Transverse Spin Structure of the Nucleon from Lattice-QCD Simulations

We present the first calculation in lattice QCD of the lowest two moments of transverse spin densities of quarks in the nucleon. They encode correlations between quark spin and orbital angular momentum. Our dynamical simulations are based on two flavors of clover-improved Wilson fermions and Wilson gluons. We find significant contributions from certain quark helicity flip generalized parton distributions, leading to strongly distorted densities of transversely polarized quarks in the nucleon. In particular, based on our results and recent arguments by Burkardt [Phys. Rev. D 72, 094020 (2005)], we predict that the Boer-Mulders function $h_1^{\perp }$, describing correlations of transverse quark spin and intrinsic transverse momentum of quarks, is large and negative for both up and down quarks.

Figure 1

Results for the generalized form factors ${\overline{B}}_{T(n=1,2)0}(t)$. The corresponding $p$-pole parametrizations are shown by the shaded error bands.

Figure 2

Study of discretization errors of the tensor charge $A_{T10}(t=0)=g_T(t=0)$ for up and down quarks at a pion mass of $m_{\pi }\approx 600\mathrm{MeV}$.

Figure 3

Pion mass dependence of the generalized form factors ${\overline{B}}_{T(n=1,2)0}(t=0)$ for up quarks. The shaded error bands show extrapolations to the physical pion mass based on an ansatz linear in $m_{\pi }^2$. The symbols are as in Fig. 2.

Figure 4

Lowest moment ($n=1$) of the densities of unpolarized quarks in a transversely polarized nucleon (left) and transversely polarized quarks in an unpolarized nucleon (right) for up (upper plots) and down (lower plots) quarks. The quark spins (inner arrows) and nucleon spins (outer arrows) are oriented in the transverse plane as indicated.

Figure 5

Second moment ($n=2$) of transverse spin densities. For details, see caption of Fig. 4.