Baryon Junction and String Interactions: Part II

Abstract

We study junctions between confining strings. These junctions arise in Yang-Mills theories, and we focus on their universal low-energy dynamics. Using open-closed duality, we map junctions with nonlinear corrections to the $s$-wave scattering amplitudes between confining string loops. In $(3+1)$ dimensions, we uncover an accidental $\mathbb{Z}_2$ symmetry. This symmetry implies novel selection rules for loop scattering amplitudes and is broken by the junction mass at subleading order. We determine the total mass of baryons up to order $(\text{baryon size})^{-3}$, providing new, testable predictions for lattice simulations.

Figures (6)

• Figure 1: Confining strings in a probe baryon. The figure shows the spatial plane determined by the insertions of three static quarks (red points). The confining strings (blue lines) are tied at the dynamical baryon junction (blue point) and terminate on the quarks at their other ends.
• Figure 2: Tree-level scattering amplitudes of massive modes in the closed channel. Interpreting one direction of the $d$-dimensional space as time, the cubic interaction vertices in equation \ref{['eq_cubic coupling def']} describe the $2\to 1$ fusion process (Left) and the $1\to 2$ decay process (Right). The external legs in this figure are generally off-shell, since all modes in the closed channel have approximately the same mass \ref{['eq_closed energy level']}.
• Figure 3: Topological defect line $\mathcal{D}$ on the confining string worldsheet. Left: the NGB field profiles are taken to be discontinuous across the line $\ell$, and the defect action is given by the bilinear coupling between $x_{i}^-$ and $x_{i}^+$. Right: local operators transform according to equation \ref{['eq_symmetry rule']} upon crossing the defect line. The $\mathbb{Z}_2$ symmetry transformation rule can be schematically written as $(\partial_tx_2,\partial_\sigma x_2)\xrightarrow{\mathcal{D}} (-\partial_\sigma x_3,-\partial_t x_3)\xrightarrow{\mathcal{D}} (\partial_tx_2,\partial_\sigma x_2)$.
• Figure 4: Merging the topological defect lines with the baryon junction worldline.
• Figure 5: Worldsheet loop diagrams. The black lines denote the propagators of the NGB fields $x_i$, $y_i$, and $z_i$. See equations \ref{['eq_app_DD green function def']}, \ref{['eq_app_ND green function def']}, \ref{['eq_app_propagators 1']}, and \ref{['eq_app_propagators 2']} in Appendix \ref{['sec_app_greens functions']} for the explicit forms of these propagators. Left: $\langle S^{(2)}_{\rm strings}\rangle$ is given by the 2-loop diagrams on the confining string worldsheets; Middle: $\langle (S^{(1)}_{\rm junction})^2\rangle$ is given by the 1-loop diagrams on the baryon junction worldline; Right: $\langle (S^{(1)}_{\rm displacement})^2\rangle$ is given by the 2-loop diagrams on the baryon junction worldline.