Evidence for a new particle on the worldsheet of the QCD flux tube

TL;DR

Improved theoretical control makes it manifest that existing lattice data provides strong evidence for a new pseudoscalar particle localized on the QCD flux tube--the worldsheet axion.

Abstract

We propose a new approach for the calculation of the spectrum of excitations of QCD flux tubes. It relies on the fact that the worldsheet theory is integrable at low energies. With this approach, energy levels can be calculated for much shorter flux tubes than was previously possible, allowing for a quantitative comparison with existing lattice data. The improved theoretical control makes it manifest that existing lattice data provides strong evidence for a new pseudoscalar particle localized on the QCD fluxtube - the worldsheet axion.

Figures (3)

• Figure 1: This plot shows $\Delta E=E-R/\ell_s^2$ as a function of the length of the flux tube $R$ for three different levels. The ground state is shown in green. States with spin 1 and with one and two units of longitudinal momentum are shown in orange and red, respectively. The value of $\ell_s$ was determined from the ground state data. The solid line shows the prediction of a derivative expansion. The dashed lines shows the prediction of the GGRT theory. For the spin 1 states the prediction for a free theory is shown as dotted lines.
• Figure 2: This plot shows $\Delta E=E-R/\ell_s^2$ as a function of the length of the flux tube for the lowest lying states containing both left- and right-movers. The scalar and pseudoscalar states are shown in blue and red, respectively. The spin-2 states are shown in green. The solid lines show the theoretical predictions derived in the remainder of the paper, including the worldsheet axion in addition to the Nambu--Goto fields. The thinner, red/blue and green dashed lines show the prediction for the pseudo-scalar/scalar and tensor channel without the axion. The dotted lines show the prediction of the $\ell_s/R$-expansion. The gray dashed line is the GGRT prediction.
• Figure 3: This plot shows the scattering phase shift $\delta$ for two Goldstone bosons as a function of the center of mass momentum in the symmetric traceless, scalar, and antisymmetric channel in the top, middle, and bottom panel, respectively. The solid and the long dashed lines show the theoretical prediction with and without the worldsheet axion, respectively.