Flavor Singlet Physics with Background Fields

**Principal Investigator:**

Arwed Schiller

**Affiliation:**

Institut für Theoretische Physik, Leipzig University, Germany (QCDSF collaboration)

**Local Project ID:**

hlz22

**HPC Platform used:**

JUQUEEN of JSC

**Date published:**

**The calculation of sea quark and gluon content of hadrons, which can be traced back to flavour singlet hadron matrix elements, is one of the greatest technical challenges left in lattice QCD. This is due to the fact that the lattice calculation of so-called "disconnected diagrams" is extremely noisy and gives a poor signal. An improved determination of these disconnected contributions was the main aim of this project. For that, physicists of the QCDSF collaboration have proposed an alternative to the conventional three-point function technique (3-pt) for the study of hadron matrix elements in lattice QCD.**

It is well known that the sea quark and gluon content of hadrons (Fig. 1) can be traced back to flavour singlet hadron matrix elements, following the operator product expansion.

The calculation of these matrix elements, also referred to as quark-line disconnected diagrams, is one of the greatest technical challenges left in lattice QCD. This is due to the fact that the lattice calculation of so-called "disconnected diagrams" is extremely noisy and gives a poor signal. An improved determination of these disconnected contributions was the main aim of this project.

For that the scientists of the QCDSF collaboration under leadership of Arwed Schiller (University of Leipzig) have proposed an alternative to the conventional three-point function technique (3-pt) for the study of hadron matrix elements in lattice QCD.

By adapting the so-called Feynman-Hellmann theorem (FH) to the lattice setting, the researchers are able to isolate matrix elements in terms of an energy shift in the presence of an appropriate weak external background field. The spin results contribute to a solution of the so-called spin crisis of the proton and allow for a direct comparison of the researchers' lattice form factor results to experimental measurements at JLab.

To generate part of the necessary lattice configurations at different lattice couplings, quark masses, sizes and background fields, the HPC system JUQUEEN served as computing platform.

**Among the results based on that technique are:**

1) Calculation of spin distributions in the hadrons including the sea quark content [1] (Fig. 2).

2) Determination of the flavor-singlet axial-vector and scalar renormalisation constants [2].

3) Elastic form factors at large momentum transfer unreachable by standard lattice techniques [3] (Fig. 3).

4) Proposal of a new approach to calculate directly the proton structure function based on a determination of the lattice forward Compton amplitude [4] (Fig. 4).

**Acknowledgements:**

The numerical configuration generation was performed using the BQCD lattice QCD program on the IBM BlueGeneQ using DIRAC 2 resources (EPCC, Edinburgh, UK), the BlueGene P and Q at Jülich Supercomputing Centre (Jülich, Germany) and the Cray XC30 at HLRN (Berlin-Hannover, Germany).

Some of the simulations were undertaken using resources awarded at the NCI National Facility in Canberra, Australia, and the iVEC facilities at the Pawsey Supercomputing Centre. These resources are provided through the National Computational Merit Allocation Scheme and the University of Adelaide Partner Share supported by the Australian Government.

**References:**

[1] A.J. Chambers et al., Phys. Rev. D90 (2014) 014510 and D92 (2015) 114517.

[2] A.J. Chambers et al., Phys. Lett. B740 (2014) 30.

[3] A.J. Chambers et al., arXiv:1702.01513 [hep-lat] (1917), to appear in Phys. Rev. D

[4] A.J. Chambers et al., Phys. Rev. Lett. 118 (2017) 242010.

**Scientific Contact:**

Arwed Schiller

Universität Leipzig

Institut für Theoretische Physik

Postfach 100 920, D-04009 Leipzig (Germany)

schiller[at]itp.uni-leipzig.de