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Gerald A. Miller

Publications and source records attributed to Gerald A. Miller.

At least 109 records · Page 6Linked to original sources
arXiv2011

Impulse approximation in nuclear pion production reactions: absence of a one-body operator

The impulse approximation of pion production reactions is studied by developing a relativistic formalism, consistent with that used to define the nucleon-nucleon potential. For plane wave initial states we find that the usual one-body (1B) expression O_1B is replaced by O_2B=-iK(m_pi/2)O_1B/m_pi, where K(m_pi/2) is the sum of all irreducible contributions to nucleon-nucleon scattering with energy transfer of m_pi/2. We show that O_2B is approximately O_1B for plane wave initial states. For distorted waves, we find that the usual operator is replaced with a sum of two-body operators that are well approximated by the operator O_2B. Our new formalism solves the (previously ignored) problem of energy transfer forbidding a one-body impulse operator. Using a purely one pion exchange deuteron, the net result is that the impulse amplitude for np --> d pi^0 at threshold is enhanced by a factor of approximately two. This amplitude is added to the larger "rescattering" amplitude and, although experimental data remain in disagreement, the theoretical prediction of the threshold cross section is brought closer to (and in agreement with) the data.

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arXiv2010

Realistic Transverse Images of the Proton Charge and Magnetic Densities

We develop a technique, denoted as the finite radius approximation (FRA), that uses a two-dimensional version of the Shannon-Nyquist sampling theorem to determine transverse densities and their uncertainties from experimental quantities. Uncertainties arising from experimental uncertainties on the form factors and lack of measured data at high $Q^2$ are treated. A key feature of the FRA is that a form factor measured at a given value of $Q^2$ is related to a definite region in coordinate space. An exact relation between the FRA and the use of a Bessel series is derived. The proton Dirac form factor is well enough known such that the transverse charge density is very accurately known except for transverse separations $b$ less than about 0.1 fm. The Pauli form factor is well known to $Q^2$ of about 10 GeV$^2$, and this allows a reasonable, but improvable, determination of the anomalous magnetic moment density.

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arXiv2010

Third Zemach Moment of the Proton

Modern electron scattering experiments have determined the proton electric form factor, G_{Ep}(Q^2), to high precision. We utilize this data, represented by the different form factor parametrizations, to compute the third Zemach moment of the proton charge distribution. We find that existing data rule out a value of the third Zemach moment large enough to explain the current puzzle with the proton charge radius determined from the Lamb shift in muonic hydrogen. This is in contrast with the recent claim of De Rujula [arXiv:1008.3861].

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arXiv2010

Impulse approximation in the n p --> d pi^0 reaction reexamined

The impulse approximation (one-body operator) in the n p --> d pi^0 reaction is reexamined with emphasis on the issues of reducibility and recoil corrections. An inconsistency when one pion exchange is included in the production operator is demonstrated and then resolved via the introduction of "wave function corrections" which nearly vanish for static nucleon propagators. Inclusion of the recoil corrections to the nucleon propagators is found to change the magnitude and sign of the impulse production amplitude, worsening agreement with the experimental cross section by approximately 30%. A cutoff is used to account for the phenomenological nature of the external wave functions, and is found to have a significant impact up to approximately 2.5 GeV.

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arXiv2010

Color Transparency at COMPASS energies

Pionic quasielastic knockout of protons from nuclei at 200 GeV show very large effects of color transparency as -t increases from 0 to several GeV^2. Similar effects are expected for quasielastic photoproduction of vector mesons.

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arXiv2010

Travels With Tony-Nucleon Structure Through Our Ages

Nucleon structure is currently understood from a unified light-front, infinite-momentum-frame framework. The specific examples of the neutron transverse charge distribution and the shape of the proton are discussed here.

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arXiv2010

Transverse Charge Densities

Electromagnetic form factors have long been used to probe the underlying charge and magnetization densities of hadrons and nuclei. Traditional three-dimensional Fourier transform methods are not rigorously applicable for systems with constituents that move relativistically. The use of the transverse charge density is a new, rigorously defined way to analyze electromagnetic form factors of hadrons.This review is concerned with the following issues: what is a transverse charge density; how is one extracted one from elastic scattering data; the existing results; what is the relationship with other observable quantities; and, future prospects.

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arXiv2010

Overview of nucleon structure

The quark-gluon properties of the nucleon are probed by a host of recent and planned experiments. These involve elastic, deep-inelastic, semi-inclusive deep-inelastic (SIDIS), and deeply-virtual Compton scattering. A light-front description is naturally applied to interpret all of these processes. The advantages of this approach will be discussed The talk will then focus on the transverse charge and magnetization densities of the nucleons and the use of SIDIS to reveal the non-spherical shape of the nucleon. We find that the central charge density of the neutron is negative, that the magnetization density of the proton extends further in space than the charge distribution, and that the shape of the nucleon, as measured by the spin-dependent density, is not spherical.

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arXiv2009

The Relation Between Equal-Time and Light-Front Wave Functions

The relation between equal-time and light-front wave functions is studied using models for which the four-dimensional solution of the Bethe-Salpeter wave function can be obtained. The popular prescription of defining the longitudinal momentum fraction using the instant-form free kinetic energy and third component of momentum is found to be incorrect except in the non-relativistic limit. The only presently known way to obtain light-front wave functions from rest-frame, instant-form wave functions is to boost the latter wave functions to the infinite momentum frame. Despite this fact, we prove a relation between certain integrals of the equal-time and light-front wave functions.

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arXiv2009

Charge Symmetry Breaking in the n p --> d pi^0 reaction

The asymmetry in the angular distribution of n p --> d pi^0 due to Charge Symmetry Breaking is calculated using Heavy Baryon Chiral Perturbation Theory. Recent developments in power counting have proven successful in describing total cross sections, and we apply them to the asymmetry calculation. Reducibility in one of the leading order diagrams is examined. We compare the updated theory with experimental results for a range of physically reasonable parameters and find over-prediction for the entire range.

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arXiv2009

Electromagnetic Form Factors and Charge Densities From Hadrons to Nuclei

A simple exact covariant model in which a scalar particle is modeled as a bound state of two different particles is used to elucidate relativistic aspects of electromagnetic form factors. The model form factor is computed using an exact covariant calculation of the lowest-order triangle diagram and shown to be the same as that obtained using light-front techniques. The meaning of transverse density is explained using coordinate space variables, allowing us to identify a true mean-square transverse size directly related to the form factor. We show that the rest-frame charge distribution is generally not observable because of the failure to uphold current conservation. Neutral systems of two charged constituents are shown to obey the 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. The non-relativistic limit is defined precisely and the ratio of the binding energy to that of the mass of the lightest constituent is shown to govern the influence of relativistic effects. The exact relativistic formula for the form factor reduces to the familiar one of the three-dimensional Fourier transform of a square of a wave function for a very limited range of parameters. For masses that mimic the quark-di-quark model of the nucleon we find substantial relativistic corrections for any value of $Q^2$. A schematic model of the lowest s-states of nuclei is used to find that relativistic effects decrease the form factor for light nuclei but increase the form factor for heavy nuclei. Furthermore, these states are strongly influenced by relativity.

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arXiv2009

Neutron Charge Density from Simple Pion Cloud Models

The physical nucleon is modeled as a bare nucleon surrounded by a pion cloud using a psuedoscalar pion-nucleon coupling to examine its implications for the neutron form factor, F_1, and the corresponding transverse charge density in the infinite momentum frame. Two versions, one with a tunable Pauli-Villars parameter, and one with light-front cloudy-bag pion-nucleon form factors, are examined. A qualitative agreement with the experimental form factor (negative definite for all Q^2) and transverse charge density are achieved when the nucleon is treated as having a finite extent. The bare nucleon must have a finite extent if this model is to account for a negative definite F_1, and consequently a negative transverse charge density of the neutron at its center.

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arXiv2009

Neutron Properties in the Medium

We demonstrate that for small values of momentum transfer, Q^2, the in-medium change of the G_E/G_M form factor ratio for a bound neutron is dominated by the change in the electric charge radius and predict in a model independent manner that the in-medium ratio will increase relative to the free result. This effect will act to increase the predicted cross-section for the neutron recoil polarization transfer process 4He(e,e'n)3He. This is in contrast to medium modification effects on the proton G_E/G_M from factor ratio, which act to decrease the predicted cross-section for the 4He(e,e'p)3H reaction. Experiments to measure the in-medium neutron form factors via neutron knockout reactions are currently feasible in the range 0.1 < Q^2 < 1 GeV^2.

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arXiv2009

The Inclusive-Exclusive Connection and the Neutron Negative Central Charge Density

We find an interpretation of the recent finding that the central charge density of the neutron is negative by using models of generalized parton distributions at zero skewness to relate the behavior of deep inelastic scattering quark distributions, evaluated at large values of Bjorken x, to the transverse charge density evaluated at small distances. The key physical input of these models is the Drell-Yan-West relation We find that the d quarks dominate the neutron structure function for large values of Bjorken x, where the large longitudinal momentum of the struck quark has a significant impact on determining the center-of-momentum of the system, and thus the "center" of the nucleon in the transverse position plane.

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arXiv2009

Elliptic flow from final state interactions in the distorted-wave emission-function model

The effect of final state interactions on the elliptic flow coefficient measured in relativistic heavy ion collisions is investigated within the DWEF formalism established by Miller and Cramer [Phys. Rev. Lett. 94, 102302 (2005), J. Phys. G34, 703 (2007), Phys. Rev. C78, 054905 (2008)]. It is found that the optical potential previously found to give the best fit of particle multiplicity and Hanbury Brown and Twiss radii in RHIC events has a moderate effect on the resulting elliptic flow coefficient v_2. This indicates that final state interactions should be taken into account to confidently predict v_2 to better than ~20% accuracy.

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arXiv2009

Singular Charge Density at the Center of the Pion?

We relate the three-dimensional infinite momentum frame spatial charge density of the pion to its electromagnetic form factor. Diverse treatments of the measured form factor data including: phenomenological fits, non-relativistic quark models, the application of perturbative QCD, QCD sum rules, holographic QCD, and the Nambu Jona-Lasinio (NJL) model all lead to the result that the charge density at the center of the pion has a logarithmic divergence. Relativistic constituent quark models do not display this singularity. Future measurements planned for larger values of momentum transfer may determine whether or not a singularity actually occurs.

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arXiv2008

Understanding the Optical Potential in HBT Interferometry

The validity of using a pion optical potential to incorporate the effects of final state interactions on HBT interferometry is investigated. We find that if the optical potential is real, the standard formalism is modified as previously described in the literature. However, if the optical potential is complex, a new term involving pion emission from eliminated states must be included. The size of such effects in previous work by Cramer and Miller is assessed.

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