Higher order string effects and the properties of the Pomeron

We revisit the description of the Pomeron within the effective string theory of QCD. Using a string duality relation, we show how the static potential maps onto the high-energy scattering amplitude that exhibits the Pomeron behavior. Besides the Pomeron intercept and slope, new additional terms stemming from the higher order string corrections are shown to affect both the growth of the nucleon’s size at high energies and its profile in impact parameter space. The stringy description also allows for an odderon that only disappears in critical dimension. Some of the Pomeron’s features that emerge within the effective string description can be studied at the future EIC collider.

Figure 1

Positive C-parity glueball according to lattice gauge simulations [21]. The lines are our fit to Regge trajectories [6].

Figure 2

Euclidean rendering of the $qq$ scattering amplitude at relative angle $\theta$ and the $q\overline{q}$ scattering amplitude at angle $\theta +\pi$. The continuation to Minkowski space follows through $\theta \to -i\chi$ with the latter as the charge conjugate of the former. The relevance of this construction for the Pomeron and the Odderon is detailed in the text.

Figure 3

$C=-1$ parity glueballs on a Regge plot, showing their angular momentum $J$ versus their squared mass $M^2(\mathrm{GeV}{)}^2$. The two upper (blue) points and lines are for the negative spatial parity $P=-1$ glueballs, and the lower (red) ones are for the $P=+1$. The masses are from lattice gauge simulations [21]. The lines shows the hypothetical behavior of the Regge trajectories.

Figure 4

The upper plot shows ${\sigma }_{\mathrm{tot}}$ in $mb$ versus the log of the collision energy $\chi =\ln (s/s_0)$. The left-side (low energy) data points at $\sqrt{s}=27,63\mathrm{GeV}$ are from the old ISR measurements, and the three right-side points, for $\sqrt{s}=2.76,7,8\mathrm{TeV}$ are from the TOTEM measurements. The dotted line in the lower plot indicates the contribution of the Reggeons other than the Pomeron (from the PDG fit.) The middle plot shows the elastic slope $B$ (${\mathrm{GeV}}^{-2}$), and the lower plot is their ratio. The curves are for the profile shown in Fig. 5.

Figure 5

The unitarized profile function $\mathrm{\Omega }=1-e^{-\mathbf{K}}$, for $\sqrt{s}=8000\mathrm{GeV}$ (upper blue curve) and 62 GeV (lower red curve), versus the impact parameter $b$ (${\mathrm{GeV}}^{-1}$). The solid curves at all plots are for the parameters $A=7.{\mathrm{GeV}}^{-2}$, $\mu =-0.04\mathrm{GeV}$, and the dashed ones are for $A=4.5{\mathrm{GeV}}^{-2}$, $\mu =0$. The dotted line in the lower plot indicate the contribution of the Reggeons other than the Pomeron.