Exclusive photoproduction of a $π^0γ$ pair in the saturation framework

TL;DR

The study addresses exclusive pi0 gamma photoproduction as a probe of gluon saturation at small x, where collinear factorization fails due to Glauber pinch and a generalized kT-factorization approach is employed. Using the shockwave formalism, the authors compute the LO projectile impact factor for gamma -> gamma q qbar, project onto pi0 via the pion DA, and assemble the full amplitude as a convolution with a dipole operator describing the saturated target, incorporating a GBW-based saturation model. A key finding is that the polarized XY amplitude changes sign with the back-to-back transverse momentum |p_t|, yielding a dip in the differential cross section, with saturation models predicting a vanishing point absent in non-saturated (linear) dynamics. This work provides a first quantitative link between exclusive small-x processes and saturation effects and lays the groundwork for further phenomenology and potential experimental exploration in ultraperipheral collisions.

Abstract

We consider the exclusive photoproduction of a $π^0 γ$ pair with large invariant mass, as a promising channel to study the effects of gluon saturation. It has recently been demonstrated that this process is incompatible with a collinear factorization approach in terms of generalized parton distributions (GPDs) at the leading twist. In such a situation, a (generalized) $k_T$-dependent factorization at small $x$ is a valid alternative approach. We perform this calculation using the shockwave formalism, which resums multiple gluon exchanges between the projectile and the dense nuclear target. We find that the polarized amplitude changes sign as a function of back-to-back transverse momentum $|\vec{p}_t|$ of the pion-photon pair, resulting in a dip-like structure in the fully differential cross section as a function of $|\vec{p}_t|$.

Figures (4)

• Figure 1: LO amplitude of photon scattering with a dense nuclear target via shockwave interaction, producing a real photon and neutral pion. Two representative diagrams are shown, for the case of photon emitted from the antiquark, after (left) and before (right) passing through the shockwave background. The total momentum transfer to the target $\Delta = -p_1-p_2$.
• Figure 2: The polarized amplitude ${\cal T}_{xy}$, convoluted with the GBW model for select values of pion rapidity $\eta$ and photon-target center of mass energy $s_{\gamma N}$, as a function of $|\vec{p}_t|$. The inset plot is the same but over a narrow range of the vertical axis to better illustrate the changing of sign.
• Figure 3: Contributions to the XY polarized amplitude split into those for photon emitted before shockwave (dashed) vs after shockwave (solid), shown as a function of $|\vec{p}_t|$, at fixed pion rapidity $\eta=3$ and for different values of center of mass energy $s_{\gamma N}$.
• Figure 4: The differential cross section for XY polarization at fixed pion rapidity $\eta=3$, and for 3 different values of center of mass energy $s_{\gamma N}$. They compare the result of convoluting the projectile impact factor with several models including those which include saturation (GBW and BK) and those that do not (BFKL) in the evolution, see main text.