Searcharxiv⌕ Search

arXiv subjects

Gerald A. Miller

Publications and source records attributed to Gerald A. Miller.

At least 37 records · Page 2Linked to original sources
arXiv2023

The Entanglement of Elastic and Inelastic Scattering

The entanglement properties of systems in which elastic and inelastic reactions occur in projectile-target interactions is studied. A new measure of entanglement, the scattering entropy, based on the unitarity of the $S-$matrix (probability conservation), is suggested. Using simple models for both low- and high-energy interactions, the amount of entanglement is found to track with the strength of the inelastic interaction. The familiar example of the classical ``black disk", total absorption, model is found to correspond to maximum entanglement. An analysis of high-energy $pp$ scattering data shows that entanglement is near maximum for lab energies greater than about 1 GeV, showing that the total absorption model is a reasonable starting point for understanding the data.

nucl-th↗
arXiv2023

Entanglement Maximization in Low-Energy Neutron-Proton Scattering

The entanglement properties of neutron-proton scattering are investigated using a measure that counts the number of entangled pairs produced by the action of a scattering operator on a given initial neutron-proton state. All phase shifts relevant for scattering at laboratory energies up to 350 MeV are used. Entanglement is found to be maximized in very low energy scattering. At such energies the Hamiltonian obeys Wigner SU(4) symmetry, and an entanglement maximum is a sign of that symmetry. At higher energies the angular dependence of entanglement is strong and the entanglement is large for many scattering angles. The tensor force is shown to play a significant role in producing entanglement at lab kinetic energies greater than about 50 MeV.

nucl-th↗
arXiv2023

Light-Front Holography Model of the EMC Effect

A new two-component model of the EMC effect based on Light-Front Holographic QCD (LFHQCD) is presented. The model suggests the EMC effect is the result of the nuclear potential breaking SU(6) symmetry. The model separates the $F_2^A$ nuclear structure function into two parts: a free contribution, involving the addition of proton and neutron structure functions weighted by the number of protons and neutrons respectively, and a nuclear/medium modified contribution that involves a universal function for all nuceli. Further, the model displays a connection with the correlation between the size of the EMC effect and the SRC pair density, $a_2$ - extracted from kinematic plateaus at around $x$ > 1 in inclusive quasi-elastic (QE) scattering.

nucl-th↗
arXiv2023

Strong Interaction Dynamics and Fermi $β$ decay in the nucleon and the nucleus

Nuclear super-allowed $β$ decay has been used to obtain tight limits on the value of the CKM matrix element $V_{ud}$ that is important for unitarity tests, and therefore important for tests of the standard model. Current requirements on precision are so intense that effects formerly thought too small to matter are now relevant. This article is a brief review of personal efforts to include the effects of strong interactions on Fermi $β$ decay. First I examine the role of isospin violation in the decay of the neutron. The size of the necessary correction depends upon detailed strong-interaction dynamics. The isospin violating parts of the nucleon wave function, important at the low energy of $β$ decay, can be constrained by data taken at much higher energies, via measurements, for example, of $ed\to e'π^\pm +\rm X $ reactions at Jefferson Laboratory. The next focus is on the role of nuclear short-ranged correlations, which affect the value of the correction needed to account for isospin violation in extracting the value of $V_{ud}$. The net result is that effects previously considered as irrelevant have become relevant for both neutron and nuclear $β$ decay.

nucl-th↗
arXiv2022

Charge Symmetry Breaking Effects on Neutron Beta Decay in Non-Relativistic Quark Models

A formalism for the study of charge symmetry breaking (CSB) effects is discussed and used to analyze the effects of charge symmetry breaking on neutron beta decay. The effect of including CSB reduces the beta decay matrix element by an amount on the order of $10^{-4}$, a value much larger than the previous estimate. A much smaller contribution due to proton recoil is treated as well, which is found to be on the order of $10^{-6}$. The current uncertainty in the value of $V_{ud}$ is also of order $10^{-4}$. An improvement of that uncertainty by an order of magnitude would require that charge symmetry breaking effects should be included in future analyses.

nucl-th↗
arXiv2022

Mass decomposition of the pion in the 't Hooft model

We obtain the energy-momentum tensor (EMT) in the 't Hooft model of two-dimensional quantum chromodynamics. The EMT is decomposed into contributions from quark and gluon fields, with all of the (plus component of) the light front momentum being carried by the quark field. The energy is split between quark and gluon fields, with the gluon field carrying the self-energy of the dressed quarks. We consider the pion in the limit of small but non-zero quark masses -- which has previously withstood numerical treatment -- as as a concrete example. We solve for the pion wave function using a variational method and obtain numerical results for its energy breakdown into quark and gluon contributions.

hep-ph↗
arXiv2022

The Fundamental Nature of Low-Energy Pion-Nucleon Interactions

A historical review of pion-nucleon interactions at low energy is presented, with aims toward an introductory, pedagogic approach focusing on issues germane to current research. These topics include the use of chiral effective field theory, the sigma term, qualitative understanding of low-energy phase shifts, the physics of the $Δ$ resonance, and isospin violation. A theme is that low-energy pion-nucleon scattering is directly related to QCD via effective field theory. Another theme is that modern needs regarding the pion-nucleon sigma term and the study of isospin violation requires a better low-energy data set.

nucl-th↗
arXiv2022

Pions in Proton Structure and Everywhere Else

The pion cloud is important in nuclear physics and in a variety of low-energy hadronic phenomena. We argue that it is natural to expect it to also be important in lepton-proton deep inelastic scattering and Drell-Yan studies of proton structure. We compute the necessary consequences of the pion cloud in connection with the recent SeaQuest data. The effects are detailed by using the exact kinematics of the experiment. Good agreement with the measurements is obtained. Thus the universality of pionic effects is understood.

nucl-th↗
arXiv2022

Nucleon-Nucleon Short-Ranged Correlations, $β$ Decay and the Unitarity of the CKM Matrix

The influence of nucleon-nucleon short-ranged correlations (SRC) on nuclear super-allowed $β$ decay is examined. The need for this is driven by the observed depletion of spectroscopic strength obtained in studies of $(e,e')$ and $(d,^3{\rm He})$ reactions on a wide variety of nuclei. We show that the influence of SRC is model-dependent, but may be very substantial. The $^{46}$V nucleus is used as an example. The resulting impact on studies of the unitarity of the Cabibbo-Kobayashi-Maskawa (CKM) matrix element is discussed.

nucl-th↗
arXiv2022

Color Transparency and Light Front Holographic QCD

Color transparency, the reduction of initial- or final-state interactions in coherent nuclear processes, is a natural prediction of QCD provided that small-sized or point-like configurations (PLCs) are responsible for high-momentum transfer, high-energy, semi-exclusive processes. I use the FMS criteria for the existence of PLCs to show that the wave functions of light front holographic QCD, as currently formulated, do not contain a PLC.

hep-ph↗
arXiv2021

Unified formalism for electromagnetic and gravitational probes: densities

The use of light front coordinates allows a fully relativistic description of a hadron's spatial densities to be obtained. These densities must be two-dimensional and transverse to a chosen spatial direction. We explore their relationship to the three-dimensional, non-relativistic densities, with a focus on densities associated with the energy momentum tensor. The two-dimensional non-relativistic densities can be obtained from the light front densities through a non-relativistic limit, and can subsequently be transformed into three-dimensional non-relativistic densities through an inverse Abel transform. However, this operation is not invertible, and moreover the application of the inverse Abel transform to the light front densities does not produce a physically meaningful result. We additionally find that the Abel transforms of so-called Breit-frame densities generally differ significantly from the true light front densities. Numerical examples are provided to illustrate the various differences between the light front, Breit frame, and non-relativistic treatment of densities.

hep-ph↗
arXiv2021

Color Transparency and the Proton Form Factor- Feynman Wins

A recent experiment [{\bf Phys. Rev. Lett. 126,082301 (2021)}] used the $(e,e'p)$ reaction on $^{12}$C to search for the effects of color transparency (the absence of final state interactions). Color transparency was said to be ruled out. The ability to observe the effects of color transparency depends on the ability of a putative point-like-configuration (PLC), formed in a high-momentum transfer coherent reaction, to escape the nucleus without expanding its size. We study the expansion aspect of color transparency using superconformal baryon-meson symmetry and light-front holographic QCD. A new formalism is obtained and used to analyze the recent experiment. The resulting conclusion is that effects of expansion would not be sufficiently significant in causing final state interactions to occur. Therefore we conclude that a PLC was not formed. This means that the Feynman mechanism involving virtual photon absorption on a single high momentum quark is responsible for high momentum electromagnetic form factor of the proton.

nucl-th↗
arXiv2021

Forces within hadrons on the light front

In this work, we find the light front densities for momentum and forces, including pressure and shear forces, within hadrons. This is achieved by deriving relativistically correct expressions relating these densities to the gravitational form factors $A(t)$ and $D(t)$ associated with the energy momentum tensor. The derivation begins from the fundamental definition of density in a quantum field theory, namely the expectation value of a local operator within a spatially-localized state. We find that it is necessary to use the light front formalism to define a density that corresponds to internal hadron structure. When using the instant form formalism, it is impossible to remove the spatial extent of the hadron wave function from any density, and -- even within instant form dynamics -- one does not obtain a Breit frame Fourier transform for a properly defined density. Within the front formalism, we derive new expressions for various mechanical properties of hadrons, including the mechanical radius, as well as for stability conditions. The multipole ansatz for the form factors is used as an example to illustrate all of these findings.

hep-ph↗
arXiv2021

Genuine empirical pressure within the proton

A phenomenological extraction of pressure within the proton has recently been performed using JLab CLAS data (arXiv:2104.02031 [nucl-ex]). The extraction used a 3-dimensional Breit frame description in which the initial and final proton states have different momenta. Instead, we obtain the two-dimensional transverse light front pressure densities that incorporate relativistic effects arising from the boosts that cause the initial and final states to differ. The mechanical radius is then determined to be $0.518~ \pm 0.062_{\mathrm{fit}} \pm 0.126_{\mathrm{sys}}~\mathrm{fm}$, which is smaller than the electric charge radius and larger than the light front momentum radius. The forces within the proton are shown to be predominantly repulsive at distances less than $0.43~\pm 0.12~\mathrm{fm}$ from the center, and predominantly attractive further out.

hep-ph↗
arXiv2021

Can a protophobic vector boson explain the ATOMKI anomaly?

In 2016, the ATOMKI collaboration announced [PRL {\bf 116}, 042501 (2016)] observing an unexpected enhancement of the $e^+-e^-$ pair production signal in one of the $^8$Be nuclear transitions induced by an incident proton beam on a $^7$Li target. Many beyond-standard-model physics explanations have subsequently been proposed. One popular theory is that the anomaly is caused by the creation of a protophobic vector boson ($X$) with a mass around 17 MeV [e.g., PRL\ {\bf 117}, 071803 (2016)] in the nuclear transition. We study this hypothesis by deriving an isospin relation between photon and $X$ couplings to nucleons. This allows us to find simple relations between protophobic $X$-production cross sections and those for measured photon production. The net result is that $X$ production is dominated by direct transitions induced by $E1^X$ and $L1^X$ (transverse and longitudinal electric dipoles) and $C1^X$ (charge dipole) without going through any nuclear resonance (i.e. Bremsstrahlung radiation) with a smooth energy dependence that occurs for all proton beam energies above threshold. This contradicts the experimental observations and invalidates the protophobic vector boson explanation.

hep-ph↗
arXiv2020

The Mystery of Bloom-Gilman Duality: A Light Front Holographic QCD Perspective

Light front wave functions motivated by holographic constructions are used to study Bloom-Gilman duality of deep inelastic scattering. Separate expressions for structure functions in terms of quark and hadronic degrees of freedom are presented, with a goal of relating the two expressions. A two-parton model is defined and resonance transition form factors are computed using previously derived light front wave functions. A new form of global duality is derived from the valence quark-number sum rule. Using a complete set of hadronic states is necessary for this new global duality to be achieved. Previous original work does not provide such a set. This is remedied by amending the model to include a longitudinal confining potential, and the resulting complete set is sufficient to carry out the study of Bloom-Gilman duality. Expressions for transition form factors are obtained and all are shown to fall asymptotically as 1/Q2. The Feynman mechanism dominates the asymptotic behavior of the model. These transition form factors are used to assess the validity of the global and local duality sum rules, with the result that both neither are satisfied. Evaluations of the hadronic expression for q(x,Q2) provide more details about this lack. This result shows that the observed validity of both global and local forms of duality for deep inelastic scattering must be related to a feature of QCD that is deeper than completeness. Our simple present model suggests a prediction that Bloom-Gilman duality would not be observed if deep inelastic scattering experiments were to be made on the pion. The underlying origin of the duality phenomenon in deep inelastic scattering is deeply buried within the confinement aspects of QCD, and remains a mystery.

hep-ph↗
arXiv2020

Unified model of nucleon elastic form factors and implications for neutrino-oscillation experiments

Precise knowledge of the nucleon's axial-current form factors is crucial for modeling GeV-scale neutrino-nucleus interactions. Unfortunately, the axial form factor remains insufficiently constrained to meet the precision requirements of upcoming long-baseline neutrino-oscillation experiments. This work studies the nucleon's axial and vector form factors using the light-front approach to build a quark-diquark model of the nucleon with an explicit pion cloud. The light-front wave functions in both the quark and pion-baryon Fock spaces are first calibrated to existing experimental information on the nucleon's electromagnetic form factors, and then used to predict the axial form factor. The resulting squared charge radius of the axial pseudo-vector form factor is predicted to be $r_A^2\! =\! 0.29\! \pm\! 0.03\, \mathrm{fm}^2$, where the small error accounts for the model's parametric uncertainty. We use our form factor results to explore the (quasi-)elastic scattering of neutrinos by (nuclei)nucleons, with the result that the the widely-implemented dipole ansatz is an inadequate approximation of the full form factor for modeling both processes. The approximation leads to a $5\!-\!10\%$ over-estimation of the total cross section, depending on the (anti)neutrino energy. We project over-estimations of similar size in the flux-averaged cross sections for the upcoming DUNE long-baseline neutrino-oscillation experiment.

nucl-th↗