# Nucleon Observables as Probes for Physics Beyond the Standard Model

**Principal Investigator:** Dr. Karl Jansen, Deutsches Elektronen-Synchrotron/DESY, Zeuthen (Germany)

**HPC Platform:** Hazel Hen of HLRS

The inner core of all matter consists mainly of protons and neutrons, the so-called nucleons. These nucleons themselves are made of three constituent quarks which are surrounded by sea quarks and gluons which are spontaneously generated through quantum fluctuations. In order to understand these complicated and non-perturbative interactions highly non-linear equations have to be solved which require the usage of supercomputers such as Hazel Hen at HLRS as employed in this project.

The main target of the computations in the project have been to reveal the quark and gluon structure of the nucleon. In particular the project has addressed the quark and gluon contributions to the spin, the angular momentum and the momentum of the nucleon. A special focus of the project has been the calculation of the scalar quark content of the proton. Such calculations will aid research of physical processes in particle physics and the as yet unknown nature of dark matter that accounts for an estimated 21 percent of matter in the universe.

The research area that can address these questions is quantum chromodynamics (QCD), which theoretically describes the strong interaction between quarks and gluons, and is expected to explain what binds together neutrons and protons in atomic nuclei. This strong interaction is responsible for the stability of atomic nuclei since, without it, the positively charged protons would repel each other leading matter to be unstable.

The strong interaction is also responsible for the fact that the binding energy of the proton is extremely large. While a quark weighs around 10 mega electron volts (MeV), a proton due to its binding energy weighs 1 GeV (giga electron volts), that is 100 times more. In fact, the strong force is so large that quarks can never be extracted from protons experimentally, a phenomenon which is called ‘confinement’. A rough picture of the confinement phenomenon is that the interaction between quarks behaves like a spring or an elastic band, where increasing energy must be invested when are quarks are pulled apart. If the band is over-stretched, it ‘rips’ and a quark-antiquark pair is formed that immediately binds via the strong interaction, and leads to a new hadron (a composite particle of quarks).

The strong force does not allow for approximate calculations, because the coupling between the quarks can grow very strong. However, with the ground-breaking formulation of the theory of quarks and gluons in a four-dimensional space-time lattice, physicist and Nobel Prize winner Kenneth Wilson succeeded in 1974 with developing the lattice theory of quantum chromodynamics (lattice QCD) – an ab initio non-perturbative method.

In the lattice QCD theory, space-time is a four-dimensional lattice, a crystal with hyper-cubic symmetry. By moving from Minkowski to Euclidean time, the theory can be considered as a statistical physical system which allows, in particular, for numerical simulations. In this project the approach of lattice QCD has been utilized to compute a number of key observables to understand better the inner structure of nucleons. A prime example is the scalar quark content of the nucleon on which we will concentrate here.

It is a fascinating and astonishing observation that the visible matter that we know seems to form only about four percent of the total matter in the universe. This calls for the existence of ‘Dark Matter’ and ‘Dark Energy’ that make the rest of about 95%, see figure 1. However, very disturbingly, we do not know at all the composition of this dark matter and dark energy. One thing known, though, is that dark matter must consist of scalar particles since otherwise an interaction with the visible matter would be observed.

The question is, of course, whether we can identify observables that can help to search for dark matter and the scalar quark content of the proton (σ_{c}, σ_{s}, σ_{πN}) is such a quantity.

The scalar quark condensate consists of a tightly coupled quark/anti-quark pair that forms a condensate, similar to a water droplet on a plane of glass. This condensate has a scalar quantum number. Therefore, it can couple to the Higgs boson, which itself is a scalar particle and, in turn, the Higgs boson could interact with scalar particles of dark matter. In order to interpret experimental results for a direct evidence of dark matter, it is essential to know the numerical value of the scalar condensate.

Using the computational resources of this project, it became possible to compute the scalar quark content of the nucleon to an unprecedented precision, see figure 2. The results of this project are already used in experiments that look for evidence of an interaction between the Higgs boson and the scalar condensate inside the nucleon. Thus, the determination of the scalar quark contents as carried out here could open a new window to finally solving the mystery of dark matter.

Figure 2: The scalar quark contents of the nucleon required for dark matter searches as computed in this project. The red stars (this work) are showing the scalar quark content of the different quark flavours. Open symbols denote previous computations within lattice QCD which did not used simulations with physical parameters of the pion mass and may thus carry a systematic error. The filled blue squares and filled black stars are calculations within lattice QCD using different discretization schemes. Green dots are the results of phenomenology using recent experimental input. *Copyright: DESY Zeuthen*

**Physical Point Papers:**

Abdel-Rehim A, Alexandrou C, Constantinou M, Hadjiyiannakou K, Jansen K, Kallidonis Ch, Koutsou G & Vaquero Aviles-Casco A: Direct evaluation of the quark content of the nucleon from lattice QCD at the physical point, Phys. Rev. Lett. (2016), 116, 252001.

**Collaborators:**

Prof. Dr. C. Alexandrou, Department of Physics, University of Cyprus, P.O. Box, 20537, 1678 Nicosia, Cyprus and Computation-based Science and Technology Research Center, The Cyprus Institute, 20 Kavafi Str., Nicosia 2121, Cyprus

Dr. A. Athenodorou, Department of Physics, University of Cyprus, P.O. Box, 20537, 1678 Nicosia, Cyprus

S. Bacchio, Department of Physics, University of Cyprus, P.O. Box, 20537, 1678 Nicosia, Cyprus

Dr. M. Constantinou, Department of Physics, University of Cyprus, P.O. Box, 20537, 1678 Nicosia, Cyprus

Dr. J. Finkenrath, Computation-based Science and Technology Research Center, The Cyprus Institute, 20 Kavafi Str., Nicosia 2121, Cyprus

Dr. K. Hadjiyiannakou, Department of Physics, Columbian College of Arts and Sciences, The George Washington University, Washington, D.C. 20052, USA

C. Kallidonis, Computation-based Science and Technology Research Center, The Cyprus Institute, 20 Kavafi Str., Nicosia 2121, Cyprus

Dr. G. Koutsou, Computation-based Science and Technology Research Center, The Cyprus Institute, 20 Kavafi Str., Nicosia 2121, Cyprus

Dr. B. Kostrzewa, Helmholtz-Institut fuer Strahlen- und Kernphysik (Theorie) and Bethe Center for Theoretical Physics, Universitaet Bonn, 53115 Bonn, Germany

Dr. K. Ottnad, Helmholtz-Institut fuer Strahlen- und Kernphysik (Theorie) and Bethe Center for Theoretical Physics, Universitaet Bonn, 53115 Bonn, Germany

Dr. M. Petschlies, Helmholtz-Institut fuer Strahlen- und Kernphysik (Theorie) and Bethe Center for Theoretical Physics, Universitaet Bonn, 53115 Bonn, Germany

A. Scapellato, Department of Physics, University of Cyprus, P.O. Box, 20537, 1678 Nicosia, Cyprus

Dr. F. Steffens, NIC, DESY, Platanenallee 6, 15738 Zeuthen, Germany

Prof. Dr. C. Urbach, Helmholtz-Institut fuer Strahlen- und Kernphysik (Theorie) and Bethe Center for Theoretical Physics, Universitaet Bonn, 53115 Bonn, Germany

Dr. A. Vaquero, INFN, Sezione di Milano-Bicocca Edificio U2, Piazza della Scienza 3 20126 Milano, Italy

J. Volmer, NIC, DESY, Platanenallee 6, 15738 Zeuthen, Germany

**Scientific Contact:**

Karl Jansen

Deutsches Elektronen-Synchrotron/DESY

Platanenallee 6, D-15738 Zeuthen (Germany)

e-mail: Karl.Jansen [at] desy.de

*January 2017*