A stochastic method for computing hadronic matrix elements

Abstract

We present a stochastic method for the calculation of baryon three-point functions that is more versatile compared to the typically used sequential method. We analyze the scaling of the error of the stochastically evaluated three-point function with the lattice volume and find a favorable signal-tonoise ratio suggesting that our stochastic method can be used efficiently at large volumes to compute hadronic matrix elements.

Disconnected quark loop contributions to nucleon observables in lattice QCD

“…In Ref. [17] we showed that a ratio of N LP to N HP of about 20 can be considered sufficient to produce an unbiased estimate for the class of observables considered here. Therefore, in this work we take N HP = 24 and choose N LP = 500 for the light quark sector.…”

“…Following Refs. [9,17], we choose a stopping condition at fixed value of the residual |r| LP ∼ 10 −2 . N HP is then selected by requiring that the bias introduced when using N LP low precision vectors is corrected.…”

“…In this paper, the aim is to use our findings on the performance of recently developed methods [17] to compute to high accuracy the disconnected contributions that enter in the determination of nucleon form factors, sigma terms and first moments of parton distributions. The evaluation will be performed using one ensemble generated with two light degenerate quarks and a strange and charm quark with masses fixed to their physical values (N f = 2 + 1 + 1) using the twisted mass fermion discretization.…”

Recent progress in hadron structure from Lattice QCD

“…In the calculation of Ref. [63] the preferred smearing is stout since it is analytically defined in both the perturbative and non-perturbative evaluations. Note, however, that in the perturbative computation of the renormalization functions introduction of smearing increases the number of algebraic expression, which explodes as the stout smearing steps increase.…”

“…For the work of Ref. [63] the renormalized matrix element at m π = 373 MeV in the MS at 2 GeV is found to be: x g = 0.309 (25). An alternative approach to extract the matrix elements of the gluon operator utilizes the Euclidean form of the Feynman-Hellman theorem.…”