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We present a systematic study demonstrating the impact of lattice QCD data on the extraction of generalised parton distributions (GPDs). For this purpose, we use a previously developed modelling of GPDs based on machine learning techniques fulfilling the theoretical requirements of polynomiality, a form of positivity constraint and known reduction limits. A special care is given to estimate the uncertainty stemming from the ill-posed character of the connection between GPDs and the experimental processes usually considered to constrain them, like deeply virtual Compton scattering (DVCS). Mock lattice QCD data inputs are included in a Bayesian framework to the prior model which is fitted to reproduce the most experimentally accessible information of a phenomenological model by Goloskov and Kroll. We highlight the impact of the precision, correlation and kinematic coverage of lattice data on GPD extraction at moderate $\xi$ which has only been brushed in the literature so far, paving the way for a joint extraction of GPDs.

We use the infinite volume reconstruction method to calculate the charged/neutral pion mass difference. The hadronic tensor is calculated on lattice QCD and then combined with an analytic photon propagator, and the mass splitting is calculated with exponentially-suppressed finite volume errors. The calculation is performed using six gauge ensembles generated with $2+1$-flavor domain wall fermions, and five ensembles are at the physical pion mass. Both Feynman and Coulomb gauge are adopted in the calculation and result in a good agreement when the lattice spacing approaches zero. After performing the continuum extrapolation and examining the residual finite-volume effects, we obtain the pion mass splitting $\Delta m_\pi = 4.534(42)(43)~\mathrm{MeV}$, which agrees well with experimental measurements., Comment: 10 pages, 5 figures