Precision study of excited state effects in nucleon matrix elements

Abstract

We present a dedicated analysis of the influence of excited states on the calculation of nucleon matrix elements. This calculation is performed at a fixed value of the lattice spacing, volume and pion mass that are typical of contemporary lattice computations. We focus on the nucleon axial charge, g A , for which we use about 7,500 measurements, and on the average momentum of the unpolarized isovector parton distribution, x u−d , for which we use about 23,000 measurements. All computations are done employing N f = 2 + 1 + 1 maximally-twisted-mass Wilson fermions and using nonperturbatively calculated renormalization factors. Excited state effects are shown to be negligible for g A , whereas they lead to an O(10%) downward shift for x u−d .

Excited state contamination in nucleon structure calculations

“…In this case, a clearer trend is visible: x u−d decreases as T /a increases, and there is no evidence that even T /a = 12 might be large enough that excited-state contamination is negligible. This result is consistent with a recent study using the open sink method, where τ is fixed in order to allow the calculation of three-point functions at all values of T [10]. Furthermore, the effect of excited states appears to be larger at smaller pion masses.…”

Hadron Structure

“…In a study by RQCD [21] at m π 300 MeV, no change of g A has been seen by varying the separation from 0.5-1.2 fm (see Fig. 4a); this is also confirmed by a high precision study at m π ∼ 370 MeV using TMF [29] in which the source-sink separation takes values within the range 0.9-1.6 fm [29]. Studying the summed ratio using TMF no curvature in the slope is observed and the result extracted for g A agrees with the plateau method as can be seen in Fig 5a. The 2-state analysis of PNDME [25] shown in Fig.…”

Sigma terms and strangeness content of the nucleon with N f = 2 + 1 + 1 twisted mass fermions

“…However they can have a non-negligible impact on the evaluation of nucleon matrix elements, as shown for instance in [40]. We are therefore planning to address this problem in a forthcoming publication.…”