**Principal Investigator:**

Karl Jansen

**Affiliation:**

Deutsches Elektronen-Synchrotron (DESY), Astroteilchenphysik, Zeuthen (Germany)

**Local Project ID:**

pr74yo

**HPC Platform used:**

SuperMUC of LRZ

**Date published:**

Lattice Quantum Chromodynamics (QCD) is a non-perturbative approach for solving QCD, our theory of the strong interaction between quarks and gluons, that starts directly from the QCD Lagrangian. It consists of discretizing the theory on a 4-dimensional Euclidean lattice. Due to most substantial advances of the employed algorithms and the advent of powerful supercomputers such as SuperMUC, lattice QCD simulations are now possible directly at physical values of the quark masses. This is a very significant step forward, since it avoids an extrapolation to the physical masses and thus eliminates a rather uncontrolled systematic uncertainty.

In this way, lattice QCD has developed into a true *ab initio* method for providing insights into the inner most structure of matter. In this project, we have focused to improve our unerstanding of hadron structure and computed observables that can probe new physics beyond the standard model (BSM).

We use a particular quark discretization, twisted mass fermions, which provides a very fast convergence to the continuum limit. Our European Twisted Mass Collaboration (ETMC), in which this project is embedded, has already simulated ensembles of gauge configurations at the physical up and down quark masses and is now calculating gauge ensembles which include *for the first time* *N _{f}* = 2+1+1 flavours of quarks comprising the physical light, strange and charm quark masses [1]. These calculations became possible by developing new algorithmic techniques within our team and which led to large improvements, see ref. [2].

½∆Σ | L | J | |

u | 0.415(13) | -0.107(40) | 0.308(40) |

d | -0.193(9) | 0.247(40) | 0.054(38) |

s | -0.021(5) | 0.067(21) | 0.046(21) |

g | - | - | 0.133(18) |

tot. | 0.201(18) | 0.207(78) | 0.541(79) |

Table 1: Numerical values of the nucleon spin decomposition, given in the ^{-}MS^{-}-scheme at 2 GeV.

**Nucleon spin.** As a first very important result we have obtained the complete decomposition of the nucleon spin into the contributions from its partons. This includes the quark intrinsic spin, the quark orbital angular momentum, and the gluon contribution. This is the first such study in lattice QCD using quarks with masses tuned to their physical values. We used Ji’s spin sum:

where ∆Σ* ^{q }*is the intrinsic spin contribution of a quark of flavor

**Direct evaluation of Parton Distribution Functions (PDF).** Another important and most remarkable result has been a direct lattice calculation of parton distribution functions. Using the pioneering method suggested by Ji in Ref. [3] we have computed nucleon parton distribution functions (PDFs) on two physical point ensembles, namely an *N _{f}* = 2 ensemble with size 48

This is the first time that by using physical values of the quark masses an agreement with phenomenological extractions of parton distribution functions could be demonstrated. This clearly constitutes a major step forward in understanding the structure of hadronic matter.

**References**

[1] Jacob Finkenrath, Constantia Alexandrou, Simone Bacchio, Panagiotis Charalambous, Petros Dimopoulos, Roberto Frezzotti, Karl Jansen, Bartosz Kostrzewa, Giancarlo Rossi, and Carsten Urbach, *Simulation of an ensemble of N _{f} *= 2 + 1 + 1

[2] Simone Bacchio, Constantia Alexandrou, and Jacob Finkerath, *Multigrid accelerated simulations for Twisted Mass fermions*, in: 35th International Symposium on Lattice Field Theory (Lattice 2017) Granada, Spain, June 18-24, 2017, 2017.

[3] Xiangdong Ji, *Parton Physics on a Euclidean Lattice*, Phys. Rev. Lett., **110**, 262002, 2013.

[4] J. F. Owens, A. Accardi, and W. Melnitchouk, *Global parton distributions with nuclear and finite-Q ^{2} corrections*, Phys. Rev.,

[5] Daniel de Florian, Rodolfo Sassot, Marco Stratmann, and Werner Vogelsang, *Extraction of Spin-Dependent Parton Densities and Their Uncertainties*, Phys. Rev., **D80**, 034030, 2009.

**Project Contributors**

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

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

M. Constantinou, Physics Department, Temple University, 1925 N. 12th Street, Philadelphia PA

J. Finkenrath, K. Hadjiyiannakou, G. Koutsou, A. Scapellato, Computation-based Science and Technology Research Center, The Cyprus Institute, 20 Kavafi Str., Nicosia 2121, Cyprus

C. Kallidonis, Department of Physics and Astronomy, Stony Brook University, New York 11794-3800

B. Kostrzewa, M. Petschlies, C. Urbach, Helmholtz-Institut für Strahlen- und Kernphysik (Theorie) and Bethe Center for Theoretical Physics, Universität Bonn, 53115 Bonn, Germany

K. Ottnad, Helmholtz-Institut Mainz, Johannes Gutenberg-Universität, 55099 Mainz

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

A. Vaquero, Department of Physics and Astronomy, University of Utah, Salt Lake City, UT 84112

**Scientific Contact**

Prof. Dr. Karl Jansen

Deutsches Elektronen-Synchrotron (DESY)

Platanenallee 6, D-15738 Zeuthen/Germany

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

**NOTE:** This report was first published in the book "High Performance Computing in Science and Engineering – Garching/Munich 2018".

*LRZ project ID: pr74yo*

*February 2020*