Backward timelike Compton scattering to decipher the photon content of the nucleon
Bernard Pire, Kirill M. Semenov-Tian-Shansky, Alisa A. Shaikhutdinova, Lech Szymanowski
备注：
33 pages, 9 figures, 1 table. A major revision of the paper. A sign mistake was corrected in amplitude calculations. This resulted in predicting higher cross section for the bTCS reaction
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 interest.
We study the timelike virtual Compton scattering process with a linearly polarized photon beam, in the generalized Bjorken scaling region and in the medium energy range which will be studied intensely at JLab12 experiments. We define new observables and show how they should help to access the polarized quark and gluon generalized parton distributions.
We review recent progress in the study of timelike Compton scattering (TCS), the crossed process of deeply virtual Compton scattering. We emphasize the need to include NLO corrections to any phenomenological program to extract Generalized Parton Distributions (GPDs) from near future experimental data. We point out that TCS at high energy should be available through a study of ultraperipheral collisions at RHIC and LHC, opening a window on quark and gluon GPDs at very small skewness.
We emphasize the complementarity of timelike and spacelike studies of deep exclusive processes, taking as an example the case of timelike Compton Scattering (TCS) i.e. the exclusive photoproduction of a lepton pair with large invariant mass, vs deeply virtual Compton scattering (DVCS) i.e. the exclusive leptoproduction of a real photon. Both amplitudes factorize with the same generalized parton distributions (GPDs) as their soft parts and coefficient functions which differ significantly at next to leading order in alpha_s. We also stress that data on TCS at very high energy should be available…
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…
Timelike Compton scattering (TCS) i.e. the exclusive photoproduction of a lepton pair with large invariant mass nicely complements the already successful experimental study of deeply virtual Compton scattering (DVCS). The same Generalized Parton Distributions enter both amplitudes, which offer a promissing way to access the quark and gluon nucleon structure. We review recent progress in this domain, emphasizing the fact that analyticity and factorization properties dictate the relation of the NLO corrections to TCS to those of DVCS. We also stress that data on TCS at high energy should be avai…
We calculate timelike virtual Compton scattering amplitudes in the generalized Bjorken scaling regime and focus on a new polarization asymmetry in the scattering process with a linearly polarized photon beam in the medium energy range, which will be studied intensely at JLab12 experiments. We demonstrate that new observables help us to access the polarized quark and gluon generalized parton distributions $\tilde H(x, ξ, t)$ and $ \tilde E(x, ξ, t)$.
We present some recent results on the analysis of hard scattering processes in the framework of Generalized Parton Distributions. In particular we compute DVCS observables on unpolarized targets with the Kroll - Goloskokov model (suited to DVMP analysis). We also discuss NLO contributions to DVCS and TCS processes for various kinematic settings.
We investigate the exclusive photoproduction of a heavy timelike photon which decays into a lepton pair, gamma p -> l+ l- p. This can be seen as the analog of deeply virtual Compton scattering, and we argue that the two processes are complementary for studying generalized parton distributions in the nucleon. In an unpolarized experiment the angular distribution of the leptons readily provides access to the real part of the Compton amplitude. We estimate the possible size of this effect in kinematics where the Compton process should be dominated by quark exchange.
Generalized Parton Distributions (GPDs) offer a new way to access the quark and gluon nucleon structure. We advocate the need to supplement the experimental study of deeply virtual Compton scattering by its crossed version, timelike Compton scattering. We review recent progress in this domain, emphasizing the need to include NLO corrections to any phenomenological program to extract GPDs from experimental data.
We present a sample of results of our work to be published soon on Timelike Compton scattering off the proton, in the framework of the Generalized Parton Distributions formalism.
In this work we consider the dilepton production via timelike Compton scattering (TCS) in electron-proton and proton-proton collisions. In particular, the differential cross section in terms of the dilepton invariant mass and rapidity is computed within the $k_T$-factorization approach. Besides, we utilize distinct unintegrated gluon distributions (UGD) in order to compare their impact on the differential cross section of TCS in $pp$ ($ep$) collisions evaluated at the LHC (LHeC), HL-LHC (LHeC), HE-LHC (LHeC) and FCC-hh (eh) center-of-mass energies.
We report on a recent work proposing measurements of the deeply virtual Compton amplitude (DVCS) $γ^* \to h \bar h γ$ in the timelike kinematic domain which is accessible at electron-positron colliders via the radiative annihilation process $e^+ e^- \to h \bar h γ$.
We study the exclusive photoproduction of an electron-positron pair on a neutron target in the Jefferson Lab energy domain. The reaction consists of two processes: the Bethe-Heitler and the Timelike Compton Scattering. The latter process provides potentially access to the Generalized Parton Distributions (GPDs) of the nucleon. We calculate all the unpolarized, single- and double-spin observables of the reaction and study their sensitivities to GPDs.
Exclusive photoproduction of dileptons, gamma N->e+e-N, is and will be measured in ultraperipheral collisions at hadron colliders, such as the Tevatron, RHIC and the LHC . We demonstrate that the timelike deeply virtual Compton scattering (TCS) mechanism gamma q -> e+e- q where the lepton pair comes from the subprocess gamma q -> gamma* q dominates in some accessible kinematical regions, thus opening a new way to study generalized parton distributions (GPD) in the nucleon. High energy kinematics enables to probe parton distributions at small skewedness. This subprocess interferes at the amplit…
We study the exclusive photoproduction of a lepton pair off the proton with the aim of studying the proton quark structure via the Generalized Parton Distributions (GPD) formalism. After deriving the amplitudes of the processes contributing to the $γP\to P' e^+e^-$, the Timelike Compton Scattering and the Bethe-Heitler process, we calculate all unpolarized, single- and double- beam-target spin observables in the valence region in terms of GPDs.
We study timelike and spacelike virtual Compton scattering in the generalized Bjorken scaling regime at next to leading order in the strong coupling constant, in the medium energy range which will be studied intensely at JLab12 and in the COMPASS-II experiment at CERN. We show that the Born amplitudes get sizeable O(α_s) corrections and, even at moderate energies, the gluonic contributions are by no means negligible. We stress that the timelike and spacelike cases are complementary and that their difference deserves much special attention.
Exclusive photoproduction of dileptons, gamma N ->l+l- N, is and will be measured in ultraperipheral collisions at hadron colliders. We demonstrate that the timelike deeply virtual Compton scattering (TCS) mechanism gamma q -> l+l- q, where the lepton pair comes from the subprocess gamma q -> gamma* q, dominates in some accessible kinematical regions, thus opening a new way to study generalized parton distributions (GPD) in the nucleon at small skewedness.
In the present work, $k_T$-factorization formalism is applied to compute the exclusive dilepton production by timelike Compton scattering (TCS) in $eA$, $pA$ and $AA$ collisions. The nuclear effects are investigated considering heavy and light ions. The production cross section in terms of invariant mass and rapidity distribution of the lepton pair is shown. The analysis is done for electron-ion collisions at the Large Hadron-Electron Collider (LHeC), its high-energy upgrade (HE-LHeC) and at the Future Circular Collider (FCC) in lepton-hadron mode. Additionally, ultraperipheral heavy ion colli…
We calculate the O(alpha_s) corrections to the timelike, spacelike and double deeply virtual Compton scattering amplitudes in the generalized Bjorken scaling region. Special attention is devoted to studies of the difference between the next to leading order timelike and spacelike coefficient functions, which plays for this process a role analogous to the large K factor which was much discussed in the analysis of inclusive Drell Yan cross sections. Also in the present studies the timelike nature of the hard scale gives rise to new absorptive part of the amplitude and to the presence of characte…
Exclusive photoproduction of dileptons, gamma N ->l+l- N, is and will be measured in ultraperipheralcollisions at hadron colliders. We demonstrate that the timelike deeply virtual Compton scattering (TCS) mechanism gamma q -> l+l- q, where the lepton pair comes from the subprocess gamma q -> gamma* q, dominates in some accessible kinematical regions, thus opening a new way to study generalized parton distributions (GPD) in the nucleon at small skewedness.
We propose measurements of the deeply virtual Compton amplitude (DVCS), gamma* to H H-bar gamma, in the timelike t = (p_{H} + p_{H-bar})^2 > 0 kinematic domain which is accessible at electron-positron colliders via the radiative annihilation process e+ e- to H H-bar gamma. These processes allow the measurement of timelike deeply virtual Compton scattering for a variety of H H-bar hadron pairs such as pi+ pi-, K+ K-, and D D-bar as well as p p-bar. As in the conventional spacelike DVCS, there are interfering coherent amplitudes contributing to the timelike processes involving C= - form factors.…
The study of exclusive processes in photon - induced interactions allow us to probe the generalized parton distributions (GPDs), which provide information about the 3 dimensional description of the quark and gluon content of hadrons. In this paper we investigate the timelike Compton scattering (TCS) in ultraperipheral $pPb$ collisions at the LHC. Such process is characterized by the exclusive dilepton production through the subprocess $γp \rightarrow γ^*p \rightarrow l^+ l^- p$, with the real photon in the initial state being emitted by the nucleus. Assuming a given model for the GPDs, the TCS…
We evaluate the leading-order QED radiative corrections to the timelike Compton scattering (TCS) process $γp \to l^- l^+ p$. We study these corrections in two energy regimes using different models for the TCS amplitude. In the low-energy regime we calculate the contribution due to the proton and its lowest-energy excitation, the $Δ(1232)$ resonance. In the high-energy near-forward kinematical regime we calculate the TCS amplitude in a handbag approach in terms of Generalized Parton Distributions (GPDs). On the level of cross sections we find the QED radiative corrections to be in the $5 -10\%$…
We emphasize how large O(α_s) corrections to timelike and spacelike virtual Compton scattering amplitudes are in the generalized Bjorken scaling regime, and in particular the gluonic contributions, even in the medium energy range which will be studied intensely at JLab12 and in the COMPASS-II experiment at CERN. We stress that the timelike and spacelike cases are complementary and that their difference deserves much special attention.
We derive the forward photoproduction amplitude for the diffractive $γp \to l^+ l^- p$ reaction in the momentum space. within the formalism of $k_\perp$- factorization. Predictions for the $γp \to l^+ l^- p$ reaction are given using unintegrated gluon distribution from the literature. We calculate the total cross section as a function of photon-proton center of mass energy and the invariant mass distribution of the lepton pair. We also discuss whether the production of timelike virtual photons can be approximated by continuing to the spacelike domain $ q^2 < 0$. The present calculation provide…
Timelike and spacelike virtual Compton scattering in the generalized Bjorken scaling regime are complementary tools to access generalized parton distributions. We stress that the gluonic contributions are by no means negligible, even in the medium energy range which will be studied intensely at JLab12 and in the COMPASS-II experiment at CERN. Ultraperipheral collisions with proton or ion beams may also be used at RHIC and at collider or fixed target experiments at LHC.
Deeply Virtual Compton Scattering in the near forward kinematic region is the golden access to Generalized Parton Distributions. We studied the O(alphaS) corrections to the scattering amplitude for both spacelike and timelike kinematics relevant respectively to the leptoproduction of a real photon and to the photoproduction of a lepton pair. It turns out that these corrections are phenomenologically important and that the gluonic contributions are by no means negligible, even in the moderate energy range of JLab12 and of the COMPASS-II experiment at CERN.
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 s…
Exclusive processes of heavy meson production and spacelike and timelike deeply virtual Compton scattering allow us to investigate the hadron structure in terms of Generalized Parton Distributions (GPDs). We review recent developments in the NLO description of such processes.
The inclusion of QCD corrections to the Born amplitude of deeply virtual Compton scattering in both spacelike (DVCS) and timelike (TCS) regimes modifies the extraction process of generalized parton distributions (GPDs) from observables. In particular, gluon contributions are by no means negligible even in the medium energy range accessible at JLab12. We emphasize the complementarity of spacelike and timelike measurements and raise the question of factorization scale dependence of the O(alpha_S) results.
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 $Q^2$. 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.
The study of $O(α_s)$ QCD contributions to the timelike and spacelike virtual Compton scattering amplitudes in the generalized Bjorken scaling regime demonstrates that gluonic contributions are by no means negligible even in the medium energy range which will be studied intensely at JLab12 and in the COMPASS-II experiment at CERN.
Exclusive photoproduction of dileptons, gamma p ->l+ l- p, will be measured in ultraperipheral collisions at LHC. The mechanism where the lepton pair comes from a heavy timelike photon radiated from a quark interferes with the pure QED process gamma gamma ->l+ l- As an analog of deeply virtual Compton scattering, this timelike Compton scattering is a way to study generalized parton distributions in the nucleon or the nucleus. High energy kinematics will enable to focus on gluon distributions. Nuclear effects may be scrutinized in heavy ion collisions.
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.
Generalized Parton Distributions (GPDs) offer a new way to access the quark and gluon nucleon structure. We review recent progress in this domain, emphasizing the need to supplement the experimental study of deeply virtual Compton scattering by its crossed version, timelike Compton scattering. We also describe the extension of the GPD concept to three quark operators and the relevance of their nucleon to meson matrix elements, namely the transition distribution amplitudes (TDAs) which factorize in backward meson electroproduction and related processes. We discuss the main properties of the TDA…
It is an empirical question whether photons always obey Bose-Einstein statistics, but devising and interpreting experimental tests of photon statistics can be a challenge. The nonrelativistic cross section for Compton scattering illustrates how a small admixture nu of wrong-sign statistics leads to a loss of gauge invariance; there is a large anomalous amplitude for scattering timelike photons. Nevertheless, one can interpret the observed transparency of the solar wind plasma at low frequencies as a bound nu < 10^(-25) if Lorentz symmetry is required. If there is instead a universal preferred …
Generalized parton distributions (GPDs) enter QCD factorization theorems for hard exclusive reactions. They encode rich information about hadron partonic structure. We explore a possibility to constrain GPDs in experiments at LHC considering two different exclusive processes: the timelike Compton scattering and the photoproduction of heavy vector mesons.
We provide predictions for the rapidity distributions of exclusive photoproduced J/psi and Upsilon mesons, and Z^0 bosons, at the Tevatron and LHC. We use the equivalent-photon approximation with the photon-proton cross sections given by the impact parameter dependent dipole saturation model, which has already been shown to give a good description of a wide variety of HERA data. We derive the quark-antiquark light-cone wave functions of timelike neutral electroweak bosons. An essential difference is pointed out between the amplitude for timelike heavy boson photoproduction and the amplitude fo…
I survey a number of interesting tests of quantum chromodynamics at the amplitude level which can be carried out in electron-positron annihilation and in photon-photon collisions at low energy, including measurements of fundamental processes such as timelike form factors and transition amplitudes, timelike Compton scattering, timelike photon to meson transition amplitudes, and two-photon exclusive processes. Many of these reactions test basic principles of QCD such as hadronization at the amplitude level, factorization, and hadron helicity conservation, tools also used in the analysis of exclu…
Exclusive proton-antiproton annihilation into two photons can be viewed as the Compton process in the crossed channel. At large s (~10 GeV^2) and |t|,|u| s this process can be described by a generalized partonic picture, analogous to the 'soft mechanism' in wide-angle real Compton scattering. The two photons are emitted in the annihilation of a single fast quark and antiquark ('handbag graph'). The transition of the p-pbar system to a q-qbar pair through soft interactions is described by double distributions, which can be related to the timelike proton elastic form factors as well as, by cross…
Using the high energy color dipole approach, we study the exclusive photoproduction of lepton pairs. We use simple models for the elementary dipole-hadron scattering amplitude that captures main features of the dependence on atomic number A, on energy and on momentum transfer t. This investigation is complementary to conventional partonic description of timelike Compton scattering, which considers quark handbag diagrams at leading order in $α_s$ and simple models of the relevant generalized parton distributions (GPDs). These calculations are input in electromagnetic interactions in pp and AA c…
Generalized parton distributions (GPDs) encoding multidimensional information of hadron partonic structure appear as the building blocks in a factorized description of hard exclusive reactions. The nucleon GPDs have been accessed by deeply virtual Compton scattering and deeply virtual meson production with lepton beam. A complementary probe with hadron beam is the exclusive pion-induced Drell-Yan process. In this paper, we discuss recent theoretical advances on describing this process in terms of nucleon GPDs and pion distribution amplitudes. Furthermore, we address the feasibility of measurin…
We develop the analysis of diphoton exclusive photoproduction in the kinematics where a collinear QCD factorization framework applies, namely nearly forward large invariant mass diphoton production. We work at the leading twist level and at the next-to-leading order (NLO) in the strong coupling constant $α_S$. We compare our predictions for cross-sections with Born order calculations for the experimental conditions accessible to JLab experiments and show the interesting sensitivity of our results to various models of generalized parton distributions (GPDs). The NLO corrections are rather large…
Exclusive proton-antiproton annihilation into two photons at large s (~10 GeV^2) and |t|,|u| ~ s can be described by a generalized parton picture analogous to the 'soft mechanism' in wide-angle real Compton scattering. The two photons are emitted in the annihilation of a single fast quark and antiquark. The matrix element describing the transition of the p-pbar system to a q-qbar pair can be related to the timelike proton elastic form factors as well as to the quark/antiquark distributions measured in inclusive deep-inelastic scattering. The reaction could be studied with the proposed 1.5-15 G…
Generalized parton distributions (GPDs) encoding multidimensional information of hadron partonic structure appear as the building blocks in a factorized description of hard exclusive reactions. The nucleon GPDs have been accessed by deeply virtual Compton scattering and deeply virtual meson production with lepton beam. A complementary probe with hadron beam is the exclusive pion-induced Drell-Yan process. We discuss recent theoretical advances on describing this process in terms of the partonic subprocess convoluted with the nucleon GPDs and the pion distribution amplitudes. Furthermore, we me…
Generalized Parton Distributions offer a new way to access the quark and gluon nucleon structure. We review recent progress in this domain, emphasizing the need to supplement the experimental study of DVCS by its crossed version, timelike Compton scattering (TCS), where data at high energy should appear thanks to the study of ultraperipheral collisions at the LHC. This will open the access to very low skewness quark and gluon GPDs. Our leading order estimates show that the factorization scale dependence of the amplitudes is quite high. This fact demands the understanding of higher order contri…
Generalized parton distributions (GPDs) encoding multidimensional information of hadron partonic structure appear as the building blocks in a factorized description of hard exclusive reactions. The nucleon GPDs have been accessed by deeply virtual Compton scattering and deeply virtual meson production with lepton beam. A complementary probe with hadron beam is shown to be the exclusive pion-induced Drell-Yan process, $π^- p \to μ^+ μ^- n$, as demonstrated by recent theoretical advances on describing this process in terms of QCD factorization as the partonic subprocess convoluted with the nucle…
Generalized distribution amplitudes (GDAs) are one type of three-dimensional structure functions, and they are related to the generalized distribution functions (GPDs) by the $s$-$t$ crossing of the Mandelstam variables. The GDA studies provide information on three-dimensional tomography of hadrons. The GDAs can be investigated by the two-photon process $γ^* γ\to h\bar h$, and the GPDs are studied by the deeply virtual Compton scattering $γ^* h \to γh$. The GDA studies had been pure theoretical topics, although the GPDs have been experimentally investigated, because there was no available expe…
