Relativistic and Nuclear Medium Effects on the Coulomb Sum Rule

Abstract

In light of the forthcoming high precision quasielastic electron scattering data from Jefferson Lab, it is timely for the various approaches to nuclear structure to make robust predictions for the associated response functions. With this in mind, we focus here on the longitudinal response function and the corresponding Coulomb sum rule for isospin-symmetric nuclear matter at various baryon densities. Using a quantum field-theoretic quark-level approach which preserves the symmetries of quantum chromodynamics, as well as exhibiting dynamical chiral symmetry breaking and quark confinement, we find a dramatic quenching of the Coulomb sum rule for momentum transfers |q| 0.5 GeV. The main driver of this effect lies in changes to the proton Dirac form factor induced by the nuclear medium. Such a dramatic quenching of the Coulomb sum rule was not seen in a recent quantum Monte Carlo calculation for carbon, suggesting that the Jefferson Lab data may well shed new light on the explicit role of QCD in nuclei.PACS numbers: 25.70.Bc, 13.40. Gp, Traditionally the nucleus is viewed as a collection of nucleons that interact via phenomenological potentials. This picture has proven successful since the establishment of the nuclear shell model and the interim has seen steady refinement, culminating today in sophisticated non-relativistic quantum-many-body approaches [1][2][3][4][5]. A key assumption of such approaches is that the internal structural properties of the nucleons which comprise a nucleus are the same as those of free nucleons. However, with the realization that quantum chromodynamics (QCD) is the fundamental theory of the strong interaction, it is natural to expect that these nucleon properties are modified by the nuclear medium [6][7][8][9]. Understanding the validity of these two viewpoints remains a key challenge for contemporary nuclear physics. Should it turn out that nucleon properties are significantly modified by the nuclear medium, this would represent a new paradigm for nuclear physics and help build a bridge between QCD and nuclei. On the other hand, if the bound nucleon is unchanged this would shed light on colour confinement in QCD and force a rethink of numerous approaches to hadron structure.Experimental evidence for explicit quark and gluon effects in nuclei remains elusive and to date the most famous example of such evidence -albeit not incontrovertible -is the EMC effect [10][11][12]. First observed in 1982 [13], the EMC effect refers to a quenching of the nuclear structure functions relative to those of a free nucleon, and demonstrates that valence quarks in a nucleus carry a smaller momentum fraction than those in a free nucleon. Numerous explanations have been proposed, ranging from nuclear structure [14][15][16][17] to QCD effects [18][19][20][21][22][23], however, no consensus has yet been reached concerning the cause of the EMC effect.Although the EMC effect is best known, the first hints of QCD effects in nuclei came from quasielastic electron scattering on nuclear targets [24][25][26]. The d...

Baryons as relativistic three-quark bound states

“…For example, the rainbow-ladder truncation becomes a vector-vector contact interaction and in the quark-diquark equation an additional static approximation for the exchange quark propagator is made. The NJL model was recently employed to calculate elastic nucleon and hyperon form factors [346,507], building upon a body of work on other structure properties such as parton distribution functions and nuclear medium effects; see also [508] and references therein. Closely related is the contactinteraction model developed in Refs.…”

Probing the low and high density nuclear matter by hadron scattering

“…In our opinion the differences between models and data are more than just an artifact of the phenomenological models and that the introduction of some new in-medium effects is really required (see also [1-3, 5, 6]). In conclusion, investigation at intermediate energy of such type "constitutes an important step for the future studies of baryons in high density matter with a strong magnetic field such as in a neutron star (or a magnetar), and in heavy ion collision experiment" [1][2][3].…”

“…Whether or not hadrons really change their properties in a nuclear medium, has been one of the longstanding problems in nuclear physics [1][2][3][4]. One of the essential assumption of long-familiar nuclear physics is that the protons and neutrons do not significantly change their properties and structure when they are in a nucleus.…”

“…As it is seen from figure 1, the structure of nucleons is modified inside the nuclear medium (in-medium effect) at density ρ ≥ 0.5ρ 0 , ρ 0 is normal nuclear matter density. Inclusion of such unconventional EMC-type effects draw greater attention in nuclear physics [1,2].…”

“…Such observations can direct to a some bridge between the investigations at intermediate and high energy. "This would represent a new paradigm for nuclear physics and help to build a bridge between QCD and nuclei " [1,2].…”