Structure Factor of the Electron Liquid from the Moment Sum Rules

Based on the light-cone (LC) framework and the kT factorization formalism, the transverse momentum effects and the different helicity components' contributions to the pion form factor Fπ(Q2) are recalculated. In particular, the contribution to the pion form factor from the higher helicity components (λ1 + λ2 = ±1), which come from the spin-space Wigner rotation, are analyzed in the soft and hard energy regions respectively. Our results show that the right power behavior of the hard contribution from the higher helicity components can only be obtained by fully keeping the kT dependence in the hard amplitude, and that the kT dependence in LC wavefunction affects the hard and soft contributions substantially. A model for the twist-3 wavefunction ψp(x,k⊥) of the pion has been constructed based on the moment calculation by applying the QCD sum rules, whose distribution amplitude has a better end-point behavior than that of the asymptotic one. With this model wavefunction, the twist-3 contributions including both the usual helicity components (λ1 + λ2 = 0) and the higher helicity components (λ1 + λ2 = ±1) to the pion form factor have been studied within the modified pQCD approach. Our results show that the twist-3 contribution drops fast and it becomes less than the twist-2 contribution at Q2~10GeV2. The higher helicity components in the twist-3 wavefunction will give an extra suppression to the pion form factor. When all the power contributions, which include higher order in αs, higher helicities, higher twists in DA and etc., have been taken into account, it is expected that the hard contributions will fit the present experimental data well at the energy region where pQCD is applicable.

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SPIN STRUCTURE FUNCTIONS AND INTRINSIC MOTION OF THE CONSTITUENTS

International Journal of Modern Physics A ◽

10.1142/s0217751x03014769 ◽

2003 ◽

Vol 18 (08) ◽

pp. 1397-1402

Author(s):

PETR ZÁVADA

Keyword(s):

Spin Structure ◽

Rest Frame ◽

Mass Shell ◽

Sum Rules ◽

Parton Model ◽

Structure Functions ◽

Quark Parton Model ◽

Intrinsic Motion ◽

Spin Structure Functions ◽

The Moment

The spin structure functions of the system of quasifree fermions on mass shell are studied in a consistently covariant approach. Comparison with the basic formulas following from the quark-parton model reveals the importance of the fermion motion inside the target for the correct evaluation of the spin structure functions. In particular it is shown, that regarding the moment Γ1, both the approaches are equivalent for the static fermions, but differ by the factor 1/3 in the limit of massles fermions (m ≪ p0, in target rest frame). Some other sum rules are discussed as well.

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Form invariance of the moment sum-rules for jellium with the addition of short-range terms in the pair-potential

Indian Journal of Physics ◽

10.1007/s12648-020-01750-2 ◽

2020 ◽

Author(s):

Riccardo Fantoni

Keyword(s):

Short Range ◽

Sum Rules ◽

Pair Potential ◽

Form Invariance ◽

The Moment

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A Perturbation Theory for the Population of Atomic Energy Levels in Non-Lte Plasmas

International Astronomical Union Colloquium ◽

10.1017/s025292110010805x ◽

1988 ◽

Vol 102 ◽

pp. 343-347

Author(s):

M. Klapisch

Keyword(s):

Perturbation Theory ◽

Small Parameter ◽

Classification Scheme ◽

Sum Rules ◽

Energy Levels ◽

Natural Classification ◽

Quantum Numbers ◽

Formal Expansion ◽

Atomic Energy Levels ◽

As Effects

AbstractA formal expansion of the CRM in powers of a small parameter is presented. The terms of the expansion are products of matrices. Inverses are interpreted as effects of cascades.It will be shown that this allows for the separation of the different contributions to the populations, thus providing a natural classification scheme for processes involving atoms in plasmas. Sum rules can be formulated, allowing the population of the levels, in some simple cases, to be related in a transparent way to the quantum numbers.

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