Connecting baryon light-front wave functions to quasi-transverse-momentum-dependent correlators in lattice QCD

Abstract

Within light-front quantization, hadrons can be represented on a Fock-space basis of configurations of elementary partons. The coefficients of the expansion are called light-front wave functions (LFWFs), and encode all the dynamical degrees of freedom. We show how to extract the LFWFs of baryons, such as the proton, from equal-time correlators suitable for Lattice QCD simulations. Using an operator product expansion, we prove the factorization of the relevant correlator in the three-quark color-singlet LFWF, a residual lattice factor, and a soft factor that systematically subtracts the additional divergences arising from the factorization. We verify up to next-to-leading order the independent renormalizability of the LFWF, and we derive the evolution equations that govern its scale dependence.

Figures (9)

• Figure 1: Baryon QTMD correlator. We consider the baryon $B$ traveling along the $y^{ 3 }$-axis, and the quark operators $\hat{ q }$ on the hypersurface $y^{ 0 } = 0$ are connected to the boundary of the lattice through Wilson lines. The lattice is bounded by $\lvert L \rvert$ along the $y^{ 3 }$-axis, and by $L_{ \perp }$ along the perpendicular spatial directions. The cases $\text{sign} \! \left( L \right) = - 1, + 1$ correspond to a baryon in the initial and final state, respectively. For simplicity, we only represent the $v$-directed gauge links, colored in red, green and blue to visually indicate the antisymmetrization of the color indices in the fundamental representation.
• Figure 2: Soft factor for the three-quark baryon LFWF. The lightlike Wilson lines orthogonal to $\bar{ n }$ and $n$ connect on the hypersurface $y^{ 3 } = 0$. They are colored in red, green and blue to visually indicate the antisymmetrization of the fundamental-representation color indices at both ends. For simplicity, the transverse gauge links at both ends are implied.
• Figure 3: One-loop diagram contributing to the quark current at next-to-leading order. The thick line is the gauge link.
• Figure 4: Leading-power baryon three-quark LFWF. The quark fields lie on the hypersurface tangent to the light cone and orthogonal to $\bar{ n }$. The lightlike Wilson lines are colored in red, green and blue to visually indicate the antisymmetrization of the fundamental-representation color indices. For simplicity, the transverse gauge links are implied.
• Figure 5: Lattice factor for the baryon three-quark LFWF. The lightlike and $v$-directed Wilson lines connect on the hypersurface $y^{ 3 } = 0$. They are colored in red, green and blue to visually indicate the antisymmetrization of the fundamental-representation color indices on both ends. For simplicity, the transverse gauge links on both ends are implied.