Effective Field Theory Factorization for Diffraction

Abstract

We derive a factorization formula for coherent and incoherent $ep$ diffraction using the soft collinear effective theory, utilizing multiple power expansion parameters to handle different kinematic regions. This goes beyond the known hard-collinear diffractive factorization to address the small-$x$ Regge dynamics and Pomeron exchange from first principles. The effective field theory analysis also uncovers and factorizes an important irreducible incoherent background generated by color-nonsinglet exchange, dubbed "quasi-diffraction", for which we calculate the associated Sudakov suppression. For unpolarized scattering we show that there are four diffractive structure functions at leading power, and point out the importance of studying $F_{3,4}^D$ through asymmetries, in addition to $F_{2,L}^D$. For the quasi-diffractive background, we make model independent predictions for ratios of the corresponding structure functions in a perturbative kinematic region. Our analysis also makes predictions for six leading-power spin-dependent structure functions. Finally, we provide connections to diffractive parton distributions, and assess the Ingelman-Schlein model. Our work lays a path for further QCD-based studies of diffraction.

Figures (19)

• Figure 1: Scheme for classifying rapidity-gapped processes in lepton-hadron colliders.
• Figure 2: $ep$ scattering producing a central jet $X$ with momentum $p_X$ and forward particles $Y$ with momentum $p'$, with a rapidity gap separating $p'$ and $p_X$. (a) Partonic diagrams for the forward scattering case, where we have either incoherent diffraction with a multi-particle state $Y$ or coherent diffraction with a proton $Y$. (b) Leading diagram for the hard scattering case for moderate $x$. This is a subleading contribution to incoherent diffraction in the small-$x$ region.
• Figure 3: The $\bar{x}$ dependence of the coefficients $c_i$ of $F_i^D$ in eq. \ref{['eq:diffcross']} for coherent diffraction with $m_Y=0$. We fix $(\sqrt{-t}/Q,\beta,x) = (0.2,0.9,0.1)$ in both plots, and take $y=\{0.1,0.5\}$ in the left and right panels, respectively. The coefficients $c_3$ and $c_4$ vanish when integrated over the full range of $\bar{x}$, whose size is proportional to $\Delta \approx \sqrt{-t}/Q$ and is centered at the point $x/\beta - (2 - y)xz$, which is plotted as a gold vertical dotted line. The purple dotted vertical lines indicate the lower and upper bounds of $\bar{x}$. The coefficients of $F_{3}^D$ (green) and $F_4^D$ (red) are large relative to that of $F_L^D$ (gray) at small $y$, which is shown at 10$\times$ scale in the left panel.
• Figure 4: Range of allowed values for $\bar{x}$ at HERA relative to the polar angle $\theta$ measured in the lab frame, with shading indicating the corresponding value of $|t|$. In both panels we fix $(x,y,\beta,m_Y) = (0.02,0.2,0.3,0)$ and the beams carry HERA energies $(E_p,E_e) = (920,27.6)$ GeV. The left panel shows the full range of possible $t$ values. The right panel zooms in to the small-$t$ regime that was the focus at HERA. Note that a finer $\theta$-resolution is required to resolve $\bar{x}$ at smaller $-t$.
• Figure 5: Range of allowed values of $\bar{x}$ at the EIC relative to the polar angle $\theta$ measured in the lab frame, with shading indicating the corresponding value of $|t|$. In both panels we fix $(x,y,\beta,m_Y) = (0.02,0.2,0.3,0)$. In the left panel the beam energies are $(E_p,E_e) = (275,2.5)$ GeV, while in the right panel they are $(E_p,E_e) = (41,10)$ GeV. Importantly, the right panel provides a parameter choice for which the outgoing hadronic state $Y$ is at an angle $\theta > 2^{\circ}$ that is observable in the main EIC detector.