Hadrons fall into two classes: baryons, such as the familiar proton, and mesons, for example the pion. Deep Inelastic Scattering was the first direct evidence that baryons really were made up of much smaller constituents, “partons”, i.e. quarks and gluons. Investigating the structure of hadrons has become a vital component of many experiments at (for example) JLAB and the LHC.
In  we have proposed an alternative method of measuring the parton distribution in hadrons. Parton distribution functions tell us how the momentum of a nucleon is shared out between its partons. The traditional lattice method of measuring parton distributions proceeds through the operator product expansion. In that approach lattice operators are constructed which correspond to moments of the distribution – each moment needs a different operator, with its individual renormalisation constant. Our new approach directly involves simulating scattering on hadrons – in essence we are repeating a deep inelastic scattering experiment on the lattice. First results of the method leading to a reconstruction of a parton distribution function (left panel) are shown above.
Other investigations are designed to determine the distribution of electromagnetic currents in hadrons due to the presence of quarks. These can be parameterised by two functions (electric and magnetic form factors). For most of the second half of the 20th century, it was believed that they both depended on momentum in the same way, so that their ratio was constant. However recent experiments have shown that at higher momentum transfer the ratio decreases and perhaps passes through zero. To investigate this theoretically is difficult (due to the larger momentum transfer). We have developed a method, , that allows this range to be considerably extended, approaching the region where the sign might change, as shown in the right panel.
Bibliography:  A. J. Chambers et al., Phys. Rev. Lett. 118 (2017) 242001.  A. J. Chambers et al., Phys. Rev. D96 (2017) 114509.