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Hannaford-Gunn, Alec; Kadir Utku Can; Horsley, Roger; Nakamura, Yoshifumi; Perlt, Holger; Rakow, Paul E L; Stüben, Hinnerk; Schierholz, Gerrit; Young, Ross D; Zanotti, James M
arXiv.org, 02/2022Paper, Journal Article
We determine the properties of generalised parton distributions (GPDs) from a lattice QCD calculation of the off-forward Compton amplitude (OFCA). By extending the Feynman-Hellmann relation to second-order matrix elements at off-forward kinematics, this amplitude can be calculated from lattice propagators computed in the presence of a background field. Using an operator product expansion, we show that the deeply-virtual part of the OFCA can be parameterised in terms of the low-order Mellin moments of the GPDs. We apply this formalism to a numerical investigation for zero-skewness kinematics at two values of the soft momentum transfer, \(t = -1.1, -2.2 \;\text{GeV}^2\), and a pion mass of \(m_{\pi}\approx 470\;\text{MeV}\). The form factors of the lowest two moments of the nucleon GPDs are determined, including the first lattice QCD determination of the \(n=4\) moments. Hence we demonstrate the viability of this method to calculate the OFCA from first principles, and thereby provide novel constraint on the \(x\)- and \(t\)-dependence of GPDs.
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