Coherent deeply virtual Compton scattering off He nuclei
OOctober 18, 2019 0:32 ws-procs961x669 WSPC Proceedings - 9.61in x 6.69in int183˙scopetta page 1 Coherent deeply virtual Compton scattering off He nuclei
S. Fucini, M. Rinaldi and S. Scopetta ∗ Dipartimento di Fisica e Geologia, University of Perugia and INFN, Perugia SectionPerugia, I-06123, Italy ∗ E-mail: [email protected]
The status of realistic calculations of nuclear generalized parton distributions, enteringthe theoretical description of coherent deeply virtual Compton scattering off nuclei, isreviewed for trinucleons and for He, also in view of forthcoming measurements at theJefferson Laboratory and at the future Electron Ion Collider.
Keywords : exclusive processes, nuclear imaging, few-body systems
1. Introduction
Nuclear modifications of the nucleon parton structures, discovered by the EuropeanMuon Collaboration several decades ago, cannot be explained by means of inclu-sive measurements only. One of the possible ways out is to perform nuclear imaging,now possible for the first time through deeply virtual Compton scattering (DVCS)and deeply-virtual meson production, using the tool of generalized parton distri-butions (GPDs) (see Refs for recent reports). The comparison of the transversespatial quark and gluon distributions in nuclei or bound nucleons (to be obtainedin coherent or incoherent DVCS, respectively) to the corresponding quantities infree nucleons, will allow ultimately a pictorial representation of the EMC effect.The relevance of non-nucleonic degrees of freedom, as addressed in Ref. , or thechange of size for bound nucleons, will be observed. The most discussed sector ofthe EMC effect is the valence region at intermediate Q , which will be investigatedby Jefferson Lab (JLab) at 12 GeV. For the lightest nuclei, H, He, He, sophisti-cated calculations of conventional effects, although challenging, are possible. Thiswould allow one to distinguish them from exotic ones, likely responsible for theobserved EMC behavior. Without realistic benchmark calculations, making use ofwave functions obtained as exact solution of the Schr¨odinger equation using real-istic nucleon nucleon potentials and three-body forces whenever appropriate, theinterpretation of experimental data is difficult. Among few-body nuclei, in this talkwe will concentrate in three- and four-body systems.
2. Coherent DVCS off He For the coherent channel of DVCS, the one where the nucleus does not break up (seeFig. 1 for a representation of the process with a generic A nucleus, in the handbagapproximation, i.e., with the interaction occurring on a leading quark), due to verysmall cross sections, the measurements addressed in the Introduction are very diffi- a r X i v : . [ nu c l - t h ] O c t ctober 18, 2019 0:32 ws-procs961x669 WSPC Proceedings - 9.61in x 6.69in int183˙scopetta page 2 Factorizatione e’ (k) (k’) x+ x x− x gg * (q ) (q ) GPDs (x, x ,t) A A A (p) (p’) D = p’ −p Fig. 1. Coherent DVCS process off a nucleus A in the handbag approximation. R q (x , x =0.2, D =-0.25 GeV ) x Fig. 2. Estimate of nuclear effects on He GPD for the d ( u ) flavor, full (dashed) line. The effectis given by the difference of the curves with respect to one. cult. In between the H nucleus, very interesting for its rich spin structure and forthe the possible extraction of neutron information, and He, ideal to study nucleareffects, being deeply-bound, scalar and isoscalar, with a simple description of its spinand flavor structure, He provides an opportunity to study the A dependence of nu-clear effects, and it could give easy access to neutron polarization properties, due toits specific spin structure. In addition, being isospin-1 /
2, it guarantees that flavordependence of nuclear effects can be studied, in particular if parallel measurementson H targets, likely possible at the Electron Ion Collider (EIC), were performed .A complete realistic study of leading twist DVCS requires the evaluation of nuclearGPDs. From the theoretical point of view, conventional effects for nuclear systemsare seen in a plane wave impulse approximation (IA) analysis, i.e., with the struckquark belonging to one nucleon in the target, and disregarding possible final stateinteraction effects between this nucleon and the remnants). This requires the eval-uation of realistic non-diagonal spectral functions . For He, a complete analysisusing the Av18 nucleon-nucleon (NN) potential is available . Nuclear GPDs arefound to be sensitive to details of the used NN interaction. In particular, nucleareffects are found to grow with the momentum transfer to the target, ∆ , and withthe longitudinal momentum asymmetry of the process (parametrized by the so-called skewness variable, ξ ). In He, nuclear effects are found to be bigger for the d ctober 18, 2019 0:32 ws-procs961x669 WSPC Proceedings - 9.61in x 6.69in int183˙scopetta page 3 -0.1 0.1 0.3 0.5 0.1 0.15 0.2 0.25 0.3 A L U H e ( ° ) x B Fig. 3. He azimuthal (with respect to the angle φ between lepton and nuclear planes) beam-spinasymmetry A LU ( φ ): results of Ref. (red stars) compared with data (black squares) . flavor than for the u one (see Fig. 2), a prediction of a realistic impulse approxima-tion (IA), where also violations of nuclear charge symmetry are considered in theAV18 NN interaction, which could be tested experimentally. Besides, the depen-dence on the excitation energy of the nuclear recoiling system in the IA description,parametrized by the so-called removal energy, is found to be bigger in nuclear GPDsthan in inclusive observables. Anyway, it is also found that close to the forwardlimit the information on neutron polarization can be safely extracted from He dataand workable extraction formulae have been proposed in this sense . Measure-ments for He and H are not planned, but could be considered as extensions ofthe impressive ALERT detector project at JLab 12 , at least in the unpolarizedsector. Polarized measurements, which could access neutron angular momentuminformation , seem very unlikely at JLab, due to the difficulty of arranging apolarized target and a recoil detector in the same experimental setup, but are inprinciple accessible at the EIC, where the extension to lower x regions will be alsopossible .
3. Coherent DVCS off He Despite the difficulty of measuring coherent DVCS off nuclei, due to small cross-sections, the first data for coherent DVCS off He collected at JLab in the 6 GeVsetup have been published . A new impressive program is on the way at JLab, car-ried on by the CLAS collaboration with the ALERT detector project . A studyfor DVCS off He with nuclear ingredients of the same quality of those summarizedabove for He is still missing and should be done, to update existing calculations,performed long time ago . The evaluation of a realistic spectral functions of He,using state-of-the-art NN potentials, will require in particular the wave function ofa nuclear three-body scattering state, which is a really challenging few-body prob-lem. An encouraging calculation has been recently performed for coherent DVCSoff He , with the aim to describe the CLAS data , as a relevant intermediate ctober 18, 2019 0:32 ws-procs961x669 WSPC Proceedings - 9.61in x 6.69in int183˙scopetta page 4 step towards a rigorous realistic evaluation. A model of the nuclear non-diagonalspectral function, based on the momentum distribution corresponding to the Av18NN interaction , has been used in the actual IA calculation. In particular thespectral function is exact in its ground state part (when the remnant is a boundthree-body system) and modelled in the complicated excited sector. As a test ofthe procedure, typical results are found for the nuclear form factor and for nuclearparton distributions, in proper limits. Nuclear GPD and the actual observable,the so-called, Compton form factor (CFF) are evaluated using a well known GPDmodel to take into account the nucleonic information . As can be seen in Fig. 2, avery good agreement is found with the data, for the so-called beam-spin asymmetry,theoretically obtained in terms of the CFF, in turn evaluated from the GPD. Onecan conclude that a careful analysis of the reaction mechanism in terms of basicconventional ingredients is successful and that the present experimental accuracydoes not require the use of exotic arguments, such as dynamical off-shellness. Morerefined nuclear calculations will be certainly necessary for the expected improvedaccuracy of the next generation of experiments at JLab, with the 12 GeV electronbeam and high luminosity, and, above all, at the EIC. Very recent results for theincoherent channel are reported in , where an encouraging comparison with datafrom JLab is presented.This work was supported in part by the STRONG-2020 project of the EuropeanUnions Horizon 2020 research and innovation programme under grant agreementNo 824093, and by the project “Deeply Virtual Compton Scattering off He”, inthe programme FRB of the University of Perugia.
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