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Nucleon Structure Using Lattice QCD Simulation with Physical Pion Mass

Principal Investigator: Constantia Alexandrou, University of Cyprus and The Cyprus Institute (Cyprus)
HPC Platform: SuperMUC of LRZ - Date published: April 2016

The goal of this project is to understand the properties of elementary particles such as the proton, which forms most of the ordinary matter around us. The fundamental theory that determines the mass and structure of such particles is the strong interaction, one of the four forces known to us, the others being electromagnetism, the weak interaction, and gravity.

Quantum Chromodynamics (QCD) is the underlying theory of the strong interactions that describe a wide range of complex processes in the universe. Among them are the fusion and fission processes that power the sun and the other stars, the formation and explosion of stars and the state of matter at the birth of the universe.

QCD is a remarkable theory that differs from the other three fundamental interactions. The basic building blocks of the theory are the quarks that are always confined inside the hadrons. The proton is a baryon made of three light quarks as shown in the picture below. However, these quarks cannot be liberated and be observed freely, a property characteristic only of QCD and known as confinement.

Furthermore, unlike a basket of apples where its weight is the sum of the weights of each apple and the empty basket, the weight or mass of the proton is almost exclusively determined by the interactions among the three quarks rather than their mass, which is approximately 200 times less than that of the proton.

Clearly to describe the properties of the proton one needs very different methods as compared to describing other physical systems such as for example the binding energy of the hydrogen atom. Thus, the challenge is to provide a quantitative description of strongly interacting particles using the underlying theory of QCD. This is done by defining the continuous equations of QCD on a discrete four-dimensional mesh or lattice and simulating it on the largest supercomputers available. This formulation, first written down by Nobel Prize winner K. Wilson, is known as lattice QCD and enables us to systematically study the properties of these particles numerically.

Baryon Structure Using Dynamical QCD Simulations With Physical Values of the Light, Strange and Charm Quark Masses

The biggest challenge in lattice QCD is to simulate the theory at physical values of the light quark masses. In addition to light quarks that make ordinary matter there are heavier quarks. Our collaboration, known as the European Twisted Mass Collaboration (ETMC), uses an improved formulation as compared to the original one by Wilson and is able to simulate QCD with physical values for the light quarks. Using computational resources allocated by PRACE, my group has pioneered the calculation of key observables that characterize the structure of protons and neutrons, collectively referred to as nucleons.

In Fig. 1 we show the axial charge of the nucleon as a function of the mass of the pion. This is a well measured quantity and serves as a check of our theoretical approach. The value obtained at physical pion mass was computed using PRACE resources and we are the first group to produce it. The value obtained agrees with the experimental value and gives confidence in our methodology although a reduction of the error is still needed.

Nucleon Structure Using Lattice QCD Simulation with Physical Pion MassFig.1: The axial charge of the nucleon as a function of the mass of the pion squared, the lightest particle in the theory. The result at the physical value of the pion mass is produced using partly PRACE resources. The experimental value is shown with the black asterisk. See C. Alexandrou et al., Phys. Rev. D92 (2015) 114513
Copyright: University of Cyprus and The Cyprus Institute

The determination of other important quantities follow the same methodology as that used for the evaluation of the axial charge. In particular, moments of parton distribution functions play a crucial role in determined properties like the momentum fraction carried by the three quarks inside the nucleon. We show in Fig. 2 the isovector momentum fraction again as a function of the pion mass. As can be seen the value obtained is higher than the one measured experimentally. This is now understood to be due to contamination from other excited sates and it is currently under investigation.

Nucleon Structure Using Lattice QCD Simulation with Physical Pion MassFig. 2: Results for the momentum fraction from our collaboration using twisted mass fermions (TMF) as compared to the results of other collaborations, see C. Alexandrou et al., Phys. Rev. D92 (2015) 114513
Copyright: University of Cyprus and The Cyprus Institute

Nucleon Structure Using Lattice QCD Simulation with Physical Pion MassFig. 3: Results on the total spin carried by quarks in the nucleon obtained using twisted mass fermions and partly PRACE computational resources. The open symbols include disconnected contributions computed using partly Piz Daint of CSCS, Switzerland. See C. Alexandrou, keynote talk at the Light Cone meeting in Rome, arXiv:1512.03924.
Copyright: University of Cyprus and The Cyprus Institute

Using the first moments we can extract information on the spin components of the proton, addressing a long-standing puzzle. We show in Fig. 3 the total spin carried by quarks in the proton. At the physical point we show the contributions from the u, d and s quarks. This was accomplished by combining PRACE resources with resources of the Piz Daint machine of CSCS, Switzerland that enabled us to compute the disconnected diagrams associate with sea quark contributions, leveraging the resources secured on SuperMUC.

In Fig. 4 we show the decomposition of the total spin into the intrinsic spin and the angular momentum carried by quarks. The results at the physical point are the first to include disconnected contributions. As can be seen, these contributions are important to bring agreement between the theoretical value and the experimental one.

Nucleon Structure Using Lattice QCD Simulation with Physical Pion MassFig 4: The intrinsic spin ?? and the angular momentum L carried by quarks in the nucleon. The open symbols include contributions from sea quarks. The open diamonds include the contributions from sea up, down and strange quarks. See C. Alexandrou, keynote talk at the Light Cone meeting in Rome, arXiv:1512.0392
Copyright: University of Cyprus and The Cyprus Institute

Scientific team:

C. Alexandrou, M. Constantinou, K. Hadjiyiannakou, K. Jansen, C. Kallidonis, G. Koutsou, A. Vaquero

Computational resources:

State‐of‐the‐art lattice QCD simulations rely on access to Tier-0 supercomputers. None of these results would have been obtained without access to SuperMUC resources, which was made possible through PRACE, the Partnership for Advanced Computing in Europe. We would like to take this opportunity to thank the Leibniz Supercomputing Centre in Munich for the very good management of the machine, which has enabled us to do internationally competitive research.

Scientific Contact:

Prof. Constantia Alexandrou
University of Cyprus
Department of Physics, Faculty of Pure and Applied Sciences
P.O.Box 20537, 1678 Nicosia/Cyprus
e-mail: alexand [at] ucy.ac.cy

April 2016

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