ELEMENTARY PARTICLE PHYSICS
Nucleon Structure Observables from Simulations of QCD on Large and Fine Lattices
Principal Investigator:
Apl. Prof. Dr. Georg von Hippel
Affiliation:
Johannes Gutenberg-Universität Mainz, Institut für Kernphysik, Mainz, Germany
Local Project ID:
NucStrucLFL
HPC Platform used:
JUWELS (CPU nodes) of JSC
Date published:
The internal structure of the proton and neutron (collectively known as the nucleon), which form the building blocks of atomic nuclei, still poses many open questions. Not only is it not completely understood how the nucleon’s spin and momentum are composed of those of its constituent particles (the quarks and gluons), but even its size is subject to significant uncertainty arising from discrepancies between different determinations: there is a decade-old inconsistency between the electric charge radius of the proton as obtained from scattering experiments in good agreement with the value from hydrogen spectroscopy on the one hand, and the most accurate determination from the spectroscopy of muonic hydrogen on the other. This significant discrepancy, which has been dubbed the “proton radius puzzle”, has given rise to a variety of initiatives to better determine the proton radius.
In the context of scattering experiments, the proton charge radius is determined from the slope of the electric form factor describing the proton’s response to being probed at different momentum transfers. In order to gain a proper understanding of the origin of the proton radius puzzle and associated questions, theoretical determinations of nucleon structure observables, and in particular of the electromagnetic form factors of the nucleon, from first principles are required.
Lattice Quantum Chromodynamics (Lattice QCD) provides a way to study such questions from first principles, and lattice QCD calculations are therefore instrumental in predicting the nucleon charge radii from QCD. This has generated lively activity on this topic within the lattice QCD community although at present, the precision of lattice results is not yet sufficient to definitely rule out either the electronic or the muonic result for the proton radius. To make further progress towards ruling out either the electronic or the muonic result for the proton radius from first-principles simulations of lattice QCD, improved control of the extrapolation to the physical point (at vanishing lattice spacing, infinite volume and physical quark masses) is required.
The Coordinated Lattice Simulations (CLS) effort combines the human and computational resources of several European teams in order to generate a set of lattice QCD ensembles that allow for a controlled extrapolation to the physical point (i.e. zero lattice spacing, physical pion mass and infinite lattice volume). For this end, it is essential to have ensembles both at fine lattice spacing and at (near-)physical pion mass, all while maintaining a large enough overall lattice volume. Simultaneously fulfilling these competing demands is very expensive computationally, so large HPC systems, such as JUWELS at JSC, are required.
In this project, nucleon structure observables were measured on the two largest (in lattice units) ensembles codenamed “E250” (at physical quark masses) and “E300” (at a very fine lattice spacing).
In Figure 1, we show the landscape of CLS ensembles in terms of lattice spacing and pion mass. All ensembles satisfy the condition mπL>4 required for good control of finite-size effects. As can be seen from the plot, the E250 and E300 ensembles are the closest to the physical point (shown as a red dot) and thus have a large impact on the extrapolation in lattice spacing and pion mass, respectively.
Figure 1: Landscape of the CLS ensembles currently used to study nucleon structure. The E250 and E300 ensembles studied in this project are the closest to the physical point and thus the most important for a controlled extrapolation.
In Figure 2, we show results for the electric and magnetic form factors of the proton and the neutron obtained from our lattice QCD simulations and extrapolated to the physical point. The orange bands show the uncertainty resulting from the extrapolation, while the black points are experimental results from scattering experiments shown for comparison. It can be seen that the lattice QCD result for the electric form factor of the proton is noticeably steeper than the experimental determination, indicating that the QCD prediction is more in line with the results from muonic hydrogen spectroscopy. On the other hand, the magnetic form factor of the proton obtained from lattice QCD is in good agreement with the experimental results by the A1 collaboration (which implies some tension with the results from other experiments), while the neutron form factors broadly agree with experiment within the much larger uncertainties [2,3].
Figure 2: The electric (left column) and magnetic (right column) form factors of the proton (top row) and the neutron (bottom row). Shown in orange are the result from our lattice QCD simulations extrapolated to the physical point, with the shaded bands indicating the statistical and systematic uncertainties of the results, while the black points are experimental results from scattering experiments, and the red crosses indicate the experimental values of the magnetic moments. Figure taken from Ref. [3].
Furthermore, we have studied the isovector matrix elements giving access to the valence-quark contributions to the overall spin and momentum of the nucleon [1], and the so-called pion-nucleon sigma term giving access to the contribution of the quark masses to the nucleon mass [4].
We currently plan to extend our analysis also to further isoscalar matrix elements, and to the axial-vector form factors of the nucleon, which are important for describing neutrino-nucleus scattering in the context of the planned long-baseline neutrino experiments that will investigate the nature of the neutrinos.
References
[1] D. Djukanovic, G. von Hippel, H. B. Meyer, K. Ottnad and H. Wittig,Improved analysis of isovector nucleon matrix elements with Nf=2+1 flavors of O(a) improved Wilson fermions,Phys. Rev. D 109 (2024) 074507, doi:10.1103/PhysRevD.109.074507 [arXiv:2402.03024].
[2] D. Djukanovic, G. von Hippel, H. B. Meyer, K. Ottnad, M. Salg and H. Wittig,Precision calculation of the electromagnetic radii of the proton and neutron from lattice QCD,to appear in Phys. Rev. Lett., arXiv:2309.07491.
[3] D. Djukanovic, G. von Hippel, H. B. Meyer, K. Ottnad, M. Salg and H. Wittig,Electromagnetic form factors of the nucleon from Nf=2+1 lattice QCD,to appear in Phys. Rev. D, arXiv:2309.06590.
[4] A. Agadjanov, D. Djukanovic, G. von Hippel, H. B. Meyer, K. Ottnad and H. Wittig,Nucleon Sigma Terms with Nf=2+1 Flavors of O(a)-Improved Wilson Fermions,Phys. Rev. Lett. 131 (2023) 261902, doi:10.1103/PhysRevLett.131.261902 [arXiv:2303.08741].