Singular charge density at the center of the pion?

Miller, Gerald A.

doi:10.1103/physrevc.79.055204

Cited by 57 publications

(52 citation statements)

References 49 publications

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“…The transverse density ρ(b) is an integral involving the singular function K 0 (x) which varies as log 1 x for x << 1. The question of the singularity of the central transverse density ρ(b) is interesting to the present author because of recent work [11] showing that for the pion ρ(b) is likely to approach infinity as b approaches zero. We may study the limit as b approaches 0 by using the asymptotic limit of the form factor Eq.…”

Section: A Singular Central Densitymentioning

confidence: 99%

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Electromagnetic form factors and charge densities from hadrons to nuclei

Miller

2009

Phys. Rev. C

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A simple exact covariant model in which a scalar particle Ψ is modeled as a bound state of two different particles is used to elucidate relativistic aspects of electromagnetic form factors F (Q 2 ). The model form factor is computed using an exact covariant calculation of the lowest-order triangle diagram. The light-front technique of integrating over the minus-component of the virtual momentum gives the same result and is the same as the one obtained originally by Gunion et al. by using time-ordered perturbation theory in the infinite-momentum-frame. The meaning of the transverse density ρ(b) is explained by providing a general derivation, using three spatial-coordinates, of its relationship with the form factor. This allows us to identify a mean-square transverse sizeThe quantity b 2 is a true measure of hadronic size because of its direct relationship with the transverse density. We show that the rest-frame charge distribution is generally not observable by studying the explicit failure to uphold current conservation. Neutral systems of two charged constituents are shown to obey the conventional lore that the heavier one is generally closer to the transverse origin than the lighter one. It is argued that the negative central charge density of the neutron arises, in pion-cloud models, from pions of high longitudinal momentum that reside at the center. The non-relativistic limit is defined precisely, and the ratio of the binding energy B to the mass M of the lightest constituent is shown to govern the influence of relativistic effects. We show that the exact relativistic formula for F (Q 2 ) is the same as the familiar one of the three-dimensional Fourier transform of a square of a wave function for very small values of B/M, but this only occurs values of B/M less than about 0.001. For masses that mimic the quark-di-quark model of the nucleon we find that there are substantial relativistic corrections to the form factor for any value of Q 2 . A schematic model of the lowest s-states of nuclei is developed. Relativistic effects are found to decrease the form factor for light nuclei but to increase the form factor for heavy nuclei. Furthermore, these lowest s-states are likely to be strongly influenced by relativistic effects that are order 15-20%.

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Section: A Singular Central Densitymentioning

confidence: 99%

“…The transverse density is also the integral of the three-dimensional infinite momentum frame density ρ(x − , b) over all values of the longitudinal position coordinate [11].…”

Section: Electromagnetic Form Factors Measure Transverse Densitiementioning

confidence: 99%

Electromagnetic form factors and charge densities from hadrons to nuclei

Miller

2009

Phys. Rev. C

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“…It has been explored in a number of recent works [26][27][28][29][30][31]. These transverse densities are obtained as twodimensional Fourier transforms of elastic form factors and describe the density of charge and magnetization in the plane transverse to the propagation direction of a fast moving nucleon.…”

Section: Introductionmentioning

confidence: 99%

Pion transverse charge density and the edge of hadrons

2014

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We use the world data on the pion form factor for space-like kinematics and a technique previously used to extract the proton transverse densities, to extract the transverse pion charge density and its uncertainty due the incomplete knowledge of the pion form factor at large values of Q 2 and the experimental uncertainties. The pion charge density at small values of impact parameter b < 0.1 fm is dominated by this incompleteness error while the range between 0.1-0.3 fm is relatively well constrained. A comparison of pion and proton transverse charge densities shows that the pion is denser than the proton for values of b < 0.2 fm. The pion and proton transverse charge densities seem to be the same for values of b=0.3-0.6 fm. Future data from JLab 12 GeV and the EIC will increase the dynamic extent of the form factor data to higher values of Q 2 and thus reduce the uncertainties in the extracted pion transverse charge density.

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“…Since the form factor involves initial and final states with different momenta, three dimensional Fourier transforms cannot be interpreted as densities. However, the transverse densities defined at fixed light-front time have a proper density interpretation [99,100,101]. The charge densities in the transverse impact parameter plane for the nucleon have been discussed extensively in various phenomenological models [63,64,74,102,103,104,105,106,107,108,109], whereas the densities in the transverse coordinate plane have been studied in [110,111,112].…”

Section: Introductionmentioning

confidence: 99%

Deuteron transverse densities in holographic QCD

2017

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Abstract. We investigate the transverse charge density in the longitudinally as well as transversely polarized deuteron using the recent empirical description of the deuteron electromagnetic form factors in the framework of holographic QCD. The predictions of the holographic QCD are compared with the results of a standard phenomenological parameterization. In addition, we evaluate GPDs and the gravitational form factors for the deuteron. The longitudinal momentum densities are also investigated in the transverse plane. PACS

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Singular charge density at the center of the pion?

Cited by 57 publications

References 49 publications

Electromagnetic form factors and charge densities from hadrons to nuclei

Electromagnetic form factors and charge densities from hadrons to nuclei

Pion transverse charge density and the edge of hadrons

Deuteron transverse densities in holographic QCD

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