Fundamental properties of the proton in light-front zero modes

Abstract To study a nuclear system in the Skyrme model one must first construct a space of low energy Skyrme configurations. However, there is no mathematical definition of this configuration space and there is not even consensus on its fundamental properties, such as its dimension. Here, we propose that the full instanton moduli space can be used to construct a consistent skyrmion configuration space, provided that the Skyrme model is coupled to a vector meson which we identify with the ρ-meson. Each instanton generates a unique skyrmion and we reinterpret the 8N instanton moduli as physical degrees of freedom in the Skyrme model. In this picture a single skyrmion has six zero modes and two non-zero modes: one controls the overall scale of the solution and one the energy of the ρ-meson field. We study the N = 1 and N = 2 systems in detail. Two interacting skyrmions can excite the ρ through scattering, suggesting that the ρ and Skyrme fields are intrinsically linked. Our proposal is the first consistent manifold description of the two-skyrmion configuration space. The method can also be generalised to higher N and thus provides a general framework to study any skyrmion configuration space.

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Construction of the light-front QCD Hamiltonian with zero modes modeling the vacuum

Theoretical and Mathematical Physics ◽

10.1007/s11232-011-0137-4 ◽

2011 ◽

Vol 169 (2) ◽

pp. 1600-1610 ◽

Cited By ~ 11

Author(s):

M. Yu. Malyshev ◽

E. V. Prokhvatilov

Keyword(s):

Light Front ◽

Zero Modes

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QUANTUM GAUGE BOSON PROPAGATORS IN THE LIGHT FRONT

Modern Physics Letters A ◽

10.1142/s021773230401566x ◽

2004 ◽

Vol 19 (38) ◽

pp. 2831-2844 ◽

Cited By ~ 5

Author(s):

A. T. SUZUKI ◽

J. H. O. SALES

Keyword(s):

Gauge Boson ◽

Degrees Of Freedom ◽

Zero Mode ◽

Light Front ◽

Gauge Fields ◽

Algebraic Condition ◽

Constant Vector ◽

Gauge Bosons ◽

Zero Modes ◽

Boson Propagator

Gauge fields in the light front are traditionally addressed via the employment of an algebraic condition n·A=0 in the Lagrangian density, where Aμ is the gauge field (Abelian or non-Abelian) and nμ is the external, light-like, constant vector which defines the gauge proper. However, this condition though necessary is not sufficient to fix the gauge completely; there still remains a residual gauge freedom that must be addressed appropriately. To do this, we need to define the condition (n·A)(∂·A)=0 with n·A=0=∂·A. The implementation of this condition in the theory gives rise to a gauge boson propagator (in momentum space) leading to conspicuous nonlocal singularities of the type (k·n)-α where α=1,2. These singularities must be conveniently treated, and by convenient we mean not only mathemathically well-defined but physically sound and meaningful as well. In calculating such a propagator for one and two noncovariant gauge bosons those singularities demand from the outset the use of a prescription such as the Mandelstam–Leibbrandt (ML) one. We show that the implementation of the ML prescription does not remove certain pathologies associated with zero modes. However we present a causal, singularity-softening prescription and show how to keep causality from being broken without the zero mode nuisance and letting only the propagation of physical degrees of freedom.

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Light-front projection of spin-1 electromagnetic current and zero-modes

Physics Letters B ◽

10.1016/j.physletb.2012.01.021 ◽

2012 ◽

Vol 708 (1-2) ◽

pp. 87-92 ◽

Cited By ~ 16

Author(s):

J.P.B.C. de Melo ◽

T. Frederico

Keyword(s):

Light Front ◽

Electromagnetic Current ◽

Zero Modes

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Decoupling of zero modes and covariance in the light-front formulation of supersymmetric theories

Physical Review D ◽

10.1103/physrevd.58.125005 ◽

1998 ◽

Vol 58 (12) ◽

Cited By ~ 1

Author(s):

M. Burkardt ◽

F. Antonuccio ◽

S. Tsujimaru

Keyword(s):

Light Front ◽

Zero Modes ◽

Supersymmetric Theories

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Current-Component Independent Transition Form Factors for Semileptonic and Rare D ⟶ π K Decays in the Light-Front Quark Model

Advances in High Energy Physics ◽

10.1155/2021/4277321 ◽

2021 ◽

Vol 2021 ◽

pp. 1-14

Author(s):

Ho-Meoyng Choi

Keyword(s):

Form Factor ◽

Quark Model ◽

Form Factors ◽

Light Front ◽

Recent Analysis ◽

Identical Result ◽

Current Component ◽

Tensor Form ◽

Zero Modes ◽

Valence Region

We investigate the exclusive semileptonic and rare D ⟶ π K decays within the standard model together with the light-front quark model (LFQM) constrained by the variational principle for the QCD-motivated effective Hamiltonian. The form factors are obtained in the q + = 0 frame and then analytically continue to the physical timelike region. Together with our recent analysis of the current-component independent form factors f ± q 2 for the semileptonic decays, we present the current-component independent tensor form factor f T q 2 for the rare decays to make the complete set of hadronic matrix elements regulating the semileptonic and rare D ⟶ π K decays in our LFQM. The tensor form factor f T q 2 are obtained from two independent sets J T + ⊥ , J T + − of the tensor current J T u v . As in our recent analysis of f − q 2 , we show that f T q 2 obtained from the two different sets of the current components gives the identical result in the valence region of the q + = 0 frame without involving the explicit zero modes and the instantaneous contributions. The implications of the zero modes and the instantaneous contributions are also discussed in comparison between the manifestly covariant model and the standard LFQM. In our numerical calculations, we obtain the q 2 -dependent form factors ( f ± , f T ) for D ⟶ π K and branching ratios for the semileptonic D ⟶ π K ℓ v ℓ ℓ = e , μ decays. Our results show in good agreement with the available experimental data as well as other theoretical model predictions.

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