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Douglas W. Higinbotham

Publications and source records attributed to Douglas W. Higinbotham.

18 recordsLinked to original sources
arXiv2026

Hofstadter-Herman Visualization as a Diagnostic Tool for Systematic Effects in Electromagnetic Form Factor Extractions

The internal charge and magnetization distributions of the proton are characterized by electromagnetic form factors GE and GM. They are experimentally extracted via Rosenbluth separation, which measures the elastic scattering of electrons and protons at multiple beam energies and angles at fixed momentum transfer Q2. Conventionally, form factor values are obtained by plotting reduced cross sections against the virtual photon polarization parameter epsilon and then extracting the slope and intercept of the best fit lines. An alternative visualization method, proposed by Hofstadter and Herman in 1960, plots GM2 vs. GE2 curves instead. The best fit values of GE2 and GM2 are immediately visible from the intersection region of the curves and their uncertainty bands. In this work, we apply both conventional and Hofstadter-Herman visualizations to classic 1994 SLAC elastic scattering data. We demonstrate that the Hofstadter-Herman method reveals previously obscured regions of form factor parameter space and highlights subtle experimental discrepancies among data sets. Our results motivate adopting this visualization method as a routine diagnostic cross-check at the Electron-Ion Collider and elsewhere to flag normalization shifts and related adjustments before they enter global fits.

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arXiv2026

Long Range Outlook for Short-Range Correlations

Short range correlated (SRC) N N pairs are pairs of nucleons with high relative momentum (prel > kF where kF ~ 250 MeV/c is the Fermi momentum in medium to heavy nuclei) and lower center of mass momentum. The motivation for studying SRC pairs ranges from a desire to achieve a more comprehensive understanding of the many-body nuclear wave-function at high-resolution to searching for explicit QCD-dynamics effects within the nuclear medium, not to mention connections to many other open problems in nuclear physics. Exploring short-range correlations was one of the physics motivations for building CEBAF (now Jefferson Lab). Scientists used the high luminosity and high energy of this cutting-edge machine to find kinematics that cleanly showed the signals of short-range correlations. This paved the way in the last two decades for tremendous progress understanding these correlations. This paper reviews recent progress and highlights outstanding questions and areas that need further study.

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arXiv2023

Proposal to PAC 51: Color Transparency in Maximal Rescattering Kinematics

With the current highest beam energy at Jefferson Lab and traditional methods, we have exhausted our sensitivity for observing the onset of proton color transparency in a nucleus in A(e,e'p) parallel scattering kinematics for up to $Q^{2}$ = 14 GeV$^{2}$ . One of the disadvantages in A(e,e'p) experiments is that even if a point-like color singlet is produced at such $Q^{2}$, its expansion is unconstrained over the full radius of the nuclei, with the potential to significantly reduce the size of the color transparency effect. Therefore, in order to be sensitive to the effects of color transparency, we enhance the sensitivity of the measurement to the production of a point-like color neutral object prior to the onset of wave-function expansion. In this experiment, we propose a color transparency measurement in maximal rescattering ("dirty") kinematics in deuterium where final-state interactions (FSIs) are known to be huge effects, thereby enhancing our sensitivity to a reduction in FSIs indicative of color transparency. The kinematics in exclusive processes in deuterium can be precisely chosen such that the inter-nucleon distances of the struck and spectator nucleon lead to well-controlled FSIs.

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arXiv2023

Direct Comparison of using a Z-Transformation instead of the traditional $Q^2$ for for Extraction of the Proton Radius from $e-p$ Scattering Data

A discrepancy in the determination of the proton's charge radius, $r_p$, between muonic hydrogen spectroscopy versus classic atomic spectroscopy and electron scattering data has become known as the proton radius puzzle. Extractions of $r_p$ from electron scattering data require determination of the slope of the proton's charge form factor, $G_E^p$, in the limit of $Q^2\rightarrow0$ through fitting and extrapolation. Some works have presented the $Z$-transformation fitting technique as the best choice for this type of extraction due to the true functional form of $G_E^p$ being mathematically guaranteed to exist within the parameter-space of the fit function. In this work, we test this claim by examining the mathematical bias and variances introduced by this technique as compared to the more traditional $Q^2$ fits using statistically sampled $G_E^p$ parameterizations with known input radii. Our tests conclude that the quality of the $Z$-transformation technique depends on the range of data used. In the case of new experiments, the fit function and technique should be selected in advance by generating realistic pseudodata and assessing the power of different techniques.

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arXiv2023

Physical Implications of the Extrapolation and Statistical Bootstrap of the Nucleon Structure Function Ratio $\frac{F_2^n}{F_2^p}$ for Mirror Nuclei $^3$He and $^3$H

A nuclear physics example of statistical bootstrap is used on the MARATHON data nucleon structure function ratio, $\frac{F_2^n}{F_2^p}$, in the quark momentum fraction $x_B\rightarrow0$ and $x_B\rightarrow1$ regions. The extrapolated $F_2$ ratio value as quark momentum fraction $x_B\rightarrow 1$ approaches 0.4 and this value is compared to theoretical predictions. The extrapolated ratio when $x_B\rightarrow 0$ favors the simple model of isospin symmetry with the complete dominance of seaquarks at low momentum fraction. At high-$x_B$, the proton quark distribution function ratio $d/u$ is derived from the $x\rightarrow 1$ ratio $\frac{F_2^n}{F_2^p}\rightarrow 0.4$ and found to be $d/u \rightarrow 1/6$. Our extrapolated values for both the $\frac{F_2^n}{F_2^p}$ ratio and the $d/u$ parton distribution function ratio most closely match perturbative QCD values from quark counting and helicity conservation arguments but still differ by roughly $7\%$. The mismatch to theoretical predictions may be ameliorated if two compatible models act simultaneously in the nucleon wavefunction. One such example is nucleon wavefunctions composed of a linear combination of a quark-diquark state and a 3-valence quark correlated state with coefficients that combine to give the extrapolated $F_2$ ratio of $0.4$.

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arXiv2022

Understanding the systematic differences in extractions of the proton electric form factors at low-$Q^2$

Systematic differences exist between values of the proton's electric form factors in the low-$Q^2$ region extracted by different experimental and theoretical groups, though they are all making use of basically the same electron-proton scattering data. To try understand the source of these differences, we make use of the analytically well-behaved rational (N=1, M=1) function, a predictive function that can be reasonably used for extrapolations at $Q^{2} \rightarrow 0$. First, we test how well this deceptively simple two-parameter function describes the extremely complex and state-of-the-art dispersively improved chiral effective field theory calculations. Second, we carry out a complete re-analysis of the 34 sets of eletron-proton elastic scattering cross-section data of the Mainz A1 Collaboration with its unconstrained 31 normalization parameters up to $Q^{2} = 0.5~{\rm (GeV/c)^{2}}$. We find that subtle shifts in the normalization parameters can result in relatively large changes in the extracted physical qualities. In conclusion, we show that by simply using a well-behaved analytic function, the apparent discrepancy between recent form-factor extractions can be resolved.

hep-ph↗
arXiv2022

EIC Detector Overview

The Electron Ion Collider will have two interaction regions that can be instrumented with detectors. The first region will be instrumented as part of the project and needs to be capable of delivering the physics that has been outlined by the National Academy of Sciences and ready at the start of beam commissioning near the end of this decade. Plans for a second complementary detector to be located at a second interaction region are already in progress and will hopefully come to fruition just a few years after the first detector comes online. While the basic parameters of these detectors are being selected using conventional approaches, the optimization of the detectors is already being enhanced by making use of advanced optimization techniques.

physics.ins-det↗
arXiv2021

Elastic Positron-Proton Scattering at Low Q$^2$

Systematic differences in the the proton's charge radius, as determined by ordinary atoms and muonic atoms, have caused a resurgence of interest in elastic lepton scattering measurements. The proton's charge radius, defined as the slope of the charge form factor at Q$^2$=0, does not depend on the probe. Any difference in the apparent size of the proton, when determined from ordinary versus muonic hydrogen, could point to new physics or need for the higher order corrections. While recent measurements seem to now be in agreement, there is to date no high precision elastic scattering data with both electrons and positrons. A high precision proton radius measurement could be performed in Hall B at Jefferson Lab with a positron beam and the calorimeter based setup of the PRad experiment. This measurement could also be extended to deuterons where a similar discrepancy has been observed between the muonic and electronic determination of deuteron charge radius. A new, high precision measurement with positrons, when viewed alongside electron scattering measurements and the forthcoming MUSE muon scattering measurement, could help provide new insights into the origins of the proton radius puzzle, and also provide new experimental constraints on radiative correction calculations.

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arXiv2021

Advanced extraction of the deuteron charge radius from electron-deuteron scattering data

To extract the charge radius of the proton, $r_{p}$, from the electron scattering data, the PRad collaboration at Jefferson Lab has developed a rigorous framework for finding the best functional forms - the fitters - for a robust extraction of $r_{p}$ from a wide variety of sample functions for the range and uncertainties of the PRad data. In this paper we utilize and further develop this framework. Herein we discuss methods for searching for the best fitter candidates as well as a procedure for testing the robustness of extraction of the deuteron charge radius, $r_{d}$, from parametrizations based on elastic electron-deuteron scattering data. The ansatz proposed in this paper for the robust extraction of $r_{d}$, for the proposed low-$Q^{2}$ DRad experiment at Jefferson Lab, can be further improved once there are more data.

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arXiv2020

How Analytic Choices Can Affect the Extraction of Electromagnetic Form Factors from Elastic Electron Scattering Cross Section Data

Scientists often try to incorporate prior knowledge into their regression algorithms, such as a particular analytic behavior or a known value at a kinematic endpoint. Unfortunately, there is often no unique way to make use of this prior knowledge, and thus, different analytic choices can lead to very different regression results from the same set of data. To illustrate this point in the context of the proton electromagnetic form factors, we use the Mainz elastic data with its 1422 cross section points and 31 normalization parameters. Starting with a complex unbound non-linear regression, we will show how the addition of a single theory-motivated constraint removes an oscillation from the magnetic form factor and shifts the extracted proton charge radius. We then repeat both regressions using the same algorithm, but with a rebinned version of the Mainz dataset. These examples illustrate how analytic choices, such as the function that is being used or even the binning of the data, can dramatically affect the results of a complex regression. These results also demonstrate why it is critical when using regression algorithms to have either a physical model in mind or a firm mathematical basis

physics.data-an↗
arXiv2020

Reinterpretation of classic proton charge form factor measurements

In 1963, a proton radius of $0.805(11)~\mathrm{fm}$ was extracted from electron scattering data and this classic value has been used in the standard dipole parameterization of the form factor. In trying to reproduce this classic result, we discovered that there was a sign error in the original analysis and that the authors should have found a value of $0.851(19)~\mathrm{fm}$. We additionally made use of modern computing power to find a robust function for extracting the radius using this 1963 data's spacing and uncertainty. This optimal function, the Padé $(0,1)$ approximant, also gives a result which is consistent with the modern high precision proton radius extractions.

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arXiv2019

The Double Spin Asymmetry of Nitrogen in Elastic and Quasielastic Kinematics from a Solid Ammonia Dynamically Polarized Target

Solid ammonia (NH$_3$) is commonly used as a dynamically polarized proton target for electron and muon scattering cross-section asymmetry measurements. As spin 1$^{+}$ particles, the $^{14}$N nuclei in the target are also polarized and contribute a non-trivial asymmetry background that should be addressed. We describe here a method to extract the nitrogen contribution to the asymmetry, and report the cross-section asymmetries of electron-nitrogen scattering at beam energies of $E=1.7$ GeV and $E=2.2$ GeV, and momentum transfer of $Q^{2}=0.023-0.080$ GeV$^{2}$.

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arXiv2019

Bias-Variance Trade-off and Model Selection for Proton Radius Extractions

Intuitively, a scientist might assume that a more complex regression model will necessarily yield a better predictive model of experimental data. Herein, we disprove this notion in the context of extracting the proton charge radius from charge form factor data. Using a Monte Carlo study, we show that a simpler regression model can in certain cases be the better predictive model. This is especially true with noisy data where the complex model will fit the noise instead of the physical signal. Thus, in order to select the appropriate regression model to employ, a clear technique should be used such as the Akaike information criterion or Bayesian information criterion, and ideally selected previous to seeing the results. Also, to ensure a reasonable fit, the scientist should also make regression quality plots, such as residual plots, and not just rely on a single criterion such as reduced chi2. When we apply these techniques to low four-momentum transfer cross section data, we find a proton radius that is consistent with the muonic Lamb shift results. While presented for the case of proton radius extraction, these concepts are applicable in general and can be used to illustrate the necessity of balancing bias and variance when building a regression model and validating results, ideas that are at the heart of modern machine learning algorithms.

physics.data-an↗
arXiv2018

Robust extraction of proton charge radius from electron-proton scattering data

Extracting the proton charge radius from electron scattering data requires determining the slope of the charge form factor at $Q^2$ of zero. But as experimental data never reach that limit, numerous methods for making the extraction have been proposed, though often the functions are determined after seeing the data which can lead to confirmation bias. To find functional forms that will allow for a robust extraction of the input radius for a wide variety of functional forms in order to have confidence in the extraction from upcoming low $Q^2$ experimental data such as the Jefferson Lab PRad experiment, we create a general framework for inputting form-factor functions as well as various fitting functions. The input form factors are used to generate pseudo-data with fluctuations intended to mimic the binning and random uncertainty of a given set of real data. All combinations of input functions and fit functions can then be tested repeatedly against regenerated pseudo-data. Since the input radius is known, this allows us to find fit functions that are robust for radius extractions in an objective fashion. For the range and uncertainty of the PRad data, we find that a two-parameter rational function, a two-parameter continued fraction and the second order polynomial expansion of $z$ can extract the input radius regardless of the input charge form factor function that is used. We have created an easily expandable framework to search for functional forms that allow for a robust extraction of the radius from a given binning and uncertainty of pseudo-data generated from a wide variety of trial functions. This method has enabled a successful search for the best functional forms to extract the radius from the upcoming PRad data and can be used for other experiments.

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arXiv2016

The Proton Radius from Electron Scattering Data

[Background] The proton charge radius extracted from recent muonic hydrogen Lamb shift measurements is significantly smaller than that extracted from atomic hydrogen and electron scattering measurements. [Purpose] In an attempt to understand the discrepancy, we review high-precision electron scattering results from Mainz, Jefferson Lab, Saskatoon and Stanford. [Method] We make use of stepwise regression techniques using the $F$-test as well as the Akaike information criterion to systematically determine the predictive variables to use for a given set and range of electron scattering data as well as to provide multivariate error estimates. [Results] Starting with the precision, low four-momentum transfer ($Q^2$) data from Mainz (1980) and Saskatoon (1974), we find that a stepwise regression of the Maclaurin series using the $F$-test as well as the Akaike information criterion justify using a linear extrapolation which yields a value for the proton radius that is consistent with the result obtained from muonic hydrogen measurements. Applying the same Maclaurin series and statistical criteria to the 2014 Rosenbluth results on $G_E$ from Mainz, we again find that the stepwise regression tends to favor a radius consistent with the muonic hydrogen radius but produces results that are extremely sensitive to the range of data included in the fit. Making use of the high-$Q^2$ data on $G_E$ to select functions which extrapolate to high $Q^2$, we find that a Padé ($N=M=1$) statistical model works remarkably well, as does a dipole function with a 0.84 fm radius, $G_E(Q^2) = ( 1 + Q^2/0.66\,\mathrm{GeV}^2)^{-2}$. [Conclusions] From this statistical analysis, we conclude that the electron scattering result and the muonic hydrogen result are consistent. It is the atomic hydrogen results that are the outliers.

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arXiv2014

The Challenge of the EMC Effect: existing data and future directions

Since the discovery that the ratio of inclusive charged lepton (per-nucleon) cross sections from a nucleus A to the deuteron is not unity - even in deep inelastic scattering kinematics - a great deal of experimental and theoretical effort has gone into understanding the phenomenon. The EMC effect, as it is now known, shows that even in the most extreme kinematic conditions the effects of the nucleon being bound in a nucleus can not be ignored. In this paper we collect the most precise data available for various nuclear to deuteron ratios, as well as provide a commentary on the current status of the theoretical understanding of this thirty year old effect.

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arXiv2010

Short-Range Nucleon-Nucleon Correlations

Valence-shell nucleon knock-out experiments, such as 12C(e,e'p)11B, measure less strength then is predicted by independent particle shell model calculations. The theoretical solution to this problem is to include the correlations between the nucleons in the nucleus in the calculations. Motivated by these results, many electron scattering experiments have tried to directly observe these correlations in order to gain new insight into the short-range part of the nucleon-nucleon potential. Unfortunately, many competing mechanisms can cause the same observable final-state as an initial-state correlation, making truly isolating the signal extremely challenging. This paper reviews the recent experimental evidence for short-range correlations, as well as explores the possibility that such correlations are responsible for the EMC effect in the 0.3 < xB < 0.7 deep inelastic scattering ratios.

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