[Paper Review] Revealing CFFs and GPDs from experimental measurements

Krešimir Kumerički, A.H. Mueller+1 more|arXiv (Cornell University)|Feb 28, 2013

Particle physics theoretical and experimental studies14 references3 citations

TL;DR

This paper presents a phenomenological framework to extract Compton Form Factors (CFFs) and Generalized Parton Distributions (GPDs) from experimental data on deeply virtual Compton scattering (DVCS) and meson electroproduction. Using HERMES data, it employs a one-to-one mapping and least-squares fitting to determine the imaginary and real parts of key CFFs, finding that $\Im\mathrm{m}\mathcal{H}$ is significantly non-zero while other components are consistent with zero, indicating $\mathcal{H}$ dominates the DVCS amplitude.

ABSTRACT

We report on the status of the phenomenological access of generalized parton distributions from photon and meson electroproduction off proton. Thereby, we emphasize the role of HERMES data for deeply virtual Compton scattering, which allows us to map various asymmetries into the space of Compton form factors.

Motivation & Objective

• To develop a phenomenological method for accessing Compton Form Factors (CFFs) and Generalized Parton Distributions (GPDs) from exclusive electroproduction experiments.
• To utilize HERMES data on deeply virtual Compton scattering (DVCS) to map measured asymmetries to CFFs, overcoming interference between Bethe-Heitler and DVCS amplitudes.
• To perform a global fit combining HERMES, HERA, and Jefferson Lab data to constrain GPD models and assess the dominance of the $\mathcal{H}$ GPD.
• To evaluate the feasibility of extracting $\mathcal{E}$ and $\widetilde{\mathcal{H}}$ GPDs from current data, identifying limitations due to experimental noise and systematic constraints.

Proposed method

• A one-to-one mapping is established between measured single- and double-spin asymmetries and the imaginary and real parts of the CFFs $\mathcal{H}$, $\widetilde{\mathcal{H}}$, $\mathcal{E}$, and $\overline{\mathcal{E}}$ using eight quadratic equations derived from the interference term in DVCS.
• Least-squares fitting is applied to all fourteen asymmetries (including $\cos\phi$, $\sin\phi$, and $\cos(\varphi)\cos(\phi)$ harmonics) to extract CFFs, with constraints applied to resolve ambiguities in the BH-dominated regime.
• A linearized map is used as a comparison to validate the non-linear fitting approach, particularly in regions where the DVCS amplitude dominates.
• A global GPD model fit is performed by combining HERMES, HERA collider, and Jefferson Lab data, using the NLO factorization framework to describe the hard scattering amplitude and GPDs.
• The analysis relies on twist-two dominated asymmetries from HERMES final data, extracted via missing-mass event selection, to ensure consistency with the collinear factorization approach.
• Systematic errors are included in the fitting procedure, and the model is tested against charge-odd and charge-even asymmetries to validate the consistency of the extracted CFFs.

Experimental results

Research questions

• RQ1 Can the full set of Compton Form Factors (CFFs) be extracted from HERMES DVCS data using measured asymmetries, including both modulus and phase information?
• RQ2 Which CFFs are significantly constrained by current experimental data, and what does this imply about the dominance of specific GPDs like $\mathcal{H}$?
• RQ3 How do different fitting strategies—direct mapping, linearization, and least-squares fitting—compare in reconstructing the CFFs from experimental asymmetries?
• RQ4 To what extent can the $\mathcal{E}$ and $\widetilde{\mathcal{H}}$ GPDs be accessed from existing data, and what are the main limitations?
• RQ5 Can a global fit to diverse DVCS data sets (HERMES, HERA, Jefferson Lab) yield a consistent and acceptable description of the data, and what is the goodness of fit?

Key findings

• The imaginary part of the $\mathcal{H}$ CFF, $\Im\mathrm{m}\mathcal{H}$, is found to be significantly non-zero, indicating a dominant contribution from the $\mathcal{H}$ GPD in the DVCS amplitude.
• The real part of $\mathcal{H}$, $\Re\mathrm{e}\mathcal{H}$, and the imaginary part of $\widetilde{\mathcal{H}}$, $\Im\mathrm{m}\widetilde{\mathcal{H}}$, are consistent with zero and well constrained by the data.
• Other CFFs, including $\Re\mathrm{e}\mathcal{E}$, $\Im\mathrm{m}\mathcal{E}$, and $\Re\mathrm{e}\widetilde{\mathcal{H}}$, are found to be noisy and compatible with zero, indicating limited phenomenological access with current data.
• The least-squares fitting procedure successfully recovers the CFFs, though in bins #3 and #8 it selects the DVCS-dominated solution over the BH-dominated one, which is corrected by constraining $\Re\mathrm{e}\mathcal{E}$ to reduce error bars.
• The global fit to world DVCS data yields a $\chi^2/\text{d.o.f.} \approx 1.6$, indicating an acceptable but not perfect description of the data across diverse experiments and observables.
• The model, which sets $\Im\mathrm{m}\mathcal{E} = 0$, still describes the transverse target HERMES data well, suggesting that the $\mathcal{E}$ GPD is not strongly constrained by current measurements.