Compton Form Factors Research Articles

Bayesian Neural Network Variational Autoencoder Inverse Mapper (BNN-VAIM) and its application in Compton Form Factors extraction

We extend the Variational Autoencoder Inverse Mapper (VAIM) framework for the inverse problem of extracting Compton Form Factors (CFFs) from deeply virtual exclusive reactions, such as the unpolarized Deeply virtual exclusive scattering (DVCS) cross section. VAIM is an end-to-end deep learning framework to address the solution ambiguity issue in ill-posed inverse problems, which comprises of a forward mapper and a backward mapper to simulate the forward and inverse processes, respectively. In particular, we incorporate Bayesian Neural Network (BNN) into the VAIM architecture (BNN-VAIM) for uncertainty quantification. By sampling the weights and biases distributions of the BNN in the backward mapper of the VAIM, BNN-VAIM is able to estimate prediction uncertainty associated with each individual solution obtained for an ill-posed inverse problem. We first demonstrate the uncertainty quantification capability of BNN-VAIM in a toy inverse problem. Then, we apply BNN-VAIM to the inverse problem of extracting 8 CFFs from the unpolarized DVCS cross section.

Accessing compton form factors at the electron ion collider in China: an impact study on {textbf {Im}} {mathcal E}

We estimate the impact of asymmetry measurements of Deeply Virtual Compton Scattering (DVCS) with transversely polarized proton beam taken at a future Electron Ion Collider in China (EicC) on the extraction of Compton Form Factors (CFFs). The CFFs extracted from an analysis based on artificial neural-network approach are reweighted by means of pseudo-data generated in the expected kinematic region of EicC. We find a remarkable improvement in the extraction of CFF Im {mathcal E}, especially at the range of parton momentum fraction x sim 0.01, thus hinting for a future experimental probe of the parton orbital angular momentum. This work casts a glance at a practical implementation of Bayesian reweighting method on CFFs’ impact study.

Deeply Virtual Compton Scattering at Next-to-Next-to-Leading Order.

Deeply virtual Compton scattering gives access to the generalized parton distributions that encode the information on the transverse position of quarks and gluons in the proton with dependence on their longitudinal momentum. In anticipation of the high-precision experimental data in a broad kinematic range from the Electron-Ion Collider, we have calculated the two-loop, next-to-next-to-leading order (NNLO) deeply virtual Compton scattering coefficient functions associated with the dominant Compton form factors H and E at large energies. The NNLO correction to the imaginary part of H appears to be rather large, up to factor 2 at the input scale Q^{2}=4 GeV^{2} for simple generalized parton distribution models, due to a cancellation between quark and gluon contributions.

On extraction of twist-two Compton form factors from DVCS observables through harmonic analysis

We investigate the exercise of locally extracting the real and imaginary parts of the four twist-2 Compton form factors (CFFs) left{mathcal{H},mathcal{E},overset{sim }{mathcal{H}},overset{sim }{mathcal{E}}right} which arise in the deeply virtual Compton scattering (DVCS) process e + p → e + p + γ. Neglecting dynamical higher-twist contributions, we find that there are a sufficient number of DVCS observables and degrees of freedom to extract all 8 leading quantities model-independently, exploiting the azimuthal dependence of the absolute cross sections across all possible beam and target polarizations at a common kinematical point in {Q, t, xB, y}. As an example, for typical JLab lab-frame kinematics, we simplify the reduced DVCS observables to their dominant terms, providing a sufficient number of equations for local determination of the twist-2 CFFs. We demonstrate the feasibility using harmonic fitting to both cross sections and beam spin asymmetries with both real and pseudo-data.

Accessing pion GPDs through the Sullivan process: is it feasible?

Describing hadronic structure is one of the most intriguing problems in physics. In this respect, generalized parton distributions (GPDs) constitute an outstanding tool, allowing to draw “three dimensional pictures” of hadron’s inside. Starting from contemporary models for pion’s GPDs fulfilling all constraints imposed by QCD, we compute Compton form factors of pions subjected to deeply virtual Compton scattering. We show CFF’s behaviour to be gluon-dominated at EIC’s kinematics. Finally we evaluate lepton-beam-spin asymmetries in the Sullivan process, demonstrating the existence of such and thus triggering optimism about the possibility of probing pion’s 3D structure at electron-ion colliders.

Pion GPDs: Constraints, modelling and experimental access

The study of Generalised Parton Distributions (GPDs) is a hot-topic in hadron physics. Due to its connection with chiral symmetry breaking, assessing those of pions is of great interest. For this reason, we present a novel model-building strategy for pion GPDs capable of fulfilling all of the theoretical constraints required by QCD: support, polynomiality, positivity and soft-pion theorem. The methodology is illustrated with a simple model, and exploited afterwards for the calculation of pions' deeply virtual Compton Scattering (DVCS) Compton Form Factors (CFFs) at NLO. The results show gluon-content to play the dominant role in pions' response to DVCS at EIC kinematics.

What do DVCS data tell us about TCS observables?

Deeply virtual Compton scattering (DVCS) and timelike Compton scattering (TCS) leading twist amplitudes are intimately related thanks to their analytic properties as a function of Q^2Q2. We exploit this feature to use Compton form factors previously extracted from available DVCS data and derive data-driven predictions for TCS observables to be measured in near future experiments. Our results quantitatively illustrate the complementarity of DVCS and TCS experiments.

Deeply Virtual Compton Scattering Cross Section at High Bjorken xB

We report high-precision measurements of the deeply virtual Compton scattering (DVCS) cross section at high values of the Bjorken variable x_{B}. DVCS is sensitive to the generalized parton distributions of the nucleon, which provide a three-dimensional description of its internal constituents. Using the exact analytic expression of the DVCS cross section for all possible polarization states of the initial and final electron and nucleon, and final state photon, we present the first experimental extraction of all four helicity-conserving Compton form factors (CFFs) of the nucleon as a function of x_{B}, while systematically including helicity flip amplitudes. In particular, the high accuracy of the present data demonstrates sensitivity to some very poorly known CFFs.

Twist-three cross-sections in deeply virtual Compton scattering

We study the deeply virtual Compton scattering process with both twist-two and twist-three Compton form factors and present our cross-sections formulas with all polarization configurations. While the twist-three contributions are generally assumed to be negligible in the literature due to the kinematical suppression, we compare them with the twist-two ones at typical JLab 6 GeV and 12 GeV kinematics as well as EIC kinematics and show their kinematical suppression explicitly, justifying the leading-twist approximation made in the literature. In addition, we also estimate the twist-three Compton form factors using Wandzura-Wilczek relations and inputs of twist-two generalized parton distributions based on a reggeized spectator model. With those estimated Compton form factors, we analyze the kinematical behavior of twist-two and twist-three cross-sections in a wide range of kinematics, and discuss the optimal regions for separating the leading-twist effects from the higher-twist ones.

Pion generalized parton distributions: A path toward phenomenology

We introduce a new family of generalized parton distribution models able to fulfill by construction all the theoretical properties imposed by QCD. These models are built on standard parton distribution functions and extended to off-forward kinematics through a well-defined procedure. We apply this strategy on the pion, first handling a simple but insightful algebraic model, and then exploiting state-of-the-art computations obtained in continuum QCD. We compare these models with a more standard one relying on an xFitter extraction of the pion parton distribution functions. The results for both quark and gluon generalized parton distributions are presented and exploited for calculation of electromagnetic, gravitational, and Compton form factors. Results on the latter highlight the relevance of next-to-leading-order corrections, even in the so-called valence region.

Novel Rosenbluth extraction framework for Compton form factors from deeply virtual exclusive experiments

We use a generalization of the Rosenbluth separation method for a model independent simultaneous extraction of the Compton Form Factors H and E, from virtual Compton scattering data on an unpolarized target. A precise evaluation of H and E, enabled by the proposed method, is the first step towards pinning down the distribution of angular momentum inside the proton.

First Measurement of Timelike Compton Scattering.

We present the first measurement of the timelike Compton scattering process, γp→p^{'}γ^{*}(γ^{*}→e^{+}e^{-}), obtained with the CLAS12 detector at Jefferson Lab. The photon beam polarization and the decay lepton angular asymmetries are reported in the range of timelike photon virtualities 2.25<Q^{'2}<9 GeV^{2}, squared momentum transferred 0.1<-t<0.8 GeV^{2}, and average total center-of-mass energy squared s=14.5 GeV^{2}. The photon beam polarization asymmetry, similar to the beam-spin asymmetry in deep virtual Compton scattering, is sensitive to the imaginary part of the Compton form factors and provides a way to test the universality of the generalized parton distributions. The angular asymmetry of the decay leptons accesses the real part of the Compton form factors and thus the D-term in the parametrization of the generalized parton distributions.

Higher-order kinematical effects in deeply virtual Compton scattering

We study the deeply virtual Compton scattering cross-section in twist-two generalized parton distribution (GPD) approximation, and show that different choices of light-cone vectors and gauges for the final photon polarization will lead to different higher-order kinematical corrections to the cross-section formula. The choice of light-cone vectors affects kinematic corrections at the twist-three level, accounting for the differences between the cross-section formulas in the literature. On the other hand, kinematical corrections from higher-twist GPDs should eliminate the light-cone dependence at twist three. Those light-cone dependencies are studied systematically at JLab 12 GeV and future EIC kinematics. They serve as the intrinsic systematic uncertainties in extracting the Compton form factors through the cross-section formula. More importantly, they are also necessary for understanding cross-section measurements with higher-twist precision and to reconstruct higher-order Compton form factors.

Deeply virtual Compton scattering off Helium nuclei with positron beams

Positron initiated deeply virtual Compton scattering (DVCS) off ^4He and ^3He nuclei is described. The way the so-called d-term could be obtained from the real part of the relevant Compton form factor is summarized, and the importance and novelty of this measurement is discussed. The measurements addressed for ^3He targets could be very useful even in a standard unpolarized target setup, measuring beam spin and beam charge asymmetries only. The unpolarized beam charge asymmetries for DVCS off ^3He and ^4He are also estimated, at JLab kinematics and, for ^4He, also at a configuration typical at the future Electron–Ion Collider. Incoherent DVCS processes, in particular the ones with tagging the internal target by measuring slow recoiling nuclei, and the unique possibility offered by positron beams for the investigation of Compton form factors of higher twist, are also briefly addressed.

Impact of a positron beam at JLab on an unbiased determination of DVCS Compton form factors

The impact of potential future measurements of beam charge asymmetries on the current knowledge of Compton form factors is evaluated. Elaborating on the results of a global neural network fit to deeply virtual Compton scattering data, a Bayesian reweighting analysis quantifies the improved determination of the real part of the Compton form factor $\mathcal{H}$. Such an improvement is particularly relevant for the experimental determination of the proton mechanical properties or for universality studies of generalized parton distributions through analyses of virtual Compton scattering in both spacelike and timelike regions.

Deeply virtual Compton scattering on the neutron with positron beam

Measuring DVCS on a neutron target is a necessary step to deepen our understanding of the structure of the nucleon in terms of Generalized Parton Distributions (GPDs). The combination of DVCS observables on neutron and proton targets allows to perform a flavor decomposition of the Compton Form Factors (CFFs), which are related to integrals of GPDs. Moreover, neutron-DVCS plays a complementary role to DVCS on a transversely polarized proton target in the determination of the CFF of the GPD E, the least known and constrained GPD that enters Ji’s angular momentum sum rule. A measurement of the beam-charge asymmetry (BCA) in the \(e^{\pm } d\rightarrow e^{\pm }n\gamma (p)\) reaction can significantly impact the experimental determination of the real CFFs of the E and, to a lesser extent, \(\widetilde{H}\) CFFs.

Separation of Quark Flavors Using Deeply Virtual Compton Scattering Data.

Using the available data on deeply virtual Compton scattering (DVCS) off protons and utilizing neural networks enhanced by the dispersion relation constraint, we determine six out of eight leading Compton form factors in the valence quark kinematic region. Furthermore, adding recent data on DVCS off neutrons, we separate contributions of up and down quarks to the dominant form factor, thus paving the way towards a three-dimensional picture of the nucleon.

Measuring the skewness dependency of Generalized Parton Distributions

Generalized Parton Distributions (GPDs) have emerged over the 1990s as a powerful concept and tool to study nucleon structure. They provide nucleon tomography from the correlation between transverse position and longitudinal momentum of partons. The Double Deeply Virtual Compton Scattering (DDVCS) process consists of the Deeply Virtual Compton Scattering (DVCS) process with a virtual photon in the final state eventually generating a lepton pair, which can be either an electron-positron or a muon-antimuon pair. The virtuality of the final time-like photon can be measured and varied, thus providing an extra lever arm and allowing one to measure the GPDs for the initial and transferred momentum dependences independently. This unique feature of DDVCS is of relevance, among others, for the determination of the distribution of nuclear forces which is accessed through the skewness dependency of GPDs. This proceeding discusses the feasibility and merits of a DDVCS experiment in the context of JLab 12 GeV based on model-predicted pseudo-data, and the capability of extraction of Compton Form Factors based on a fitter algorithm.

Data-driven study of timelike Compton scattering

In the framework of collinear QCD factorization, the leading twist scattering amplitudes for deeply virtual Compton scattering (DVCS) and timelike Compton scattering (TCS) are intimately related thanks to analytic properties of leading and next-to-leading order amplitudes. We exploit this welcome feature to make data-driven predictions for TCS observables to be measured in near future experiments. Using a recent extraction of DVCS Compton form factors from most of the existing experimental data for that process, we derive TCS amplitudes and calculate TCS observables only assuming leading-twist dominance. Artificial neural network techniques are used for an essential reduction of model dependency, while a careful propagation of experimental uncertainties is achieved with replica methods. Our analysis allows for stringent tests of the leading twist dominance of DVCS and TCS amplitudes. Moreover, this study helps to understand quantitatively the complementarity of DVCS and TCS measurements to test the universality of generalized parton distributions, which is crucial e.g. to perform the nucleon tomography.

Deeply virtual Compton scattering off the neutron

The three-dimensional structure of nucleons (protons and neutrons) is embedded in so-called generalized parton distributions, which are accessible from deeply virtual Compton scattering. In this process, a high energy electron is scattered off a nucleon by exchanging a virtual photon. Then, a highly-energetic real photon is emitted from one of the quarks inside the nucleon, which carries information on the quark's transverse position and longitudinal momentum. By measuring the cross-section of deeply virtual Compton scattering, Compton form factors related to the generalized parton distributions can be extracted. Here, we report the observation of unpolarized deeply virtual Compton scattering off a deuterium target. From the measured photon-electroproduction cross-sections, we have extracted the cross-section of a quasi-free neutron and a coherent deuteron. Due to the approximate isospin symmetry of quantum chromodynamics, we can determine the contributions from the different quark flavours to the helicity-conserved Compton form factors by combining our measurements with previous ones probing the proton's internal structure. These results advance our understanding of the description of the nucleon structure, which is important to solve the proton spin puzzle.