Intrinsic quark transverse momentum in the nucleon from lattice QCD

Abstract

A better understanding of transverse momentum (k_T-) dependent quark distributions in a hadron is needed to interpret several experimentally observed large angular asymmetries and to clarify the fundamental role of gauge links in non-abelian gauge theories. Based on manifestly non-local gauge invariant quark operators we introduce process-independent k_T-distributions and study their properties in lattice QCD. We find that the longitudinal and transverse momentum dependence approximately factorizes, in contrast to the behavior of generalized parton distributions. The resulting quark k_T-probability densities for the nucleon show characteristic dipole deformations due to correlations between intrinsic k_T and the quark or nucleon spin. Our lattice calculations are based on N_f=2+1 mixed action propagators of the LHP collaboration.

Figures (3)

• Figure 1: Illustration of the transverse momentum distribution of quarks in the proton.
• Figure 2: Real parts of the amplitudes $\tilde{A}_i(l^2,l {\cdot} P{=}0)$, for $m_\pi {\approx} 500\,\mathrm{MeV}$. The solid lines and error bands are Gaussian fits to the renormalized lattice data above $\sqrt{-l^2}{=}0.25\,\mathrm{fm}$.
• Figure 3: Quark densities in the $\boldsymbol{k}_\perp$-plane, for $m_\pi {\approx} 500\,\mathrm{MeV}$. (a) $\rho_L$ for $u$-quarks and $\lambda=1$, $\boldsymbol{S}_\perp=(1,0)$, (b) the same for $d$-quarks, (c) $\rho_T$ for $u$-quarks and $\Lambda=1$, $\boldsymbol{s}_\perp=(1,0)$, (d) the same for $d$-quarks. The error bands show the density profile at $\boldsymbol{k}_y=0$ as a function of $\boldsymbol{k}_x$ (scale not shown).