Tomography of the Rho meson in the QCD Instanton Vacuum: Transverse Momentum Dependent Parton Distribution Functions

Abstract

We analyse the rho meson unpolarized and polarized transverse momentum dependent parton distribution functions (TMDPDFs) in the instanton liquid model (ILM). The corresponding TMDs in ILM are approximated by a constituent quark beam function in the leading Fock state multiplied by a rapidity-dependent factor resulting from the staple-shaped Wilson lines, for fixed longitudinal momentum, transverse separation, and rapidity. At the resolution of the ILM, all of the rho meson TMDs are symmetric in parton x for fixed transverse momentum, and Gaussian-like in the transverse momentum for fixed parton x. The latter is a direct consequence of the profiling of the quark zero modes in the ILM. The evolved TMDs at higher rapidity using the Collins-Soper kernel, and higher resolution using the renormalization group (RG), show substantial skewness towards low parton x.

Figures (8)

• Figure 1: Rho meson TMD $f_1^{q/\rho}$ (left) \ref{['F1QR']} and $f_{1\mathrm{LT}}^{q/\rho}$ (right) \ref{['F1LTQR']} beam functions with only constituent quark contribution at low resolution $\mu=1/\rho$ with $\rho=0.313$ fm: (a,b) are the density plots, (c,d) the 3D plots, (e,f) the longitudinal momentum dependence for fixed $k_\perp$, and (g,h) the transverse momentum dependent plots for fixed $x$. The rho LFWF parameters are $C_{\rho}=1.9888$, $m_\rho=791.0$ MeV, $M=398.17$ MeV.
• Figure 2: Rho meson tensor-polarized TMD $f_{1LL}^{q/\rho}$ (left) \ref{['F1LLQR']} and $f_{1TT}^{q/\rho}$ (right) \ref{['F1TTQR']} beam functions with only constituent quark contribution at low resolution $\mu=1/\rho$ with $\rho=0.313$ fm: (a,b) are the density plots, (c,d) the 3D plots, (e,f) the longitudinal momentum dependence for fixed $k_\perp$, and (g,h) the transverse momentum dependent plots for fixed $x$. The rho LFWF parameters are $C_{\rho}=1.9888$, $m_\rho=791.0$ MeV, $M=398.17$ MeV.
• Figure 3: Rho meson TMD $g_1^{q/\rho}$ (left) \ref{['G1QR']} and $g_{1T}^{q/\rho}$ (right) \ref{['G1TQR']} beam functions with only constituent quark contribution at low resolution $\mu=1/\rho$ with $\rho=0.313$ fm: (a,b) are the density plots, (c,d) the 3D plots, (e,f) the longitudinal momentum dependence for fixed $k_\perp$, and (g,h) the transverse momentum dependent plots for fixed $x$. The rho LFWF parameters are $C_{\rho}=1.9888$, $m_\rho=791.0$ MeV, $M=398.17$ MeV.
• Figure 4: Rho meson TMD $h_1^{q/\rho}$ (left) \ref{['H1QR']} and $h_{1L}^{q/\rho}$ (right) \ref{['H1LQR']} beam functions with only constituent quark contribution at low resolution $\mu=1/\rho$ with $\rho=0.313$ fm: (a,b) are the density plots, (c,d) the 3D plots, (e,f) the longitudinal momentum dependence for fixed $k_\perp$, and (g,h) the transverse momentum dependent plots for fixed $x$. The rho LFWF parameters are $C_{\rho}=1.9888$, $m_\rho=791.0$ MeV, $M=398.17$ MeV.
• Figure 5: The rho parton distribution $f_{1LL}^{q/\rho}$ at $\mu\simeq1/\rho$ (a), and after DGLAP evolution (b).