Origin of the nucleon gravitational form factor $B_N(t)$

Abstract

Recent lattice QCD simulations and phenomenological models indicate that the nucleon's gravitational form factor $B_N(t)$ remains remarkably small at finite momentum transfer $t$. While $B_N(0) = 0$ is a known consequence of the equivalence principle, the physical origin of its suppression at finite $t$ has not been fully elucidated. In this work, we demonstrate that the smallness of $B_N(t)$ arises from a fundamental cancellation within the nucleon's wave functions. Using light-front holographic QCD, we show that $B_N(t)$ is governed by an antisymmetric factor in the longitudinal dynamics that leads to an exact vanishing in the symmetric limit and significant suppression for realistic nucleon structures. Our results suggest that the smallness of $B_N(t)$ is a signature of the nucleon's dominant S-wave character, providing a formal justification for its frequent omission in practical applications like near-threshold $J/ψ$ production.

Figures (3)

• Figure 1: The longitudinal wave function $X_\pm(x) = X(x)$, the corresponding suppression factor $X^2(x)-X^2(1-x)$, and the integrand of Eq. (\ref{['eqn:holographic_current']}) at $zQ = 1$ with two sets of mass parameters: (Top) $m_q = 46$ MeV and $m_D = 140$ MeV; (Bottom) $m_q = 300$ MeV, $m_D = 600$ MeV. The former are the values adopted in light-front holographic QCD and the latter are typical values adopted in constituent quark model.
• Figure 2: The gravitational form factor $B_N(t)$ of the nucleon obtained from light-front holographic QCD (LFHQCD) incorporating longitudinal dynamics. The theoretical prediction is shown in comparison with recent lattice QCD results from Ref. Hackett:2023rif.
• Figure 3: Different partial waves of the longitudinal wave function $X_\pm(x) = X(x)$, and the corresponding suppression factor $X^2(x)-X^2(1-x)$ and the integrand of Eq. (\ref{['eqn:holographic_current']}) at $zQ = 1$. From Top to Bottom, the partial waves are: S-wave ($n=0$), P-wave ($n=1$) and D-wave ($n=2$). The S-wave is given by Eq. (\ref{['eqn:IMA']}), with $m_q = 46$ MeV and $m_D = 140$ MeV. The $n$-th partial wave is given by multiplying the Eq. (\ref{['eqn:IMA']}) by the Legendre polynomial $P_n(2x-1)$ with a proper normalization.