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Resonance parameters of the vector charmoniumlike state $G(3900)$

T0 review · 4 major / 4 minor · reviewed 2026-08-16 · deepseek-v4-flash

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Pith's one-line read This paper claims that the broad G(3900) bump seen in $e^+e^-\to D\bar D$ is a P-wave dynamically generated state of the $(D,D^*)$ meson doublet, not an ordinary charmonium, and supports that claim with a global coupled-channel fit.

desk verdict Solid coupled-channel case for G(3900) as a dynamically generated P-wave molecule, with a useful pole-trajectory diagnostic; the quantitative pole is regulator-dependent and needs a sensitivity study before it is quoted. read the letter →

arxiv 2504.17431 v3 pith:CI2OHI5M submitted 2025-04-24 hep-ph

Quanxing Ye , Zhenyu Zhang , Meng-Lin Du , Ulf-G. Mei{ss}ner , Peng-Yu Niu , Qian Wang This is my paper · ORCID
classification hep-ph
keywords G(3900)dynamicallygeneratedstateP-wavehadronicmoleculeheavyquarkspinsymmetryLippmann-Schwingerequationcharmoniumlikestateselectron-positronannihilationopencharmmesonpairs
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

The paper analyzes the most precise electron-positron annihilation cross sections into open-charm meson pairs in the energy region 3.7 to 4.25 GeV and asks what the bump called G(3900) actually is. Its answer is that the bump is a P-wave state generated dynamically by the rescattering of $D$ and $D^*$ mesons, rather than a conventional quark-antiquark charmonium state or a mere threshold artifact. The evidence comes from a global fit whose scattering amplitudes, obtained by solving the Lippmann-Schwinger equation, contain a pole near 3.9 GeV in two different model settings, one with three and one with two bare charmonia. If the claim is right, G(3900) joins the family of hadronic molecules formed from charmed meson pairs, and the same dynamics predicts exotic $1^{-+}$ partners that could be searched for in radiative electron-positron processes.

What carries the argument

The engine of the argument is a separable $P$-wave contact interaction between the $(D,D^*)$ doublet and its antiparticle, built in the heavy quark spin symmetry limit and decomposed into SU(3) flavor singlet, octet, and isospin-triplet channels. This interaction feeds a Lippmann-Schwinger equation with twelve open-charmed channels and either two or three bare vector charmonia, regulated by a Gaussian form factor with cutoff $\Lambda=0.50$ GeV. The decisive diagnostic is the pole-trajectory plot: each pole of the $T$-matrix is followed as the bare charmonium couplings are gradually reduced to zero, so that poles that remain stationary are identified as dynamically generated while poles that migrate to the bare mass are identified as renormalized charmonia.

What would settle it

Repeat the coupled-channel fit with a different regulator, for example varying $\Lambda$ from 0.4 to 0.6 GeV or using a sharp cutoff, and check whether a pole near 3830 to 3890 MeV persists on the relevant unphysical Riemann sheet; if it disappears or moves to one of the bare charmonium masses, the claim that G(3900) is dynamically generated fails.

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Extended reading notes

Core claim

The central claim is that G(3900) is a dynamically generated P-wave state of the $(D,D^*)$ heavy-quark-spin doublet and its antiparticle. When the scattering amplitudes for $e^+e^-\to D\bar D$, $e^+e^-\to D\bar D^*+\text{c.c.}$, and $e^+e^-\to D^*\bar D^*$ are fitted globally, a pole near 3.9 GeV appears regardless of whether three bare charmonia ($\psi(1D)$, $\psi(3S)$, $\psi(2D)$) or only two are included. Pole-trajectory analysis shows that this pole stays essentially fixed as the charmonium couplings are switched off, which is the paper's criterion for a dynamically generated state, whereas the ordinary charmonium poles move back to their bare masses. The paper reports a candidate pole at roughly $3832.6-74.5i$ MeV in Model I and $3883.9-46.5i$ MeV in Model II, and it argues that the Model II result is the more reliable one because Model I shows signs of overfitting.

Load-bearing premise

The classification leans on a single Gaussian cutoff of 0.50 GeV standing in for all omitted higher-order effects; the paper itself concedes that without the omitted counterterms the description of the data relies on that cutoff, so if the near-3.9 GeV pole vanishes or moves to a charmonium mass under a different regulator, the claim would lose its support.

Editorial extensions

If this is right

  • The broad structure near 3.9 GeV should be classified as a $P$-wave $D\bar D^*/\bar D D^*$ hadronic molecule rather than a missing charmonium state, so searches for a conventional charmonium assignment there are unnecessary.
  • Two bare charmonia, $\psi(1D)$ and $\psi(3S)$, are sufficient to describe the data in the energy region considered; the additional $\psi(2D)$ in Model I is redundant and its fitted pole has no physical significance.
  • Within this framework the $\psi(4040)$ pole is also dynamically generated, with its bare input shifted to a higher pole around 4.23 to 4.28 GeV, which changes how its width should be interpreted near threshold.
  • The same low-energy constants predict several dynamically generated $1^{-+}$ exotic states, which should be looked for in electron-positron annihilation accompanied by a single photon.
  • For near-threshold states such as G(3900) and $\psi(4040)$, Breit-Wigner masses and widths are not reliable resonance parameters; pole positions on the relevant Riemann sheets are the more appropriate quantities.

Reading between the lines

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

  • If the mechanism is correct, the same $P$-wave contact dynamics should generate partner molecules in the bottom sector, such as $B\bar B^*$ and $B^*\bar B^*$ states near their thresholds, offering a test at a different heavy-quark mass.
  • The pole-trajectory diagnostic could be applied to other vector charmoniumlike states to decide, case by case, which are renormalized quarkonia and which are dynamically generated hadronic molecules.
  • A decisive next step would be to repeat the fit with a different regulator or with the omitted higher-order counterterms included; if a pole near 3.9 GeV survives such changes, the molecule interpretation would cease to be regulator-dependent.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 4 minor

Summary. The paper performs a global fit to the BESIII, Belle, and BaBar cross-section data for e+e- -> D Dbar, D Dbar* + c.c., and D* Dbar* in the energy region 3.7-4.25 GeV, using a coupled-channel Lippmann-Schwinger equation with P-wave contact interactions built from the heavy-quark spin symmetry doublet (D, D*) and its antiparticle in an SU(3) flavor extension of earlier work. Three bare charmonia (psi(1D), psi(3S), psi(2D)) are included in Model I and two in Model II. The main claim is that a pole near 3.9 GeV, at 3832.57(+0.91,-0.79) - 74.53(+0.68,-2.15)i MeV in Model I and 3883.91(+0.38,-0.46) - 46.53(+1.22,-1.22)i MeV in Model II, is dynamically generated rather than a renormalized bare charmonium, based on pole-trajectory analysis that switches off the bare couplings. The same fitted parameters are used to predict dynamically generated states in the JPC = 1-+ channel, which are proposed as search targets in single-photon e+e- processes.

Significance. If the central claim is correct, the paper provides a quantitative identification of G(3900) as a P-wave D Dbar*/Dbar D* hadronic molecule rather than a conventional charmonium state, with the BESIII lineshape explained as a threshold-coupled-channel effect. The work is a serious contribution: it uses up-to-date experimental cross sections, implements a consistent SU(3) generalization of the HQSS contact formalism, solves the full coupled-channel LSE with an explicit production amplitude, and provides a non-circular pole-trajectory diagnostic for distinguishing dynamically generated poles from renormalized bare states. The predictions for JPC = 1-+ exotic states are falsifiable and give the paper additional value beyond the G(3900) interpretation. The main limitation, acknowledged in the text, is that the pole extraction is cutoff-dependent because higher-order counterterms are omitted; this is the key issue that determines whether the dynamical-generation classification is robust.

major comments (4)
  1. [Section III, discussion after Eq. (66) and the renormalization paragraph near the end of Section III A] The paper explicitly states that 'The description of the data thus relies on the choice of the cutoff as a consequence of omitting these necessary counter terms.' Since the central conclusion that G(3900) is dynamically generated rests entirely on the pole obtained with Lambda = 0.50 GeV and a Gaussian separable regulator, the manuscript should demonstrate that the existence, Riemann-sheet assignment, mass, and width of this pole are stable under reasonable variations of Lambda and of the form-factor shape, or under inclusion of the minimal higher-order counterterms. Without such a study, the pole trajectory analysis in Fig. 5 varies only the bare charmonium couplings and does not address the regulator sensitivity that is the load-bearing uncertainty of the claim.
  2. [Tables II and III and the accompanying discussion] The two models give materially different candidates for the same physical state: 3832.52 +/- 74.53i MeV on the (-, +, -, +, +, +) sheet in Model I versus 3883.91 +/- 46.53i MeV on the (-, -, +, +, +, +) sheet in Model II. The difference in the real part is about 50 MeV and the widths differ by roughly 28 MeV, both much larger than the quoted statistical uncertainties. The choice to emphasize Model II is justified by fit quality and residual behavior, but the manuscript does not provide a quantitative estimate of the model systematic uncertainty or a criterion that would decide when the difference between models undermines the extraction. This should be addressed before the pole parameters are presented as the definitive G(3900) resonance parameters.
  3. [Section III, chi2/d.o.f. values in Table I and residual plots in Fig. 3] The reduced chi-square values are 2.17 (Model I) and 2.66 (Model II), and the standardized residuals in panels (c) and (d) of Fig. 3 are not randomly distributed around zero, as the authors themselves note. This moderate fit quality means that the pole parameters, including the dynamically generated G(3900) candidate, are not tightly constrained by the data alone. The paper should quantify the impact of the residual non-randomness, for example by adding a systematic uncertainty associated with the inconsistent BESIII and Belle data sets or by fitting with and without the problematic channels, to show that the dynamical-generation conclusion survives such changes.
  4. [Section III A, pole trajectory method and Fig. 5] The distinction between dynamically generated and renormalized bare charmonium poles is made by switching off g0_2D, g0_1D, and g0_3S and observing which poles move toward the bare masses. This is a valid self-consistency test, but it tests only one combination of parameters. The same classification should be checked against variations of the contact LECs and of the regulator, since a dynamically generated pole in a P-wave contact theory can move across Riemann sheets or vanish when the short-distance physics is changed. A short appendix with such sensitivity scans would substantially strengthen the central claim.
minor comments (4)
  1. [Section II B] There is a typo in 'Moldel I or II' in the paragraph following Eq. (26); it should read 'Model I or II'.
  2. [Section II C, sentence after Eq. (37)] The phrase 'one we get' should be 'one gets' or 'one obtains the physical production amplitude'.
  3. [Section III A] The text writes 'Breit-Winger' where 'Breit-Wigner' is intended.
  4. [Tables VII and VIII] The fit parameters are reported with statistical uncertainties but no correlation matrix is given; given the large number of correlated LECs and bare parameters, a correlation matrix or at least a statement about the strongest correlations would help assess the stability of the pole extraction.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: the G(3900) classification rests on a fitted coupled-channel model with pole-trajectory diagnostics, not on an input–output identity; the only self-citation (Ref. [31]) is non-load-bearing.

full rationale

The central claim is that a pole surviving when charmonium couplings are switched to zero is dynamically generated. This is a model-internal diagnostic applied to amplitudes whose parameters are fitted to the BESIII, Belle, and BaBar cross sections; the pole is not equal by construction to any fitted parameter, and the paper reports two models (I and II) with different pole positions and selects Model II by goodness-of-fit and residual analysis, which is model comparison rather than circularity. The formalism is explicitly an SU(3) extension of the same authors' Ref. [31], but the contact potentials, loop functions, production amplitudes, and Lippmann-Schwinger equations are re-derived in the text, and the conclusion is cross-checked against independent analyses (Refs. [20,29,32]) and external data. The paper's admission that 'the description of the data thus relies on the choice of the cutoff as a consequence of omitting these necessary counter terms' is a regulator-dependence caveat and a correctness risk, not a circular step. The 1-+ predictions reuse the same fitted LECs in a channel without bare states; the label 'dynamically generated' is definitional there, but the pole positions are genuine derived predictions. No quoted equation reduces to its own input, so the paper is a self-consistent phenomenological fit with only a minor non-load-bearing self-citation.

Assumptions & free parameters 28 free parameters · 6 assumptions · 1 invented entities

The central claim rests on a phenomenological Lagrangian with 28 fitted parameters (12 contact LECs, 3 bare couplings, 3 bare masses, 9 photon couplings, 1 cutoff), an SU(3) and HQSS flavor decomposition, a nonrelativistic loop function, and a Gaussian regulator. The paper acknowledges regulator dependence and that psi(2D) appears redundant. The 1-+ predictions transfer the same fitted LECs, giving them no independent fitted parameters.

free parameters (28)
  • C0_1 (SU(3) singlet LEC) = Model I: -672.91 ± 8.39 GeV^-4; Model II: -593.56 ± 17.11 GeV^-4
    Fitted contact LEC in the SU(3) basis; part of the potential in Eq. (20).
  • C0_2 (SU(3) singlet LEC) = Model I: 182.93 ± 15.36 GeV^-4; Model II: -109.96 ± 16.28 GeV^-4
    Fitted contact LEC in the SU(3) basis; part of the potential in Eq. (20).
  • C0_3 (SU(3) singlet LEC) = Model I: -0.11 ± 10.60 GeV^-4; Model II: 797.37 ± 32.52 GeV^-4
    Fitted contact LEC in the SU(3) basis; part of the potential in Eq. (20).
  • C0_4 (SU(3) singlet LEC) = Model I: 613.97 ± 17.17 GeV^-4; Model II: 9.28 ± 9.4 GeV^-4
    Fitted contact LEC in the SU(3) basis; part of the potential in Eq. (20).
  • C8_1 (SU(3) octet LEC) = Model I: -208.49 ± 16.96 GeV^-4; Model II: -357.46 ± 15.66 GeV^-4
    Fitted contact LEC in the SU(3) basis; part of the potential in Eq. (20).
  • C8_2 (SU(3) octet LEC) = Model I: 15.25 ± 9.82 GeV^-4; Model II: -63.08 ± 12.13 GeV^-4
    Fitted contact LEC in the SU(3) basis; part of the potential in Eq. (20).
  • C8_3 (SU(3) octet LEC) = Model I: -33.28 ± 9.43 GeV^-4; Model II: 109.12 ± 26.50 GeV^-4
    Fitted contact LEC in the SU(3) basis; part of the potential in Eq. (20).
  • C8_4 (SU(3) octet LEC) = Model I: 638.27 ± 26.30 GeV^-4; Model II: 475.96 ± 38.51 GeV^-4
    Fitted contact LEC in the SU(3) basis; part of the potential in Eq. (20).
  • C1_1 (isospin triplet LEC) = Model I: -1159.87 ± 19.31 GeV^-4; Model II: -739.76 ± 23.82 GeV^-4
    Fitted contact LEC in the SU(3) basis; part of the potential in Eq. (20).
  • C1_2 (isospin triplet LEC) = Model I: 321.28 ± 17.50 GeV^-4; Model II: 263.68 ± 21.22 GeV^-4
    Fitted contact LEC in the SU(3) basis; part of the potential in Eq. (20).
  • C1_3 (isospin triplet LEC) = Model I: 375.02 ± 25.13 GeV^-4; Model II: -292.25 ± 8.56 GeV^-4
    Fitted contact LEC in the SU(3) basis; part of the potential in Eq. (20).
  • C1_4 (isospin triplet LEC) = Model I: 438.66 ± 17.70 GeV^-4; Model II: -223.61 ± 8.68 GeV^-4
    Fitted contact LEC in the SU(3) basis; part of the potential in Eq. (20).
  • g0_1D (bare coupling of psi(1D)) = Model I: 0.66 ± 0.04 GeV^-1; Model II: -12.93 ± 0.26 GeV^-1
    Coupling between the bare psi(1D) charmonium and open charmed channels; fitted.
  • g0_3S (bare coupling of psi(3S)) = Model I: -14.66 ± 0.37 GeV^-1; Model II: -14.11 ± 0.96 GeV^-1
    Coupling between the bare psi(3S) charmonium and open charmed channels; fitted.
  • g0_2D (bare coupling of psi(2D)) = Model I: -17.09 ± 0.23 GeV^-1; Model II: not included
    Coupling between the bare psi(2D) charmonium and open charmed channels; fitted in Model I, absent in Model II.
  • m0_1D (bare mass of psi(1D)) = Model I: 3.807 ± 0.001 GeV; Model II: 3.804 ± 0.001 GeV
    Bare charmonium mass that is renormalized by the coupled-channel dynamics; fitted.
  • m0_3S (bare mass of psi(3S)) = Model I: 4.229 ± 0.002 GeV; Model II: 4.253 ± 0.005 GeV
    Bare charmonium mass that is renormalized by the coupled-channel dynamics; fitted.
  • m0_2D (bare mass of psi(2D)) = Model I: 3.692 ± 0.003 GeV; Model II: not included
    Bare charmonium mass in Model I; the text later argues this state acts as a redundant free parameter.
  • f0_S (photon coupling to SU(3) singlet S-wave) = Model I: -12.82 ± 0.34; Model II: -4.92 ± 0.48
    Bare production amplitude coupling of the virtual photon to charmed meson pairs; fitted.
  • f0_D (photon coupling to SU(3) singlet D-wave) = Model I: 10.16 ± 0.28; Model II: -4.62 ± 0.29
    Bare production amplitude coupling of the virtual photon to charmed meson pairs; fitted.
  • f8_S (photon coupling to SU(3) octet S-wave) = Model I: -16.72 ± 0.30; Model II: -20.63 ± 0.76
    Bare production amplitude coupling of the virtual photon to charmed meson pairs; fitted.
  • f8_D (photon coupling to SU(3) octet D-wave) = Model I: 8.75 ± 0.24; Model II: 7.3 ± 0.46
    Bare production amplitude coupling of the virtual photon to charmed meson pairs; fitted.
  • f1_S (photon coupling to isospin triplet S-wave) = Model I: 10.13 ± 0.21; Model II: 21.75 ± 0.45
    Bare production amplitude coupling of the virtual photon to charmed meson pairs; fitted.
  • f1_D (photon coupling to isospin triplet D-wave) = Model I: -3.01 ± 0.11; Model II: -5.38 ± 0.16
    Bare production amplitude coupling of the virtual photon to charmed meson pairs; fitted.
  • f0_1D (photon coupling to bare psi(1D)) = Model I: -0.30 ± 0.02; Model II: 0.13 ± 0.00
    Coupling between the virtual photon and the bare psi(1D) charmonium; fitted.
  • f0_3S (photon coupling to bare psi(3S)) = Model I: -11.96 ± 0.63; Model II: -0.47 ± 0.05
    Coupling between the virtual photon and the bare psi(3S) charmonium; fitted.
  • f0_2D (photon coupling to bare psi(2D)) = Model I: -0.15 ± 0.00; Model II: not included
    Coupling between the virtual photon and the bare psi(2D) charmonium in Model I; fitted.
  • Lambda (Gaussian cutoff) = 0.50 ± 0.00 GeV (both models)
    Regulator for the separable P-wave interaction; effectively fixed by the fit, with no systematic variation performed.
assumptions (6)
  • domain assumption Heavy quark spin symmetry (HQSS) holds for the (D,D*) doublet in the energy region studied.
    Used in Section II.A to decompose charmed meson pairs into heavy-light basis and define the contact potential with four LECs.
  • domain assumption SU(3) flavor symmetry relates the D, D_s charmed meson channels.
    Used to build the 3x3 flavor transformation in Eqs. (1)-(6) and include D_s D_s channels.
  • domain assumption The two-body loop can be treated nonrelativistically.
    The nonrelativistic Green function in Eq. (29) is used; text estimates relativistic correction at most 12 percent.
  • ad hoc to paper A separable Gaussian form factor with cutoff Lambda regularizes the amplitude.
    Introduced in Eq. (29); the cutoff is treated as a fit parameter and regulator dependence is acknowledged.
  • ad hoc to paper Leading-order contact interaction alone, with no higher-order counterterms, is sufficient for pole extraction.
    The authors intentionally bypass the renormalization debate in Section III, stating that the description relies on the cutoff choice as a consequence of omitting necessary counter terms.
  • domain assumption Isospin symmetry: D+ and D0 masses are taken equal.
    Stated in Section III.A before the pole search.
invented entities (1)
  • Predicted JPC = 1-+ exotic charmonium-like states independent evidence
    purpose: Dynamically generated by the same fitted LECs; predicted as a bound state near 3836-3870 MeV and resonances around 3885-4224 MeV (Model I) or 3892-4214 MeV (Model II); searchable in e+e- annihilation with a single photon in the final state.
    The paper gives specific pole masses and a concrete production channel, so the states are falsifiable, but they have not yet been observed.

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Pith. "Pith review of Resonance parameters of the vector charmoniumlike state $G(3900)$." pith.science (2026). https://pith.science/paper/CI2OHI5M

@misc{pith2026250417431,
  author       = {Pith},
  title        = {Pith review of: Resonance parameters of the vector charmoniumlike state $G(3900)$},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/CI2OHI5M}},
  note         = {Machine review of arXiv:2504.17431}
}
abstract

Motivated by the updated analysis of the $G(3900)$ by the BESIII collaboration, we perform a global analysis of the cross sections of the $e^+e^-\to D\bar{D}$, $e^+e^-\to D\bar{D}^*+c.c.$, $e^+e^-\to D^*\bar{D}^*$ processes, especially focusing on the properties of the $G(3900)$. As the energy region of interest is limited by the next opening threshold, i.e. the $D_1\bar{D}$ threshold, we focus on the energy region $[3.7,4.25]~\mathrm{GeV}$, where three charmonia $\psi(1D)$, $\psi(3S)$ and $\psi(2D)$ explicitly contribute to the cross sections. By constructing the $P$-wave contact interaction between the $(D,D^*)$ doublet and its antiparticle in the heavy quark limit, we extract the physical scattering amplitude by solving the Lippmann-Schwinger equation. No matter whether three or two charmonium states are included in our framework, we always find a dynamically generated state corresponding to the $G(3900)$, which suggests it to be a $P$-wave dynamically generated state. We also predict several dynamically generated states in the corresponding $1^{-+}$ channel. These states can be further searched for in the electron-positron annihilation process involving the emission of a single photon.

Figures

Figures reproduced from arXiv: 2504.17431 by the authors.

Figure 1
Figure 1. FIG. 1: Feynman diagram for the processes [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2: Pole positions on the complex energy [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3: The line shapes of Model I (solid curve) and Model II (dashed curve) in comparison with the experimental [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figures from the paper (7 more)
Figure 4
Figure 4. Figure 4: FIG. 4: Paths from poles in Model I on unphysical RSs [PITH_FULL_IMAGE:figures/full_fig_p010_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5: Left: The trajectories of the poles in Model I on various RSs with the coupling constants [PITH_FULL_IMAGE:figures/full_fig_p012_5.png]
Figure 7
Figure 7. Figure 7: FIG. 7: The pole positions of Model I (purple hollow [PITH_FULL_IMAGE:figures/full_fig_p013_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8: The zoomed-in trajectory of poles in Model I on various RSs with the couplings [PITH_FULL_IMAGE:figures/full_fig_p024_8.png]
Figure 9
Figure 9. Figure 9: FIG. 9: The [PITH_FULL_IMAGE:figures/full_fig_p024_9.png]
Figure 10
Figure 10. Figure 10: FIG. 10: The distribution of the standardized residuals for Models I (orange) and II (green). There are 15 bins in [PITH_FULL_IMAGE:figures/full_fig_p025_10.png]
Figure 11
Figure 11. Figure 11: FIG. 11: The distribution of the standardized residuals for Models I (orange) and II (green). There are 20 bins in [PITH_FULL_IMAGE:figures/full_fig_p025_11.png]

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Reference graph

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    +iε+) =i Z b a d4q (2π)4 f(|⃗ q|2) (q2 0−ω2 1 +iε+)((E−q0)2−ω2 2 +iε+), (C1) where E is the center-of-mass energy and ωi = p |⃗ q|2 +m2 i with i = 1, 2. Here, f(|⃗ q|2) is a form factor, whose specific form depends on the truncation scheme. In the non-relativistic approximatio...

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