,4$. Used methods, as well as possible extensions for higher orders, are presented.