Nucleon form factors and moments of generalized parton distributions using $N_f=2+1+1$ twisted mass fermions

TL;DR

This study computes nucleon axial and electromagnetic form factors and the first moments of generalized parton distributions using maximally twisted mass fermions with $N_f=2+1+1$ on two ensembles down to $m_\pi\approx210$ MeV. The authors extract $G_E$, $G_M$, $G_A$, $G_p$, and the one-derivative Q^2-dependent GFFs $A_{20}, B_{20}, C_{20}, \tilde{A}_{20}, \tilde{B}_{20}$ from connected nucleon matrix elements, renormalize nonperturbatively in RI$'$-MOM and convert to $\overline{\rm MS}$ at $\mu=2$ GeV, with scale setting via the nucleon mass and cross-checks against other discretizations. Their analysis of the isovector and isoscalar channels yields insights into the spin decomposition via Ji's sum rule, suggesting $J^u>J^d$ and a near-zero $J^d$ at the lightest pion mass, while indicating small strange/charm sea effects on these quantities. The results show general agreement with other lattice actions at $m_\pi$ down to ~200 MeV, but persistent gaps remain in reproducing the experimental $g_A$ and in fully accounting for disconnected contributions and excited-state contamination, motivating future work toward a complete nucleon spin picture from first principles.

Abstract

We present results on the axial and the electromagnetic form factors of the nucleon, as well as, on the first moments of the nucleon generalized parton distributions using maximally twisted mass fermions. We analyze two N_f=2+1+1 ensembles having pion masses of 210 MeV and 354 MeV at two values of the lattice spacing. The lattice scale is determined using the nucleon mass computed on a total of 18 N_f=2+1+1 ensembles generated at three values of the lattice spacing, $a$. The renormalization constants are evaluated non-perturbatively with a perturbative subtraction of ${\cal O}(a^2)$-terms. The moments of the generalized parton distributions are given in the $\bar{\rm MS}$ scheme at a scale of $ μ=2$ GeV. We compare with recent results obtained using different discretization schemes. The implications on the spin content of the nucleon are also discussed.

Figures (27)

• Figure 1: Connected nucleon three-point function.
• Figure 2: Ratios for the matrix elements of the local axial-vector operator (upper) and one derivative vector operator (lower) for a few exemplary choices of the momentum. The solid lines with the bands indicate the fitted plateau values with their jackknife errors. From top to bottom the momentum takes values $\vec{p}=(0,0,0),\,(1,0,0),\, (0,-1,0)$ and $(1,0,1)$.
• Figure 3: Nucleon mass at three lattice spacings. The solid lines are fits to ${\cal O}(p^3)$ (upper panel) and ${\cal O}(p^4)$ (lower panel) HB$\chi$PT with explicit $\Delta$ degrees of freedom in the so called small scale expansion(SSE). The dotted lines denote the error band. The physical point is shown with the asterisk.
• Figure 4: Upper panel: One derivative renormalization functions for $\beta=2.10,\,a\,\mu=0.0015$ using $N_f{=}4$ gauge configurations, where $Z_{DV1}\, (Z_{DA1}) \equiv Z_{DV}^{\mu\mu}\, (Z_{DA}^{\mu\mu})$ and $Z_{DV2}\, (Z_{DA2}) \equiv Z_{DV}^{\mu\neq\nu}\, (Z_{DA}^{\mu\neq\nu})$. Black circles are the unsubtracted data and the magenta diamonds the data after subtracting the perturbative ${\cal O}(a^2)$-terms. For comparison, we show the subtracted data using $N_f{=}2{+}1{+}1$ gauge configurations at the same value of the quark mass and $\beta$ (blue crosses). Lower panel: One derivative renormalization functions for $\beta=1.95$ using $N_f{=}4$ gauge configurations as a function of the twisted quark mass.
• Figure 5: Upper panel: $Z_A,\,Z_V$ for $\beta=1.95,$ and $a\mu=0.0055$; Lower panel: Renormalization constants for one derivative operators for $\beta=1.95,$ and $a\mu=0.0055$, where $Z_{DV1}\, (Z_{DA1}) \equiv Z_{DV}^{\mu\mu}\, (Z_{DA}^{\mu\mu})$ and $Z_{DV2}\, (Z_{DA2}) \equiv Z_{DV}^{\mu\neq\nu}\,(Z_{DA}^{\mu\neq\nu})$. The lattice data are shown in black circles and the data after the ${\cal O}(a^2)$-terms have been subtracted are shown in magenta diamonds. The solid diamond at $(a\,p)^2=0$ is the value obtained after performing a linear extrapolation of the subtracted data.