First moments of the nucleon transverse quark spin densities using lattice QCD

Abstract

We present a calculation of the Mellin moments of the transverse quark spin densities in the nucleon using lattice QCD. The densities are extracted from the unpolarized and transversity generalized form factors extrapolated to the continuum limit using three N f = 2 + 1 + 1 twisted mass fermion gauge ensembles simulated with physical quark masses and spanning three lattice spacings. The first moment of transversely polarized quarks in an unpolarized nucleon shows an interesting distortion, which can be traced back to the sharp falloff of the transversity generalized form factor BT n0(t). The isovector tensor anomalous magnetic moment is determined to be κT = 1.051(94), which confirms a negative and large Boer-Mulders function, h ⊥ 1 , in the nucleon.

Nucleon transverse quark spin densities

“…Results are shown for the cB211.072.64 (top), cC211.060.80 (middle) and cD211.054.96 (bottom) ensemble. For the latter, we are still increasing statistics for the three largest values of 𝑡 𝑠 , see Table . 2. obtain a value of 𝑔 𝑢−𝑑 𝑇 = 0.924(54) [5]. In Fig.…”

“…This requires the computation of disconnected contributions. We use hierachical probing to improve from ETMC [5,6] using only physical mass point ensembles; PNDME [7]; 𝜒QCD [8]; NME [9]; and CLS-Mainz [10]. Open green and yellow symbols denote lattice QCD results without continuum extrapolation.…”

Selected lattice QCD results on hadron structure

“…3, we show the strange nucleon electromagnetic form factors, demonstrating that sea quark effects can be accurately determined and showing non-zero strangeness in the nucleon. (left) from: ETMC [12,13] using only physical mass point ensembles, PNDME [14], χQCD [15], NME [16], and CLS-Mainz [17] (green symbols for N f = 2 + 1 + 1 and yellow for N f = 2 + 1 ensembles). Open green and yellow symbols denote lattice QCD results without continuum extrapolation.…”

Off-forward anomalous dimensions of non-singlet transversity operators

“…The matrix elements themselves are again to be calculated non-perturbatively, see e.g. [11][12][13] for recent progress in lattice QCD. They are related to the transversity distribution (TDF) of partons inside hadrons.…”