Octet baryon electromagnetic form factor double ratios $(G_E^\ast/G_M^\ast)/(G_E/G_M)$ in a nuclear medium

The ratios of the baryon electric ($G_E$) to magnetic ($G_M$) form factors, $G_E/G_M$, can provide us with important information on the structure of baryons in vacuum as demonstrated in recent studies for the proton and neutron systems. It has been argued that the corresponding in-medium ratios, $G_E^\ast/G_M^\ast$, can also provide useful information on the electromagnetic structure of baryons in a nuclear medium. Although the ratios may not be measured directly in experiments except for the proton at present, the double ratios $(G_E^\ast/G_M^\ast)/(G_E/G_M)$ can be directly related to the polarization-transfer measurements of bound baryons. In the present work we estimate, for the first time, the double ratios $(G_E^\ast/G_M^\ast)/(G_E/G_M)$ for all the members of octet baryons in symmetric nuclear matter in the range $Q^2=0$--3 GeV$^2$, where $Q^2=- q^2$ with $q$ being the four-momentum transfer.


I. INTRODUCTION
The issue of whether or not hadrons change their properties in a nuclear medium, has been one of the longstanding problems in nuclear physics [1][2][3]. Quantum chromodynamics (QCD) is established as the theory of strong interaction, and quarks and gluons are the degrees of freedom in the QCD Lagrangian. It is natural that in the strong mean fields which pervade nuclear matter, the motion of the quarks and gluons inside hadrons should be modified. Such changes are what is meant by the nuclear modification of hadron properties, and studying the effects is clearly central to the understanding of hadron properties in a nuclear medium within QCD.
In the last few decades new experimental methods have been proposed to probe the electromagnetic structure of baryons in a nuclear medium. The measurements made at JLab [4] and MAMI for polarization-transfer double ratio for a bound proton, which can be directly connected with the electromagnetic form factor (EMFF) double ratio (G * E /G * M )/(G E /G M ) [5][6][7][8][9], showed that the ratio is not unity, and imply the medium modifications of the bound proton electromagnetic form factors.
The results motivated further theoretical studies of the double ratios, not only for the proton but also the neutron, using different frameworks [13][14][15][16][17][18][19][20][21]. These studies predict a surprising fact that, while the double ratio for the proton is quenched, that for the neutron is enhanced in a nuclear medium [18][19][20]. Thus, one can suspect that the in-medium modifications of the electromagnetic form factors may be different for the charged and charge neutral particles. One of the important and interesting motivations of this study is, to explore systematically the medium modifications of the octet baryon electromagnetic form factors focusing on the differences between the charged and charge neutral baryons.
In high energy heavy-ion collisions and in the core of a neutron star and a compact star, the formation of baryon-nucleus bound states are less expected due to the disappearance of nuclei into nuclear, hadron, or quark matter. However, the matter produced in heavy-ion collisions and expected to exist in the core of neutron and compact stars, the medium effects that are similar to the system of the baryon-nucleus bound states may be produced. Thus, as a first step, we consider the situation that the octet baryons are immersed in symmetric nuclear matter, and study the medium effects on the electromagnetic form factors of them. Such a study may provide us with very important information for understanding better heavy-ion collisions, neutron stars and compact stars.
In the present work we estimate the EMFF double ratios of octet baryons in symmetric nuclear matter. In addition to the nucleons, we predict the double ratios of the charged baryons Σ + , Σ − , and Ξ − , as well as the charge neutral baryons Λ, Σ 0 , and Ξ 0 . We consider, in particular, nuclear matter densities ρ = 0 and 0.5ρ 0 , and ρ 0 , with ρ 0 = 0.15 fm −3 being the normal nuclear matter density. The present estimates are based on the model results in Ref. [19]. In this work however, we estimate directly the double ratios (G * E /G * M )/(G E /G M ) of octet baryons, since these quantity can possibly be compared with the polarization-transfer double ratio measurements, when the experimental technique advances in the future.
Our estimates are based on the combination of the covariant spectator quark model and the quark-meson coupling (QMC) model, extended in symmetric nuclear matter [19]. The free parameters of the covariant spectator quark model in vacuum are calibrated using lattice QCD EMFF data for the octet baryons avoiding the contamination from the meson cloud effects. The meson cloud contributions for the EMFFs are estimated based on an SU (6) symmetry for the meson-baryon couplings.
Since the meson cloud is expected to be dominated by the lightest meson, the pion, we reduce the calculations to the pion cloud contributions. The parameters associated with the pion cloud are fitted to the available physical data for the octet baryons including the nucleon EMFFs, octet baryon magnetic moments, and the electric and magnetic radii. The extension for symmetric nuclear matter is made based on the QMC model [2,14], taking into account the medium modifications of the relevant hadron masses and the pion-baryon coupling constants [19].
This article is organized as follows. In Sec. II, we introduce nomenclature associated with the octet baryon electromagnetic form factors in vacuum and in medium. In Sec. III, we discuss briefly the properties of the theoretical model used, and explain the model extension for symmetric nuclear matter. The results for the octet baryon EMFF double ratios are presented and analyzed in Sec. IV. Finally, we give outlook and conclusions in Sec. V.

II. ELECTROMAGNETIC FORM FACTORS IN VACUUM AND IN MEDIUM
The electromagnetic current for the interaction between an octet baryon B and a virtual photon with momentum q in vacuum, can be written as where M B is the baryon mass, Q 2 = −q 2 is the photon virtuality and, F 1B and F 2B are the Dirac and Pauli form factors, respectively. In Eq. (2.1) we represent the current in units e = √ 4πα, where α ≃ 1/137 is the electromagnetic fine structure constant. For simplicity, we omit the projection with the initial u B and finalū B Dirac spinors.
At Q 2 = 0 the baryon form factors are normalized as F 1B (0) = e B and F 2B (0) = κ B , where e B is the baryon charge in units of e, and κ B is the baryon anomalous magnetic moment in natural units e 2MB . An alternative representation of EMFFs for a spin 1/2 particle is the Sachs representation: the electric G EB and magnetic G MB form factors. These form factors are defined by [19]: Note that the expression for G MB includes the factor MN MB , where M N is the free nucleon mass, in order to convert to the nucleon natural units ( e 2MN ). If we omit the conversion factor MN MB , we have the usual relation, G MB = F 1B +F 2B in the baryon B natural units ( e 2MB ), and in the limit Q 2 = 0 we obtain the baryon magnetic moment µ B = G MB (0) e 2MB . To summarize, the inclusion of the extra factor MN MB in Eq. (2.3) is to convert G MB to the nucleon natural units, allowing a simpler comparison among the magnetic form factors of different baryons.
By assuming a spin 1/2 baryon B in a nuclear medium (nuclear matter) as a quasi-particle which has an effective mass (Lorentz scalar) and an effective vector potential or four-momentum (Lorentz vector) due to the medium effects satisfying the quasi-particle Dirac equation, we can also define the bound baryon B EMFFs in a nuclear medium [22] as F * 1B and F * 2B , respectively, corresponding to those in vacuum without the asterisk *. The Sachs form factors G * EB and G * MB in medium can also be obtained using the corresponding relations of Eqs. For convenience we use also e * B = F * 1B (0) and κ * B = F * 2B (0) to represent the charge and anomalous magnetic moments in medium, where e * B = e B . Note in particular that according to our convention, the in-medium magnetic form factor takes the form In this way, we represent the octet baryon in-medium magnetic form factors in natural units of the nucleon in vacuum, where M N is the free nucleon mass. For the magnetic moment of an octet baryon B in medium we use µ * B = G * MB (0) e 2MN . Since the effective baryon mass is expected to be smaller than that in vacuum (M * B < M B ), G * MB (Q 2 ) is expected to be enhanced in medium relative to that in vacuum. In particular, one has |µ * B | > |µ B |.

III. DESCRIPTION OF THE MODEL
We explain in this section briefly the properties of the model used in the present work. We start with the description of the model in vacuum, and in the end, discuss the extension to the nuclear medium.
The electromagnetic interaction of a baryon B with a photon, can be decomposed into the photon interaction with the valence quarks, and the photon interaction with the (bare baryon)-meson system. Since the pion is the lightest meson, we consider only the pion cloud effects as a first, reasonable approximation. Then, we decompose the electromagnrtic current into where J µ 0B stands for the electromagnetic interaction with the baryon core (valence quarks without pion cloud), and the remaining terms represent the interaction with the intermediate pion-baryon (πB) states, displayed in Fig. 1. In particular, J µ π represents the direct interaction with the pion [diagram (a)], and the J µ γB the interaction with the baryon while one pion is in the air [diagram (b)]. Z B is a normalization constant associated with the baryon B bare wave function. For more details, see Refs. [19,[23][24][25].

Valence quark contribution
The valence quark contributions for the octet baryon electromagnetic form factors are determined by the current J µ 0B based on the covariant spectator quark model in Refs. [19,23].
In the covariant spectator quark model the structure of the baryon wave functions is based on an SU (3) symmetry, which is broken by the quark masses, namely by the heavier strange quark mass. In the relativistic impulse approximation we can separate the degrees of freedom of the interaction-acting quark from the spectator quarkpair (diquark), and integrate into the internal degrees of freedom of the quark-pair to obtain an effective radial wave function [11,12,[26][27][28]. Then, the SU (3) symmetry breaking in the model is included at the level of the octet baryon radial wave functions approximated by an S-wave state of the quark-diquark system [19,23]. The octet baryon radial wave functions are characterized by the Hulthen form associated with the two momentum-range scales and depend also on the baryon mass (M B ) [11]. We consider a common long-range scale for all octet baryons, and a shorter-range scale associated with the number of strange quarks, namely, zero, one, or two [23,29]. Since we use different momentum-range scales for the different octet baryon families, we break the SU (3) symmetry at the level of the radial wave functions. Overall, one has four momentum-range scales for the octet baryon radial wave functions, and break the SU (3) symmetry. The SU (3) symmetry breaking effect has a strong impact on the baryon systems with two strange quarks.
The electromagnetic structure of the valence constituent quarks is described by effective quark form factors, which can be parametrized in terms of the vector meson dominance (VMD) mechanism.
For the flavor SU (2) sector, we represent the quark current based on the isoscalar (isovector) decomposition into an ω-meson (ρ-meson) associated term which parametrizes the long-range structure, and a term associated with a heavy effective meson (mass M h ) to simulate the short-range structure. In numerical calculation we approximate m ω ≃ m ρ , and fix M h as M h = 2M N (twice the nucleon mass).
For the strange quark, we replace the ρ-term (ππ channel) by a term associated with the φ meson (KK channel). One obtains in the end a quark current with five adjustable parameters, combined with three bare-quark anomalous magnetic moments, κ u , κ d and κ s . The five parameters were determined in the study of the nucleon physical EMFFs [11], and in the study of decuplet baryon EMFFs in lattice QCD [12]. The quark bare-anomalous magnetic moments are readjusted in the study of octet baryon EMFFs in Ref. [19].
The covariant spectator quark model can be extended to the lattice QCD regime. In this extension, we generalize the quark currents and the radial wave functions to the lattice QCD conditions, in general, characterized by the value of the pion mass. The extension to lattice QCD regime assumes that the effect of the meson cloud is suppressed for simulations with large pion masses and that only the effect of the valence quark is relevant.
In the extension to the lattice QCD regime, the radial wave function is determined using the baryon mass M B associated with the lattice QCD regime and the quark currents are determined using a VMD parametrization where the physical masses (M N , m ρ , m φ and M h = 2M N ) are replaced by the corresponding masses in the lattice QCD regime [30,31]. The parameters of the wave function and the parameters of the quark current are the same in the physical and in the lattice QCD regimes. The extension to lattice QCD regime was proved to be successful for the nucleon and ∆(1232) systems [30,31]. The method has been used in several studies of the octet and decuplet baryons in order to estimate the valence quark contributions for the EMFFs [12,19,23,32].
An important characteristic of the covariant spectator quark model is that, it breaks SU (2) symmetry in the u and d light-quark sector at the level of quark current. In the present model the strength of the isoscalar current is larger than that of the isovector compared with the other models [16,[33][34][35]. This isovector-isoscalar asymmetry has an impact on the results of the neutron electric form factor, and is responsible for the dominance of valence quark component in the neutron electric form factor [11,19].

Pion cloud contribution
The pion cloud contributions for the octet baryon EMFFs are estimated using an SU (3) symmetry-based model for the pion-baryon interaction parametrized by the constant α ≡ D/(D + F ) = 0.6 (SU (6) symmetrylimit value). We use the framework of Ref. [24], where all the couplings (πB, eB and κB) are determined by the SU (6) symmetry model, apart the six independent functions of Q 2 [19]. Those functions are parametrized in terms of five independent coefficients, and two cutoffs which regulate the falloff of the pion cloud contributions [19,23]. In the parametrizations we include a dependence on the pion mass in order to reproduce the leading order chiral behavior of the nucleon electromagnetic isovector square charge radii, corresponding to the Dirac and Pauli EMFFs [19].

Calibration of the model in vacuum
The parameters of the present model in vacuum are calibrated using lattice QCD EMFF data for the baryons p, n, Σ + , Σ 0 , Σ − and Ξ − [36]. Only for Λ and Ξ 0 there are no representative lattice QCD data 1 . In addition to the lattice QCD data, we use also physical data to constrain the model in vacuum, namely, EMFF data for p and n, the magnetic moments of octet baryons except for Σ 0 , which is unknown, and the electric square charge radii of p, n and Σ − as well as the magnetic square radii of p and n. The physical data are used to fix the parameters associated with the pion cloud, while the lattice data are used to fix the parameters associated with the valence quarks. The normalization constant Z B is determined by the combination of the bare and pion cloud components. Details of the model calibration can be found in Ref. [19].

Extension to the nuclear medium
As discussed already, for the extension of the model in vacuum for the nuclear medium, we assume that the proprieties of the octet baryons are modified in medium, and they are described by the modified Dirac equations for quasi-particles with the modified masses (M * B ), and the modified pion-baryon coupling constants (g * πBB ′ ). The medium modifications of the masses and the coupling constants versus nuclear matter density, are calculated by the QMC model [2].
The medium modifications of the valence quark contributions for the EMFFs are estimated as follows: the effects of masses M * B are included in the octet baryon radial wave functions Ψ B , and in the quark electromagnetic (EM) currents. In the extension of the quark EM currents to the nuclear medium, we take the advantage of the VMD parametrization in vacuum with the free masses m ρ (≃ m ω ), m φ and M h = 2M N , and in medium we re- 1 The lattice QCD simulations are more difficult to perform for charge neutral baryons, and thus have poorer statistics. For these reasons the neutral baryons are in general excluded from the simulations. In the present case there are results for n and Ξ 0 , although errors are large [36].
place these masses by the respective values in medium, m * ρ (≃ m * ω ), m * φ and M * h = 2M * N . Concerning the medium modification of the pion cloud contribution, it is performed taking into account the medium modification of the pion-baryon coupling constants g * πBB ′ . For estimating the in-medium pion-baryon coupling constants g * πBB ′ , we use Goldberger-Treiman relation, and an estimate of the in-medium pion decay constant f * π [19]. The numerical values for the in-medium baryon (M * B ) and meson masses, and coupling constants (g * πBB ′ ) used in the present work, can be found in Tables 3 and 4 in Ref. [19], respectively.

Properties of the model in medium
Before presenting the results for the G E /G M double ratios of octet baryons, it is important to review briefly the properties of the model derived and calibrated in Ref. [19]. This will help better to understand the results of double ratios presented in this article.
From the calibration of the model in vacuum [19], it is clear that the fit to the lattice data provides a good description for the N and Σ systems, but not so good for the Ξ systems. This may be the consequence of the SU (3) symmetry breaking, which has a stronger impact on the systems with two strange quarks.
It was also concluded that the calibration provided only a crude estimate of the quark core effect for the charge neutral baryons, since these systems are not well constrained by lattice QCD data, except for the neutron and the Ξ 0 . For the neutron, fortunately, there are physical data to be used. Nevertheless, the separation between the quark core and pion cloud contributions should be taken with care, particularly for G EB , whose magnitudes are in general small for charge neutral baryons, where the small pion cloud effects and residual quark core effects cannot be separated with a good precision. The estimates for the charge neutral baryons can in principle be improved with the explicit inclusion of the kaon cloud as well. Although the effect of the kaon cloud is expected to be smaller than that of the pion due to the large kaon mass, it may still be relevant in the cases when both the bare quark core and the pion cloud contributions are small.
Based on the SU (3) scheme applied in the present model, we conclude, in general, that the valence quark contribution is more than 80% of the total contribution for each octet baryon EMFFs in vacuum, as well as in medium [19]. The exceptions are the charge neutral baryons which deserve specific discussions.
In general we notice that the ratio G * E /G E decreases from the unity as Q 2 increases except for the charge neutral baryons, which means that the magnitudes of the electric form factors decrease in symmetric nuclear matter faster than those in vacuum in the low Q 2 region. [See Figs. 4,7,9 and 11 in Ref. [19] (but the effect is less  [19].] In vacuum as well as in-medium cases we have falloffs with Q 2 . The falloffs are faster for larger nuclear densities. In the region near Q 2 = 0, however, the magnitude of G * M /G M is, in general, determined by the valence quark contributions, which are dominated by the in-medium masses of the baryons. The expressions for the valence quark contributions for the in-medium magnetic form factor G * M at Q 2 = 0 are presented in Table I. We can notice in Table I  . These results are the consequence of our extension of the covariant spectator quark model to symmetric nuclear matter, based on a quark current which has the dependence of the quark anomalous magnetic moment (κ q ) in the form κ q /(2M * N ). Note that in the case of the nucleon we need to take into account only one term. One has then is less sensitive to the mass variations in medium. The magnetic form factors in larger densities (or smaller effective masses) are more enhanced than those in smaller densities.
Once discussed the properties of the model in medium, we can present our estimates for the octet baryon G E /G M double ratios for the nuclear matter densities 0.5ρ 0 and ρ 0 with ρ 0 = 0.15 fm −3 .

IV. OCTET BARYON EMFF DOUBLE RATIOS
We present here our estimates of the octet baryon electromagnetic form factor double ratios In the cases of proton and neutron, we have experimental data for the ratio G E /G M in vacuum [19]. The estimates for G E /G M in vacuum and in symmetric nuclear matter for these cases are presented in Fig. 2. The results for the vacuum (dotted line) are in agreement with the corresponding experimental data (see Ref. [19]). The results of the double ratios for the proton and neutron can be better understood when we know the results for the proton and neutron single ratios G E /G M in vacuum and in symmetric nuclear matter.
For the discussion in symmetric nuclear matter, it is important to recall that the magnetic form factors are converted into the units of nuclear magneton in vacuum, µ N = e 2MN . In the case of the nucleon the magnetic form factor near Q 2 = 0 can be expressed in the form  Table I). For the EMFFs of charge neutral baryons, it is also important to notice that, in the low-Q 2 region, the electric form factor of a baryon B can be expressed as G EB ≃ − 1 6 r 2 EB Q 2 , where r 2 EB is the electric charge square radius of the baryon B. Then, we can write in the low-Q 2 region, EB is the in-medium electric charge square radius.
Our results for the octet baryon double ratios are displayed in Figs. 3-6. We discuss separately each case in the following for proton, neutron, Σ ± and Ξ − , and the other charge neutral baryons (Λ, Σ 0 and Ξ 0 ).

Proton double ratios
We start our discussion with the proton double ratios displayed in the left panel of Fig. 3.  [19].
From the results of the single ratio G * E /G * M , the left panel of Fig. 2, one can see that the single ratio in vacuum (ρ = 0) decreases almost linearly with Q 2 (dotted line). A simple analysis of the result in vacuum for G E /G M can be made using the low-Q 2 expansion discussed in Ref. [18]: Ep and r 2 Mp are, respectively, the proton electric charge and magnetic dipole square radii in vacuum. This estimate also holds in symmetric nuclear matter by replacing the in-vacuum quantities by the corresponding in-medium quantities: µ * p , r * 2 Ep and r * 2 Mp . The nearly linear falloff with Q 2 in vacuum is the consequence of the small magnitude of the factor (r 2 Ep − r 2 Mp ), which means that the values of r 2 Ep and r 2 Mp are close. Although this analysis is only valid in the low-Q 2 region (say Q 2 < 1 GeV 2 ) [18], it is interesting to notice that the approximated linear dependence is observed also for large Q 2 in the present model. From Fig. 2, one can also conclude that the falloff increases with the nuclear matter density ρ, suggesting that (r * 2 Ep − r * 2 Mp ) increases also with the nuclear matter density ρ.
Looking now the double ratios, in the left panel of Fig. 3, we can see that the magnitudes at Q 2 = 0 are less than unity for both 0.5ρ 0 and ρ 0 . These results are essentially a consequence of the enhancement of the in-medium magnetic form factor, since The results for the proton double ratios indicate that the factor (r * 2 Ep −r * 2 Mp ) is enhanced in symmetric nuclear matter. As a consequence, the falloff of G * E /G * M increases in symmetric nuclear matter.
Our results for 0.5ρ 0 are similar to those in Ref. [20], for ρ = 0.4ρ 0 . However, our estimates for both 0.5ρ 0 and ρ 0 give slower falloff rates with Q 2 compared with the estimates based on the Nambu-Jona-Lasinio model in Ref. [18]. A relativistic light-front constituent quark model [33] predicts an almost constant double ratio. Other studies predict different Q 2 -dependence [14,16,33].

Neutron double ratios
We now discuss the results for the neutron double ratios presented in the right panel of Fig. 3. It is worth to recall that, although there is no experimental extraction for the neutron double ratio at the moment, the double ratio results are expected from the 2 H( e, e ′ n)p and 4 He( e, e ′ n) 3 He reactions in the near future [9,18,37].
The results for the neutron double ratios are also very interesting. Contrary to the case of the proton, the neutron double ratios increases in the region Q 2 < 2.8 GeV 2 . The medium effects enhance the neutron double ratios up to 7% for 0.5ρ 0 and 15% for ρ 0 near Q 2 = 0.3 GeV 2 , before starting to fall down slowly up to Q 2 ≃ 2.8 GeV 2 , where the double ratios become closer to the unity. Beyond the point Q 2 = 3 GeV 2 , the double ratios become smaller than unity (not shown in this article).
It is worth noticing that, in general, the amounts of increase in the neutron double ratios are smaller than those of the reduction in the proton double ratios for the corresponding nuclear densities. The important conclusion is that, contrary to the proton, the neutron double ratio  [18,20], although the shapes are different. The magnitude of the enhancement for the neutron double ratios is, in general, smaller than the estimates made in other studies with similar nuclear densities [18,20].
The significant difference between the double ratios of proton and neutron for a given density (0.5ρ 0 and ρ 0 ) can be understood by the different behaviors of G E /G M in vacuum as well as in medium. In the right panel of Fig. 2, we can see that the neutron single ratio G * E /G * M decreases monotonously with Q 2 starting from Q 2 = 0, the point G * E /G * M = 0, for the three densities. The differences among the different densities are the slops. The derivatives increase in absolute values with the density ρ. The common starting point (G * E /G * M = 0) is the consequence of G En ∝ r 2 En Q 2 , near Q 2 = 0. The slopes of G En and G * En can be estimated by r 2 En and r * 2 En , respectively. Those slopes have an important role in the double ratios 2 .
Since the neutron is a charge neutral baryon, the medium modification of G E can be estimated using the low-Q 2 relation:

En
. One can then reduce the analysis of the effects in medium to the study of the variation of the neutron electric charge square radius in symmetric nuclear matter. The enhancement (faster falloff) of the electric form factors in medium at low Q 2 can be understood by the increasing of the neutron electric charge square radius in symmetric nuclear matter. In this aspect the medium effect in the electric form factor GEn ≃ 1.16 for 0.5ρ 0 and G * En GEn ≃ 1.33 for ρ 0 . These results show that the electric charge square radius increases 16% for 0.5ρ 0 , and 33% for ρ 0 relative to that in vacuum. In both cases, we conclude that the neutron electric charge square radius is enhanced in symmetric nuclear matter. The enhancement increases as nuclear density increases.
Different from the proton case, one can conclude that to estimate the medium modifications of the neutron EMFF double ratio, it is not sufficient to take into account only the medium modification of the magnetic form factor. The medium modifications of G M are given by the factor (∝ MN The particular Q 2 -dependence obtained for the neutron EMFF double ratio (non linear shape) is a consequence of the properties of the model. Contrary to the analysis made in Ref. [18], which is restricted to the low-Q 2 region, our analysis cannot be exclusively restricted to the variables µ * B , r * 2 EB and r * 2 MB , since we take into account the medium modifications in a wider range of Q 2 .
As mentioned in Sec. III, the covariant spectator quark model breaks the SU (2) symmetry at the level of the quark EM currents. The main consequence is that the neutron form factors in vacuum are dominated by the valence quark contributions. In particular the valence quark contribution to G En is about 86% near Q 2 = 0. In the extension for the symmetric nuclear matter we still have a dominance of the valence quark contributions. Since the impact of the in-medium effects are different for the valence and for the pion cloud components, we obtain non-linear results for the neutron EMFF double ratios. In this aspect the present model differs from the usual other models in the literature, where the models for nucleons are based on an almost exact SU (2) symmetry [16,[33][34][35], We now focus on the Σ ± and Ξ − EMFF double ratios displayed in Figs. 4 and 5.
The results for the Σ + and Σ − EMFF double ratios shown in Fig. 4 are very similar, which may reflect the SU (3) symmetry. Our first note goes to the reduction in the magnitude of the single ratio G * E /G * M in symmetric nuclear matter compared to that in vacuum. The reduction increases with the nuclear density ρ.
The Q 2 -dependence of the Σ ± EMFF double ratios is very similar to the case of the proton except for the slower falloff. The reduction of the falloff for Σ ± with Q 2 , in comparison with the proton case, reflects the presence of strange quarks. It is expected that baryons containing more strange quarks have smaller medium modifications due to the small modifications in the baryon masses. The small modification in the baryon mass has a small impact on the baryon wave function as well as on the pion cloud contributions. The final effect is the reduction in the falloff of the double ratio with Q 2 . As in the proton case, the falloff increases with nuclear density.
The results of the Ξ − EMFF double ratios are presented in the left panel of Fig. 5. One can immediately notice that, contrary to the charged baryons discussed so far p, Σ + and Σ − , the double ratio increases with Q 2 , starting from values smaller than unity. The magnitude of the double ratio can be explained by observing that are partially canceled by the effects of the in-medium nucleon mass ∝ MN M * N for the two densities, which correspond to a 10% correction for 0.5ρ 0 , and a 20% for ρ 0 . Then the Ξ 0 double ratio can be estimated in a simple form, In the present model, these results are the consequence of the dominance of the valence quark contribution, since the pion cloud contribution is negligible for Ξ 0 (see Fig. 10 of Ref. [19]).
To summarize, our estimates of the Ξ 0 EMFF double ratios are based on the dominance of the valence quark contribution in both the electric and magnetic form factors. We then predict a significant enhancement of the double ratios in the nuclear medium, and a weak Q 2dependence.

V. OUTLOOK AND CONCLUSIONS
We have estimated, for the first time, the electromagnetic form factor double ratios, GE /GM , namely the inmedium electric to magnetic form factor ratio to that ratio in vacuum, for all the octet baryon members. The es-timates are based on the covariant spectator quark model plus an SU (3) symmetry-based parametrization for the pion cloud contributions. The extension of the model for symmetric nuclear matter is performed using the inmedium inputs for the octet baryons, ρ-and ω-meson effective masses calculated in the quark-meson coupling model, as well as the in-medium pion-baryon coupling constants obtained using the Goldberger-Treiman relation. The model parameters in vacuum are calibrated by the lattice QCD simulation data with large pion masses for the valence quark part, and by physical nucleon electromagnetic form factor data and octet baryon magnetic moments for the pion cloud part. Our estimates are covariant and are performed for a wide range of Q 2 , and not restricted to the low-Q 2 region.
One of our main interests are originated from the different behaviors of the electromagnetic form factor double ratios for the proton and neutron, which, so far, only a few studies have been made. While the double ratio of the proton decreases with Q 2 as was observed in the JLab experiments, that for the neutron is predicted to increase in medium in the low and intermediate Q 2 region (Q 2 < 2.8 GeV 2 ). This prediction can be tested in the near future with the advanced polarization-transfer experiment, or the developments of other new experimental methods.
The first estimates for the neutron electromagnetic form factor double ratio has motivated us to study the double ratios of the charge neutral particles in the octet baryon members. Our present estimates suggest that, contrary to the case of the neutron double ratio, those of the Λ and Σ 0 are suppressed in medium in the low-Q 2 region. On the other hand, for larger Q 2 region, we expect the enhancement of the double ratios for Λ and Σ 0 .
For the electromagnetic form factor double ratios of the charged particles Σ − and Σ + , we predict that they are quenched, and become less than the unity as in the case of the proton. The Q 2 -dependence is weaker than the case of the proton, mainly because, the systems with strange quarks are less affected by medium modifications.
As for the Ξ − and Ξ 0 baryons containing two strange quarks, we conclude that the electromagnetic form factor double ratios have a weaker Q 2 -dependence compared with those of the baryons containing a smaller number of strange quarks, although, we admit that our estimates for the Ξ − and Ξ 0 are less precise.
The medium effects, as the ones estimated by the present study, have an important impact on the baryons immersed in a nuclear medium, such as in heavy ion collisions, and in the core of a neutron star and a compact star. In order to better understand those effects the measurement of octet baryon electromagnetic form factor double ratios are very important in order to test and constrain our theoretical estimates. At the moment, the measurement of the electromagnetic form factor double ratios are restricted to the case of the proton based on the polarization-transfer method, although the results for the neutron are expected in the near future. There is then some hope that the polarization-transfer method or new methods can be used to directly extract the in-medium modifications of the octet baryon electromagnetic form factors.