A glimpse of gluons through deeply virtual compton scattering on the proton

Abstract

The internal structure of nucleons (protons and neutrons) remains one of the greatest outstanding problems in modern nuclear physics. By scattering high-energy electrons off a proton we are able to resolve its fundamental constituents and probe their momenta and positions. Here we investigate the dynamics of quarks and gluons inside nucleons using deeply virtual Compton scattering (DVCS)-a highly virtual photon scatters off the proton, which subsequently radiates a photon. DVCS interferes with the Bethe-Heitler (BH) process, where the photon is emitted by the electron rather than the proton. We report herein the full determination of the BH-DVCS interference by exploiting the distinct energy dependences of the DVCS and BH amplitudes. In the regime where the scattering is expected to occur off a single quark, measurements show an intriguing sensitivity to gluons, the carriers of the strong interaction.

Fig. 1

A few examples of DVCS diagrams. At leading-order in perturbative quantum chromodynamics (QCD) (a), the virtual photon with four-momentum q interacts with a single quark (single straight line) from the proton p, in the limit Q ² = −q ² much larger than the proton mass squared. Subsequently, the active quark emits a real photon with four-momentum q′. The recoil proton has four-momentum p′. Perturbation theory can be used to calculate the part of the amplitude above the (dashed) factorization line, whereas GPDs encode the non-perturbative structure of the nucleon. At next-to-leading order in perturbative QCD (b), a gluon (curly line) from the proton splits into a quark-antiquark pair and the quark absorbs the virtual photon. c An example of deeply virtual Compton scattering (DVCS) diagram at next-to-leading twist illustrating a quark-gluon correlation. The average longitudinal momentum fraction carried by the active parton (quark/gluon) is x and −2ξ is the longitudinal momentum transfer. The helicity of the photons contributing to the leading-twist amplitudes are specified in parenthesis

Fig. 2

Lowest-order diagrams for ep → epγ. The momentum four-vectors of external particles are labeled on the left. The net four-momentum transfer to the proton is Δ_μ = (q − q′)_μ = (p′ − p)_μ. In the virtual Compton scattering (VCS) amplitude, the (spacelike) virtuality of the incident photon is Q ² = −q ² = −(k − k′)². The Bjorken variable x _B is defined as x _B = Q ²/(2q ⋅ P). In the Bethe-Heitler amplitude, the virtuality of the incident photon is −Δ² = −t

Fig. 3

Missing mass squared distribution. The black histogram presents the raw data. Accidental and π ⁰ backgrounds are shown in green and orange, respectively. The subtraction of the accidental and π ⁰ contributions from the raw data is displayed in blue. The Monte-Carlo simulation is represented by the open crosses, whereas the triangles show the estimated inclusive yield obtained by subtracting the simulation from the background-subtracted data. The vertical dotted lines illustrate the two cuts applied on $M_{\mathrm{X}}^2$ in the analysis. This figure corresponds to the kinematic setting E ^beam = 4.455 GeV and Q ² = 1.75 GeV², integrated over t

Fig. 4

Beam helicity-dependent and helicity-independent cross sections. Unpolarized cross sections are represented with black circles and polarized cross sections with black triangles. The kinematic setting shown corresponds to Q ² = 1.75 GeV², x _B = 0.36, and t = −0.30 GeV². The beam energies are E ^beam = 4.455 GeV (a) and E ^beam = 5.55 GeV (b). Bars show s.d. statistical uncertainties, calculated as the squared root of the number of detected events and propagated to the measured cross sections. Dashed lines represent the result of the LT/LO fit with ${\mathbb{H}}_{++}$, ${\mathbb{E}}_{++}$, ${\tilde{\mathbb{H}}}_{++}$, and ${\tilde{\mathbb{E}}}_{++}$. Solid lines show the result of the HT fit with ${\mathbb{H}}_{++}$, ${\tilde{\mathbb{H}}}_{++}$, ${\mathbb{H}}_{0+}$, and ${\tilde{\mathbb{H}}}_{0+}$. Curves for the NLO fit (${\mathbb{H}}_{++}$, ${\tilde{\mathbb{H}}}_{++}$, ${\mathbb{H}}_{-+}$, and ${\tilde{\mathbb{H}}}_{-+}$) overlap with the HT fit and are not shown. Results of the KM15 fit to previously published DVCS data are also presented

Fig. 5

A generalized Rosenbluth separation. DVCS² and DVCS-BH interference contributions are shown at Q ² = 1.75 GeV², x _B = 0.36, t = −0.30 GeV², and E ^beam = 5.55 GeV for the helicity-independent (a) and helicity-dependent (b) cross sections. Solid and dotted lines represent these contributions for the twist-3 (HT) scenario; dashed and dashed-dotted lines correspond to the NLO scenario. Bands show s.d. statistical uncertainties. A DVCS² contribution appears in the helicity-dependent cross section only if there is a contribution from the longitudinal polarization of the virtual photon (HT scenario)