[Paper Review] Measurements of the Electron-Helicity Dependent Cross Sections of Deeply Virtual Compton Scattering with CEBAF at 12 GeV

J. Roche, C. E. Hyde-Wright+2 more|ArXiv.org|Sep 11, 2006

Quantum Chromodynamics and Particle Interactions18 citations

TL;DR

This paper proposes high-precision measurements of electron-helicity-dependent cross sections in deeply virtual Compton scattering (DVCS) using the CEBAF 12 GeV electron beam and a polarized hydrogen target. By detecting the scattered electron in the Hall A high-resolution spectrometer and the emitted photon in a PbF₂ calorimeter, the experiment aims to extract generalized parton distributions (GPDs) with 3% systematic precision, enabling the first transverse spatial imaging of quark distributions in the proton as a function of light-cone momentum fraction.

ABSTRACT

We propose precision measurements of the helicity-dependent and helicity independent cross sections for the ep->epg reaction in Deeply Virtual Compton Scattering (DVCS) kinematics. DVCS scaling is obtained in the limits Q^2>>Lambda_{QCD}^2, x_Bj fixed, and -Δ^2=-(q-q')^2<2 GeV^2, W>2 GeV, and -Δ^21 GeV^2. We will use our successful technique from the 5.75 GeV Hall A DVCS experiment (E00-110). With polarized 6.6, 8.8, and 11 GeV beams incident on the liquid hydrogen target, we will detect the scattered electron in the Hall A HRS-L spectrometer (maximum central momentum 4.3 GeV/c) and the emitted photon in a slightly expanded PbF_2 calorimeter. In general, we will not detect the recoil proton. The H(e,e'g)X missing mass resolution is sufficient to isolate the exclusive channel with 3% systematic precision.

Motivation & Objective

• To measure helicity-dependent and helicity-independent cross sections for the ep → epγ reaction in DVCS kinematics at 12 GeV CEBAF.
• To extract generalized parton distributions (GPDs) with high precision to image the transverse spatial structure of quarks in the proton as a function of their light-cone momentum fraction.
• To test the factorization theorem and quantify higher-twist contributions (e.g., hadronic photon content) via Q²-dependent analysis of DVCS observables.
• To separate real and imaginary parts of Compton form factors, enabling access to GPDs in regions not directly probed by imaginary parts alone.
• To calibrate future measurements of relative asymmetries through precise determination of σ_LT, σ_TT, and σ_LT′ cross sections.

Proposed method

• Use polarized 6.6, 8.8, and 11 GeV electron beams incident on a liquid hydrogen target in Hall A at Jefferson Lab.
• Detect the scattered electron using the Hall A HRS-L spectrometer, with a maximum central momentum of 4.3 GeV/c.
• Detect the emitted photon using a slightly expanded PbF₂ calorimeter with high hermeticity and energy resolution.
• Employ missing mass reconstruction to isolate the exclusive ep → epγ channel with 3% systematic uncertainty.
• Measure the helicity-dependent cross sections σ_LT, σ_TT, and σ_LT′, and the longitudinal cross section σ_L + σ_T/ε_L to access real and imaginary parts of Compton form factors.
• Apply DGLAP evolution to parton distributions and use the factorized ansatz in the b → ∞ limit to model GPDs and predict cross sections.

Experimental results

Research questions

• RQ1 How do the helicity-dependent cross sections σ_LT, σ_TT, and σ_LT′ vary with Q² and t in the DVCS regime?
• RQ2 What is the Q² dependence of the DVCS amplitude, and how does it test the factorization theorem and constrain higher-twist contributions?
• RQ3 How do the real and imaginary parts of the Compton form factors constrain the spatial distribution of quarks in the proton as a function of light-cone momentum fraction?
• RQ4 To what extent can the transverse profile of the proton be reconstructed from the t-dependence of the DVCS observables at fixed x_Bj?
• RQ5 How do the measured observables compare to predictions from the VGG model, and what does this reveal about model uncertainties at the 10–20% level?

Key findings

• The experiment is projected to achieve 3% systematic precision in missing mass reconstruction, enabling clean isolation of the exclusive ep → epγ channel.
• The Q² dependence of the DVCS observables will allow stringent tests of the factorization theorem and quantification of higher-twist contributions, which scale as 1/Q² or faster.
• The t-dependence of the observables at fixed x_Bj will provide the first direct study of the transverse spatial profile of quark distributions in the proton as a function of their light-cone momentum fraction.
• The separation of real and imaginary parts of the Compton form factors will extend access to GPDs beyond the x = ±ξ region probed by the imaginary part alone.
• The measured cross sections σ_L + σ_T/ε_L, σ_LT, σ_TT, and σ_LT′ will provide a calibration for future relative asymmetry measurements in DVCS.
• The experiment is expected to require 88 days of production running, with an additional 12 days for optical curing of the PbF₂ calorimeter.