We calculate the nucleon resonance contributions to nucleon Compton scattering, including all states with J^P = 1/2^{+-} and J^P = 3/2^{+-} where experimental data for their electromagnetic transition form factors exist. To this end, we construct a tensor basis for the Compton scattering amplitude based on electromagnetic gauge invariance, crossing symmetry and analyticity. The corresponding Compton form factors provide a Lorentz-invariant description of the process in general kinematics, which reduces to the static and generalized polarizabilities in the appropriate kinematic limits. We derive the general forms of the offshell nucleon-to-resonance transition vertices that implement electromagnetic and spin-3/2 gauge invariance, which automatically also defines onshell transition form factors that are free of kinematic constraints. We provide simple fits for those form factors, which we use to analyze the resulting Compton form factors and extract their contributions to the nucleon's polarizabilities. Apart from the Delta(1232), the resonance contributions to the scalar and spin polarizabilites are very small, although the N(1520) could play a role for the proton's magnetic polarizability.
We analyze the nucleon's Compton scattering amplitude in the Dyson-Schwinger/Faddeev approach. We calculate a subset of diagrams that implements the nonperturbative handbag contribution as well as all t-channel resonances. At the quark level, these ingredients are represented by the quark Compton vertex whose analytic properties we study in detail. We derive a general form for a fermion two-photon vertex that is consistent with its Ward-Takahashi identities and free of kinematic singularities, and we relate its transverse part to the onshell nucleon Compton amplitude. We solve an inhomogeneous…
We consider the spin-averaged nucleon forward Compton scattering amplitude in heavy baryon chiral perturbation theory including all terms to order ${\cal O} (q^4)$. The chiral prediction for the spin-averaged forward Compton scattering amplitude is in good agreement with the data for photon energies $ω\le 110$ MeV. We also evaluate the nucleon electric and magnetic Compton polarizabilities to this order and discuss the uncertainties of the various counter terms entering the chiral expansion of these quantities.
Chiral effective field theories have a long history studying the process of Compton scattering on the nucleon. In this contribution I want to focus on the new developments that have occured since the last Chiral Dynamics conference in Mainz 1997. I will focus exclusively on the spin-dependent sector, where most of the recent work has been done.
We discuss the low-energy behavior of the spin-averaged amplitude of virtual Compton scattering (VCS) off a nucleon. Based on gauge invariance, Lorentz invariance and the discrete symmetries, it is shown that to first order in the frequency of the final real photon only two generalized polarizabilities appear. Different low-energy expansion schemes are discussed and put into perspective.
Virtual Compton scattering off nucleons and pions at low energies is discussed. Predictions for the generalized polarizabilities of the nucleon are presented within the framework of heavy-baryon chiral perturbation theory and the linear sigma model. First results for the generalized polarizabilities of the charged pion in chiral perturbation theory at ${\cal O}(p^4)$ are shown.
We summarize results from our recent paper* on nucleon Compton scattering in the Dyson-Schwinger approach. We study the Compton scattering phase space and its various kinematic limits, and we introduce a covariant, transverse tensor basis for the scattering amplitude that is free of kinematic singularities. We illustrate the decomposition of the Compton amplitude at the quark-gluon level and calculate its nonperturbative handbag part, which also includes all t-channel meson resonances. The calculation requires numerical solutions for the dressed quark propagator, the nucleon's Faddeev amplitud…
We calculated two--photon exchange effects for elastic electron--proton scattering at high momentum transfers. The corresponding nucleon Compton amplitude is defined by two space--like virtual photons that appear to have significant virtualities. We make predictions for a) a single--spin beam asymmetry, and b) a single--spin target asymmetry or recoil proton polarization caused by an unpolarized electron beam.
Two different topics relevant for DA$Φ$NE and CEBAF, respectively, are covered. First we analyze the rare radiative eta decay mode $η\toππγγ$ within the framework of chiral perturbation theory at ${\cal O}(p^4)$. We then discuss virtual Compton scattering off the nucleon at low energies. Predictions for the two spin-independent generalized polarizabilities are shown.
We analyze polarized Compton scattering which provides information on the spin-structure of the nucleon. For scattering processes with photon energies up to 100 MeV the spin-structure dependence can be encoded into four independent parameters-the so-called spin-polarizabilities $γ_i, i=1...4$ of the nucleon, which we calculate within the framework of the "small scale expansion" in SU(2) baryon chiral perturbation theory. Specific application is made to "forward" and "backward" spin- polarizabilities.
We consider deeply virtual Compton scattering and deep inelastic scattering in presence of Regge exchanges that are part of the non-perturbative quark-nucleon amplitude. In particular we discuss contribution from the Pomeron exchange and demonstrate how it leads to Regge scaling of the Compton amplitude. Comparison with HERA data is given.
We present fixed-$t$ subtracted dispersion relations for Compton scattering off the nucleon at energies $E_γ\leq$ 500 MeV, as a formalism to extract the nucleon polarizabilities with a minimum of model dependence. The subtracted dispersion integrals are mainly saturated by $πN$ intermediate states in the $s$-channel $γN \to πN \to γN$ and $ππ$ intermediate states in the $t$-channel $γγ\to ππ\to N \bar N$. For the subprocess $γγ\to ππ$, we construct a unitarized amplitude and find a good description of the available data. We show results for Compton scattering using the subtracted dispersion re…
We study the deeply-virtual Compton scattering (DVCS) process $e^- N \to e^- γπN$ involving the transition between a nucleon and a nucleon resonance in the $πN$ system, within the framework of generalized parton distributions (GPDs). For the four lowest-lying nucleon resonances, $Δ(1232)$, $P_{11}(1440)$, $D_{13}(1520)$, and $S_{11}(1535)$, we express the DVCS amplitude in the Bjorken limit in terms of corresponding nucleon-to-resonance GPDs. Building upon the knowledge of the well studied electromagnetic nucleon-to-resonance transition form factors, which map the quark charge densities in tra…
We present a projector formalism which allows to define dynamical polarizabilities of the nucleon from a multipole expansion of the nucleon Compton amplitudes. We give predictions for the energy dependence of these dynamical polarizabilities both from dispersion theory and from leading-one-loop chiral effective field theory. Based on the good agreement between the two theoretical frameworks, we conclude that the energy dependence of the dynamical polarizabilities is dominated by chiral dynamics, except in those multipole channels where the first nucleon resonance Delta(1232) can be excited. Bo…
We formulate the low energy theorem for virtual Compton scattering off a nucleon and examine its consequences for generalized nucleon polarizabilites. As a result of a new, model independent definition of the low energy limit for VVCS reaction, all generalized sum rules of the nucleon have continuous limit for real photons and obtain contributions from the $t$-channel that were not included previously.
We compute the Compton scattering off the nucleons in the framework of manifestly covariant baryon chiral perturbation theory (B$χ$PT). The results for observables differ substantially from the corresponding calculations in heavy-baryon chiral perturbation theory (HB$χ$PT), most appreciably in the forward kinematics. We verify that the covariant $p^3$ result fulfills the forward-Compton-scattering sum rules. We also explore the effect of the $Δ$(1232) resonance at order $p^4/\varDelta$, with $\varDelta\approx 300$ MeV, the resonance excitation energy. We find that the substantial effect of the…
We propose a new way to experimentally determine the subleading low-energy structure constant of doubly-virtual Compton scattering on a proton. Such empirical determination will reduce the theoretical model error in estimates of the hadronic correction to the muonic hydrogen Lamb shift. We demonstrate that the di-lepton forward-backward asymmetry in the $e^- p \to e^- p \, e^- e^+$ process, which can be accessed at electron scattering facilities, yields a large sensitivity to this so far unknown low-energy constant.
The nucleon spin-averaged forward virtual Compton tensor determines important physical quantities such as electromagnetically-induced mass differences of nucleons, and two-photon exchange contributions in hydrogen spectroscopy. It depends on two kinematic variables: $ν$, the virtual photon energy in the proton rest frame, and $Q^2$, the photon's invariant four-momentum squared. Using the operator product expansion, we calculate the tensor's large-$Q^2$ behavior for $ν=0$, including for the first time the full spin-2 contribution and correcting a previous result in the literature for the spin-0…
We formulate a new power-counting scheme for a chiral effective field theory of nucleons, pions, and Deltas. This extends chiral perturbation theory into the Delta-resonance region. We calculate nucleon Compton scattering up to next-to-leading order in this theory. The resultant description of existing $γ$p cross section data is very good for photon energies up to about 300 MeV. We also find reasonable numbers for the spin-independent polarizabilities $α_p$ and $β_p$.
We investigate the low-energy behavior of the four-point Green's function $Γ^{μν}$ describing virtual Compton scattering off the nucleon. Using Lorentz invariance, gauge invariance, and crossing symmetry, we derive the leading terms of an expansion of the operator in the four-momenta $q$ and $q'$ of the initial and final photon, respectively. The model-independent result is expressed in terms of the electromagnetic form factors of the free nucleon, i.e., on-shell information which one obtains from electron-nucleon scattering experiments. Model-dependent terms appear in the operator at $O(q_αq'…
A review is given of the very recent developments in the fields of real and virtual Compton scattering off the nucleon. Both real and virtual Compton scattering reactions are discussed at low outgoing photon energy where one accesses polarizabilities of the nucleon. The real Compton scattering at large momentum transfer is discussed which is asymptotically a tool to obtain information on the valence quark wave function of the nucleon. The rapid developments in deeply virtual Compton scattering and associated meson electroproduction reactions at high energy, high photon virtuality and small mom…
As guideline for forthcoming experiments, we present predictions from Chiral Effective Field Theory for polarized cross sections in low energy Compton scattering for photon energies below 170 MeV, both on the proton and on the neutron. Special interest is put on the role of the nucleon spin polarizabilities which can be examined especially well in polarized Compton scattering. We present a model-independent way to extract their energy dependence and static values from experiment, interpreting our findings also in terms of the low energy effective degrees of freedom inside the nucleon: The pola…
I give a summary of recent results on nucleon polarizabilities, with emphasis on chiral perturbation theory. The predictive calculations of Compton scattering off the nucleon are compared to recent empirical determinations and lattice QCD calculations of the polarizabilities, thereby testing chiral perturbation theory in the single-baryon sector.
We investigate the spin-independent part of the virtual Compton scattering (VCS) amplitude off the nucleon within the framework of chiral perturbation theory. We perform a consistent calculation to third order in external momenta according to Weinberg's power counting. With this calculation we can determine the second- and fourth-order structure-dependent coefficients of the general low-energy expansion of the spin-averaged VCS amplitude based on gauge invariance, crossing symmetry and the discrete symmetries. We discuss the kinematical regime to which our calculation can be applied and compar…
The spin-independent part of the virtual Compton scattering (VCS) amplitude from the nucleon is calculated within the framework of heavy baryon chiral perturbation theory (HBChPT). The calculation is performed to third order in external momenta according to chiral power counting. The relation of the tree-level amplitudes to what is expected from the low-energy theorem is discussed. We relate the one-loop results to the structure coefficients of a low-energy expansion for the model-dependent part of the VCS amplitude recently defined by Fearing and Scherer. Finally we discuss the connection of …
We review theoretical progress and prospects for determining the nucleon's static dipole polarisabilities from Compton scattering on few-nucleon targets, including new values; see Refs. [1-5] for details and a more thorough bibliography.
During the workshop "Compton Scattering off Protons and Light Nuclei: pinning down the nucleon polarisabilities" (ECT*, Trento, Italy, 29 July -- 2 August 2013, http://www.ectstar.eu/node/98), recent developments had been reviewed in experimental and theoretical studies of real and virtual Compton scattering, static and generalized dipole scalar and spin polarisabilities of nucleons, as well as related phenomena in physics of muonic atoms. A vivid topic at the workshop was pathways towards the most precise extraction of the static polarisabilities from low-energy Compton cattering---including …
Virtual Compton scattering off the nucleon (VCS) is studied in the regime of low energy of the outgoing real photon. This regime allows one to directly access the generalized polarizabilities of the nucleon in a VCS experiment. In the derivation of the low energy theorem for VCS that exists in the literature, the low energy limit taken for virtual initial photons does not match on that for real photons, when one approaches the initial photon's mass shell. While this problem has for a long time been attributed to the non-analyticity of the Compton amplitude with respect to the photon virtuality…
Fixed-$t$ subtracted dispersion relations are presented for Compton scattering off the nucleon at energies $E_γ\leq 500$ MeV, as a formalism to extract the nucleon polarizabilities from the data with a minimum of model dependence. The scalar polarizabilities difference $α- β$ and the backward spin polarizability $γ_π$ enter directly as fit parameters in this formalism.
We present QCD results for the exclusive processes $γ{\rm N}\rightarrowγ{\rm N}$ ($\rm N=p,\;n$) at large momentum transfer and compare them to data for the proton. TALK given at DPF meeting, November 10-14, Fermilab.
The differential cross section for gamma-deuteron Compton scattering is computed to next-to-leading order (NLO) in an effective field theory that describes nucleon-nucleon interactions below the pion production threshold. Contributions at NLO include the nucleon isoscalar electric polarizability from its 1/m_pi behavior in the chiral limit. The parameter free prediction of the gamma-deuteron differential cross section at NLO is in good agreement with data.
In the following, the subject of Deep Virtual Compton Scattering on the nucleon and its relation to the recently introduced concept of Generalized Parton Distributions are briefly reviewed. The general theoretical framework and the links between theory and experiment will be outlined and the recently published data which look promising for the development of this field will be discussed. Finally, the experimental prospectives of the domain will be presented.
Using hydrogen and deuterium targets, Compton scattering by the proton and neutron have been studied at the tagged photon beam of the MAMI (Mainz) accelerator using different experimental setups. The theoretical tools for the analysis of the experimental data have been investigated, as there are the nonsubtracted dispersion theory and the theory of quasi-free reactions on the proton and neutron bound in the deuteron. Experimental Compton scattering data are understood in the first and second resonance region with good precision. Precise electromagnetic polarizabilities and spin polarizabilitie…
We derive two new sum rules for the unpolarized doubly virtual Compton scattering process on a nucleon, which establish novel low-$Q^2$ relations involving the nucleon's generalized polarizabilities and moments of the nucleon's unpolarized structure functions $F_1(x,Q^2)$ and $F_2(x,Q^2)$. These relations facilitate the determination of some structure constants which can only be accessed in off-forward doubly virtual Compton scattering, not experimentally accessible at present. We perform an empirical determination for the proton and compare our results with a next-to-leading-order chiral pert…
A unified presentation is given on the use of dispersion relations in the real and virtual Compton scattering processes off the nucleon. The way in which dispersion relations for Compton scattering amplitudes establish connections between low energy nucleon structure quantities, such as polarizabilities or anomalous magnetic moments, and the nucleon excitation spectrum is reviewed. We discuss various sum rules for forward real and virtual Compton scattering, such as the Gerasimov-Drell-Hearn sum rule and its generalizations, the Burkhardt-Cottingham sum rule, as well as sum rules for forward n…
We outline a microscopic framework to calculate nucleon Compton scattering from the level of quarks and gluons within the covariant Faddeev approach. We explain the connection with hadronic expansions of the Compton scattering amplitude and discuss the obstacles in maintaining electromagnetic gauge invariance. Finally we give preliminary results for the nucleon polarizabilities.
This review gives an update on virtual Compton scattering (VCS) off the nucleon, $γ^* N \to N γ$, in the low-energy regime. We recall the theoretical formalism related to the generalized polarizabilities (GPs) and model predictions for these observables. We present the GP extraction methods that are used in the experiments: the approach based on the low-energy theorem for VCS and the formalism of Dispersion Relations. We then review the experimental results, with a focus on the progress brought by recent experimental data on proton generalized polarizabilities, and we conclude by some perspect…
Virtual Compton Scattering on the nucleon: $γ^* N \to γN$ is a new and rapidly developing field at low and high energies. This lecture is about the low energy part, i.e. for energies in the $(γp)$ center-of-mass mainly up to the $Δ(1232)$ resonance region. I review the concept of Generalized Polarizabilities of the Nucleon, and the experiments dedicated to their measurement.
In addition to the E2/M1 ratio of the N->$Δ$ transition, the electromagnetic polarizabilities and spin-polarizabilities are important structure constants of the nucleon which serve as sensitive tests of chiral perturbation theory and of models of the nucleon. Recently, these quantities have been investigated experimentally at MAMI (Mainz) by high-precision Compton scattering using hydrogen and deuterium targets, where for the latter the method of quasi-free scattering has been applied.
We analyze virtual Compton scattering off the nucleon at low energies in a covariant, model-independent formalism. We define a set of invariant functions which, once the irregular nucleon pole terms have been subtracted in a gauge-invariant fashion, is free of poles and kinematical zeros. The covariant treatment naturally allows one to implement the constraints due to Lorentz and gauge invariance, crossing symmetry, and the discrete symmetries. In particular, when applied to the $ep\to e'p'γ$ reaction, charge-conjugation symmetry in combination with nucleon crossing generates four relations am…
Standard parton distribution functions contain neither information on the correlations between partons nor on their transverse motion, then a vital knowledge about the three dimensional structure of the nucleon is lost. Hard exclusive processes, in particular DVCS, are essential reactions to go beyond this standard picture. In the following, we examine the most recent data and their implication on the quarks/gluons imaging (tomography) of the nucleon.
We study twist-three effects in deeply virtual Compton scattering on an unpolarized spin-1/2 target. A careful definition of observables as Fourier moments w.r.t. the azimuthal angle allows for a clear separation of twist-two and -three effects. Although the latter are power suppressed, they give leading contributions to the twist-three asymmetries and do not affect the twist-two observables.
We review the current state of knowledge of the nucleon polarizabilities and of their role in nucleon Compton scattering and in hydrogen spectrum. We discuss the basic concepts, the recent lattice QCD calculations and advances in chiral effective-field theory. On the experimental side, we review the ongoing programs aimed to measure the nucleon (scalar and spin) polarizabilities via the Compton scattering processes, with real and virtual photons. A great part of the review is devoted to the general constraints based on unitarity, causality, discrete and continuous symmetries, which result in m…
A dispersion relation formalism for the virtual Compton scattering (VCS) reaction on the proton is presented, which for the first time allows a dispersive evaluation of 4 generalized polarizabilities at a four-momentum transfer $Q^2 \leq$ 0.5 GeV$^2$. The dispersive integrals are calculated using a state-of-the-art pion photo- and electroproduction analysis. The dispersion formalism provides a new tool to analyze VCS experiments above pion threshold, thus increasing the sensitivity to the generalized polarizabilities of the nucleon.
We study the double deeply virtual Compton scattering (DDVCS) process off the nucleon, through the scattering of a spacelike virtual photon with large virtuality resulting in the production of a timelike virtual photon, decaying into an e^+ e^- pair. This process is expressed in the Bjorken regime in terms of generalized parton distributions (GPDs) and it is shown that by varying the invariant mass of the lepton pair, one can directly extract the GPDs from the observables. We give predictions for the DDVCS cross section and beam helicity asymmetry and discuss its experimental feasibility.
At moderate and large momentum transfer, high energy vector meson photoproduction and Compton scattering can be consistently explained by mechanisms based on interactions and exchanges of constituent quarks and gluons. This opens an original window on the partonic structure of hadronic matter by emphasizing the role of quark correlations, quark exchange as implemented through saturating Regge trajectories and non-perturbative effects in the gluon propagator, which provides us with a bridge with lattice calculations. Compton scattering is directly related to vector meson photoproduction and enl…
We give an overview of low-energy Compton scattering (gamma^(*) p --> gamma p) with a real or virtual incoming photon. These processes allow the investigation of one of the fundamental properties of the nucleon, i.e. how its internal structure deforms under an applied static electromagnetic field. Our knowledge of nucleon polarisabilities and their generalization to non-zero four-momentum transfer will be reviewed, including the presently ongoing experiments and future perspectives.
Coherent Deeply virtual Compton scattering off the $^4$He nucleus is studied in impulse approximation. A convolution formula for the nuclear Generalized Parton Distribution (GPD) is derived in terms of the $^4$He non-diagonal spectral function and of the GPD of the struck nucleon. A model of the nuclear non diagonal spectral function, based on the momentum distribution corresponding to the AV18 nucleon-nucleon interaction, is used in the actual calculation. Typical impulse approximation results are reproduced, in proper limits, for the nuclear form factor and for nuclear parton distributions. …
In recent work, Hill and Paz apply the operator product expansion to forward doubly virtual Compton scattering. The resulting large-$Q^2$ form of the amplitude $W_1(0,Q^2)$ is compatible with the one we obtain by extrapolation of low-$Q^2$ results from a chiral effective field theory, providing support for our approach. That paper also presents a result for the two-photon contribution to the Lamb shift in muonic hydrogen that has a much larger uncertainty than in previous work. We show that this an overestimate arising from the inclusion of the proton pole term in the subtracted dispersion rel…
The exclusive photoproduction off nucleon of a large invariant mass lepton pair in the backward region specified by the small Mandelstam variable $-u$ is discussed in the framework of collinear QCD factorization. The amplitude is factorized in terms of photon-to-nucleon Transition Distribution Amplitudes (TDAs) which encode the photon content of the nucleon. Model estimates of these new non-perturbative objects are described and the corresponding cross sections calculated. The background due to the electromagnetic Bethe-Heitler process is shown to be negligible in the kinematical regime of int…
The status of Compton scattering by the nucleon at energies of the first and second resonance is summarized. In addition to a general test of dispersion theories and a precise determination of polarizabilities, the validities of four fundamental sum rules are explored. {\it Recommended} averages of experimental values for the electromagnetic polarizabilities and spin-polarizabilities of the nucleon are determined: $α_p=12.0\pm 0.6$, $β_p=1.9\mp 0.6$, $α_n= 12.5 \pm 1.7$, $β_n= 2.7 \mp 1.8$ (unit $10^{-4}$fm$^3$), $γ^{(p)}_π= -38.7 \pm 1.8$, $γ^{(n)}_π= 58.6 \pm 4.0$ (unit $10^{-4}$fm$^4$).
It is shown that the Quark-Level Linear $σ$ Model (QLL$σ$M) leads to a prediction for the diamagnetic term of the polarizabilities of the nucleon which is in excellent agreement with the experimental data. The bare mass of the $σ$ meson is predicted to be $m_σ=666$ MeV and the two-photon width $Γ(σ\toγγ)=(2.6\pm 0.3)$ keV. It is argued that the mass predicted by the QLL$σ$M corresponds to the $γγ\toσ\to NN$ reaction, i.e. to a $t$-channel pole of the $γN\to Nγ$ reaction. Large -angle Compton scattering experiments revealing effects of the $σ$ meson in the differential cross section are discuss…
I consider Compton scattering off the nucleon in the presence of $CP$ violation. I construct the Compton tensor which possesses these features and consider low energy expansion (LEX) of the corresponding amplitudes. It allows to separate out the Born contribution which only depends on the static properties of the nucleon, such as the electric charge, the mass, the magnetic moment, and the electric dipole moment (EDM). I introduce new structure constants, the $T$-odd nucleon polarizabilities which parametrize the unknown non-Born part. These constants describe the response of the $T$-violating …
Compton scattering off the proton in the third resonance region is analyzed for the first time, owing to the full combined analysis of pion- and photo-induced reactions in a coupled-channel effective Lagrangian model with K-matrix approximation. Two isospin $I=3/2$ resonances $D_{33}(1700)$ and $F_{35}(1930)$ are found to be essential in the range of 1.6 - 1.8 GeV. The recent beam asymmetry data of Compton scattering from the GRAAL facility are used to determine the helicity couplings of these resonances, and strong constraints are coming also from $πN$ and $KΣ$ photoproduction data. The possi…
This PhD thesis is devoted to the low-energy structure of the nucleon (proton and neutron) as seen through electromagnetic probes, e.g., electron and Compton scattering. The research presented here is based primarily on dispersion theory and chiral effective-field theory. The main motivation is the recent proton radius puzzle, which is the discrepancy between the classic proton charge radius determinations (based on electron-proton scattering and normal hydrogen spectroscopy) and the highly precise extraction based on first muonic-hydrogen experiments by the CREMA Collaboration. The precision …
We consider Deeply Virtual Compton Scattering (DVCS) on nucleons and nuclei in the framework of generalized vector meson dominance (GVMD) model. We demonstrate that the GVMD model provides a good description of the HERA data on the dependence of the proton DVCS cross section on Q^2, W (at Q^2=4 GeV^2) and t. At Q^2 = 8 GeV^2, the soft W-behavior of the GVMD model somewhat underestimates the W-dependence of the DVCS cross section due to the hard contribution not present in the GVMD model. We estimate 1/Q^2 power-suppressed corrections to the DVCS amplitude and the DVCS cross section and find th…
The generalized parton distributions (GPDs) of the meson and nucleon at small and large values of the momentum transfer were determined on the basis of the comparative analysis of different sets of experimental data of electromagnetic form factors of the proton and neutron, using the different sets of the parton distribution functions (PDFs). As a result, different form factors of the nucleons and meson were calculated. The t-dependence of these form factors was checked up in the description of the nucleon-nucleon and meson-nucleon elastic scattering and the differential cross sections of the …
We review the recent developments of virtual Compton scattering. We focus on the kinematical regimes which look the most promising. The threshold regime gives access to the generalized polarizabilities of the proton. The hard scattering regime allows tests of perturbative QCD predictions and of the valence quark wave function. The Bjorken regime is closely related to deep inelastic scattering. It gives access to the off-forward parton distributions which generalize the ordinary parton distributions and may shed a new light on the spin problem. For each regime we discuss the experimental perspe…
Structure functions are the essential objects for understanding the deep inelastic scattering processes, providing valuable insight into the partonic structure of hadrons. A direct calculation of the Compton amplitude provides a complementary way to accessing the structure functions, circumventing the operator mixing and renormalisation issues of the standard operator product expansion approach. We describe the connection between the Compton amplitude and the structure functions, and describe a Feynman-Hellmann approach to calculate the amplitude directly. As an application, we extract the mom…
