Mass structure of hadrons and light-front sum rules in the 
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 Hooft model

Ji, Xiangdong; Liu, Yizhuang; Zahed, Ismaïl

doi:10.1103/physrevd.103.074002

Cited by 17 publications

(7 citation statements)

References 32 publications

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“…In the case of QED, the electron mass is the only mechanical scale that, together with the dimensionless coupling α ∼ 1/137, sets the energy scale for atomic physics, chemistry and biology. In cases like 1+1 dimensional QCD, the dimensional coupling introduces scalar energy as well [23]. An important mechanism to generate a new source of scalebreaking is through the condensates of scalar fields in the ground states of QFTs.…”

Section: Scalar and Tensor Energy And Relativistic Virial Theoremmentioning

confidence: 99%

Quantum anomalous energy effects on the nucleon mass

Liu

2021

Sci. China Phys. Mech. Astron.

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Apart from the quark and gluon kinetic and potential energies, the nucleon mass includes a novel energy of pure quantum origin resulting from anomalous breaking of scale symmetry. We demonstrate the effects of this quantum anomalous energy (QAE) in QED, as well as in a toy 1+1 dimensional non-linear sigma model where it contributes non-perturbatively, in a way resembling the Higgs mechanism for the masses of matter particles in electro-weak theory. The QAE contribution to the nucleon mass can be explained using a similar mechanism, in terms of a dynamical response of the gluonic scalar field through Higgs-like couplings between the nucleon and scalar resonances. In addition, the QAE sets the scale for other energies in the nucleon through a relativistic virial theorem, and contributes a negative pressure to confine the colored quarks.

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Section: Scalar and Tensor Energy And Relativistic Virial Theoremmentioning

confidence: 99%

Quantum anomalous energy effects on the nucleon mass

Liu

2021

Sci. China Phys. Mech. Astron.

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“…On the light front, the old lore was that the QCD vacuum is trivial owing to the vanishing of the backward diagrams in perturbation theory [50]. However, more carefull analyses reveal that the vacuum physics is encoded in the longitudinal zero modes of the fields [51], which is rather manifest in twodimensional QCD [52] (and references therein). In effective models of QCD such as the NJL model, the non-trivial aspects of the vacuum on the light front are explicitly tied to the tadpole contributions, generated by the constrained part of the fermion field [38][39][40].…”

Section: T Hooft Effective Lagrangian On the Light Frontmentioning

confidence: 99%

“…For convenience the spin-flavor part is made explicit using the light front spinors u s (k) for a particle spinor, and v s (k) for an anti-particle spinor, with the remaining φ X a scalar-isoscalar wavefunction. The spinors are explicity given in Appendix A. Inserting (55) in (52) and then in (51), and unwinding the various contractions from the 4-Fermi interaction terms, yield the boost invariant eigenvalue equation…”

Section: Light Front Spectrummentioning

confidence: 99%

Hadronic structure on the light-front VII. Pions and kaons and their partonic distributions

Liu¹,

Shuryak²,

Zahed³

2023

Preprint

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This work is a continuation in our series of papers, that addresses quark models of hadronic structure on the light front, motivated by the QCD vacuum structure and lattice results. The spontaneous breaking of chiral symmetry on the light front, is shown to parallel that in the rest frame, where the non-local instanton induced t Hooft interaction plays a central role. By rewriting this interaction solely in terms of the good component of the fermionic field, a scalar chiral condensate emerges in the mean-field approximation, which is identical to the one obtained in the rest frame. The pions and kaons emerge as deeply bound Goldstone modes in the chiral limit, with the scalarisoscalar sigma meson mode as a threshold state with zero binding. We explicitly derive the light front distribution amplitudes (DAs) and partonic functions (PDFs) for these mesons. The DAs and PDFs are in good agreement with those extracted from the QCD instanton vacuum in the rest frame, using the large momentum effective theory (LaMET). The QCD evolved DAs and PDFs compare well with available measurements, as well as recent lattice results.

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“…We use the 't Hooft Equation for baryons and tetraquarks by making the successive substitutions q → [qq] and q → [q q]. The 't Hooft Equation has been extensively studied in the literature [23][24][25][26][27][28][29][30] and it is worth noting that, in the conformal limit, it possesses a gravity dual on AdS 3 [31]. Here, we only highlight how it is both complementary and consistent with the holographic Schrödinger Equation.…”

Section: The 'T Hooft Equationmentioning

confidence: 99%

Hadron spectroscopy using the light-front holographic Schrödinger equation and the 't Hooft equation

Ahmady,

Kaur,

MacKay

et al. 2021

Preprint

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Light-front holographic QCD provides a successful first approximation to hadron spectroscopy in the chiral limit of (3 + 1)-dim light-front QCD, where a holographic Schrödinger-like Equation, with an emerging confining scale, κ, governs confinement in the transverse direction. In its supersymmetric formulation, light-front holography predicts that each baryon has two superpartners: a meson and a tetraquark, with their degenerate masses being generated by the same scale, κ. In nature, this mass degeneracy is lifted by chiral symmetry breaking and longitudinal confinement.In this paper, we show that the latter can be successfully captured by the 't Hooft Equation of(1 + 1)-dim, large N c , QCD. Together, the holographic Schrödinger Equation and the 't Hooft Equation, provide a good global description of the data across the full hadron spectrum with a universal κ.

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Mass structure of hadrons and light-front sum rules in the t′ Hooft model

Cited by 17 publications

References 32 publications

Quantum anomalous energy effects on the nucleon mass

Quantum anomalous energy effects on the nucleon mass

Hadronic structure on the light-front VII. Pions and kaons and their partonic distributions

Hadron spectroscopy using the light-front holographic Schrödinger equation and the 't Hooft equation

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