In-medium electromagnetic form factors of pseudoscalar mesons from the quark model

Ahmad Jafar Arifi; Kazuo Tsushima; Parada T. P. Hutauruk

REVIEW 2 major objections 5 minor 2 cited by

In-medium electromagnetic form factors of pseudoscalar mesons from the quark model

T0 review · 2 major / 5 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read Meson charge radii grow with nuclear density, fastest for pions.

desk verdict New heavy-light in-medium form factor predictions with a honestly stated but load-bearing constant-beta assumption; worth a serious referee. read the letter →

arxiv 2412.09883 v2 pith:Q7ALIQAB submitted 2024-12-13 hep-ph nucl-th

Ahmad Jafar Arifi , Parada T. P. Hutauruk , Kazuo Tsushima This is my paper · ORCID

classification hep-phnucl-th

keywords in-mediumformfactorslight-frontquarkmodelquark-mesoncouplingchargeradiipseudoscalarmesonssymmetricnuclearmatterheavy-lightpionandkaon

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper predicts how the electromagnetic form factors of pseudoscalar mesons change when the meson sits in symmetric nuclear matter, using a light-front quark model fed by quark-meson coupling model mean fields. It claims that with rising density the form factors of charged mesons fall off faster with momentum transfer, neutral meson form factors rise, and the absolute charge radius of every meson grows. The growth rate is flavor dependent: pions change most, charged D mesons least, kaons and B mesons at nearly the same rate. The authors argue the medium acts mainly on light quarks, leaving heavy-quark contributions almost untouched, which gives a clean quark-level signature of nuclear medium effects.

What carries the argument

The engine is a light-front quark model (a constituent-quark description of mesons as quark-antiquark bound states on a fixed light-front plane) with a Gaussian radial wave function of width $\beta_{q\bar q}$, combined with the quark-meson coupling model (a relativistic mean-field description in which nuclear scalar and vector fields act on light quarks). The scalar mean field reduces the light-quark mass to $m_q^*$, and the vector mean field shifts quark energies and the longitudinal momentum variable $x$ to $\tilde{x}^*$; the vector shift cancels for equal-mass $q\bar q$ pairs and does not affect heavy quarks. The form factor is a convolution of initial and final wave functions with the shifted variables, and its slope at $Q^2=0$ yields the charge radius. The paper keeps $\beta_{q\bar q}$ fixed at its free-space value, so the entire density dependence enters through the quark mass and energy shifts.

What would settle it

Measure the pion charge radius in nuclear matter at saturation density, for example through the energy shifts of deeply bound pionic atoms or electron scattering on nuclei: the central claim predicts $r_\pi^2 \simeq 0.897$ fm$^2$ at $\rho_0$, and a measured value close to the free-space $0.427(10)$ fm$^2$ would falsify it.

Watch

Extended reading notes

Core claim

The paper's central claim is that the in-medium modifications of the spacelike electromagnetic form factors are controlled by the light-quark sector. In symmetric nuclear matter the light quark acquires an effective mass $m_q^*$ smaller than its free value, and this alone makes the form factor of a charged meson drop more steeply with $Q^2$ as the density rises, while a neutral meson's form factor rises with density. The corresponding absolute charge radii therefore increase with density: at saturation density the pion radius squared reaches $0.897$ fm$^2$ against $0.427(10)$ fm$^2$ in free space, and the kaon reaches $0.697$ fm$^2$. The flavor decomposition shows the heavy-quark ($s$, $c$, $b$) contribution is nearly density independent, so the ordering of radii and the charged-versus-neutral asymmetry are carried by the light quark.

Load-bearing premise

The load-bearing assumption is that the Gaussian width $\beta_{q\bar q}$ of the meson wave function is unchanged in the medium; if the medium alters that transverse size, the predicted growth of the charge radii and its flavor ordering could change.

Editorial extensions

If this is right

At saturation density the pion's charge radius squared is about 1.45 times its free-space value, so measurements of pionic atoms or electron scattering on nuclei could see a clearly inflated pion in matter.
The charged-versus-neutral asymmetry (faster fall-off for charged, rising form factor for neutral kaons and D mesons) offers a distinctive experimental signature that does not depend on the overall normalization.
Because heavy-quark form factors are nearly unchanged, observables built from heavy-light mesons in nuclei isolate the light-quark medium response.
Medium effects fade at higher $Q^2$, so upcoming electron scattering measurements should target the low-$Q^2$ region to test these predictions.
The nearly identical growth of kaon and B-meson radii, despite very different quark masses, is a parameter-free feature of the model that a measurement could confirm or rule out.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

Our inference: the constant-$\beta_{q\bar q}$ assumption is the main lever; if the medium changes the transverse size of the wave function, the direction of the radius change could survive but the flavor ordering and the kaon-B coincidence could shift.
Our inference: applying the same machinery to distribution amplitudes or generalized parton distributions would predict that medium effects concentrate in the light-quark partonic content, linking these radius changes to nuclear partonic modifications.
Our inference: because the model's pion decay constant turns negative above $1.5\rho_0$, the density trend beyond that point is not trustworthy; testing the trend would require a model that stabilizes the decay constant.
Our inference: a finite-density lattice calculation of the neutral kaon form factor, once the sign problem is bypassed, would be a sharp check, since the predicted increase with density is opposite to naive screening intuition.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Put it on the pile. The genuinely new content is the in-medium D and B meson electromagnetic form factors and the flavor decomposition showing medium effects sit almost entirely in the light quark sector. The free-space form factors are anchored to data and lattice results, the QMC sector reproduces saturation, and the authors state their main caveats up front: beta held fixed, densities capped at 1.5 rho0, no error bars. That is honest work, not a dressed-up fit.

The paper extends the earlier Arifi-Hutauruk-Tsushima framework to heavy-light mesons, so the novelty is real but incremental for the pion and kaon, which already show similar trends in NJL and BSA-LFQM papers. The heavy-light results are what is new.

The soft spots are what the reader flagged. The constant-beta assumption is explicitly stated, and it is load-bearing because the charge radius slope scales roughly as 1/beta^2. The authors justify it by saying beta is a short-distance scale, but the QMC model itself allows bag radii and effective masses to move with density, so freezing the transverse width is a choice, not a derivation. A density-dependent beta could shift the magnitudes in Table IV by the same order as the predicted 50-100% increases, and flavor-dependent changes could reorder the pion/kaon/B pattern. That does not kill the qualitative claim that charge radii grow with density—the effective light-quark mass dropping pushes that direction in every variant—but it does mean the quantitative table is not secured. The pion decay constant turning negative above 1.5 rho0 is an honest limitation, and the authors point to the BSA treatment for higher densities. The difference from the BSA pion EMFF is noted but not resolved; the reader should know the in-medium pion result is treatment-sensitive.

One more thing: the paper averages over K+ and K- and takes absolute values to cancel the vector potential. That is a modelling choice that hides the vector-potential dependence except in the radius differences in Fig. 9. It is presented clearly, so no foul, but it means the 'unified' in-medium radii are scalar-only quantities.

Bottom line: this deserves a serious referee. The calculation is transparent, the limitations are stated, the heavy-light predictions are new, and the qualitative medium trend is robust even if the quantitative slope is not. A referee should push for a sensitivity study on beta and for error estimates, but this is not a desk reject. I would bring it to reading group and probably cite the heavy-light tables.

Referee Report

2 major / 5 minor

Summary. This paper combines the light-front quark model (LFQM) with the quark-meson coupling (QMC) model to compute the spacelike electromagnetic form factors (EMFFs) and charge radii of the pion, kaon, D mesons, and B mesons in symmetric nuclear matter. The LFQM parameters are fixed to free-space meson observables and the QMC parameters are fixed to nuclear saturation properties. The authors find that with increasing nuclear density the charged-meson EMFFs fall faster with Q^2, the neutral-meson EMFFs rise, and the absolute values of the charge radii increase, with the rate depending on the quark flavor content. They also decompose the EMFFs into light- and heavy-quark sector contributions and conclude that the medium affects mainly the light-quark sector. The calculation is restricted to densities up to 1.5 rho0 because the pion decay constant becomes negative at higher densities, and the Gaussian width beta is assumed to be density independent.

Significance. If the quantitative predictions are robust, this is a useful model study of in-medium hadron structure in a regime where lattice QCD is not directly applicable and where JLab 12 GeV and EIC programs may eventually provide constraints. The paper has clear strengths: the free-space EMFFs are benchmarked against experimental and lattice data, the quark-flavor decomposition is systematic, and the main assumptions and limitations are stated explicitly. However, the central quantitative content is the density dependence of the charge-radii slope near Q^2=0, and this content is controlled by an assumption that is not yet tested in the manuscript. The conclusions should therefore be regarded as conditional until the sensitivity to that assumption is quantified.

major comments (2)

[Sec. III B, Eqs. (56), (59), Table IV, Fig. 9] The Gaussians width beta_{q qbar} in Eq. (7) controls the transverse size of the meson wave function and therefore the slope of the EMFF at Q^2=0, i.e., the charge radius in Eq. (48). In the in-medium calculation the authors modify the effective light-quark mass m*_q and the vector-potential shifts, but keep beta fixed, stating in Sec. III B that "for simplicity, we assume it to be constant in the present work." No sensitivity estimate is given. Since |<r^2>| scales approximately as 1/beta^2, a density-dependent change of beta of only 10% changes the predicted radius by about 20%, which is the same order as the reported 50-100% increases at rho=rho0 in Table IV. A flavor-dependent beta* could also alter the claimed ordering, for example the near equality of the K and B meson radii. I ask the authors to add a sensitivity analysis, for example by varying beta by plausible amounts or by estimating beta* from the QMC bag radius or the in-medium meson mass, and to state explicitly which conclusions survive.
[Sec. III B, Eqs. (54), (57), (59), and text after Eq. (59)] The definitions of the plus-momentum variables are ambiguous. Equation (51) defines p*0_i as the in-medium energy including the vector potential, while Eq. (54) adds V_qomega to p*+_q, and Eq. (57) does the same in the numerator of the shifted variable. The text after Eq. (59) states that in the meson rest frame P*+ = M*, which appears inconsistent with Eq. (52), where P*0 = E*_M +/- V_qomega for q Qbar and Q qbar systems. If p*+_q and P*+ already contain the vector potential, the shifts in Eqs. (54) and (57) double-count it; if they do not, this should be stated explicitly. Because the individual K+ and K- radii and the vector-potential-induced splitting shown in Fig. 9 depend on these shifts, the derivation should be clarified before the individual-meson results can be assessed.

minor comments (5)

[Sec. IV B] The text says the pion charge radius increases to approximately 1.45 times its free-space value, with <r*2_pi> = 0.897 fm^2 at rho=rho0. This factor refers to the radius sqrt(<r^2>), not to <r^2> itself, whose ratio is about 2.1; please phrase this as sqrt(<r*2>) to avoid confusion.
[Sec. IV C and Figs. 5, 7] The text refers to the quark-sector curves as "blue line" and "red line," while the figure legends and captions use orange and green; please make the color references consistent.
[Sec. III B] The in-medium meson masses M* from Ref. [58] enter P*+ and the light-front variable in Eqs. (52) and (57), but the present paper does not tabulate their density dependence. A short table or a reminder of the relevant values would improve reproducibility.
[Sec. IV B] The authors note that the calculation is limited to rho <= 1.5 rho0 because the pion decay constant may become negative at higher densities. It would be helpful to state how close the 1.5 rho0 results are to that breakdown, so that the reader knows whether the highest-density predictions are already in a regime where the model is strained.
[References] Reference [25] appears incomplete: it lists the journal and article number but no year or volume; please complete the entry.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: in-medium EMFFs and charge radii are genuine hybrid-model predictions, not re-fitted inputs.

full rationale

The paper's derivation chain is self-contained against its own inputs. Free-space LFQM parameters (quark masses and Gaussian widths beta) are fitted to free-space meson observables (masses, decay constants, charge radii) as in Ref. [26], and QMC parameters are fitted to nuclear saturation properties. The in-medium EMFFs in Eqs. (56) and (59) then use only the QMC-generated in-medium light-quark mass m_q^* = m_q - V_q^sigma, with beta held constant by an explicitly stated assumption (Sec. III B: 'for simplicity, we assume it to be constant'). The predicted density dependence of the charge radii (Table IV and Fig. 9) follows from Eq. (48) applied to the computed form factors; no parameter is fitted to in-medium EMFF or radius data. The self-citations, especially to Ref. [58] for the in-medium momentum-fraction shift, are not load-bearing because the governing equations are reproduced in the present paper. The constancy of beta is a modeling assumption that could affect quantitative robustness, but it is a stated approximation, not a circular reduction of the predicted quantity to a fitted one. The consistency checks against free-space experimental and lattice data further confirm that the model is not tuned to the target in-medium results.

Assumptions & free parameters 4 free parameters · 8 assumptions · 0 invented entities

The calculation inherits a large set of fitted parameters from the LFQM and QMC models and several modeling assumptions, including the Gaussian wave function, a medium-independent beta, and the mean-field treatment. No new particles, forces, or dimensions are introduced.

free parameters (4)

Constituent quark masses m_q, m_s, m_c, m_b = 0.22, 0.45, 1.80, 5.20 GeV (Table I)
Control the LFWF and the in-medium effective light-quark mass m_q^*; taken from fits to meson spectra and decay constants in Ref. [26].
Gaussian scale parameters beta_{q\bar q}, beta_{q\bar s}, beta_{q\bar c}, beta_{q\bar b} = 0.3659, 0.3886, 0.4679, 0.5266 GeV (Table I)
Set the transverse size of the meson wave function and therefore the charge radii and EMFF slopes; fitted in free space.
MIT bag parameters B^{1/4}, Z_N, x_q, S_N(0) = 148 MeV, 4.327, 2.368, 0.609 (Table II)
QMC inputs that determine m_q^* and the scalar polarizability; fixed by requiring free nucleon mass 939 MeV and bag radius 0.8 fm.
QMC coupling constants g_{N sigma}^2/(4 pi), g_{N omega}^2/(4 pi) = 6.40, 7.57 (Table III)
Fit the saturation binding energy -15.7 MeV at rho0 = 0.15 fm^-3; they set the mean-field potentials V_q^sigma and V_q^omega that drive the in-medium effects.

assumptions (8)

domain assumption The Gaussian LFWF (Eq. 7) is a valid phenomenological representation of the ground-state meson wave function.
No derivation from QCD; beta is fitted, and the choice of Gaussian form affects the Q^2 dependence of form factors.
domain assumption The Bakamjian-Thomas construction preserves Poincare invariance and frame independence.
Used to build meson states in Sec. II A; underpins the light-front calculation but is not proven in this paper.
domain assumption The EMFF is computed in the impulse approximation with only the plus current and helicity-nonflip contributions.
Standard LFQM simplification in Eqs. (45) and (46); other current components may require additional Lorentz structure, as the authors note from Ref. [67].
domain assumption The sigma mean field couples only to light u and d quarks; s, c, and b quarks are unaffected in medium.
Core QMC premise in Eqs. (29) to (31); it produces the key result that heavy-quark form factors are nearly unchanged.
ad hoc to paper The Gaussian width beta_{q\bar q} is unchanged in the nuclear medium.
Stated in Sec. III B as a simplicity assumption; if beta changed with density, the charge radius predictions would shift.
domain assumption The vector potential V_q^omega has the same magnitude for every meson containing one light quark or antiquark.
Adopted in Sec. III B from QMC; used in the unequal-mass meson formulas and the K plus versus K minus radius splitting.
domain assumption Relativistic mean-field approximation: meson field operators are replaced by their constant mean-field values.
Sec. II B.1, standard QMC treatment; neglects quantum fluctuations of the sigma and omega fields.
domain assumption The in-medium LFWF is normalized with the same condition as Eq. (10) so that quark-sector form factors remain F_i^*(0) = 1.
Required for charge conservation; the paper does not explicitly show the in-medium normalization, but Eqs. (56) and (59) imply it.

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Cite this review

Pith. "Pith review of In-medium electromagnetic form factors of pseudoscalar mesons from the quark model." pith.science (2026). https://pith.science/paper/Q7ALIQAB

@misc{pith2026241209883,
  author       = {Pith},
  title        = {Pith review of: In-medium electromagnetic form factors of pseudoscalar mesons from the quark model},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/Q7ALIQAB}},
  note         = {Machine review of arXiv:2412.09883}
}

read the original abstract

We explore the modifications of hadron structure in a nuclear medium, focusing on the spacelike electromagnetic form factors (EMFFs) of light and heavy-light pseudoscalar mesons. By combining the light-front quark model (LFQM) with the quark-meson coupling (QMC) model, which reasonably reproduces EMFFs in free space and the saturation properties of nuclear matter, respectively, we systematically analyze the in-medium EMFFs and charge radii of mesons with various quark flavors. Our findings show that the EMFFs of charged (neutral) mesons exhibit a faster fall-off (increase) with increasing four-momentum transfer squared and nuclear density. Consequently, the absolute value of the charge radii of mesons increases with nuclear density, where the rate of increase depends on their quark flavor contents. We observe that the EMFFs of pions and kaons undergo significant modifications in the nuclear medium, while heavy-light mesons are only slightly modified. By decomposing the quark flavor contributions to EMFFs, we show that the medium effects primarily impact the light-quark sector, leaving the heavy-quark sector nearly unaffected. The results of this study further suggest the importance of the medium effects at the quark level.

Figures

Figures reproduced from arXiv: 2412.09883 by the authors.

**Figure 2.** FIG. 2. Density dependence of the scalar (blue dashed [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗

**Figure 3.** FIG. 3. In-medium EMFFs of the pion (upper panel) and [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗

Figures from the paper (4 more)

**Figure 4.** Figure 4: FIG. 4. In-medium EMFFs of the charged kaon (upper [PITH_FULL_IMAGE:figures/full_fig_p009_4.png]

**Figure 6.** Figure 6: FIG. 6. In-medium EMFFs of the neutral kaon (upper panel) [PITH_FULL_IMAGE:figures/full_fig_p010_6.png]

**Figure 8.** Figure 8: FIG. 8. In-medium EMFFs of the charged and neutral [PITH_FULL_IMAGE:figures/full_fig_p012_8.png]

**Figure 9.** Figure 9: FIG. 9. Density dependence of the charge radii for mesons [PITH_FULL_IMAGE:figures/full_fig_p013_9.png]

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Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Valence quark properties of charged kaons in symmetric nuclear matter
hep-ph 2025-05 conditional novelty 4.0 of 10

Charged kaon valence-quark TMDs and GPDs are computed with the light-cone quark model using in-medium quark masses from the chiral SU(3) quark mean field model, producing density-dependent form factors and charge radii.
Effect of nuclear medium on the spatial distribution of pions
hep-ph 2025-01 conditional novelty 4.0 of 10

Using a light-cone quark model fed with chiral mean-field quark masses, the authors compute pion GPDs and find the pion charge radius increases with nuclear density.

Reference graph

Works this paper leans on

90 extracted references · 72 canonical work pages · cited by 2 Pith papers

[1]

Relativistic mean-field approximation The effective Lagrangian density for the symmetric nu- clear matter at the hadronic level is given by [8, 69–71] LQMC = Lnucleon + Lmeson + Lint, (11) with each component defined as follows Lnucleon = ¯ψ[i /∂ − mN ]ψ, (12) Lmeson = 1 2 (∂µ ˆσ∂ µ ˆσ − m2 σ ˆσ2) − 1 2 ∂µ ˆων(∂µ ˆων − ∂ν ˆωµ) − m2 ω ˆωµ ˆωµ , (13) where ...
[2]

This is done by using the MIT Bag model for hadrons, and solving the Dirac equations for the quarks and antiquarks in the presence of meson mean fields in nuclear matter

MIT bag model In the standard QMC model [8, 56, 70, 71], the nucleon-meson couplings are derived from the quark- meson couplings. This is done by using the MIT Bag model for hadrons, and solving the Dirac equations for the quarks and antiquarks in the presence of meson mean fields in nuclear matter. The meson potentials are given by Vqσ = gqσ σ, V qω = gq...
[3]

The in-medium effective mass of light quarks, mod- ified by the scalar σ mean-field
[4]

The in-medium energy of light quarks, modified by the vector potential. Note that the Gaussian parameter βq ¯q may be modified in the medium; however, for simplicity, we assume it to be constant in the present work, as it is expected to re- main and not largely changed in the medium because it is associated with the short-range scale of the meson wave fun...
[5]

In this new definition, the longitudinal momentum x is shifted due to the differ- ence between ( p+ q , P+) and ( p∗+ q , P∗+) when computing the form factor in the medium

Equal quark mass case For the q ¯q mesons, the longitudinal momentum of the quark (antiquark) is modified by the vector potential +Vqω (−Vqω), with the new definition of the “quark” lon- gitudinal momentum given by [58] x → ˜x∗ = p∗+ q + Vqω P ∗+ = x∗ + Vqω P ∗+ , (54) The vector potentials for the quark and antiquark cancel out in the case of the q ¯q me...
[6]

Unequal quark mass case For the q ¯Q and Q¯q mesons, the scalar and vector po- tentials affect both the meson four-momenta. The lon- gitudinal momenta of the quark and antiquark in the 7 medium are given by x →    ˜x∗ = p∗+ q + Vqω P ∗+ + Vqω = x∗ + Vqω /P ∗+ (1 + Vqω /P ∗+) for (q ¯Q), ˜x∗ = p∗+ q − Vqω P ∗+ − Vqω = x∗ − Vqω /P ∗+ (1 − Vqω /P ...
[7]

As shown in the inset of the up- per panel, the model agrees well with the lattice data in the low- Q2 region, though some discrepancies persist at higher Q2

Charged kaon Figure 4 presents the results for the K ± EMFFs along- side the older experimental data [80] and recent lattice QCD results [46]. As shown in the inset of the up- per panel, the model agrees well with the lattice data in the low- Q2 region, though some discrepancies persist at higher Q2. We also found that the in-medium kaon EMFFs decrease wi...
[8]

Neutral Kaon Besides computing the K ± EMFFs, we also compute the K 0 EMFFs in the nuclear medium as a function of the Q2 for a few different nuclear densities as shown in Fig. 6. The upper panel of Fig. 6 shows that the totalK 0 EMFFs increase as the density increases, which is different from what we found in the K ± EMFFs. A similar indication is found ...

2023

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Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.

[1] [1]

Relativistic mean-field approximation The effective Lagrangian density for the symmetric nu- clear matter at the hadronic level is given by [8, 69–71] LQMC = Lnucleon + Lmeson + Lint, (11) with each component defined as follows Lnucleon = ¯ψ[i /∂ − mN ]ψ, (12) Lmeson = 1 2 (∂µ ˆσ∂ µ ˆσ − m2 σ ˆσ2) − 1 2 ∂µ ˆων(∂µ ˆων − ∂ν ˆωµ) − m2 ω ˆωµ ˆωµ , (13) where ...

[2] [2]

This is done by using the MIT Bag model for hadrons, and solving the Dirac equations for the quarks and antiquarks in the presence of meson mean fields in nuclear matter

MIT bag model In the standard QMC model [8, 56, 70, 71], the nucleon-meson couplings are derived from the quark- meson couplings. This is done by using the MIT Bag model for hadrons, and solving the Dirac equations for the quarks and antiquarks in the presence of meson mean fields in nuclear matter. The meson potentials are given by Vqσ = gqσ σ, V qω = gq...

[3] [3]

The in-medium effective mass of light quarks, mod- ified by the scalar σ mean-field

[4] [4]

The in-medium energy of light quarks, modified by the vector potential. Note that the Gaussian parameter βq ¯q may be modified in the medium; however, for simplicity, we assume it to be constant in the present work, as it is expected to re- main and not largely changed in the medium because it is associated with the short-range scale of the meson wave fun...

[5] [5]

In this new definition, the longitudinal momentum x is shifted due to the differ- ence between ( p+ q , P+) and ( p∗+ q , P∗+) when computing the form factor in the medium

Equal quark mass case For the q ¯q mesons, the longitudinal momentum of the quark (antiquark) is modified by the vector potential +Vqω (−Vqω), with the new definition of the “quark” lon- gitudinal momentum given by [58] x → ˜x∗ = p∗+ q + Vqω P ∗+ = x∗ + Vqω P ∗+ , (54) The vector potentials for the quark and antiquark cancel out in the case of the q ¯q me...

[6] [6]

Unequal quark mass case For the q ¯Q and Q¯q mesons, the scalar and vector po- tentials affect both the meson four-momenta. The lon- gitudinal momenta of the quark and antiquark in the 7 medium are given by x →    ˜x∗ = p∗+ q + Vqω P ∗+ + Vqω = x∗ + Vqω /P ∗+ (1 + Vqω /P ∗+) for (q ¯Q), ˜x∗ = p∗+ q − Vqω P ∗+ − Vqω = x∗ − Vqω /P ∗+ (1 − Vqω /P ...

[7] [7]

As shown in the inset of the up- per panel, the model agrees well with the lattice data in the low- Q2 region, though some discrepancies persist at higher Q2

Charged kaon Figure 4 presents the results for the K ± EMFFs along- side the older experimental data [80] and recent lattice QCD results [46]. As shown in the inset of the up- per panel, the model agrees well with the lattice data in the low- Q2 region, though some discrepancies persist at higher Q2. We also found that the in-medium kaon EMFFs decrease wi...

[8] [8]

Neutral Kaon Besides computing the K ± EMFFs, we also compute the K 0 EMFFs in the nuclear medium as a function of the Q2 for a few different nuclear densities as shown in Fig. 6. The upper panel of Fig. 6 shows that the totalK 0 EMFFs increase as the density increases, which is different from what we found in the K ± EMFFs. A similar indication is found ...

2023